Prediction of road texture influence on rolling resistance

Transcription

1 Prediction of road texture influence on rolling resistance Stijn Boere DCT Master s thesis Coach(es): Supervisor: dr. ir. I. Lopez dr. ir. A. Kuijpers prof. dr. H. Nijmeijer Eindhoven Universiy of Technology Department Mechanical Engineering Dynamics and Control Group Eindhoven, December, 2009

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3 Contents 1 Introduction Motivation Goals Thesis structure Literature review Empirical approach Numerical approach Finite element methods Kropp et al O boy and Dowling Brinkmeier et al Lopez et al Conclusion JSV paper Abstract Introduction Modeling approach Smooth-road rolling resistance Road texture rolling resistance Model validation Influence of road texture on rolling resistance Conclusion Conclusions and Recommendations Conclusions Recommendations Bibliography 30 A FE model 35 B Tyre/road interaction model 43 C Regression Analysis 59 3

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5 Chapter 1 Introduction 1.1 Motivation Recently, vehicle energy consumption and related CO 2 emissions have gained much attention due to the global warming awareness and rising oil prices. The European Union is committed under the Kyoto protocol to reduce CO 2 emissions by 20% in 2020 compared to 1990 levels. In Europe, 18% of the total CO 2 emission originates from road transport [1]. Reduction in CO 2 emissions of road transport can be achieved by technical or non-technical measures [2]. Examples of non-technical measures include the education in fuel efficient driving and CO2 based taxation schemes for passenger cars. Technical measures are for example the use of alternative fuels, vehicle weight reduction, increased engine efficiency and decreased vehicle resistance factors. The EU policy on CO 2 reduction of road vehicles by technical measures has long been based on voluntary commitment of road vehicle manufacturers. However, the industry has failed to meet the 1998 target of reducing the average CO 2 emissions of cars to 130 g/km in Instead, emissions are still lagging behind at a level of g/km. The EU therefore agreed on a regulation to reduce fleetaverage CO 2 emissions to 140 g/km in 2015 and 95 g/km on This requires an improvement of 15% over the next five years and in improvement of 38% over the next ten years. Putting this in perspective, the achieved reduction for the last 15 years was no more than 20%. Therefore, increasing efforts have to be made in the coming years. One of the possibilities to reduce fuel consumption and CO 2 emissions is the reduction of rolling resistance. The relative importance of rolling resistance with respect to fuel consumption depends on the vehicle velocity and driving pattern. Rolling resistance in an average set of tyres accounts for approximately 20% to the fuel consumption for motor way driving and 30% to the fuel consumption for an urban driving cycle [3, 4]. Therefore, it is generally estimated that decreasing rolling resistance by 10% will result in a fuel and CO 2 reduction of about 2-3 %. Rolling resistance is influenced by several parameters. Tyre loading and deformation. Rolling resistance in car tyres increases with increasing tyre deformation resulting from high vehicle weight or low inflation pressure. It is estimated that 50% of the passenger cars in The Netherlands suffer from underinflated tyres. This results in a significant increase in fuel consumption and CO 2 emission [2]. Furthermore, underinflated tyres have a negative influence on vehicle handling, grip and noise emission. Public education could increase the awareness of the importance of properly inflated tyres. Tyre characteristics. Reduction of visco elastic losses by improved rubber compounds and improved tyre structures can significantly reduce rolling resistance. Tyre manufacturers have developed so called green tyres which promise a lower rolling resistance without comprising on grip, skid resistance and tyre/road noise. Recently, mandatory tyre labels were introduced for tyre suppliers which indicate the fuel-efficiency, grip and noise emission characteristics of tyres. This enables tyre buyers to make an educated choice between different sets of tyres. 5

6 6 CHAPTER 1. INTRODUCTION Road characteristics. Road irregularities induce vibrations. Road unevenness, large wavelength irregularities (wavelengths: m), causes vibrations in the suspension of a car. Smaller wavelength irregularities result in internal tyre vibrations. These vibrations result in energy dissipation. The influence of road characteristics on rolling resistance should therefore be a consideration in road constructions. Improved tyre characteristics have a large potential in reducing the CO 2 emission of road transport. Various models have been developed to predict the rolling resistance as a function of tyre design parameters. However, the effect of road characteristics is largely unknown. Most of the current knowledge on this topic is based on empirical studies. However, results between studies often show a poor comparison. Therefore, there is a need to study the effects of road characteristics more systematically. This project focuses on the development of a numerical model to predict the influence of small wavelength (<0.5m) road irregularities on tyre vibrations and inherent energy losses. A numerical model that predicts the influence of road characteristics on greenhouse gas emissions can help in the design or selection of "green" road surfaces. Nowadays, the European emission rights system enables emissions to be converted into monetary terms. Therefore, an accurate numerical model has, besides environmental benefits, also financial implications as it could change the outcomes of a cost/benefit comparison in new road constructions. 1.2 Goals The goals of this project are as follows: 1. Establish an empirical correlation between rolling resistance and road texture using experimental data. The experimental data is acquired on a test track located in Kloosterzande, The Netherlands by M+P consulting engineers. Texture profiles and rolling resistance are measured on 40 different test tracks. 2. Develop a numerical model that predicts the influence of road irregularities on rolling resistance of pneumatic tyres. The basis of the numerical model in this project is a tyre/road noise model developed at Eindhoven University of Technology in the last five years. In this project, an additional module is developed which predicts the rolling resistance on an arbitrary road surface. 3. Study the correlation between rolling resistance and tyre/road noise, between rolling resistance and skid resistance and between rolling resistance and mechanical impedance of the road surface. Regression analyses are used to determine whether there are conflicting requirement between optimizing rolling resistance and optimizing the other tyre characteristics. Furthermore, the effect of mechanically flexible, noise reducing, road surfaces on rolling resistance is examined. 1.3 Thesis structure This report is organized as follows. The next chapter presents a review of the literature on empirical and numerical research on the influence of road texture on rolling resistance. Chapter 3 contains a draft paper which is submitted to the Journal of Sound and Vibrations and which should be considered as the core of this report. Chapter 4 concludes with extensive conclusions and recommendations. The remaining of the report should be considered to be a working document for further improvements of the model. Appendix A provides more information on the FEM analysis. Appendix B describes the tyre/road interaction model in detail. Appendix C contains a detailed report on the experimental data analysis and covers the third goal of this project which is not treated in the journal paper. Regression analyses between rolling resistance, tyre/road noise, skid resistance and mechanical impedance of the road are discussed. Finally, the numerical model, measurement data and animations are attached digitally.

7 Chapter 2 Literature review Rolling resistance of pneumatic tyres has been the subject of extensive study in the past. Correlations with various parameters are found such as inflation pressure, tyre material properties and tyre temperature [5, 6, 7, 8]. Most of these studies use either experimental data, analytical derivations on equivalent structures or finite element method (FEM) analysis to predict rolling resistance. Road texture is one of the parameters that has received less attention in the past. Most of the current knowledge on this topic is based in empirical studies. Section 2.1 reviews the literature based on empirical observations. Road texture induces tyre vibrations which results in energy dissipation. Section 2.2 reviews the numerical attempts to predict the influence of road texture on these tyre vibrations. Section 2.2 also includes a review of the tyre model developed at Eindhoven University of Technology which is used as the basis of the current work. 2.1 Empirical approach In the past, several attempts have been made to find correlations between road texture and rolling resistance. One of the problems in this respect is the characterization of road texture. Often a distinction is made between different wavelengths regions as shows in Table 2.1. Name Table 2.1: Wavelength regions Wavelengths Micro texture <0.5 [mm] Macro texture [mm] Mega texture [m] Unevenness [m] These texture regions are graphically illustrated in Fig. 2.1 The SILVIA project [10], a European Commission Program, provides an interesting overview of the empirical studies up till One of the first attempts to study the relationship between road characteristics and rolling resistance was carried out by the Swedish National Road and Transport Institute (VTI) in Sweden in the 1980th [11]. Texture profiles and fuel consumption were measured on 20 different surfaces with constant speed (50-70 km/h). Positive correlations were observed between all texture wavelengths and fuel consumption. However, difficulties were found in identifying causal relationships due to strong inter correlations between the different wavelengths. It is estimated that the shortwave unevenness can have an effect up to 10% in fuel economy. However, as the driving speed increases, smaller texture wavelengths increase in importance. 7

8 8 CHAPTER 2. LITERATURE REVIEW Unevenness Mega texture Macro texture Micro texture Figure 2.1: Wavelength regions redrawn from [9] Another Swedish VTI report [12] also summarizes earlier work. Possible correlations were suggested between all spectra bands including micro texture. It is noted that rough macro texture (wavelengths > 5mm) can have a positive effect on rolling resistance on wet roads. Furthermore, it is suggested that the stiffness and softening behavior of road surfaces can be a significant factor concerning rolling resistance. Belgian data [13] showed positive correlations between unevenness, mega texture, macro texture and rolling resistance. Mega texture was shown to have the strongest correlation unlike the study performed by VTI which showed stronger correlations in the unevenness texture region. A New Zealand study [14] compares rolling resistance on road surface with varying macro texture and unevenness. Variations up till 40 % in rolling resistance were found. Positive correlations between short wave unevenness and mega texture and macro texture were found. Concluding, there seems no general consensus in the relative importance of texture wavelengths. Correlations have been reported between shortwave unevenness, mega texture, macro texture and even micro texture. However, results between studies often show a poor comparison. Therefore, there is a need to study the effects of road characteristics on rolling resistance more systematically. 2.2 Numerical approach In the past several attempts have been made to model the behavior of tyres. However, few models consider the effects of road irregularities on internal tyre vibrations. At this point five research methodologies can be identified that are employed in the area of tyre/road contact analysis Finite element methods Finite element methods are extensively used to model tyre behavior [15, 16, 17]. The advantage of FEM is that design data is used and results are easy to interpret. The models vary in complexity: steady state or transient behavior, elastic or visco-elastic material models and iso-thermal analysis or thermal mechanic analysis. Finite element methods require great computational effort and will become more popular as computational power increases over the years. However, transient dynamic FEM analysis of rolling tyres which are detailed enough to capture the small deformation caused by road texture are currently out of reach. Therefore, alternative techniques have to be developed that require less computational effort.

9 2.2. NUMERICAL APPROACH Kropp et al. The tyre/road noise group of the Applied Acoustics department at Chalmers University of Technology, Sweden, focusses on the modeling of tyre/road interaction and related phenomena such as tyre/road noise, rolling resistance, traction and wear. Several models have been developed varying in complexity [18, 19]. An overview of the approach is shown in Fig The basis of the approach is an orthotropic pretensioned Kirchhoffs plate on a stiffness bedding shown in Fig From this simplified equivalent tyre structure the impuls response functions (Green s functions) at the contact nodes of the tyre are pre-calculated. Elastic half-space stiffness Road texture profile Tyre geometry Material data Tyre model Green s functions Rolling contact model 3D contact (iterative process) Wullens Belt and tread deformations Noise generation model Tyre/road noise Dynamic contact forces Material data Tyre model Waveguide finite elements Fraggstedt Dissipated power (rolling resistance) Figure 2.2: Overview of the tyre/road interaction approach from [18] A full 3D contact model is developed by Wullens [18]. The plate includes the rolling band and the sidewalls but the curvature of the tyre is not taken into account, other than the cyclic boundary conditions connecting the ends of the plate. The inflated air stiffness and the rigidity of the sidewalls are implemented in the form of a spring bedding. The material properties like the bending stiffness, the spring stiffness, and the tension are obtained by measurements. Tyre structure Rolling band Sidewalls Z Circumferential direction Y X Air and sidewalls stiffness Lateral direction Figure 2.3: Pretensioned Kirchhoffs plate on a stiffness bedding shown from [18] The belt displacement ζ e is determined by the convolution ζ e (t) = m F m (t) g m,e (t) = m t 0 f(τ)g(t τ)dτ (2.1) in which g m,e (t) represents Green s functions expressing the normal displacement of a point e on the belt due to a unit force at point m. F m (t) represents the contact forces. The contact forces are by indenting a rough road surface into an elastic half space. Since the tread material is not modeled in the equivalent Kirchhoffs plate it has to be accounted for in the choice of the elastic half space properties. A sound generation model finally determines the actual noise production. A more recent method to obtain the Green s function of a rotating tyre is the use of waveguide finite elements. The obtained contact forces using this method are used by Fraggstedt [20]. This

10 10 CHAPTER 2. LITERATURE REVIEW model predicts the energy dissipation of a tyre which is rolling on a rough road surface. The energy dissipation is shown to be comparable to measurement results. The tyre dissipates more power on a rough road surface than on a smooth road surface. The advantage of the model is that it shows the elements within the tyre with the highest energy dissipation. It is also shown that most of the energy is dissipated at frequencies below 250 Hz O boy and Dowling O boy and Dowling [21, 22] at the engineering department at the University of Cambridge use a multi layer viscoelastic cylindrical representation of the tyre belt shown in Fig. 2.4 to determine the vibration characteristics of a tyre. The parameters in the model are defined solely by design data. This model of the tyre belt is then used to determine the parameters of an equivalent simple bending plate model. From this result the Green s functions for the contact nodes are determined using the same approach as at Chalmers University. The tyre is rolled over a textured road surface. The contact forces are determined using the belt displacement, the undeformed tread block height and the tread block stiffness. This method is used to predict tyre/road noise. Rolling resistance is not yet examined using this approach. Figure 2.4: Complete viscoelastic cylindrical model of the tyre belt from [21] Brinkmeier et al. In Germany Brinkmeier et al. also aim at the prediction of rolling noise. However, finite element methods are used instead of simplified equivalent structures or waveguide finite elements [23]. An Arbitrary Lagrangian Eulerian (ALE) approach is employed to describe the steady state rolling on a smooth road surface [24]. This approach uses a reference frame that removes the explicit time dependence from the problem so that a purely spatially dependent analysis can be performed. This choice of reference frame allows the finite element mesh to remain stationary. Transfer functions are determined which relate a force input at the contact nodes to the tyre vibrations in a rotating tyre. Finally, a linear tyre/road interaction model is defined in the frequency domain. A discrete Fourier analysis of texture measurements results in a frequency spectrum. Using the contact patch stiffness this is transferred into an excitation function. By combining the transfer functions and excitation functions the tyre vibrations can be determined. Subsequently, a sound generation analysis is performed. However, there has been no attempt to study the energy dissipation due to the tyre vibrations Lopez et al. At Eindhoven University of Technology a methodology to model tyre vibrations has been developed in recent years [25, 26, 27]. In this approach, a transformation on the modal representation of a static deformed tyre is used to account for the rotation of the tyre. First, the tyre is inflated and pressed against a smooth road surface and the highly nonlinear stationary tyre deformations are determined. A modal base is constructed around the deformed state. Subsequently, reduction techniques are applied to reduce the amount of computational effort and

11 2.2. NUMERICAL APPROACH 11 storage capacity. The reduced mass matrix, eigenmodes and eigenvectors are extracted from the FEM environment. A coordinate transformation is applied to account for the rotation of the tyre which is illustrated in Fig e 1 z e 2 z e 2 x t e 1 x e 1 y e 2 y Figure 2.5: Reference e 1 and body fixed e 2 coordinate systems with β = α + Ωt. The equation of motion of the tyre in the body fixed frame can be written as, Mẍ(t) + Dẋ(t) + Kx(t) = f(α + Ωt, t) (2.2). In which M, D and K represent the mass, damping and stiffness matrix respectively. f(α + Ωt, t) are the applied forces in the body fixed frame, α is the angular coordinate in the body fixed frame and Ω is the rotating velocity of the tyre. Rayleigh damping is considered: D mod = αm + βk (2.3) The system can be rewritten in modal coordinates using the transformation x(t) = Φη(t) (2.4) In which Φ represents the matrix of eigenvectors and η represents the modal coordinates. Subsequently the equation of motion can be written as η η η(t) + D mod η η η(t) + K mod η(t) = Φ T f(α + Ωt, t) (2.5) where K mod is a diagonal matrix with elements k ii = ω 2 i, ω i are the eigen frequencies of the system and D mod is a diagonal matrix with elements d ii = 2ξ i ω i where ξ i are the modal damping ratios. To obtain the equation of motion of the tyre in a reference coordinate system the material derivative can be used: D Dt = t + Ω β with β = α + Ωt (2.6) and in which the left-hand side represents the time derivative in the body fixed (Lagrangian) coordinates, the first term on the right-hand side is the time derivative in the reference (Eulerian) coordinates, Ω is the rotational speed and β is the circumferential angle in the reference frame (Fig. 2.5). The equation of motion of the tyre in a fixed reference frame can be obtained by transforming the material (Lagrangian) derivatives into time (Eulerian) derivatives using Eq. (2.6): where η η η(t) + D(Ω) η η η(t) + K(Ω)η(t) = Φ T f(t) (2.7)

12 12 CHAPTER 2. LITERATURE REVIEW D = 2P(Ω, M, Φ) + D mod (2.8) K = S(Ω, M, Φ) + D mod P(Ω, M, Φ) + K mod (2.9) The matrices S,P are added stiffness and damping terms due to the rotation: ( P(Ω, M, Φ) = Φ T (β)m ˆΩˆΩˆΩΦ(β) + Ω Φ(β) ) β ( ) S(Ω, M, Φ) = Φ T (β)m ˆΩˆΩˆΩ 2 Φ(β) + 2ΩˆΩˆΩˆΩ Φ(β) + Ω 2 2 Φ(β) β β 2 (2.10) (2.11) Equations (2.4) and (2.7) now give a the response of the tyre in a fixed reference frame. From this point either transfer function or Green s function can be determined. The Green s function s can be used in a tyre/road interaction model. An advantage of the approach at Eindhoven University of Technology is that it is solely based on design data in a FEM environment. Furthermore, the applied reduction techniques limit the required computational effort. Kersjes [28] has successfully combined the method of Lopez et al. with the tyre/road contact model of Wullens [18] to predict tyre vibrations. However, no attempts have yet been made to determine the energy dissipation due to these tyre vibrations Conclusion The influence of road texture on rolling resistance is still rather unclear. Empirical studies do not always agree and measurements are often unreliable and time consuming. Few numerical models have been designed to predict the influence of road texture on rolling resistance. A full finite element analysis requires great computational effort and is therefore still out of reach. The only existing model which is able to predict rolling resistance on arbitrary road surfaces is the model of Fraggstedt [20]. The current work focusses on extending the tyre/road noise model developed at Eindhoven University of Technology with a new rolling resistance prediction module.

13 Chapter 3 JSV paper Tyre/road interaction model for the prediction of rolling resistance due to texture induced tyre vibrations Stijn Boere, Ines Lopez, Ard Kuijpers, Henk Nijmeijer As submitted to the Journal of Sound and Vibrations November 30, Abstract This work aims at predicting the influence of road texture on the rolling resistance of car tyres. A new modeling approach is proposed in which the large steady state tyre deformations are decoupled from the small texture induced tyre vibrations. The total rolling resistance is approximated as the sum of the smooth-road rolling resistance and the road texture rolling resistance. The smooth-road rolling resistance represents the energy dissipation due to the large continuous deformation of the cross section of the tyre. A nonlinear steady-state rolling analysis on a FEM tyre model is used to determine this energy dissipation. The road texture rolling resistance is the additional energy dissipation resulting from road texture induced tyre vibrations. A reduced modal representation is extracted from the FEM tyre model and is used to calculate the texture induced tyre vibrations. The inherent energy dissipation is determined and expressed as a rolling resistance coefficient. The predicted rolling resistance coefficients are compared to experimental data obtained at a test location at Kloosterzande, The Netherlands. A measurement trailer is used to determine the rolling resistance on 30 test tracks with different texture properties. Road texture profiles are measured using a stationary laser profile meter. The measurement data show a constant smooth road rolling resistance which supports the proposed modeling approach. A clear correlation is found between rolling resistance and road texture in both simulations and experiments. Increasing texture severity results in higher rolling resistance. The model predicts the correct trend regarding the increase of rolling resistance with increasing texture severity although a discrepancy in the absolute rolling resistance levels can be observed. The simulation outcomes are promising and the results support the validity of the proposed modeling approach. Future developments of the model can improve the rolling resistance prediction by including more accurate tyre data. 13

14 14 CHAPTER 3. JSV PAPER 3.2 Introduction In Europe, 18% of the total CO 2 emission originates from road transport [1]. Aerodynamic resistance, inertial forces, climbing forces and rolling resistance contribute to the total force a vehicle has to overcome to maintain constant speed. Rolling resistance is an important factor in this respect since it accounts for approximately % to the energy consumption of a typical passenger car [3, 4]. Lowering rolling resistance in pneumatic tyres can therefore greatly contribute to the reduction of greenhouse gas emissions. Rolling resistance of pneumatic tyres has been the subject of extensive study in the past. Correlations with various parameters are found such as inflation pressure, tyre material properties and tyre temperature [5, 6, 7, 8]. Most of these studies use either experimental data, analytical derivations on equivalent structures or finite element method (FEM) analyses to predict rolling resistance. Road texture is one of the parameters that has received less attention in the past. Instead, smooth road surfaces are used as an approximation which is probably due to the high computational effort involved in using the necessary detailed time domain FEM models. In order to study the effects of road texture on rolling resistance a thorough understanding of tyre and contact dynamics is required. Existing literature on the influence of road texture on rolling resistance mainly uses experimental data to relate various texture metrics to the rolling resistance level. The SILVIA project [10] provides an interesting overview of the empirical work done up till Significant increases in rolling resistance and fuel consumption are found for increasing texture severity [11, 13]. No general consensus can be found on the relative importance of different texture wavelength bands. Moreover, rolling resistance often shows a poor measurement reproducibility. Therefore, this paper proposes a modeling approach to study the effects of road texture on rolling resistance more systematically. A variety of tyre models have been developed to analyze vehicle handling, comfort and tyre wear [29, 30]. Few models are able to predict the effect of road irregularities [31]. Models that do consider the effects of road texture often aim at the prediction of tyre/road noise. The relevant frequencies concerning tyre/road noise are approximately khz. These frequencies are much higher than the frequencies that influence rolling resistance, Hz [21, 20]. Many of the existing dynamic tyre models are based on equivalent tyre structures such as plates and rings [19, 32, 33]. The parameters in these equivalent structure models have to be determined through a comparison with experimental data. This limits the use of these simplified models since every new tyre design needs prototyping in order to find the appropriate model parameters. An alternative approach is the use of finite element methods to model the dynamic behavior of the tyre. The advantage of FEM above equivalent structure methods is that representative design data is used. This allows the tyre manufacturer to assess the dynamic tyre properties without prototyping. However, due to the large number of degrees of freedom, a full scale FEM analysis requires great computational effort. Therefore, a time domain analysis using FEM is still out of reach. A time independent solution can be obtained by a steady state rolling analysis which uses an Arbitrary Lagrangian Eulerian formulation (ALE) [24, 23]. A steady-state rolling analysis allows for local mesh refinement of the contact region which is essential for accurate contact analysis. However, a steady state rolling analysis can only be performed on an axi-symmetric tyre. Therefore, it is not possible to include tread blocks. Furthermore, the effects of road texture can not be taken into account since a smooth road surface is required. This work focuses on texture induced tyre vibrations and the inherent energy dissipation which contributes to the total rolling resistance. The goal of this paper is to predict the influence of road texture on rolling resistance. A new computationally efficient modeling approach is proposed in which the large steady state tyre deformations are decoupled from the small texture induced tyre vibrations. The total rolling resistance is approximated as the sum of the smooth-road rolling resistance and the road texture rolling resistance. The two parts of the rolling resistance are analyzed separately. The smoothroad rolling resistance is the energy dissipation due to the continuous deformation of the cross section of the tyre. A nonlinear steady-state rolling analysis on a FEM tyre model is used to determine this energy dissipation. The road texture rolling resistance is the additional energy dissipation resulting from road texture induced tyre vibrations. A reduced modal representation is extracted from the FEM tyre

15 3.3. MODELING APPROACH 15 description. This modal representation is used as a boundary impedance condition in a tyre/road interaction model. This paper is organized as follows: in Section 3.3 the modeling approach is discussed in detail. The smooth-road rolling resistance is analyzed in Section 3.4. The road texture rolling resistance is analyzed using a tyre/road interaction model which is presented in Section 3.5. The results of the tyre/road interaction model are compared to results found in literature in Section 3.6. A comparison of the numerical results with measurements is given in Section 3.7. In Section 3.8 conclusions are drawn and future work is discussed. 3.3 Modeling approach There are a number of definitions of rolling resistance: it can be expressed as either a resisting force at the wheel axle, a resisting moment around the wheel axle or a power dissipation. To avoid confusion, an accurate definition of rolling resistance is important. Rolling resistance can be defined as the power dissipation P dis at a certain axle load N axle. The power dissipation depends on the resistant force F res acting on the wheel axle and the vehicle velocity v. In this study, the rolling resistance coefficient, RRC, is used to quantify rolling resistance: RRC = F res = P dis N axle N axle v. (3.1) It has been shown that the resistant force F res is linearly dependent on the applied axle load N axle in the practical range of axle loads [4]. Therefore, the rolling resistance coefficient does not change with changing axle loads. Furthermore, the rolling resistance coefficient has been shown to be fairly constant with increasing velocity [13]. This simplifies the comparison between results found in literature. Rolling resistance coefficients generally range from to for tyres on modern passenger cars [4]. Existing tyre models that predict rolling resistance assume a smooth road surface. Tyre vibrations due to road texture are therefore neglected. In order to asses the influence of road texture on rolling resistance, the vibrations in the tyre and the inherent energy dissipation should be taken into account. Therefore, this paper proposes a new computationally efficient modeling approach in which the large steady state tyre deformations are decoupled from the small texture induced tyre vibrations. The total rolling resistance is approximated as the sum of two parts (illustrated in Fig. 3.1): Smooth-road rolling resistance. The rubber elements in the tyre undergo large deformation within the contact patch as the tyre rolls over a smooth road surface. The energy which is required for this deformation is not fully recovered when the elements return to their original state. The visco-elastic rubber material dissipates energy. In a fixed reference frame, the deformation of the tyre and the tyre/road contact forces are constant in time. The power dissipation due to the large deformation of the tyre is time independent. Road texture rolling resistance. Road texture results in time varying tyre/road contact forces in the contact patch. These variations in contact forces cause vibrations in the tyre. The vibration energy is dissipated due to damping in the tread and the tyre structure. The next section describes the analysis of the smooth-road rolling resistance using a steady state rolling analysis on a FEM tyre model. The road texture rolling resistance is analyzed using a time domain tyre/road interaction model described in Section Smooth-road rolling resistance The energy dissipation in a tyre which is rolling on a smooth road surface can be modeled using a steady state rolling analysis [24, 23]. This analysis uses an Arbitrary Langrangian Eulerian reference

16 16 CHAPTER 3. JSV PAPER (a) (b) ( c) Figure 3.1: Schematic representation of the proposed modeling approach. (a) Base state (b) The smooth-road rolling resistance resulting from steady state tyre deformations. (c) The road texture rolling resistance due to texture induced tyre vibrations. frame which removes the explicit time dependency from the problem so that a purely spatially dependent analysis can be performed. The reference frame moves at the speed of the ground velocity but does not spin along with the tyre. This choice of reference frame allows the finite element mesh to remain stationary so that only the part of the body in the contact zone requires fine meshing [34]. Fig. 3.2 displays the finite element discretization of the tyre (185 SR14). The simplified model consists of a tyre belt with internal reinforcement bars. Figure 3.2: Tyre discretization The material parameters are extracted from literature [20, 19]. The rubber material in the tyre is described by a second order Prony series to model the visco-elastic modulus E(t). The rubber material parameters are condensed from data used by Fraggstedt [20] which are valid for the tread compound. For simplification, the tread compound is used to model all the rubber compounds in the tyre. This is a rough estimate since the tread compound generally has a higher loss modulus than the belt compound [20]. The tyre is loaded with an axle load of N axle = 4100N and pressed against a rigid smooth road surface. The reaction forces on the road are shown in Fig Subsequently, a steady state rolling analysis is performed at vehicle speeds, v, ranging from 20 to 100 km/h. The deformation in the tyre changes since the rotation causes a stiffening effect in the tyre. Therefore, multiple iterations are required to balance the axle forces and the reaction forces. Fig. 3.4 shows the rolling resistance coefficient (RRC) in the tyre at different vehicle velocities. The RRC increases with increasing velocity. This is unexpected since literature suggest a fairly constant rolling resistance coefficient up till 100 km/h [4, 13]. A possible explanation is that the simulations run at a constant tyre temperature. However, in reality the temperature rises when the velocity increases. Increasing temperature results in lower visco-elastic losses which significantly decreases the rolling

17 3.4. SMOOTH-ROAD ROLLING RESISTANCE 17 Contact force, Magnitude [N] e e e e e e e e e e e e e+00 Figure 3.3: Contact force distribution for a tyre load of 4100 N resistance coefficient [13]. At 80 km/h the RRC equals approximately This exceeds the expected values reported in literature [4]. This could either be a result of the mismatched temperature or the relatively high loss modulus of the tyre tread compound which is used to model all the rubber compounds in the tyre. In the future, the steady state rolling analysis can be used on improved FEM models which include more accurate tyre data and temperature effects Rolling resistance coefficient [-] Vehicle velocity [km/h] Figure 3.4: Rolling resistance coefficient as a function of vehicle velocity There is little computational effort involved in computing the smooth-road rolling resistance since the mesh remains stationary and only the contact patch requires a fine discretization. However, a steady state rolling analysis can only be performed on an axi-symmetric tyre. Therefore, it is not possible to include tread blocks. Furthermore, since this analysis is time independent it is not possible to predict road texture induced tyre vibrations. In the next section the road texture rolling resistance is analyzed using a tyre/road interaction model. The basis of the interaction model is a modal representation of the same FEM model as presented in this section. The tread blocks are modeled as separate subsystems since they are not included in the FEM model.

18 18 CHAPTER 3. JSV PAPER 3.5 Road texture rolling resistance Due to nonlinear phenomena such as the varying size of the contact patch, a tyre/road interaction model has to be represented in the time domain. Tyre/road interaction models often use Winkler beddings or elastic half spaces to describe the contact characteristics between the tyre belt and the road [35, 18]. In this work, a tyre/road interaction model is developed which is based on the approach by Andersson and Kropp [36]. The advantage of this approach is that it accounts for small wavelength road texture by applying a nonlinear contact stiffness to the road. Fig. 3.5 presents a schematic overview of the tyre/road interaction model. Dynamic response of deformed rotating tyre Tread dynamics Contact stiffness The model consists of three layers: Figure 3.5: Schematic overview of the tyre/road model Dynamic response of the deformed rotating tyre: Green s functions are used to represent the deformed rotating tyre. These Green s functions serve as a boundary impedance condition. Tread dynamics: The tread dynamics are modeled using a linear spring damper system. Contact mechanics: The contact mechanics between the tread blocks and the road surface are modeled using a nonlinear stiffness function which accounts for the indentation of the tread block by the road asperities. Fig. 3.6 shows the components of a contact subsystem in detail. The two degrees of freedom [x 1 (t), x 2 (t)] represent the position of the lowest point on the tread block and the position of the tyre belt respectively. Furthermore, p(t) represents the height of the road profile and z 1 and z 2 represent the rest positions of the tread blocks and belt respectively. The initial forces F init are imported from the FEM analysis and are shown in Fig x (t) 2 Green s functions k l d F init x (t) 1 z 2 f(p-z -x ) z p(t) Figure 3.6: Graphical representation of a contact subsystem

19 3.5. ROAD TEXTURE ROLLING RESISTANCE Dynamic response of the deformed rotating tyre The starting point for the description of the deformed rotating tyre dynamics is a FEM description of the deformed non-rotating tyre. The deformation of the tyre results from the reaction forces F init which replace the rigid smooth road discussed in the previous section. A modal analysis is performed which results in the eigenmodes and eigenfrequencies of the deformed tyre [27]. Model reduction techniques are applied in order to reduce the number of degrees of freedom and inherent computational effort. The approach proposed in Lopez et al. [25] is used to derive the dynamic equations of the deformed rotating tyre in a fixed (Eulerian) reference frame. The equation of motion becomes η(t) + D(Ω) η(t) + K(Ω)η(t) = Φ T f(t) (3.2) where η represent the modal coordinates and Φ represent the eigenmodes of the tyre. The vector f(t) contains the applied forces in the reference frame and Ω is the rotating velocity of the tyre. The modified damping and stiffness matrices D and K are defined as D = 2P(Ω, M, Φ) + D mod (3.3) K = S(Ω, M, Φ) + D mod P(Ω, M, Φ) + K mod (3.4) The reduced mass matrix, M, is extracted from the finite element discretization. The reduced stiffness matrix K mod is a diagonal matrix with elements k ii = ω 2 i, where ω i are the eigenfrequencies of the tyre. In this work, Rayleigh damping is considered: D mod = αm + βk (3.5) in which α = 500 and β = 0 to obtain the appropriate damping characteristics. For definitions of the additional stiffness and damping matrices caused by tyre rotation, S and P, the reader is referred to Lopez et al. [25]. It is stressed that for the proposed transformation only the eigenfrequencies, eigenmodes and the mass matrix are required. Future development of the model will replace the Rayleigh damping by a generalized damping matrix which is exported from the FEM environment. The dynamic behavior of the tyre as a result of applied forces in the contact patch has to be analyzed in the time domain. Therefore, the Green s functions of the system in Eq. (3.2) can be determined by solving η(t) + D(Ω) η(t) + K(Ω)η(t) = Φ T j δ(t) (3.6) where Φ T j is the jth row of Φ and δ(t) represents the Dirac delta function. The solution to this equation is determined using the method of Lopez et al. [26]. The response of the tyre to an arbitrary force input can now be determined by the convolution of the forces f i and the Green s functions g ij (t). x i (t) = j g ij (t) f i (3.7) In order to save calculation time and storage capacity only the Green s functions of potential contact nodes are determined. After all, there will be no forces acting on nodes without road contact. The obtained Green s functions model the dynamic behavior of the rotating tyre and can now be used as boundary impedance conditions in the local tyre/road interaction model. The proposed concept to acquire the Green s functions of a rotating tyre could be replaced by other methods that lead to the same result. However, the advantage of the proposed method is that it uses a FEM model which includes representative design data. Furthermore, by applying reduction techniques there is little computational effort involved.

20 20 CHAPTER 3. JSV PAPER Tread dynamics The mechanical behavior of the tread material is represented by spring damper systems. A tread block is represented by an array of such systems (Fig. 3.5). The reaction force of a spring damper system can be written as F = k l (x 1 x 2 ) + d(ẋ 1 ẋ 2 ) (3.8) in which k l represents the stiffness and d represent the damping of the tread material. These parameters are estimated based on the properties of a single tread block which are reported in literature [19]. Table 3.1 summarizes the main parameters Table 3.1: Tread layer parameters Par. Description Value l tread Length of a tread block 15 [mm] w tread Width of a tread block 20 [mm] t tread Thickness of a tread block 6 [mm] N tread Number of spring damper systems in one tread block 7 [-] E Modulus of the tread compound 20e6 [Pa] k l Spring stiffness 1.5e5 [Ns/m] d Damping 5 [Ns/m] Contact mechanics between tread blocks and road surface The contact stiffness between the tread blocks and the road surface is modeled by a nonlinear spring to account for small wavelength texture components. Due to indentation of the tread elements by road asperities the equivalent stiffness of the tread material is much lower than the bulk stiffness of the rubber. The force generated by the nonlinear spring is defined as: { f(p z1 x F (p, z 1, x 1 ) = 1 ) (p z 1 x 1 ) > 0 (3.9) 0 (p z 1 x 1 ) 0 The contact force becomes zero when the tread block loses contact with the road. This prevents the tread block from sticking to the road. On a rough road the road asperities indent the tread elements. At first contact, stiffness is low since the contact area is small. However, when full indentation occurs the stiffness must reach infinity. To fulfill these requirements, the spring characteristic f(p z 1 x 1 ) is defined as a nonlinear function of the indentation depth as described by Andersson and Kropp [36]. This approach uses a scan of the geometry of the road surface, the elastic properties of the tread compound and a model of a flat circular punch indenting an elastic layer [37]. This results in an approximate stiffness function that is unique for every pair of contact elements. A schematic representation of such a function is given in Fig In the present work only 2D texture profiles are considered. However, the model can easily be extended to be used with full 3D texture data Iterative solving routine The force equilibrium of the described system has to be determined in every time step. A graphical representation of the iterative solving routine to determine the equilibrium state is shown in Fig The routine starts at an initial guess of the vector of tread element positions at the current time step x 1 (N). Subsequently, the contact force F (N) can be determined by Eq. (3.9). The state derivatives in Eq. (3.8) can be approximated using the finite difference method. The vector of belt deformations x 2 (N) can by approximated by rewriting Eq. (3.8)

21 3.5. ROAD TEXTURE ROLLING RESISTANCE 21 treadblock Contact force treadblock Full indetation Indentation of road surface Figure 3.7: Schematic representation of the nonlinear function between the contact force and the indentation of the road surface x 1 F Update x 1 x 2 A + - x 2 B Error Figure 3.8: Graphical representation of the iterative simulation process x A 2 (N) = d(x 1(N) x 1 (N 1)) F (N)δ t + dx 2 (N 1) + δ t k l x 1 (N) d + δ t k l (3.10) in which δ t represents the time step. Alternatively, the deformation of the belt can be determined by the convolution integral of the contact forces with the Green s function in Eq. (B.2). This can be approximated in discrete time by x B 2 (N) N 1 = F (N)g(1) t + F (n)g(n n + 1) t (3.11) in which g(n) represents the discretized Green s function at time point N. This results in an error between the displacements in Eqs. (3.10) and (B.2), x A 2 (N) x B 2 (N), which should be minimized to find the solution of the problem. Therefore, the sum of squared errors is determined. Subsequently, the algorithm updates the initial guess of positions x 1 and iterates until the squared error meets the desired solution criterion. For this iterative routine the nonlinear least square solver in MATLAB is used. A graphical representation of the simulation in subsequent time steps is given in Fig Every time step, the road shifts n t number of elements forward. This results in a time step δ t n=1

22 22 CHAPTER 3. JSV PAPER δ t = n t δx v (3.12) in which v represents the forward velocity of the vehicle and δx represent the length of an element. The tread blocks move along with the road. New (undeformed) tread blocks enter at the leading edge. Tread blocks leave the contact patch at the trailing edge. The voids in between tread blocks are modeled as tread elements with a zero stiffness. t =1 ±t n+4 n+3 n+2 n+1 n n-1 n-2 n-3 n-4 n-5 n-6 n-7 n-8 n-9 n-10 t =2 ±t n+4 n+3 n+2 n+1 n n-1 n-2 n-3 n-4 n-5 n-6 n-7 n-8 n-9 n-10 t =3 ±t n+4 n+3 n+2 n+1 n n-1 n-2 n-3 n-4 n-5 n-6 n-7 n-8 n-9 n-10 Figure 3.9: Graphical representation of the simulation in subsequent time steps The proposed numerical procedure is carried out during multiple rotations of the tyre. During initialization of the simulation the sum of contact forces is monitored. If necessary, the indentation of the road p(t) is increased to match the desired axle load N axle. The simulations show good convergence although on rough road surfaces more iterations are needed. Nevertheless, the simulations require an acceptable computational effort Road texture rolling resistance The road texture rolling resistance can now be determined using the obtained force and displacement P dis = Cn i=1 1 t 2 t 1 t2 t 1 F i (t)ẋ i 1(t)dt (3.13)

23 3.6. MODEL VALIDATION 23 in which the time interval < t 1, t 2 > represents the time of one tyre revolution in which the averaged total contact force has converged to the desired load. Furthermore, Cn represent the total number of contact nodes in the contact patch. The starting time t 1 is chosen such that transient effects from axle load changes have faded out. 3.6 Model validation The simulation results presented in this section correspond to a tyre load of 4100 N and a traveling velocity of 80 km/h Influence of time discretization The effects of the time step on the simulation results are examined by comparing time histories of the belt and tread displacements. Fig shows the time history of the belt displacement of a contact node on an ISO road surface. Two simulations with different time steps are compared. The first simulation uses the smallest time step possible. In this case the tread elements shift one position (n t = 1) every time step (Fig. 3.9). The second simulation uses a double time step. In this case the tread elements shift two positions (n t = 2) in every time step and thereby skip one position. The result shows that doubling of the time step has little influence on the deformation of the tyre belt. 3.4 x 10-3 Time step δ = 0.2 ms (n =1) t t Time step δ t = 0.4 ms (n t=2) 3.2 Belt displacement x 2 [m] Time [s] Figure 3.10: Time history of the belt displacement in a contact node for two different time steps Fig shows the time history of the tread block deformation on an ISO road surface with the two different time steps. The peaks in the deformation are caused by the zero stiffness of a tread element which represents the void between two tread blocks. The results of the simulations are very similar. However, the tread elements clearly oscillate more using a small time step. A larger time step results in less tread block oscillation since half of the texture data is skipped in this case. Obviously, this influences the analysis of the level of road texture rolling resistance. Therefore, in subsequent analyses, the numerical simulations are performed with a small time step (n t = 1).

24 24 CHAPTER 3. JSV PAPER 5 x 10-3 Time step δ = 0.2 ms (n =1) t t Time step δ t = 0.4 ms (n t=2) Tread block displacement x 1 [m] Time [s] Figure 3.11: Time history of the tread block displacement in a contact node for two different time steps Tread block contact force Fig shows the contact force of a tread block as it travels through the contact patch. The time-axis is normalized with the time needed for one complete revolution (T rev ). The predicted force is similar to the results found by O Boy and Dowling [21]. In their work, the tread block forces oscillate more which is probably a result of neglecting tread damping. Experimentally recorded tread block forces found by O Boy and Dowling do show the sharp first peak which is probably caused by the sudden compression of the undeformed tread blocks entering the contact patch. However, the second peak is not present in their experimental results and the contact force slowly decreases while traveling through the contact patch. This could indicate that the damping of the tread blocks is underestimated in the present work. 3.7 Influence of road texture on rolling resistance Road texture measurements Road texture profiles are measured using a stationary laser profile meter and used as input into the numerical model. The laser profile meter has a resolution of 0.2 mm and a measurement length of 2.8 m. The 2D measurements are taken on a test site at Kloosterzande, The Netherlands. The test site contains 30 road surfaces with different texture properties. These road surfaces can be divided into six road structure categories shown Table B.2. To quantify the road texture in one single measure, the root mean square texture depth is used: RMS tex = 1 l l 0 Z(x) 2 dx (3.14) where Z(x) represents the height of the profile with respect to the average level within the length of the profile l.

25 3.7. INFLUENCE OF ROAD TEXTURE ON ROLLING RESISTANCE Contact Force [N] Time/T rev Figure 3.12: Contact force on a tread block traveling through the contact patch Table 3.2: Road structure categories Pavement type Designation ISO10844 standardized road surface ISO Stone Mastic Asphalt SMA Dense Asphalt Concrete DAC Thin Layered Asphalt TLA Single layer Porous Asphalt Concrete PAC Double layer Porous Asphalt Concrete DPAC Influence of road texture on total rolling resistance Numerical simulations on the 30 texture profiles are carried out to determine the road texture rolling resistance. The smooth-road rolling resistance remains constant on all surfaces. Fig shows the rolling resistance coefficient (RRC) as a function of the texture depth RMS tex. There is a clear correlation between road texture and rolling resistance. Rolling resistance increases linearly with texture depth. A decrease in RMS tex of 1mm results in a decrease in rolling resistance of approximately 7% Rolling resistance measurements The numerical results are compared to measurements performed on a test site at Kloosterzande, The Netherlands. The rolling resistance is measured using a trailer from the University of Gdansk, Poland. This trailer measures the ratio between the rolling resistance force and the axle force, i.e. the rolling resistance coefficient RRC. The trailer is equipped with a Continental 225/60 R16 test tyre. The measurements are taken at a velocity of 80 km/h and an axle load of 4100 kg. Fig shows the total rolling resistance on 30 different road surfaces in both the numerical simulations and the experimental measurements. The measurements clearly indicate the presence of a smooth-road rolling resistance and a road texture rolling resistance. This observation supports the proposed modeling approach. The smooth-

26 26 CHAPTER 3. JSV PAPER Rolling Resistance Coefficient [-] ISO SMA DAC TLA PAC DPAC Trendline numerical results RMS [m] tex x 10-3 Figure 3.13: Rolling resistance in simulations with 30 texture profiles at 80 km/h Rolling Resistance Coefficient [-] ISO SMA DAC TLA PAC DPAC Trendline numerical results Trendline experimental results RMS [m] x 10-3 tex Figure 3.14: Rolling resistance simulations and measurements on 30 test tracks at 80 km/h road rolling resistance is approximately and is therefore in the same order as in the numerical FEM simulations. The road texture rolling resistance clearly grows with increasing texture depth. The

27 3.8. CONCLUSION 27 trends in the numerical and experimental results match despite the rough estimation of the model parameters. Absolute rolling resistance levels do not match. This is probably a result of neglecting temperature changes or the high loss factor of the rubber compound used in the model. Nevertheless, the numerical results are promising as they illustrate the potential of the proposed modeling concept. 3.8 Conclusion This work aims at predicting the influence of road texture on rolling resistance in car tyres. A new modeling approach is proposed in which the large steady state tyre deformations are decoupled from the small texture induced tyre vibrations. The total rolling resistance is approximated as the sum of the smooth-road rolling resistance and the road texture rolling resistance. Both parts of the rolling resistance are analyzed separately. However, both the analyses are based on the same FEM model. The advantage of the proposed approach is that a reduced FEM tyre model can be used in the interaction analysis between the road and the tread blocks which reduces the computational effort. The smooth-road rolling resistance is the energy dissipation due to the continuous deformation of the cross section of the tyre. This energy dissipation is analyzed using a nonlinear steady-state rolling analysis on the FEM model. The road texture rolling resistance is the additional energy dissipation resulting from road texture induced tyre vibrations. A tyre/road interaction model is developed which uses a reduced modal representation of the deformed tyre. The modal representation is extracted from the FEM environment and transformed to represent a deformed rolling tyre. Green s functions are constructed and used as a boundary impedance condition for the tyre road interaction model. The tread elements are modeled by linear spring damper systems. Measured texture profiles are used as input for the tyre/road interaction model. Small wavelength texture components are included by a non-linear contact stiffness formulation. The simulations show good convergence and require an acceptable computational effort. Simulated forces in the contact patch show good resemblance with results found in literature. The numerical results are compared to measurements on 30 test tracks on a test location at Kloosterzande, The Netherlands. Road texture profiles are measured using a stationary laser profile meter. The measurement data shows a constant steady state rolling resistance which supports the modeling approach. A good correlation is found between rolling resistance and texture severity in both simulations and experiments. Increasing texture depth results in higher rolling resistance. The numerical results show good resemblance with the experimental results although absolute rolling resistance levels do not match. However, the outcomes of the simulation are promising as they support the validity of the proposed modeling concept. The proposed concept can be used to develop an interaction model which includes the use of relevant design data. Acknowledgements The authors wish to thank DVS (Dienst Verkeer en Scheepvaart) for their financial support.

28 28 CHAPTER 3. JSV PAPER

29 Chapter 4 Conclusions and Recommendations 4.1 Conclusions This work extends the tyre/road noise model developed at Eindhoven University of Technology with a rolling resistance prediction module. A new three dimensional tyre/road interaction model is implemented which is able to account for small wavelength road texture. The energy dissipation is determined for several different road surfaces. The numerical results are compared to rolling resistance measurements. The main conclusions of this project are: The influence of road texture on rolling resistance is still rather unclear in literature. Empirical studies do not always agree and measurements are often unreliable and time consuming. There seems to be no general consensus in the relative importance of different texture wavelength regions. Therefore, there is a need to study the effects of road characteristics on rolling resistance more systematically. Since a full scale FEM analysis requires great computational effort, more efficient modeling techniques have to be developed. Measurements of rolling resistance on 30 test tracks indicate that the total rolling resistance can be approximated as the sum of the smooth road rolling resistance and the road texture rolling resistance. The smooth road rolling resistance is the energy dissipation due to the continuous deformation of the cross section of the tyre. The road texture rolling resistance is the additional energy dissipation resulting from road texture induced tyre vibrations. The smooth road rolling resistance can successfully be determined using a nonlinear steadystate rolling FEM analysis. This computationally efficient analysis accounts for the large nonlinear tyre deformations. The energy dissipation levels found in the steady state rolling analysis are in the same order of magnitude as the measurements results. Better results could be obtained by a more detailed FEM model and better estimates of the material properties. The road texture rolling resistance can successfully be determined by the developed three dimensional tyre/road interaction model. A modal superposition approach is used to model the dynamic behavior of the tyre. The assumption is that the small scale transient dynamic behavior due to road texture can be decoupled and superimposed onto the steady state tyre deformations resulting from a smooth road surface. The numerical results are in accordance with the experimental data with regard to the increase in rolling resistance with increasing texture depth. Time histories of contact forces in a single tread block show good resemblance with results found in literature. The tyre/road interaction simulations show good convergence and require little computational effort. Mesh refinements are therefore within reach using the current computational resources. Mesh refinement in the circumferential direction allows for smaller time steps. Mesh refinement in the axial direction allows for the implementation of detailed tread block patterns and full 3D road texture profiles. 29

30 30 CHAPTER 4. CONCLUSIONS AND RECOMMENDATIONS The relative contribution of road texture rolling resistance grows up to 20% with respect to the total rolling resistance for rough (commonly used) road surfaces. There exists a linear correlation between rolling resistance and RMS road texture depth. An increase in texture depth of 1 mm results in an increase of rolling resistance of approximately 7%. 4.2 Recommendations This thesis presents several interesting issues that deserve further research. Model extensions and refinements are the most important in this respect. Furthermore, the experimental verification of the model needs more work. Finally, the model offers the opportunity to examine the effects of road texture parameters which can not be tested in a test setup. Some specific recommendations include: Improve the FEM tyre model with more accurate material properties and by including temperature effects. This will give a more realistic prediction of the smooth road rolling resistance. Furthermore, it improves the estimated Green s function used in the tyre/road interaction model. Use a generalized damping model in both the smooth road rolling resistance analysis and the road texture rolling resistance analysis. Instead of using Rayleigh damping, a generalized damping matrix could be extracted from the FEM environment. Develop a method to accurately determine the properties of the springs and dampers in the tyre/road interaction model. A detailed FEM model of a tread block could be used to further examine the parameters of the tread block model used in the tyre/road interaction simulation. Develop a laboratory environment in which the dynamics and the rolling resistance of different tyres on different road surfaces can be tested under controlled test conditions. The reproducibility of the current measurement method is insufficient. Furthermore, the rolling resistance trailer provides little insight into the dynamics of the rolling tyre. To fully understand the dynamics of a rolling tyre, the tread block forces and tyre vibrations should be recorded and compared to numerical simulations. Therefore, a more robust measurement method is required which is able to record the tyre dynamics and in which test conditions such as temperature, vehicle velocity and axle load can be monitored and controlled. Use the tyre/road interaction model to determine the relative importance of different texture wavelength regions on rolling resistance. This analysis is very difficult on a physical setup since there is a large inter-correlation between texture wavelength regions in measured road profiles. The advantage of the numerical model is that the rolling resistance can be determined on synthesized profiles. Decrease the element size in the contact patch of the FEM model. Smaller elements allow for smaller time steps in the tyre road interaction simulation and therefore higher frequency tyre vibrations can be captured. Ultimately, one arrives at a model that predicts tyre vibrations which are important in tyre/road noise generation mechanisms.

31 Bibliography [1] European Environment Agency. Greenhouse gas emission trends and projections in Europe [2] R. Smokers and R. Vermeulen et al. Review and analysis of the reduction potential and costs of technological and other measures to reduce co2-emissions from passenger cars Contract nr. SI , Final Report. TNO Report, Oct 31, [3] Forum of European National Highway Research Laboratories (FEHRL). FEHRL study SI Tyre/Road Noise. volume 1, [4] Société de Technologie Michelin. The Tyre - Rolling resistance and Fuel Savings [5] J. D. Clark and D. J. Schuring. Load, speed and inflation pressure effects on rolling loss distribution in automobile tires. Tire Science and Technology, 16(2):78 95, [6] Z. Shida, M. Koishi, T. Kogure, and K. Kabe. A rolling resistance simulation of tires using static finite element analysis. Tire Science and Technology, 27(2):84 105, [7] W. V. Mars and J. R. Luchini. An analytical model for the transient rolling resistance behavior of tires. Tire Science and Technology, 27(3): , [8] D.S. Stutts and W. Soedel. A simplified dynamic model of the effect of internal damping on the rolling resistance in pneumatic tires. Journal of Sound and Vibration, 155(1): , [9] U. Sandberg and J.A. Ejsmont. Tyre/road noise reference book. INFORMEX Ejsmont & Sandberg Handelsbolag, SE Kisa, Sweden, first edition, [10] H. Bendtsen. SILVIA PROJECT REPORT, Rolling Resistance, Fuel Consumption and Emissions: A Literature Review Danish Road Institute, Technical Note. [11] U.S.I. Sandberg. Road macro- and megatexture influence on fuel consumption. ASTM Special Technical Publication, (1031): , [12] Anita Ihs and Georg Magnusson. The significance of various road surface properties for traffic and surroundings VTI notat, 71A Swedish National Road and Transport Institute. [13] Guy Descornet. Road-surface influence on tire rolling resistance. ASTM Special Technical Publication, (1031): , [14] P.D. Cenek and P.F. Shaw. Investigation of new zealand tyre/road interactions Road Research Bulletin. [15] M.H.R. Ghoreishy. A state of the art review of the finite element modelling of rolling tyres. Iran Polymer and Petrochemical Institute, 17(8): , [16] G. Meschke, H. J. Payer, and H. A. Mang. 3d simulations of automobile tires: Material modeling, mesh generation, and solution strategies. Tire Science and Technology, 25(3): , [17] W. Hall, J. T. Mottram, and R. P. Jones. Tire modeling methodology with the explicit finite element code ls-dyna. Tire Science and Technology, 32(4): ,

32 32 BIBLIOGRAPHY [18] F. Wullens and W. Kropp. A three-dimensional contact model for tyre/road interaction in rolling conditions. ActaAcustica/Acustica, 90: , [19] K. Larsson, S. Barrelet, and W. Kropp. The modelling of the dynamic behaviour of tyre tread blocks. Applied Acoustics, 63: , [20] M. Fraggstedt. Vibrations, damping and power dissipation in Car Tyres Doctoral Thesis. [21] D.J. O Boy and A.P. Dowling. Tyre/road interaction noise numerical noise prediction of a patterned tyre on a rough road surface. Journal of Sound and Vibration, 323(1-2): , [22] D.J. O Boy and A.P. Dowling. Tyre/road interaction noise a 3d viscoelastic multilayer model of a tyre belt. Journal of Sound and Vibration, 322(4-5): , [23] Maik Brinkmeier, Udo Nackenhorst, Steffen Petersen, and Otto von Estorff. A finite element approach for the simulation of tire rolling noise. Journal of Sound and Vibration, 309(1-2):20 39, [24] U. Nackenhorst. The ale-formulation of bodies in rolling contact: Theoretical foundations and finite element approach. Computer Methods in Applied Mechanics and Engineering, 193(39-41): , [25] I. Lopez, R. Blom, N. Roozen, and H.Nijmeijer. Modelling vibrations on deformed rolling tyres - a modal approach. Journal of Sound and Vibration, 307(3-5): , [26] I. Lopez, S.H.M. Kersjes, N.B. Roozen, A.J.C. Schmeitz, and H. Nijmeijer. Green s functions for a rotating tyre: A semi-analytical approach , Proceedings of Euronoise 2006, Tampere, Finland. May 30 - Jun 1. [27] I. Lopez, R.R.J.J. van Doorn, R. van der Steen, N.B. Roozen, and H. Nijmeijer. Frequency loci veering due to deformation in rotating tyres. Journal of Sound and Vibration, 324(3-5): , [28] S.H.M. Kersjes. Tire/road contact modelling for a rolling tire Master Thesis, DCT [29] Hans B. Pacejka. Tyre and vehicle dynamics. Butterworth Heinemann, Oxford, [30] H. Lupker, F. Cheli, F. Braghin, E. Gelosa, and A. Keckman. Numerical prediction of car tire wear. Tire Science and Technology, 32(3):., [31] A.J.C. Schmeitz, S.T.H. Jansen, H.B. Pacejka, J.C. Davis, N.M. Kota, C.G. Liang, and G. Lodewijks. Application of a semi-empirical dynamic tyre model for rolling over arbitrary road profiles. International Journal of Vehicle Design, 36(2-3): , [32] Y. J. Kim and J. S. Bolton. Effects of rotation on the dynamics of a circular cylindrical shell with application to tire vibration. Journal of Sound and Vibration, 275(3-5): , [33] P. Kindt, P. Sas, and W. Desmet. Development and validation of a three-dimensional ring-based structural tyre model. Journal of Sound and Vibration, 326(3-5): , [34] SIMULIA. Steady-state transport analysis, Section of the Abaqus Analysis User s Manual [35] J.F. Hamet and P. Klein. Use of a rolling model for the study of the correlation between road texture and tire noise Proceedings of Internoise 2001, The Hague, The Netherlands. [36] P.B.U. Andersson and W. Kropp. Time domain contact model for tyre/road interaction including nonlinear contact stiffness due to small-scale roughness. Journal of Sound and Vibration, 318(1-2): , 2008.

33 BIBLIOGRAPHY 33 [37] Fuqian Yang. Indentation of an incompressible elastic film. Mechanics of Materials, 30(4): , 1998.

34 34 BIBLIOGRAPHY

35 Appendix A FE model This chapter will provide a detailed description of the finite element analysis which is performed in the software package Abaqus. The complete analysis can be executed with the Matlab script run_abaqus _analysis.m which executes the Abaqus input files from the command prompt. The analysis consists of three stages: 1. In the first stage the mesh of the tyre is constructed, the static tyre is loaded and the contact forces are recorded and saved to the Matlab workspace. 2. In the second stage the steady state rolling resistance is determined and exported to the Matlab workspace. 3. In the third stage the recorded contact forces obtained in the first stage are applied to the static tyre and a modal analysis is performed. Subsequently, the system matrices are imported into the Matlab workspace. In the remaining of this section the three stages will be described in more detail. 35

36 36 APPENDIX A. FE MODEL Stage 1: Tyre mesh, loading and contact forces determine_cf_a.inp The first step in the construction of the finite element model is the definition the cross section of the tyre. Fig. A.1 shows the tyre cross section which is used in this project. The cross section consists of 152 nodes which are defined in the Abaqus input file tiretransfer_node.inp. The first 105 nodes define the base (rubber) elements. Nodes construct the fiber-reinforced rubber elements of the tyre belt and carcass. Rubber elements Fiber-reinforcent belt elements Carcass elements X Z Y Figure A.1: Cross section of the tyre The material properties of the three materials are defined: Belt: A linear elastic material with an elastic modulus of GPa. Carcass: A linear elastic material with an elastic modulus of 9.87 GPa. Rubber: A visco-elastic material modeled by means of a Prony series: E(t) = E 0 (1 n (p i (1 e t τ i ))) i=1 (A.1) To obtain the parameters E 0, p i and τ i the Prony series is fitted against data from Fraggstedt [20] using the fitting routine optimize.m. Fig. A.2 shows the fitting result. It has to be noted that the moduli of Fraggstedt are scaled so that the tyre eigenfrequencies match the ones found in literature. However, the loss ratio is kept equal. The Prony parameters can be found in Table A. Table A.1: Prony parameters E 0 3.3e6[N/m 2 ] p [ ] p [ ] τ e-5[s] 1.20e-3[s] τ 2 Finally, the 2D cross section is inflated with a pressure of 2 bar while the nodes in contact with the rim are tied to the axle node.

37 x Storage modulus 106 Fraggstedt Fit 3 Re(E) [Pa] Im(E) [Pa] Frequency [Hz] (a) 9 x Loss modulus 105 Fraggstedt 8 Fit Frequency [Hz] (b) Fraggstedt Fit Tan(δ) Loss ratio [-] Frequency [Hz] (c) Figure A.2: Prony series material model in the frequency domain (a) Storage modulus (b) Loss modulus (c) Lossfactor.

38 38 APPENDIX A. FE MODEL determine_cf_b.inp The 2D cross tyre cross section is revolved around the center node. The contact patch has a finer discretization than the rest of the tyre. In this project the contact mesh is modeled using a mesh size of 1.25 in circumferential direction in the contact patch (32 elements within 40 ). The mesh size in circumferential direction outside the contact patch is 4 (41 elements within 164 on both sides of the contact patch). Fig. A.3 shows the resulting three dimensional tyre mesh. Figure A.3: 3D tyre mesh The three dimensional tyre mesh is inflated with an internal pressure of 2 bar. The long term deflection of the tyre is determined and subsequently the tyre is pressed against a rigid plane road. The initial contact is made using a predefined displacement of 1 mm to avoid numerical problems. Subsequently, the tyre is pressed against the rigid plane road with a force of 4350 N using load control. The contact forces are recorded and stored in the output database. The footprint of the tyre is shown in Fig. A.4. CNORMF, Magnitude e e e e e e e e e e e e e+00 Figure A.4: Footprint of the tyre on the road The contact forces can be extracted using the Python script extract_cf.py. The Python script exports the contact forces at the contact nodes to the data file CNORMF.dat from which they can be imported into Matlab.

39 39 Stage 2: Steady state rolling analysis SST_axleforce.inp First, the tyre mesh is constructed from the start using the results from determine_cf_a. The tyre is loaded as described in the previous section only now a load of 4100 N is applied. Friction of the road is set to zero. The steady state rolling analysis is performed at a velocity of 80 km/h which, at a tyre radius of 316 mm, corresponds to an angular velocity of 70.2 rad/s. The tyre stiffens during rotation. Therefore, the position of the tyre with respect to the road is load controlled. The total reaction force should therefore remain at 4100 N and is exported to the database for verification. Furthermore, the resisting moment around the central rim node is exported to the database to determine the energy dissipation in the tyre. In the steady state rolling analysis a zero friction between the road and the tyre is assumed. In reality this is obviously not the case as the tyre would not create any traction. This analysis therefore does not simulate a free-rolling tyre: the resisting forces are not equal to the traction forces. However, in the current analysis the focus lies on rolling resistance forces instead of traction forces. The assumption is that with friction the contact patch has approximately the same shape as without friction. Therefore, the rolling resistance is assumed to be the same in both cases. The total contact force and the resisting moment around the central rim node can be imported into Matlab using the Python script extract_rrmoment.py. The Python script extracts the forces and moments to a data file moment.dat from which they can be imported into Matlab. The energy dissipation RR SST power can be determined by: RR SST power = RR SST momentv r tyre (A.2) in which v represents the velocity and r tyre represents the tyre radius. The rolling resistance coefficient RR SST rrc can be determined by: in which N axle represents the axle load. RR SST rrc = RR SST power N axle v (A.3)

40 40 APPENDIX A. FE MODEL Stage 3: Modal analysis Ab_ex_tire_1.inp The tyre is constructed constructed again from scratch. The only difference is the definition of the material parameters. During a modal analysis the visco-elastic material must be evaluated at a predefined frequency. Therefore, the visco-elastic material properties are replaced by a linear elastic material model. The elasticity is chosen to be equal to 1.4 MPa which is the storage modulus in the visco-elastic material at a frequency of 100 Hz. Furthermore, a new node set is defined which contains the master nodes. The master nodes will be retained in subsequent model reduction techniques. The master nodes can be divided into two categories. The boundary master degrees of freedom (6 nodes) are used to fix the tyre to the rim. The internal master degrees of freedom give a reduced representation of the tyre. The master nodes are illustrated in Fig. A.5. Internal master degrees of freedom Boundary master degrees of freedom X Z Y Figure A.5: Masternodes in a cross section of the tyre make_modal_analysis.m The rim nodes are untied to the axle node. The recorded contact forces from the first section are applied to the contact nodes. These forces are therefore written to the Abaqus input file using the the Matlab script make_modal_analysis.m. This script adapts the Abaqus file modal_analysis.inp so that it contains the appropriate contact forces from the data file CNORMF.dat.

41 41 modal_analysis.m In the modal analysis the first 600 eigenfrequencies and eigenmodes are determined and written to the output database. Fig. A.6 shows one such eigen mode at a frequency of 129 Hz. Additionally, the reduced mass matrix which only contains the master nodes is exported to the output file modal_analysis.fil. Figure A.6: Eigenmode of the tyre at 129 Hz. The output file can be imported using the Matlab script ab2mat.m. It has to be noted that this is a process which requires a lot of computational effort. ab2mat.m outputs the structure model that contains the base coordinates of the mesh, the mass matrix, eigenmodes and eigenfrequencies. This structure is saved as a Matlab file system_matrices.mat for further use.

42 42 APPENDIX A. FE MODEL

43 Appendix B Tyre/road interaction model This chapter provides a detailed description of the tyre/road interaction model. First, the global structure of the model is discussed and then the individual Matlab functions will be discussed in detail. A graphical overview of the numerical model with the different functions is given in Fig. B.1. The basis of the code is the file start_up.m which runs the entire analysis. The complete analysis can be divided into three stages which will be discussed separately.: 1. The first stage is the modal transformation of the system matrices and the construction of the Green s functions. 2. The second stage is the tyre/road interaction model. 3. The third stage consists of postprocessing and visualization of the results. During these stages the results and variables will be stored in different structures as shown in Table B.1 Table B.1: Road structure categories Matlab structure var model modtrans green road simu anim results Content Input and dependent variables System matrices and coordinates Matrices used in the modal transformation Green s functions and time vector Raw and discretized road data Tyre/road interaction simulation results Animation data Results from the rolling resistance analysis Before the first stage starts in the function start_up.m, the data from the FEM analysis is loaded into Matlab: Mass matrix, eigen modes and eigen frequencies in model Node coordinates and indices in model Road data in road Contact forces in contact 43

44 44 APPENDIX B. TYRE/ROAD INTERACTION MODEL 1. Modal transformation and Green s functions Input_ variables.m Contact_ nodes.m Timestep.m Load_ modes_ 3d.m Modal_ transform.m Rotate_ modes2.m Spat_ der_ ruud_ nonuni_ cond.m Green_ func_ analytic.m 2. Tyre/road interaction modeling Road_ texture.m Solve_ contact_ problem.m Green_ eval.m Start_ up.m Lsqnonlin.m Contact_ problem.m Nonlinearspring.m Springdamper.m 3. Postprocessing Rolling_resistance.m Tyre_deformation.m Animate_patch.m Animate_tyre.m Figure B.1: File structure of the tyre/road interaction model

45 45 Stage 1. Modal transformation and Green s function The eigenmodes, eigenfrequencies and mass matrix exported from the FEM analysis represent a deformed static tyre. It is well known that rotation of the tyre influences these characteristics and should be taken into account. The goal of the first stage is to apply a modal transformation to account for rotation in the tyre and subsequently to determine the Green s functions of the contact nodes. These Green s functions form the basis of the tyre/road interaction model which is described in the next section. The first stage is computationally not very demanding. The calculation of the Green s functions requires most effort and increases with increasing contact nodes and decreasing time steps. However, the bottleneck in this stage is the storage capacity of the system. The mass matrix in the current simulation has dimensions 7686 by 7686 elements. In other words, the mass matrix consist of almost 60 million entries. The current mass matrix uses approximately 500 megabytes of RAM memory. During the analysis on 32 bit operating systems, out-of-memory problems might occur. On Windows XP this can be solved by the 3Gb memory switch (edit the boot.ini file). A better solution is to work on a 64 bit machine. This section will discuss the functions in the first stage which are called by the the function start_up.m. input_variables.m A number of variables are defined in the structure var. These variables control the entire analysis. File reference Input: Output: model Variables that control the simulation Table B.2: Simulation parameters Variable Meaning Default value nom The number of modes taken into account 100 alpha Rayleigh damping parameter [-] 300 d Linear damping coefficient for tyre tread elements 5 [Ns/m] kl Linear spring constant for tyre tread elements 0.15e5 [N/m] G Shear modulus tread rubber [Pa] 0.6e6 [Ns/m] n_rev Time span of the simulation [tyre revolutions] 10 nodes_per_timestep Nodes that are shifted per timestep 1 nps Number of nodes per segment (cross section) 21 tyre_radius Tyre radius [m] /2; width_treadblock Treadblock width in axial direction [m] 15e-3 height_treadblock Treadblock height [m] 6e-3 nr_nodes_treadblock Number of subsystems within one treadblock 7 z3 Initial position of the belt A [m] z2 Initial position of the belt B [m] z1 Initial position of the tread indentation Indentation of the tyre by the road

46 46 APPENDIX B. TYRE/ROAD INTERACTION MODEL contact_nodes.m The contact patch can vary in size with respect to time. Therefore, the nodes are determined which potentially make contact with the road. This is done in the function contact_nodes.m. File reference Input: Output: model,contact Potential contact nodes Contact node indices First, the structure model.base_co is adjusted so it contains the coordinates of the reduced set of tyre nodes instead of all nodes. Then the structure model.def_coord is created so that is consists the deformed coordinates of the subset of tyre nodes. In Abaqus an axle load of 4350 N was applied to the tyre. However, the desired axle load is only 4100 N. Therefore, all the nodes that potentially make contact with the road are already identified. The node numbers and forces are stored in the structure contact.force. The position of these nodes in the coordinate matrix model.base_co is determined and stored in the vector contact.node_indices_all_vec The rows on which the contact nodes are located are identified. These rows are illustrated in Fig. B.2 and stored in the vector contact.node_row. Every node has three coordinates. The position of the first coordinate of each node in the eigenmode matrix is determined. Finally the contact forces are conveniently stored in the vector F_init Contact node row Figure B.2: Simplified illustration of the contact patch, node numbers and contact rows

47 47 timestep.m The frequency is determined at which the Green s function are sampled. This depends on the length of an element in circumferential direction, the vehicle velocity and the number of nodes that are shifted per time step. File reference Input: Output: model,var,contact Time step Length of a contact patch element in circumferential direction First, the length of an element is determined by taking the difference between the maximum and minimum of the x coordinate in model.def_coord and dividing this by the number of contact rows. The time step is defined as the length of an element divided by the vehicle velocity. The length of a treadblock is determined as the amount of nodes per treadblock times the length of an element. load_modes3d.m The eigen modes and eigen frequencies are loaded. File reference Input: Output: model,var Base coordinates of the nodes modtrans.base_co_full Matrix with eigenvectors modtrans.u Sparse matrix of eigenfrequencies modtrans.v The base coordinates are stored in a new vector modtrans.base_co_full and the eigenmodes are stored in a new matrix modetrans.u. This matrix has the dimension 3*var.non time var.nom: Mode 1 Mode 2 Mode 3 Mode i x 1 y 1 z 1 x 1 y 1 z 1 x 1 y 1 z 1 x 1 y 1 z 1 base_ co_ full = x 2 y 2 z 2 U = x 2 y 2 z 2 x 2 y 2 z 2 x 2 y 2 z 2 x 3 y 3 z 3 x 3 y 3 z 3 x 3 y 3 z 3 x 3 y 3 z 3 The eigen frequencies are stored in a sparse matrix var.v

48 48 APPENDIX B. TYRE/ROAD INTERACTION MODEL modal_transform.m The modal transformation is applied to the system matrices. File reference Input: Output: model,modtrans,var Matrix of right and left eigenvectors modtrans.u_1 and modtrans.u_2 Vector with (left) eigen frequencies modtrans.s_1 The (near diagonal) matrix modtrans.a First, the Rayleigh damping matrix D is defined with the Rayleigh variable var.alpha Next the system matrices are modified to account for the rotation of the tyre. The time derivatives of the eigenmodes are determines in rotate_modes2.m. Therefore, the spatial derivatives of the eigenmodes have to be determined by spat_der_nonuni_cond_ruud.m. For further reference on the transformation the reader is referred to [26, 25, 28, 27]. The system is rewritten in a first order form. Subsequently, the matrix of right and left eigenvectors modtrans.u_1 and modtrans.u_2 is constructed, the vector with eigen frequencies modtrans.s_1 is constructed and the (near diagonal) matrix modtrans.a is determined. green_func_analytic.m The Green s function are precalculated. File reference Input: Output: modtrans,contact,var Matrix (size: non*non*time_samples) with green s function green.functions Time samples for Green s functions Matrix with green s function shifted 1 dimension green.functions_shiftdim First, the time is defined in green.time. In the default case 200 time samples are chosen. However, is the damping is decreased or increased this should be changed. The amount of time samples has to be sufficient for the Green s functions to fully attenuate to zero. Too many time samples will decrease the efficiency of the model. The Green s function are constructed in green.functions using the eigenmodes of the original system modtrans.u, the right and left eigenvalues of the first order system modtrans.u_1 and modtrans.u_2, the eigenfrequencies of the first order system modtrans.s_1 and the diagonal entries of the matrix modtrans.a. Again, for further reference on the construction of these Green s functions the reader is referred to [26, 28]. The Green s function are modified for increased efficiency during the tyre/road interaction simulation. First, the beginning zero entry of the Green s functions is deleted. This zero entry would prevent a force in a time step to have any effect on the deformation in the same time step. This approach is in accordance to Kropp and Andersson. [36].

49 49 The Green s functions matrix is 3 dimensional with the time on the third dimension. During the tyre/road interaction simulation the Green s function will have to be convoluted with the contact forces. Therefore, the Green s functions should be easily accessible. A call for the Green s function green.functions_shiftdim(1,1,:) (force on the first node - excitation of the first node) does not result in a normal vector but to entries in the third dimension. In Matlab squeeze commands would be required to overcome this problem. Since the squeeze command is computationally inefficient the dimensions of the Green s function matrix are shifted to the left by one dimension. Now a call to green.functions_shiftdim(1,:,1) provides the correct (vector) result without the need for squeeze commands. Finally an example of the Green s function is plotted to check whether the correct amount of time samples is chosen. An example of a Green s function with the default parameters is given in Fig. B.3; 8 x 10-3 Green s function of node to node Amplitude [m] Time [s] Figure B.3: Example of a Green s function

50 50 APPENDIX B. TYRE/ROAD INTERACTION MODEL Stage 2: Tyre/road interaction The second stage of the analysis covers the interaction between the road surface and the tyre. In this section a global overview of the model is provided. Subsequently, the different parts of the simulation will be discussed in more detail. The tyre/road interaction model can be executed with the function solve_contact_problem.m. Fig. B.4 provides an overview of the tyre/road contact model. x (t) 2 Green s functions x (t) 3 k l d F init x 1(t) z 2 f(p-z -x ) z 3 z p(t) Figure B.4: Graphical representation of the contact model Fig. B.5 shows the algorithm which is used to solve the contact problem. Important to note is that the forces and displacements in this diagram all represent vectors with the size of the number of contact nodes. 1. The algorithm starts at time N with an initial guess of the displacement at the surface of the tread block x Using the displacement x 1, the rest rest position z 1, the road profile p(t) and the corresponding nonlinear stiffness function f(p z 1 x 1 ), the force in the nonlinear contact spring can be determined by the function nonlinearsping.m. 3. Using the obtained force F and the displacement from the previous time step x 1,old and x 2,old the displacement of the upper side of the treadblock can be determined by springdamper.m. 4. By subtracting the initial force F i nit from the force F the force on the belt is determined. Note: since the forces applied to the tyre in Abaqus were larger than required the outcome is a negative force pulling the belt down. Using the force and the position of the belt in the previous time step, the position of the belt in the current time step can be determined by green.m. 5. Adding the rest position and subtracting the result from (3) and (4) results in an error which should be minimized. Therefore, the nonlinear least square solver lsqnonlin.m of Matlab is used. The optimization routine squares and sums the error. 6. The Matlab optimization routine updates the position x 1 and iterates until the error is minimized and the problem has converged.

51 After the problem has converged the treadblocks and the road are shifted in position. The current positions x 1 and x 2 become the old position x 1,old and x 2,old. 8. Finally x 1,old is taken as a first guess of the next N + 1 iteration and the restart at (1). The remaining of this section will describe the subsequent functions called by start_up.m during the second stage. START Take x1,old as first guess x z 1 p(t) k (t) nl nonlinearspring.m F + - F init x 2,old x 1,old x 2,old springdamper.m green.m Update x 1 x 2 x 3 z z 3 Error Shift road and treadblocks Converged? YES NO Figure B.5: Algorithm to solve the contact problem

52 52 APPENDIX B. TYRE/ROAD INTERACTION MODEL road_texture.m First, the road is divided into road sections with the length of one element. Next, the contact stiffness of the road sections is determined. File reference Input: Output: var,road Discretized profile height of road sections road.profile_road_disc_repmat Contact stiffness related to the road sections road.profile_road_disc The resolution of the data initialized. With the data measured by M+P this is 0.2 mm. One road texture line is extracted from the data. In future version multiple line could be taken into account. However, the model currently uses a 2D extruded texture profile. The rounded number of texture points within one element is determined as the element size divided by the data resolution. With the default simulation parameters there are 22 points within one element. Next, the road elements are processed. The midpoint of a road section is determined and the maximum of 22 points is determined. The points within one section are stored and the minimum and maximum is determined. Next, an indentation array d_vec is constructed which runs from zero indentation to half indentation and consists of 100 points. Half indentation has shown to produce sufficient forces. The force for every indentation is determined using the function [37]: F = 3πµr4 eqd vec 2h(d) 3 (B.1) in which r e q is the radius of a circle with the same surface area as a contact element. The height h(d) is the un-indented part of the tread block. An exponential function is fitted through the contact force points. Monotonicity is crucial for the fitted function as non-monotonic function will cause convergence problems in the solution algorithm. A fifth order fit in the form F fit = a d 5 vec is used which is always monotonically increasing if a is positive. A few examples of the fitted function are plotted for a visual verification of the fit. One data line consists of 2.8 meters of road texture data. In one rotation the tyre already travels more than two meters. Therefore, to allow for multiple tyre rotation, the texture and contact stiffness data is copied multiple times and stored in road.profile_road_disc and road.contact _stiffness.

53 53 solve_contact_problem.m In every time step the contact problem is solved. The results are stored, the tyre is rotated and a new time step begins. File reference Input: Output: var,contact,road,green,simu Displacement of the tyre belt and tread in simu.x1_store and simu.x2_store Contact forces in simu.f. First, the options for the optimization routine lsqnonlin are defined. In the default case the Display parameter is set to Iter so that the iteration progress can be monitored. The output matrices are filled with zero entries to decrease the computational effort. In the beginning of a time step, the road profile and the contact stiffness are defined for each element depending on the contact row of the element. The excitation of the belt by previously determined forces is determined by the function green.m. In the first step these forces equal zero and therefore also excitation equals zero. Next, the actual contact problem is solved by the Matlab optimization function lsqnonlin which calls the function contact_problem.m. After convergence this results in the vector of displacements x1_new From the vector x1_new all the displacement and forces in the current time step are determined and stored. After each tyre rotation, the sum of the contact forces is compared to the desired load var.axle _load. If needed, the indentation of the road surface is adjusted. The position of the tread elements are shifted. First, the node is identified from which another node has to inherit its displacements (from_which). To identify these neighboring nodes the incrementation between nodes numbers in circumferential direction is used (+500). Some nodes will not be able to inherit displacements from other nodes because they are on the trailing edge of the contact patch. These notes therefore inherit a zero displacement.

54 54 APPENDIX B. TYRE/ROAD INTERACTION MODEL green.m The displacement of the belt due to forces in previous time steps is determined. The contact forces and Green s function are convoluted. File reference Input: Output: simu, contact, green, var Displacement of the tyre belt due to forces in previous time steps. The force at a contact node k is convoluted with the Green s function of all the contact nodes according to: x B 2 (N) N 1 = F (N)g(1) t + F (n)g(n n + 1) t n=1 (B.2) The resulting displacements for all forces are summed to determine the overall displacement simu.x3_greenold. contact_problem.m The error is calculated between the displacement of the belt determined by the Green s function x2 and the displacement of the belt determined by the spring-damper system x3. File reference Input: Output: x1,simu.x3_greenold,simu.x_old,var,simu,contact,green The vector of errors between x2 and x3 Given a displacement x1, the force F in the nonlinear spring is determined by nonlinearsptring.m. The additional force F_add is determined with respect to the static force F_init. The displacement of the belt is determined resulting from additional belt forces in the current time step according to: x 3 = F add (N)g(1) t (B.3) The displacement of the belt is determined due to the force in the spring damper system by the function springdamper. The error between x2 and x3 is determined

55 55 nonlinearspring.m The force generated by the nonlinear spring is determined given a displacement x1 and a nonlinear stiffness parameter simu.nlstiffness. File reference Input: Output: x1,var,simu The force in the nonlinear spring F The indentation of the road surface d is determined. The force in the nonlinear spring F is calculated and divided by the number of nodes within one tread block. The nonlinear stiffness approximation only holds for complete treadblocks. However, in this project the treadblocks are divided into multiple elements. Therefore, the force is divided by the number of nodes per treadblock. This is a very rough estimation which needs improvement in future versions of the model. springdamper.m Given the force generated by the nonlinear spring, the displacement due to deformation of the spring damper system x2 is determined. File reference Input: Output: F,x1,x_old,var.kl,var.d,var.delta_t The displacement of the belt x2 The displacement of the belt is approximated according to x A 2 (N) = d(x 1(N) x 1 (N 1)) F (N)δ t + dx 2 (N 1) + δ t k l x 1 (N) d + δ t k l (B.4)

56 56 APPENDIX B. TYRE/ROAD INTERACTION MODEL Stage 3: Postprocessing In the third stage of the simulation the rolling resistance is determined, the vibrations in the complete tyre are calculated and finally the simulation outcomes are visualized. Calculating the complete vibrations is a computationally intensive process. The Green s functions of all nodes have to be determined and convoluted with the recorded contact forces. Therefore, visualization of the complete tyre should only be performed for presentational purposes. Instead, the contact patch visualization can be used which is much faster. This section will discuss the subsequent functions called in the third stage. rolling_resistance.m Given the displacement of the belt and the contact forces the rolling resistance is determined. The timeframe in which the rolling resistance is calculated is very important. When the beginning state of x1 is different from the end state there is a difference in potential energy between the states which is not lost but can be recovered. Hence, rolling resistance will not be approximated correctly. File reference Input: Output: simu,var,from_index,nr_rev The energy dissipation during nr_rev revolution results.e_dissipation The power dissipation results.rollingresistance_watts The rolling resistance coefficient results.rollingresistance_coefficient The end time is defined between n_rev and n_rev+1 revolutions after from_index. The end time is chosen such that the difference between the beginning and end state is minimal. The dissipated energy is determined according to E dis = t2 t 1 F i (t)ẋ i 1(t)dt (B.5) The power dissipation is determined by dividing by the time frame and the rolling resistance is calculated by RRC = P dis (B.6) N axle v

57 57 tyre_deformation.m To analyze the vibrations of the complete tyre, the contact forces have to be convoluted with the Green s functions. Therefore, the Green s functions of all the tyre nodes have to determined. The Green s functions matrix determined earlier in the analysis (173 by 173 by 200) only covers the contact nodes and is approximately 50 Mb in size. The Green s function matrix of the complete tyre (7686 by 7686 by 200) would therefore approximately equal 100 Gb in data. Obviously, such a file can not be handled properly and therefore the Green s function are determined one by one and immediately convoluted with the appropriate contact forces. File reference Input: Output: modtrans,sim,var The deformation of the tyre nodes at each time step in deformation Initialize the Green s functions matrix which is two dimensional: the number of nodes time number time samples in the Green s function The force on every node j is treated separately analogue to green_func_analytic.m. For every time step N, the contact forces on node j are convoluted with all the Green s function at all the time steps and stored in deformation(n,:). animate_patch.m and animate_tyre.m By visualization of the contact patch a quick visual inspection of the simulation result can be performed. There is no need to recalculate the tyre deformation and therefore little computational effort is required. File reference Input: Output: simu,contact,model,road,var Animation (avi) file of the contact patch A movie object is created which is encoded by a Cinepak codec which can be played on most computers without additional software. Note: When errors occur in animate_patch the movie object is not closed and errors will occur if not closed properly before proceeding. The displacement in the tread elements with a zero contact stiffness is increased so that tread blocks are visible. Every time step the figure is updated and the frame is captured and added to the movie file.

58 58 APPENDIX B. TYRE/ROAD INTERACTION MODEL

59 Appendix C Regression Analysis 59

60 M+P consulting engineers Müller-BBM group noise - vibrations - air quality Wolfskamerweg 47, Vught P.O. Box CB Vught The Netherlands T +31 (0) F +31 (0) Vught@mp.nl Final report Influence of Road Surface Properties on Rolling Resistance of Car Tyres Prepared for Report No. Authors Dienst Verkeer en Scheepvaart M+P.DVS Postbus GA DELFT Revision 1 S.W. Boere Order No. Page Bestelnummer: of 45 Date 23 January 2008 Dr. G.J. van Blokland M+P consulting engineers No part of this publication may be used for purposes other than agreed upon by client and M+P (DNR 2005 Art. 46). Offices in Aalsmeer and Vught Member of ONRI ISO 9001

61 Summary Rolling resistance is one of the main factors concerning vehicle energy consumption. Together with aerodynamic resistance, inertial forces and climbing forces it constitutes to the total force a vehicle has to overcome to maintain constant speed. The relative importance of rolling resistance compared to the other factors varies with the vehicle velocity and driving pattern. On a level road with constant speed ( km/h) the relative importance varies from 60-38% respectively. On uneven roads with uneven driving patterns the averaged relative fuel consumption due to rolling resistance is approximately 14%. Lowering rolling resistance forces can therefore contribute to energy efficient transportation. It is often estimated that lowering the rolling resistance by 10% could give a reduction in fuel consumption of 2-3 %. This project focuses on the influence of road surface properties on rolling resistance. Additionally, possible conflicting requirements concerning tyre/road noise and skid resistance are examined. Measurements on rolling resistance, texture, mechanical impedance, skid resistance and noise were carried out on a test track with 41 different road surfaces in Kloosterzande. Amongst those surfaces is a number of unconventional noise reducing surfaces. The rolling resistance measurements were carried out with a specially designed trailer from the University of Gdansk (Poland). The observed rolling resistance coefficients are comparable to the ones found in literature. Outliers come from rarely used and very rough surface dressings and unconventional flexible surfaces. Some measurements appear to have a large spread which poses questions on the accuracy of the results. Strong correlations between texture spectra levels and rolling resistance are found in both macro (wavelengths mm) and mega ( mm) texture regions. However, there appears to be a strong inter-correlation between these texture regions and therefore the independent relative influence remains unclear. Literature sources even suggest a stronger influence from shortwave unevenness (wavelengths 0.5 5m) although these sources include suspension losses Texture amplitude characteristics appear to have a good correlation with rolling resistance. Varying Rms texture levels for conventional surfaces by 50% can have a reduction of the rolling resistance of 7-10%. Outliers in this correlation are caused by rarely used surface dressings and flexible rubber surfaces. The off-trend behavior of the surface dressing can probably be related to the nonskew texture profiles. For the flexible rubber surfaces the mechanical impedance is measured by excitation of the surface using a shaker. A simple dynamic system is proposed to model the surface dynamics containing a characteristic rubber mass. The acquired frequency response functions are reproducible and give valuable information on the dynamic behavior of the surface. The real part of the admittance (the inverse of the impedance) provides a measure of the frequency dependent energy dissipation. The relevant frequency range is estimated to be Hz. In this range, higher energy dissipation corresponds with higher rolling resistance. Further research is required to determine the relevant frequency range and to study the velocity dependency of the results. However, measuring mechanical impedance seems to be a promising method for the analysis and optimization of flexible road surfaces. 61

62 No conflicting requirements were found between skid resistance and rolling resistance. Skid resistance is assumed to depend on micro texture levels (wavelengths <0.5mm). Rolling resistance however depends on larger wavelengths. Further research is required to study the correlation between wet skid resistance and rolling resistance. No clear correlation can be found between rolling resistance and tyre/road noise. However, amongst surfaces that share the same structure, a higher Rms texture depth will result in a higher tyre/road noise level. Therefore, no conflicting requirements are found between lowering rolling resistance and decreasing tyre/road noise. 62

63 Contents Summary 61 1 Introduction Literature Review Objectives 66 2 Rolling resistance Background Measurement setup Measurement results Measurement Limitations 73 3 Road texture Background Measurement setup Measurement results Measurement limitations 78 4 Mechanical impedance Background Measurement setup Measurement results Dynamic road surface model 82 5 Skid resistance Background Measurement setup Measurement results Measurement limitations 86 6 Tyre/road noise Background Measurement setup Measurement results 87 7 Regression analysis Influence of surface texture on rolling resistance Influence of mechanical impedance on rolling resistance Correlation between skid resistance and rolling resistance Correlation between rolling resistance and tyre/road noise 99 8 Conclusion 100 References

64 1 Introduction Rolling resistance is one of the main factors concerning vehicle energy consumption. Together with aerodynamic resistance, inertial forces and climbing forces it constitutes to the total force a vehicle has to overcome to maintain constant speed. The relative importance of rolling resistance compared to the other factors varies with the vehicle velocity and driving pattern. On a level road with constant speed ( km/h) the relative importance varies from 60-38% respectively. On uneven roads with uneven driving patterns the averaged relative fuel consumption due to rolling resistance is approximately 14%. Lowering rolling resistance forces can therefore greatly contribute to energy efficient transportation. It is often estimated that lowering the rolling resistance by 10% could give a reduction in fuel consumption of 2-3 %. Although tyre design has a large influence on the reduction of rolling resistance, road surface properties cannot be neglected. This study focuses on the road surface influence on rolling resistance. For this purpose measurements are carried out on a test track located in Kloosterzande. The Kloosterzande test track contains 41 different conventional and unconventional road surfaces of approximately 60 meter each. The road surfaces differ in structure, material and chipping size. A number of noise reducing surfaces containing rubber are included. These surfaces are generally assumed to have higher rolling resistance. Numerous properties of the road surfaces, such as macro and mega texture, unevenness, skid resistance and mechanical impedance, have already been measured for other purposes. Appendix A lists all the road surfaces and gives a short description. The rolling resistance measurements are carried out with a trailer designed by the University of Gdansk (Poland). 1.1 Literature Review There is limited information available in literature on the reduction of rolling resistance. Due to the increased interest in the reduction of fuel consumption and CO 2 emissions the topic becomes increasingly important. The SILVIA project [1], a European Commission Program, provides an interesting overview of the work done up till One of the first and still very relevant attempts to study the relationship between road surface properties and fuel consumption was carried out by the Swedish National Road and Transport Institute (VTI) in Sweden in the 1980 th [2]. Texture profile and fuel consumption were measured on 20 different surfaces with constant speed (50-70 km/h). Positive correlations were observed between shortwave unevenness, megatexture, macrotexture and fuel consumption. However, strong inter correlations were found between those texture regions. It is shown that larger wavelengths have a higher influence on rolling resistance. The amount of shortwave unevenness can have an effect up to 10% in fuel economy. However, as the driving speed increases, macro texture levels increase in importance. Report [3] from the VTI summarizes earlier work. Possible correlations were suggested between all spectra bands including microtexture and rolling resistance. It is noted that rough macro texture can have a positive effect on rolling resistance on wet roads. Furthermore, it is suggested that the stiffness and softening behavior of road surfaces can be a significant factor in rolling resistance. A study based on French data [4] indicates the relationship between rolling resistance and fuel consumption. On average is shown that a doubling in rolling resistance increases the fuel economy 64

65 by about 10%. A Michelin Tyre Guide suggest a slightly higher fuel reduction: on average lowering the rolling resistance by 30% will improve fuel economy by 3-6%. Belgian data [4] showed positive correlations between unevenness, megatexture, macrotexture and rolling resistance. Megatexture was shown to have the strongest correlation unlike the study performed by VTI which showed stronger correlations in the unevenness texture region. Figure 1 shows rolling resistance increases with texture depth (correlation coefficient 0.75). figure 1 Rolling resistance coefficient and texture depth from [4] A New Zealand study [5] compares rolling resistance on road surface with varying macro texture and unevenness. Variations up till 40% in rolling resistance were found. Positive correlation between short wave unevenness and megatexture and macrotexture were found. A Swedish and Polish measurement program [6] examined the correlation between rolling resistance and tyre/road noise. It is concluded that for passenger cars there is no significant correlation between rolling resistance and tyre/road noise. Concluding, most studies agree that decreasing tyre rolling resistance can have a significant effect on fuel economy. There seems no general consensus in the relative importance of texture wavelengths. However, correlations have been reported between shortwave unevenness, megatexture and macrotexture. Microtexture seems less important. Mechanical impedance is assumed to have some influence on rolling resistance though it is never studied quantitatively. No conflicts in requirements were found in literature between noise, skid resistance and rolling resistance. 65

66 1.2 Objectives The objective of this project is threefold: - Establish a relationship between road texture and rolling resistance - Study the correlation between mechanical impedance and rolling resistance. - Examine the possible conflict in requirements between noise reduction and the reduction of rolling resistance. This report is organized as follows. First, Chapter 2 provides a theoretical background on rolling resistance and discusses the rolling resistance measurement setup. Furthermore, the measurement results are presented and the limitations of the measurements are discussed. Chapter 3 presents the road texture measurements and introduces multiple measures to characterize texture. Next, Chapter 4 introduces a method to measure the dynamic behavior of a road surface, the mechanical impedance. Subsequently, Chapter 5 discusses the measurements on skid resistance. Chapter 6 provides a brief background on tyre/road noise and presents the measurements results using the CPX method. Further, Chapter 7 provides an analysis of the correlations between rolling resistance, road texture, mechanical impedance, skid resistance and tyre/road noise. Finally, Chapter 8 contains a conclusion and discussion. 66

67 2 Rolling resistance 2.1 Background Rolling resistance is generally defined as the energy consumed by a tyre per unit of distance covered [9]. The main source of energy consumption is the continuous deformation of the tyre. The rubber elements deform in the contact patch and thereby consume energy as a result of their viscoelastic properties. This energy is not fully recovered when the elements return to the original state. The consumed hysteresis energy is converted to heat. The amount of energy loss due to rubber element deformation depends on the tyre geometry, tyre material properties, tyre temperature, tyre inflation pressure and road surface properties. This project concerns the influence of the road surface properties on the rolling resistance. Road texture is assumed to be the most important in this sense. Figure 2 shows a graphical representation of the mechanical manifestation of rolling resistance. The part of the tyre which makes contact with the road is called the contact patch. The force distribution within the contact patch as the tyre is rolling is not uniform [10]. The resultant force is located in the front of the contact patch. This resultant force acts as a torque that opposes the wheel rotation. This torque can also be represented by the rolling resistance force F r which has to be overcome to maintain constant speed. figure 2 Graphical representation of the rolling resistance force Rolling resistance forces linearly depend on the applied axle load in the practical range of axle loads [10]. Consequently, a dimensionless rolling resistance coefficient, RRC, can be introduced in which N represents the axle load and F r represents the rolling resistance force: F r (1) RRC [ ] = N 67

68 The rolling resistance coefficient in this project is measured by Gdansk University at the Kloosterzande test track. The following section will introduce the measurement setup, the measurement results and the limitation of the measurements. 2.2 Measurement setup The trailer designed by the University of Gdansk is shown in figure 3.. figure 3 Rolling resistance measurement trailer from the University of Gdansk The design consists of a 3 wheeled trailer. The first pair of wheels is self steering and provides support and stabilization. Figure 4 shows a schematic overview of the working principles of the trailer. The trailing wheel is the testing wheel and is mounted to the front wheels by means of two hinged arms. A vertical load is produced by a mass which is supported by a spring and damper. The rolling resistance coefficient is determined by the orientation of arm (1) by F (2) RRC = r = tan(θ ) N 68

69 figure 4 Schematic representation of the measurement trailer The angle between the two arms is measured by an inductive sensor. The system is compensated for tilt of arm (2) and for possible acceleration or road surface gradients. The advantage of this method is that only the angle θ has to be monitored which gives a direct measure of the rolling resistance coefficient. The trailer is driven at a constant speed of 80 km/h over the test track. A trigger records the transition from one road surface test section to the other. Multiple test runs in both directions are averaged to compensate for road surface gradients. The two tyres that are used are listed in table I. table I Two tyres used to measure the rolling resistance Tyre Size Continental CPC2 LI98 225/60 R16 Uniroyal Tiger Paw (SRTT) 225/60 R16 97S 69

70 2.3 Measurement results Figure 5 shows an example of the measurement results on one single test section. The rolling resistance coefficient of the two tyres is plotted as a function of the distance travelled over section 1. The complete overview of the measurement results over all 41 test sections is digitally provided. figure 5 Example of rolling resistance measurement test track 1, the white area represents the data window The magnitude of the rolling resistance coefficient appears to be in the order of 1% which agrees with other literature [10]. A window is applied to the raw data to account for transient effects in the results. The gray area indicates data which is neglected in the analysis. Subsequently the windowed data is averaged and the results are shown for both tyres in figure 6 and figure 7. The results are ordered according to the surface category depicted in appendix AC. The vertical line on top of each bar indicates the minimum and maximum recorded rolling resistance within the window. 70

71 figure 6 Averaged rolling resistance for different road surfaces in categorical sequence. Continental Tyre 71

72 figure 7 Averaged rolling resistance for different road surfaces in categorical sequence. SRTT Tyre 72

73 On all tested surfaces the Continental tyre appears to have a slightly higher rolling resistance (8-15%). However, the differences between the surfaces appear to be approximately the same for both tyres. Therefore, in further analysis only the Continental tyre data will be shown. The results show that the variance within one category can be quite significant compared to the differences between categories. Two surface categories, the flexible rubberized surfaces and the surface dressings, differ greatly ins size. Interestingly, some of the rubberized surfaces perform really well in terms of rolling resistance compared to more conventional surfaces. 2.4 Measurement Limitations The minimum and maximum recorded rolling resistance within the measurement window gives an indication of the reliability of the data which in some cases is quite low (surfaces 37 and 41 for example). Therefore, one has to be careful drawing hard conclusion based on these data. One of the main flaws of the measuring method is the length of the road sections: approximately 60 meter. At a speed of 80 km/h this corresponds to a measuring time of 2.7 seconds per section. In some situations this time span is too short to reach a steady state situation. Little is known about the accuracy of the trailer of the Technical University of Gdansk. The system is compensated for accelerations and road surfaces gradients. However the system is unable to correct both effects at the same time. Because road surface gradients are present at the Kloosterzande test track this may increase measuring errors. Further research is required to study the accuracy of the measuring trailer. 73

74 3 Road texture 3.1 Background Road texture can be subdivided in the following categories depending on the typical size of the wavelengths [7]. table II Texture categories and descriptions Category Micro texture Macro texture Mega texture Description Corresponds to wavelengths up to 0.5 mm. Formed by the roughness of the individual chippings. Usually too small to be observed by the eye. Typical peak-to-peak amplitude: mm Corresponds to wavelengths from 0.5 mm to 50 mm. Formed by the individual chippings. Important for water drainage. Same order of size as the tyre tread elements Typical peak-to-peak amplitude: mm Corresponds to wavelengths from mm. Formed by unwanted defects in the road surface. Same order of size as the tyre/road contact patch. Typical peak-to-peak amplitude: mm Unevenness Corresponds to wavelengths m. Wavelengths considered to be above that of texture 74

75 Rolling resistance is often considered to be affected by the rough end of the macro texture, the mega texture and the low end of unevenness as depicted in figure 8 [7] Tyre Wear Rolling resistance Tyre/road friction Exterior tyre/road noise Noise in Vehicles Discomfort & wear in vehicles Unevennes Mega Macro Micro Texture Wavelength 50 m 5 m 0.5 m 50 mm 5 mm 0.50 mm figure 8 Effect of texture on numerous phenomena as a function of wavelength range There are numerous methods to characterize texture. Most of these methods are based on 2D measurements using a laser profilometer. This chapter will introduce the measurement setup, the measurement results and the limitations of the measurements. 3.2 Measurement setup Figure 9 shows the measurement setup used to measure macro and mega texture. figure 9 A profilometer on the Kloosterzande test track 75

76 This device uses a laser interferometer which measures the height of the surface as a function of the longitudal position. The resolution in the longitudal direction is 0.2mm. The resolution in the lateral direction is 1 mm. 3.3 Measurement results A typical output of the profilometer is shown in figure 10: x Profile height [mm] Distance [m] figure 10 A typical texture output from the profilometer There are numerous ways to quantify texture. These include measures based on texture amplitude and spectral analysis of the texture [11] : - Texture wavelength spectrum - Mean profile depth (MPD) - Mean absolute deviation of the profile (Ra) - Root mean square deviation of the profile (RMS) - Skewness of the profile (Rsk) - Kurtosis of the profile (Rku) Texture wavelength spectrum Using a Fourier transform the amplitude as a function of wavelength is determined. Usually the wavelength resolution is 1/3 octave. The amplitudes are given on a logarithmic scale using a reference value of 10-6 m. a a (3) L 20log( db tx, o = ) ref 76

77 A special kind of texture wavelength level is the micro, macro and mega texture levels (Lmi, Lma and Lme respectively). These levels are determined by energetic averaging of the appropriate 1/3 octave bandpass levels. Mean Profile Depth MPD The mean profile depth is an amplitude characteristic of the texture profile. According to ISO :1997 the signal is high pass filtered to cancel unevenness of the profile and low pass filtered to reduce noise. Figure 11 shows a graphical representation of the process to determine the Mean Profile Depth. Baseline sections of 100 mm are taken and split up in two equally sized sections. The peak levels of the two sections are averaged and the average level of the complete baseline section is subtracted. This results in the Mean Profile Depth for one baseline section. The process is repeated over multiple sections and averaging is applied resulting in an average Mean Profile Depth and a standard deviation. figure 11 A graphical representation of the mean profile depth characteristics Estimated Texture Depth ETD The estimated texture depth, ETD, is a measure for macro texture and is determined by spreading a material (sand or glass spheres) in a patch. By dividing the volume of material by the area covered, the ETD is obtained which represents the average depth of the layer. The ETD characteristic is rarely used nowadays but can approximately be determined by means of the MPD value: (4) ETD = 0,2 + 0,8 MPD Mean absolute deviation of the profile Ra The average absolute value of the profile height Z(x) within evaluation length l provides a measure for the profile depth. This measure is rarely used. 77

78 1 l (5) Ra = l 0 Z( x) dx Root mean square deviation of the profile Rms The root mean square of the profile height Z(x) within evaluation length l provides a measure for the texture depth. This is a common measure to characterize texture. 1 l (6) Rms = l 0 Z( x) 2 dx Skewness of the profile Rsk Skewness is a measure for the asymmetry of the amplitude distribution. This indicates whether the profile curve exhibits a majority of peaks directed upwards (positive skew) or downwards (negative skew). For a normal distribution Rsk is zero. 1 1 Z( x) 3 Rms l (7) Rsk = l 0 3 dx Kurtosis of the profile Rku: Kurtosis refers to the weighting of the tails of a distribution and is a measure of how flat or sharp it is in relation to a normal distribution. For example, a distribution with long and thick tails will have a high Kurtosis value 1 1 Z( x) 4 Rms l (8) Rku = l 0 4 dx 3.4 Measurement limitations The profilometer is a 2D measuring device because the resolution in the lateral direction is insufficient to obtain a full 3D texture spectrum. However, under the assumption of an isotropic surface this might not be a problem. The resolution of the profilometer in longitudal directions is 0.2 mm. This resolution would allow to measure wavelengths up to 0.4 mm. The microtexture range is the wavelength region below 0.5 mm. Consequently the longitudal direction of the profilometer is insufficient for measuring micro texture. 78

79 4 Mechanical impedance 4.1 Background In the past, tyre/road research assumed the road surface to be perfectly rigid since the large difference between the road and the rubber stiffness. However, modern literature in tyre/road noise indicates that road stiffness is in fact an important design factor. Whether road stiffness in conventional surfaces influences rolling resistance is yet to be determined. However, the high rolling resistance of the noise reducing rubber surfaces may intuitively be related to the dynamic road properties. The dynamic properties of a road can be determined by applying a harmonic excitation on the road surface and by measuring the resulting force and acceleration. From these force and acceleration measurements a transfer function can be determined. In this report the transfer function from force to position is used. Using a model of the road surface the road parameters can be estimated. 4.2 Measurement setup Figure 12 shows a schematic view of the measurement setup. A shaker excites the impedance head which measures the acceleration and force applied to the baseplate. The shaker is attached to the frame by springs. The base plate is glued to the road surface and a constant preload is applied. The shaker generates a sinusoidal excitation sweep from Hz. One measurement consists of 20 frequency sweeps of which the transfer functions are averaged. figure 12 Schematic overview of the measurement setup Figure 13 and figure 14 show pictures of the measurement setup. 79

80 figure 13 Mechanical impedance measurement setup figure 14 Impedance head (left) base plate (right) 4.3 Measurement results The mechanical impedance is measured on the noise reducing surfaces (32-36) and one porous surface for reference. Figure 15 plots the amplitude and phase angle of the complex stiffness as a function of frequency. 80

81 Surface 32 Surface 33 Surface 34 Surface 35 Surface 36 Porous Surface frequency [Hz] Surface 32 Surface 33 Surface 34 Surface 35 Surface 36 Porous Surface frequency [Hz] phase angle [ ] magnitude [db] figure 15 Frequency response functions of 6 flexible rubberized surfaces 81

82 The measurement results clearly show differences in dynamic response. The differences between the noise reducing surfaces and the conventional porous road surface are significant. 4.4 Dynamic road surface model The frequency response functions in figure 15 typically show one frequency peak at Hz However, in some cases a second peak appears in the Hz range. Therefore a two dimensional dynamic model is introduced in figure 16. The model consists of two masses connected to the ground and to each other by springs and dampers. The springs and dampers have the same characteristics. In physical terms, the first mass represents the impedance head and base plate and the second mass represents the characteristic mass of the rubber surface. The springs and dampers represent the stiffness and viscoelastic behavior of the rubber. figure 16 Road surface dynamic model Figure 17 shows the frequency response function of surface 34 together with a model fit. In this model fit the mass, stiffness and damping parameters are adjusted in order to match the measured frequency response function. 82

83 stiffness amplitude [db] frequency [Hz] stiffness phase angle frequency [Hz] figure 17 Measured transfer function and model transfer function of surface 34 Table III lists the fit parameters table III Model parameters for surface 34 Surface nr Name m1 m2 d k 34 Pers 3 0,015 0, ,20E+05 The results can be verified by looking at mass 1 which represents the combination of both the impedance head (4.8 g), the baseplate (7.7 g) and the glue used to attached the baseplate to the surface ( approx. 2 g). This totals 14.5 g which is indeed approximately the mass found in the fitting process. 83

84 The model fitting procedure seems useful in further research into the dynamic characterization of road surfaces. However, the fitting procedure is highly sensitive to errors and it should therefore be automated. Additionally, more measurements at different spots on the surface should be performed and averaged to obtain more accurate measuring results. The impedance mass clearly influences the measurement results. This influence grows when the mass of the impedance head and the characteristic mass of the surface are similar. Therefore, a compensation technique should be applied [14]. This compensation is subject to current research. 84

85 5 Skid resistance 5.1 Background Skid resistance is an important safety consideration in the selection of road surfaces nowadays. Skid resistance is highly related to tyre characteristics. However, road properties can also have a significant effect. Skid resistance is generally associated with micro-texture of the road surface. On wet surfaces, the effect of texture and other surface properties become increasingly important as they facilitate the drainage of water. Wet skid resistance is hard to measure due to variable conditions. Therefore, this study will only consider dry friction using a standard measuring method. 5.2 Measurement setup Skid resistance can be measured with the British pendulum test. The measurement setup is shown in figure 18. figure 18 British pendulum test setup Under dry conditions the British pendulum test gives an indication of the friction coefficient of a road surface which in turn gives an indication of micro texture. However, the values acquired by the British pendulum have no absolute meaning and can only be used for relative comparison between the road surfaces. 5.3 Measurement results The averaged measurement results for surfaces 1 to 31 are shown in figure 19. The minimum and maximum values of the skid resistance are indicated with the error bars. 85

86 figure 19 Skid resistance measured with a British pendulum for road surfaces Measurement limitations The British Pendulum test is an empirical test and only provides indications of the skid resistance and micro texture of a surface. The test condition can vary greatly as no temperature correction is applied. The test results show a relatively large standard deviation within one road section compared to the differences between road sections. Additionally, the test results give no information of the skid resistance under wet conditions which is generally a more critical design criterion. 86

87 6 Tyre/road noise 6.1 Background A number of road surface properties have been identified that influence tyre/road noise: road texture, mechanical impedance and acoustic impedance. The acoustic impedance characterizes the frequency dependent energy absorption of the road surface. This energy absorption is for example influenced by the structure and the amount of voids in the road surface. Tyre/road noise is an important factor in the selection of road surfaces nowadays. A number of measuring methods are available to measure the noise exterior to the vehicle. In this study the noise level is measured in close proximity of the tyre. 6.2 Measurement setup The tyre road noise is measured in close proximity (CPX) of the tyre with a structure containing 11 microphones (figure 20). This method is related to the Close Proximity (CPX) method, as described in ISO/CD [12]. For each microphone the A-weighted equivalent sound level LA,eq is measured (the overall level and the 1/3-octave bands between 50 and 5000 Hz) along with the vehicle speed. figure 20 The close proximity measuring method to study tyre/road noise A number of different tyres is used for the measurements and averaged for each road section. 6.3 Measurement results It has been shown that there is a linear relation between velocity and tyre/road noise [13]. Therefore a speed correction is applied prior to analysis. Figure 21 shows the sound levels of each section on which a speed correction has been applied. The results clearly show the positive effect of the flexible road surface on the tyre/road noise. 87

88 (A B l [d e v e L d n u o S )] ISO SMA DAC Thin layered asphalt PAC double layer PAC rubberized surfacessurface dressin Section figure 21 A-weighted equivalent sound level in the range Hz for all road section. Sound levels are corrected for speed. 88

89 7 Regression analysis The goal of this project is to find correlations between road surface properties and rolling resistance. In Chapter 3, Chapter 4 and Chapter 5 a number of road surface properties is described: road texture, mechanical impedance and skid resistance. This chapter studies empirical relations between those properties and rolling resistance. 7.1 Influence of surface texture on rolling resistance Texture amplitude characteristics Figure 22 plots the root mean square (Rms) texture depth and the corresponding rolling resistance coefficient for a Continental tyre on all surfaces. Each point represents a road surface and the points are color coded according to the road category as shown in Appendix C. There appears to be a clear correlation between rolling resistance and Rms texture depth. However, the rubberized surfaces and the surface dressings do not correspond to this relation. Therefore, in subsequent regression analysis these surfaces will be excluded. Figure 22 also shows the linear regression trend line obtained by a least squares regression procedure. The slope of the regression line is approximately 0.78 [1/mm] and the regression line crosses the vertical axis at approximately A correlation coefficient of R 2 =0.89 indicates a rather good correlation between Rms texture depth and rolling resistance. A t-test is applied to test whether the slope of the regression line differs significantly from zero (nullhypothesis). Under the assumption of the null hypothesis the t-score is approximately 15.7 with 28 degrees of freedom. These values indicate that it is highly unlikely that there is in fact no relationship between Rms texture depth and rolling resistance. Therefore, the null hypothesis has to be rejected. Within a 95% confidence it can be stated that the slope of the regression line lies in the interval [0.68;0.88]. It has to be noted that the correlation between Rms texture depth and rolling resistance does not necessarily indicate a causal relationship between those two. However, it can be concluded that selecting a conventional surface with 1 mm less Rms texture depth can give a reduction in rolling resistance of approximately % which results in a potential fuel reduction of approximately 1-2%. 89

90 figure 22 Rms texture values and rolling resistance for all surfaces for a Continental tyre. Color coded per category according to appendix C Figure 23 provides more insight into the reliability of the data. Each point corresponds to a road surface texture. Each box corresponds to the spread in the data used to determine the mean value. The width of the box corresponds to a 95% interval (+/- 2 standard deviations) around the mean RMS texture depth. The height of the box corresponds to the difference between the maximum and minimum recorded rolling resistance. Figure 15 clearly shows that, however the spread in the data is quite significant, the correlation between RMS texture depth and rolling resistance remains present. 90

91 Continental Rolling Resistance Coefficient [-] ISO SMA DAC Thin layered asphalt PAC Double layer PAC Rubberized surfaces Surface dressings Rms texture depth [m] x 10-3 figure 23 Rms texture depth and rolling resistance for all surfaces for a Continental tyre. Color coded by category according to appendix C. The box size indicates the spread in data. As illustrated by figure 23, the rubberized surfaces and the surface dressing do not follow the trend of the other surfaces.. To study the abnormal behavior of the surface dressing these profiles are examined more thoroughly. Figure 24 plots two surface profiles that have approximately the same RMS value of 1.5 mm. x x figure 24 Two texture profiles having approximately the same Rms values Surface number 7 is a surface that obeys the common trend. Surface number 40 is a surface dressing that showed a significantly higher rolling resistance. The difference between the two profiles is significant. Surface 7 seems flat and has many pockets whereas surface 40 seems to have more spikes. These differences in texture profile can quantitatively be described by the profile skewness Rsk as explained in Section 3. Figure 25 shows an overview of the skewness of 91

92 all the surfaces. Negative skewness corresponds to more holes and a zero skewness corresponds to a homogenous distribution of the profile which contains relatively more peaks. figure 25 Skewness Rsk for different road surfaces. Color coded according to appendix C. Figure 25 clearly shows the low skewness of the surface dressings. Due to holes and peaks in the texture profile, the rubber of the tyre in the contact patch is not completely in contact with the road. Therefore the profile which is felt by the tyre is different from the profile determined by a profilometer. The tyre envelopes the road surface texture. This effect is amplified as the skewness of the profile approaches zero. The enveloping phenomenon is for example described by Meier [8] who studies the correlation between tyre/road noise and texture. Meier suggests a possible solution by running the profile through a numerical algorithm which filters steep slopes in the data. In this study, the enveloping algorithm has indeed shown to increase the correlation when surface dressing are included in the analysis. However, the correlation between the conventional surfaces rapidly decreases probably because the algorithm filters a lot of valuable texture information. Therefore, in further analysis no enveloping algorithm will be applied and the surface dressing will be excluded from the analysis. 92

93 7.1.2 Spectral texture characteristics It is generally assumed that rolling resistance depends on the rough end of the macro texture (wavelengths: mm), the mega texture (wavelengths: mm) and short wave unevenness (wavelengths: m) [7]. This section studies the correlation between texture spectrum bands and rolling resistance. However, the texture spectrum bands may not be treated as independent variables. Therefore, the inter correlations between the spectra bands is examined first. Figure 26 shows an inter correlation diagram which provides an idea of the correlation between the spectra bands. The squared correlations coefficient, R 2, represents the goodness of the linear regression between two wavelengths presented on the horizontal and vertical axis. A correlation coefficient of R 2 =1 represent a perfect fit. On the diagonal the correlation coefficient is always 1 as the same band spectra are compared. However, for the spectrum bands to be independent variables the offdiagonal values should be as low as possible. 0.5mm 30 Mega texture Macro texture 50mm 5mm 500mm mm 50mm 5mm 0.5mm Mega texture Macro texture figure 26 Inter correlation between spectra bands. A correlation value of 1 corresponds to a perfect correlation Figure 26 shows clear correlations between texture wavelengths in the mega and rough macro spectrum. In other words, a texture with a high macro texture level will generally give a corresponding mega texture level. 93

94 Table IV indicates the correlations between the overall macro texture level Lma, mega texture level Lme and the rolling resistance. Additionally the inter correlation between those two texture parameter is presented. table IV Correlation between macro texture, mega texture and rolling resistance Linear regression Correlation coefficient R Lma v.s. rolling resistance 0.91 Lme v.s. rolling resistance 0.90 Lma v.s. Lme 0.96 Table IV indeed shows that there is a strong correlation between both macro and mega texture and rolling resistance. However, due to the strong inter correlation no conclusion can be drawn on the relative influence of both texture regions. 94

95 7.2 Influence of mechanical impedance on rolling resistance In order to study the influence of mechanical impedance on rolling resistance, the rolling resistance data of the noise reducing surfaces is corrected for Rms texture depth. Figure 27 shows the rolling resistance data for a corrected Rms texture depth of 1 mm. 0,016 0,014 0,012 Rolling resistance coefficient [-] 0,01 0,008 0,006 0,004 0, Section figure 27 Rolling resistance of noise reducing surfaces after regression Figure 15 in section 4.3 plotted the transfer function between the indentation of the surface and the applied force. This figure showed clear differences in dynamic behavior between the road surfaces. It is hypothesized that stiffness does not affect rolling resistance since an ideal spring does not consume energy. Therefore, in this section the energy consumption of the surfaces as a result of the rolling tyre is studied. The real part of the mechanical admittance, the equivalent of the inverse of mechanical impedance, provides a measure of the energy dissipation at a given frequency: ω 2 F( ω) Z( ω) 2 (9) P ( ) = Re( A( ) F( ) ) = Re( ) ω ω 95

96 Figure 28 plots the real part of the admittance as a function of the frequency. Given an input force equal to 1 N the admittance gives a measure of the energy dissipation in Watts for given frequencies. 0 Real part of admittance for 1 N input [W] Surface 32 Surface 33 Surface 34 Surface 35 Surface 36 Porous Surface Frequency [Hz] figure 28 Power dissipation as a function of frequency for the six different surfaces. Looking at figure 28 the question arises which frequency range affects the rolling resistance. The tyre excites the surface in the contact patch. Figure 29 provides an indication of the surface pressure profile within the contact patch. figure 29 Pressure spectrum of a car tyre at the surface patch. 96

97 The lowest frequency which could affect rolling resistance, f min, is the frequency which corresponds to the length of the contact patch l c at a given speed v (10) f = min v l c For a contact patch of 100 mm and a speed of 80 km/h this corresponds to a frequency of 222 Hz. However, considering that the pressure only varies over a part of the contact patch l cp the maximum frequency that could affect rolling resistance could be (11) f = max v l cp For l cp as one third of the contact patch (100 mm) and a speed of 80 km/h this corresponds to a frequency of 666 Hz. Combining figure 27, figure 28 and looking at the relevant frequency range there seems to be a clear correlation between energy dissipation and rolling resistance. A higher energy dissipation in the Hz range appears to correspond to a higher rolling resistance. This result can potentially be used in the design of new low rolling resistance, noise reducing and flexible road surfaces. It has to be noted that the relevant frequency range is highly dependent of the vehicle speed. Therefore, it may be useful to measure the rolling resistance at varying speed to study this effect. Additionally, the static stiffness of the road surface may cause a change in contact patch size and may thereby shift the relevant frequency range. Further, decreasing the static stiffness potentially lowers the resonant frequency which increases the energy dissipation at lower frequencies. These topics should be further addressed in future research. 7.3 Correlation between skid resistance and rolling resistance. Skid resistance is assumed to give an indication of the amount of micro texture on a surface. Figure 30 shows a scatter diagram of the skid resistance values obtained by a British Pendulum test and the rolling resistance. From this figure it can be concluded that no clear correlation can be found between skid resistance/micro texture and rolling resistance. Therefore, the requirements of improving skid resistance and reducing rolling resistance do not conflict. 97

98 figure 30 Skid resistance BPM values and rolling resistance.. Additional regression analysis with roughness on a wet road and vehicle deceleration has shown to result in similar results. The absence of a significant relation can be related to the wavelength dependency of both rolling resistance and grip. Grip is generally assumed to be affected by small wavelengths, rolling resistance is generally affected by larger wavelengths (figure 8). 98

99 7.4 Correlation between rolling resistance and tyre/road noise Figure 31 shows the sound level measurements using the CPX method compared with the rolling resistance. This figure seems to indicate that there is no strong correlation between rolling resistance and tyre/road noise. This may seem counter intuitive as rolling resistance has a strong correlation with texture depth and it is commonly assumed that texture depth and exterior noise are strongly correlated as well. figure 31 Sound level measurement based on CPX method and rolling resistance measurements The previous paradox can be explained by looking at the different generating mechanisms that cause tyre/road noise [13]. Due to all these effects, there seems to be no correlation between texture depth and tyre/road noise. However, by eliminating some of these generating mechanisms and comparing the surfaces within one category and layer thickness, the correlation between texture depth and tyre/road noise becomes clear. This method indeed shows that larger chipping size leads to higher Rms texture depths and louder tyre/road noise. Therefore, optimizing tyre/road noise by decreasing texture depth will also contribute to the reduction of rolling resistance. 99

100 8 Conclusion This project focuses on the influence of road surface properties on rolling resistance. Additionally, possible conflicting requirements concerning tyre/road noise and skid resistance are examined. Measurements on rolling resistance, texture, mechanical impedance, skid resistance and tyre/road noise are carried out on a test track with 41 different road surfaces in Kloosterzande. Amongst those surfaces is a number of unconventional noise reducing surfaces. The rolling resistance measurements are carried out with a specially designed trailer from the University of Gdansk (Poland). The observed rolling resistance coefficients are comparable to the ones found in literature. Outliers come from rarely used and very rough surface dressings and unconventional flexible surfaces. Some measurements appear to have a large spread which poses questions on the accuracy of the results. Strong correlations between texture spectra levels and rolling resistance are found in both macro (wavelengths mm) and mega ( mm) texture regions. However, there appears to be a strong inter-correlation between these texture regions and therefore the independent relative influence remains unclear. Literature sources even suggest a stronger influence from shortwave unevenness (wavelengths 0.5 5m) which is not observable with the current measurement setup. Texture amplitude characteristics appear to have a good correlation with rolling resistance. Varying Rms texture levels for conventional surfaces by 50% can have a reduction of the rolling resistance of 7-10%. Outliers in this correlation are caused by rarely used surface dressings and flexible rubber surfaces. The off-trend behavior of the surface dressing can probably be related to the nonskew texture profiles. For the flexible rubber surfaces the mechanical impedance is measured by excitation of the surface using a shaker. A simple dynamic system is proposed to model the surface dynamics containing a characteristic rubber mass. The acquired frequency response functions are reproducible and give valuable information on the dynamic behavior of the surface. The real part of the admittance (the inverse of the impedance) provides a measure of the frequency dependent energy dissipation. The relevant frequency range is estimated to be Hz. In this range, higher energy dissipation corresponds with higher rolling resistance. Further research is required to determine the relevant frequency range and to study the velocity dependency of the results. However, measuring mechanical impedance seems to be a promising method for the analysis and optimization of flexible road surfaces. No conflicting requirements were found between skid resistance and rolling resistance. Skid resistance is assumed to depend on micro texture levels (wavelengths <0.5mm). Rolling resistance however depends on larger wavelengths. Further research is required to study the correlation between wet skid resistance and rolling resistance. No clear correlation can be found between rolling resistance and tyre/road noise. However, amongst surfaces that share the same structure, a higher Rms texture depth will result in a higher tyre/road noise level. Therefore, no conflicting requirements are found between lowering rolling resistance and decreasing tyre/road noise. 100

101 References [1] Hans Bendtsen, European Commission, SILVIA PROJECT REPORT, Rolling Resistance, Fuel Consumption and Emissions: A Literature Review, [2] Ulf Sandberg, Road Macro- and Megatexture Influence on Fuel Consumption, Surface Characteristics of Roadways: International Research and Technologies, ASTM STP 1031, W.E. Meyer and J. Reichert, Eds., American Society for Testing and Materials, Philadelphia, 1990, pp [3] Anita Ihs, Magnusson, Georg, The significance of various road surface properties for traffic and surroundings. VTI notat, 71A Swedish National Road and Transport Institute. [4] Guy Descornet, Road Surface Influence on Tyre Rolling Resistance. Surface Characteristics of Roadways: International Research and Technologies, ASTM STP 1031, W. E. Mayer and J. Reichert, Eds., American Society for testing and Materials, Philadelphia, 1990, pp [5] P.D. Cenek, P.F. Shaw, Investigation of New Zealand Tyre/Road Interactions, Road Research Bulletin,1990 [6] Ulf Sandberg, Jerzy A. Ejsmont, 2000, Noise emission, Friction and Rolling Resistance of car Tyres summary of an experimental study. Paper from NOISE-CON 2000, Newport Beach, California, December 2000 [7] Ulf Sandberg, Jerzy A. Ejsmont, 2002, Tyre/Road reference book, Informex, SE-59040, Sweden [8] A. von Meier, G.J. van Blokland, G. Descornet, The influence of texture and sound absorption on the noise of porous road surfaces, 1992, Second International Symposium on Road surface Characteristics [9] ISO International Standard. Passenger car tyres Methods of measuring rolling resistance. Reference number ISO 8767:1992 (E) [10] The Tyre, Rolling resistance and fuel savings, Societe de Technologie Michelin, Clermont-Ferrand, 2003 [11] ISO International Standard. Characterization of pavement texture by use of surface profiles. Reference number: ISO :1997(E) [12] ISO International Standard. Method for measuring the influencceof road surfaces on traffic noise Part 2: The close proximity method (CPX) [13] Acoustic Optimization Tool, M+P report DWW , November 2007 [14] O. Cakar, K.Y. Sanliturk, 2005, Elimination of transducer frequency response functions, Mechanical Systems and Signal Precessing, Vol. 19, Issue 1, p

102 APPENDIX A Road surfaces per category 102

103 Section km Picture Black/white squares are 1cm 2 section 1 30 mm ISO-surface section 2 25 mm Thin Layered Asphalt 2/4 (12%) section 3 25 mm Thin Layered Asphalt 2/6 (8%) section 4 25 mm Thin Layered Asphalt 2/6 (12%) section 5 25 mm Thin Layered Asphalt 4/8 (12%)

104 Section km Picture Black/white squares are 1cm 2 section 6 50 mm PAC 0/ section 7 50 mm PAC 0/ section 8 50 mm PAC 4/ section 9 25 mm PAC 4/ section mm PAC 4/ mm PAC 11/

105 Section km Picture Black/white squares are 1cm 2 section mm PAC 4/ mm PAC 11/ section mm PAC 8/ mm PAC 11/ section mm PAC 2/ mm PAC 8/ section mm PAC 2/ mm PAC 8/ section mm PAC 2/

106 Section km Picture Black/white squares are 1cm 2 section mm PAC 2/ mm PAC 11/ section mm PAC 2/ mm EPAC 0/16 (3m%) section mm PAC 2/ mm EPAC 0/16 (10 m%) section mm SMA 0/ section mm SMA 0/

107 Section km Picture Black/white squares are 1cm 2 section mm SMA 0/ section mm SMA 0/ section mm DAC 0/ section mm PAC 4/ section mm PAC 4/ mm PAC 4/

108 Section km Picture Black/white squares are 1cm 2 section mm PAC 4/ mm PAC 8/ section mm PAC 4/ mm PAC 8/ section mm PAC 4/ mm PAC 8/ section mm PAC 8/ mm PAC 8/ section mm PAC 8/ mm PAC 4/

109 Section km Picture Black/white squares are 1cm 2 section mm PAC 8/ section 32 PERS section 33 PERS section 34 PERS section 35 regupol 6010 MF

110 Section km Picture Black/white squares are 1cm 2 section 36 regupol 6510 G section 37 regupol 6510 G + 45 mm PAC 11/ section mm PAC 8/ section 39 acoustic intermediate section section 40 5/8 surface dressing

111 Section km Picture Black/white squares are 1cm 2 section 41 11/16 surface dressing

112 APPENDIX A Rolling resistance measurements 112

113 Surface 1 Surface 2 Surface 3 113

114 Surface 4 Surface 5 Surface 6 114

115 Surface 7 Surface 8 Surface 9 115

116 Surface 10 Surface 11 Surface

117 Surface 13 Surface 14 Surface

118 Surface 16 Surface 17 Surface

119 Surface 19 Surface 20 Surface

120 Surface 22 Surface 23 Surface

121 Surface 25 Surface 26 Surface

122 Surface 28 Surface 29 Surface

123 Surface 31 Surface 32 Surface

124 Surface 34 Surface 35 Surface

125 Surface 37 Surface 38 Surface

126 Surface