The influence of strong crosswinds on safety of different types of road vehicles

Transcription

1 ( ().,-volV) ( ().,-volV) STOCHASTICS AND PROBABILITY IN ENGINEERING MECHANICS The influence of strong crosswinds on safety of different types of road vehicles Xiaoyu Zhang. Carsten Proppe Received: 4 October 2018 / Accepted: 22 January 2019 Ó Springer Nature B.V Abstract Strong crosswinds have a great influence on the safety of road vehicles. Different vehicle types may have different behavior under strong crosswinds, thereby leading to different dominant accident modes and accident risks. In order to compare the crosswind stability of road vehicles, a probabilistic method based on reliability analysis has been applied in this paper. The crosswind is simulated as a stochastic gust model with nonstationary wind turbulence. The vehicles are classified into several categories. For each vehicle type, a worst case vehicle model and the corresponding aerodynamic coefficients have been identified. Dominant accident modes and failure probabilities have been computed and are compared. The influence of road conditions (dry/wet) and wind directions on the crosswind stability has been taken investigated. The proposed model makes it possible to compare the effect of crosswind on different vehicle types based on a risk analysis. Keywords Crosswind stability Vehicle dynamics Failure probability X. Zhang C. Proppe (&) Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany carsten.proppe@kit.edu X. Zhang zxykar@163.com 1 Introduction Strong crosswinds play an important role in the lateral stability of road vehicles. They may cause accidents or make the driver and passengers feel uncomfortable or insecure. In the past few decades, a lot of work has been carried out to study the crosswind stability of road vehicles and the critical wind speed (vehicle speed limit) which may lead to an accident of the vehicle has also been investigated, cf. [2, 4, 11, 12]. So far, simulation models for the study of crosswind stability of road vehicles can be generally divided into two groups. The first group focuses on deterministic parameters and computes the critical wind speed for vehicles at different vehicle speeds (e.g. [3, 5]) while the second group takes stochastic parameters into account and yields only average results or probabilities (e.g. [26, 28]). Baker [2] presented a method for predicting the critical wind speed of road vehicles based on a simplified vehicle model with deterministic wind speeds. A four-wheel, single-mass vehicle was considered and the suspension dynamics were neglected. For vehicles entering into a sudden gust, a step function for the simulation of the wind speed has been utilized. Three accident modes (overturning, sideslip and rotation) were taken into consideration and the wind angle of attack is assumed to be time-independent. Neither the stochastic characteristics of the wind speed nor the driver behavior were taken into account.

2 Later, Baker [3] applied the vehicle model of [2] to other vehicle types, including passenger cars, coaches, large vans and tractors with trailers. Based on the analysis of critical wind speeds for different vehicles at various vehicle velocities, a two-level wind warning system for the safety of high-sided vehicles at exposed sites during windy periods has been proposed. It was suggested that when the gust speed is above 17.5 m/s, a speed limit of 105 m/s for all high-sided vehicles should be proposed. When the gust speed reaches m/s, closure of the traffic route for all vehicles was recommended. In [4], Baker extended his method by investigating the parameters that affect windinduced accidents and by considering driver vehicle interactions. Guo and Xu [19, 30] presented critical wind speeds for road vehicles running on long bridges by using a quasi-steady wind vehicle model, while Dai and Young [17] proposed a wind warning system with three levels based on a statistical analysis of vehicleaccident data and meteorological data. Recently, Chen and Cai [13] developed a simulation framework for the coupled bridge vehicle wind system. Critical wind speeds for the vehicle running at different vehicle speeds were reported. Studies show that reducing vehicle speed is an effective way to lower the accident risk when the wind speed is not extremely high. When the wind speed is high enough, the vehicle should be prohibited to pass through the bridge no matter what speed it runs at, since the vehicle may be blown over even if it does not move. Similar studies can also be found in [5, 10, 15]. These investigations take the wind turbulence into account and compute the critical wind speeds with deterministic parameters and scenarios. However, they usually focus on a certain vehicle type and the underlying assumption for them is that the wind is a stationary process and the mean gust amplitude and duration are usually assumed to be constant. In reality, due to the nonlinear character of the relationship between vehicle dynamics and wind speed, a deterministic gust shape is a simplification that is not justified. It has been found that the flow field created by extreme wind events (e.g. thunderstorm winds, sudden gusts) is quite different from the traditional atmospheric boundary layer wind flow due to the rapidly time-varying wind speed and the spatially correlated wind fluctuations [14]. The extreme wind event usually shows nonstationary features which may significantly influence the wind vehicle interaction. In fact, realistic wind is usually a nonstationary process, and simulations of the crosswind have to take its nonstationary character into account. In this regard, nonstationary wind turbulence has to be modeled and the gust characteristics, including the gust amplitude and duration, have to be considered as stochastic parameters. Besides the nonstationary wind model, models of various vehicle types, including the driver model and road conditions (wet or dry) have to be considered. For each vehicle type, the corresponding aerodynamic coefficients must be identified. In general, there are many parameters that significantly influence the crosswind stability of vehicles, such as the vehicle geometrical features, the vehicle physical characteristics and the wind condition (wind speed, relative wind angle and wind duration, etc.). To get an accurate assessment for the crosswind stability of various different road vehicles, all these factors have to be taken into consideration. Due to the influence of uncertainties, it is not possible to determine an exact failure boundary for the wind speed at which the vehicle fails. Instead, a risk assessment has to be carried out, for which failure conditions have to be established and failure probabilities have to be computed. In this way, the influence of various parameters on the crosswind stability of different road vehicles can be judged on an objective basis. In summary, this paper is organized as follows. The following section gives a description for the modeling aspect of the vehicle wind system. Firstly, different road vehicle models and corresponding failure criteria of the vehicles are described. Then, a stochastic gust model with nonstationary wind turbulence is introduced. The wind excitation caused by nonstationary crosswind will be presented at the end of this section. Next, Sect. 3 introduces the risk assessment for road vehicles under crosswind based on a reliability analysis. Corresponding results for the failure probability of different vehicles will be presented and compared in Sect. 4. Finally, in Sect. 5, conclusions of this study will be drawn.

3 2 Modeling aspects of the vehicle wind system In general, the vehicle wind system can be divided into three parts: the nonlinear vehicle model, the nonstationary wind model and the interaction force between wind and vehicle. 2.1 Vehicle models and corresponding failure criteria In order to investigate the influence of strong crosswind on different road vehicles, several different vehicle categories are modeled and simulated. The studied vehicle types comprise passenger cars, trucks, buses, large vans and a car with trailer. They are simulated in Matlab/Simulink. Equations of motion for the coupled vehicle wind system are based on and developed from foregoing studies, cf. [9, 13, 27, 29]. Vehicles are modeled as a combination of rigid bodies with lumped masses. The rotational displacements, including yaw, pitch and roll motion are fully considered. Figure 1 shows a sketch of the 2-axle, 4-wheel vehicle model. As can be seen, the characteristics of vehicle suspensions are simulated as springs and dampers. When a car trailer is taken into account, the car and the trailer will be connected by a hitch force (cf. the hitch point in Fig. 2). In addition, driver models and road conditions have also been considered. The driver model is developed based on the idea that the steering angle should be adjusted to keep the vehicle running on a desired route (here, the route is assumed to be straight). This can be realized by a classical control method, namely the PID control method, cf. [1, 4, 13]. For the tyre road interaction (see Figs. 1, 2), a friction coefficient of 0.9 for dry conditions and 0.5 for wet conditions has been assumed. Only the worst-case vehicle model (i.e. the unloaded vehicle model) for each vehicle class has been taken into consideration. Main parameters that characterize the vehicle model are listed in Table 1. They are chosen to represent a broad range of vehicles within each vehicle category and taken mainly from published papers (e.g. [3, 6, 9]) or based on experience. Corresponding aerodynamic coefficients used for each vehicle type are obtained from wind tunnel measurements of Baker [3], Baker and Reynolds [6], Cheli et al. [12] and Juhlin [20]. Furthermore, accident modes have to be defined. According to Baker [4], the accident modes of road vehicles caused by strong crosswind can be stated as follows: Sideslip accident: the lateral displacement of the vehicle exceeds 0.5 m. Overturning accident: one of the vehicle tire forces falls to zero. Rotational accident: the yaw displacement exceeds 0.2 rad. 2.2 Wind model For a fixed point in space, the wind speed is composed of two parts: the mean wind speed u 0 and the turbulent wind speed u 0 ðtþ, which acts in the same direction as u 0. This can be expressed as follows: V x z z F wz M wy G c x y M wx G c mg s lr l f T Fig. 1 A sketch of the 2-axle, 4-wheel vehicle model

4 y G c z Hitch point x G c l rt l ft lr l f Fig. 2 A sketch of the car with trailer which is connected by a hitch point Table 1 Main parameters used for the simulation of different road vehicles Vehicle type Truck Bus Van Car Trailer Mass (kg) , Length (m) Height (m) Distance from CG to front axle (m) Distance from CG to rear axle (m) Rotational inertia (kg m 2 ) 50,000 60,000 20, uðtþ ¼u 0 þ u 0 ðtþ ð1þ where t refers to an instant of time and u(t) is the total wind speed. The mean wind speed is evaluated by the wellknown logarithmic wind profile [21] while the wind turbulence is described by the power spectral density (PSD) (e.g. von Kármán PSD [22] and Simiu PSD [7], etc.). To simulate the wind turbulence, many methods can be applied, e.g. the spectral representation method, the wavelet method and the auto-regressive moving average (ARMA) method, etc. However, these methods are mainly based on the assumption of stationary processes. In order to produce the nonstationary wind turbulence, a nonstationary auto-regressive (NONAR) method has been utilized in this paper. For details, the reader is referred to [18, 24]. Additionally, in order to model extreme wind conditions, a gust scenario is applied. The gust is defined as the maximum deviation of the wind speed between two consecutive mean wind crossings. Until now, most of the gust models are obtained either by convention or by selecting a reference model from a statistical distribution, such that the gust shape itself is deterministic and thus fixed. Its use for the simulation of realistic gust events seems to be limited. A way to extend this approach would be the simulation of gusts with stochastic amplitudes and durations. Correspondingly, a probabilistic simulation for the wind model has to be carried out. Examples for these probabilistic approaches can be found in [8] for wind turbines and in [23], where the artificial gust scenario is superposed to turbulent fluctuations and modeled by means of the so called constrained simulation approach. Figure 3 shows a typical realization of the gust model based u(t) [m/s] t [s] Fig. 3 An example of the gust model with nonstationary wind turbulence at u 0 ¼ 17 m/s

5 on the above mentioned simulation method with nonstationary wind turbulence at u 0 ¼ 17 m/s. 2.3 Wind excitation The wind excitation acting on a vehicle is represented by means of concentrated forces and moments. They can be described as follows: FðtÞ ¼ 1 2 q LA C C F ðb x ðtþþv 2 res ðtþ MðtÞ ¼ 1 2 q LA C L C C M ðb x ðtþþv 2 res ðtþ ð2þ ð3þ where F(t) and M(t) are the wind force and moment, respectively. q L refers to the air density; A C and L C are the characteristic area and length of the vehicle. The dimensionless aerodynamic coefficients C F ðb x ðtþþ and C M ðb x ðtþþ, which are nonlinear functions of the relative wind angle b x ðtþ, can be obtained by means of wind tunnel tests or CFD simulations. V res ðtþ is the relative wind speed which is defined as V 2 res ðtþ ¼vðtÞ2 þ uðtþ 2 þ 2uðtÞvðtÞ sinða x ðtþþ; ð4þ cf. Fig. 4. Considering a moving vehicle with spatial extension, the turbulent wind excitation can be calculated based on an equivalent wind spectrum, which can be described as follows [25]: spectrum and thus depends on the relative wind speed, the length scale of the turbulence and the variance of the wind fluctuations. 3 Failure probability analysis To evaluate the failure probability of vehicles running under strong crosswind, a risk analysis has been carried out. Figure 5 shows a diagram for the risk analysis. As can be seen, the process is mainly composed of two parts, that is, the nonlinear vehicle wind system and the reliability analysis. The nonlinear vehicle wind system has already been described above and the reliability analysis can be implemented with FORM or Monte Carlo methods with variance reduction, e.g. Line sampling (LS). More details about the risk analysis by using FORM and LS methods can be found in [23]. 4 Results and analysis A series of different simulations has been carried out and the influence of different parameters (e.g. different vehicle speeds, wind directions and wind turbulence) on the crosswind stability of vehicles has been studied. ~S u 0 u 0ðf Þ¼v2 ðf ÞS u 0 u 0ðf Þ ð5þ where f refers to the frequency (in Hz), v 2 ðf Þ is a correction factor, namely the aerodynamic admittance function that depends in general on the length and height of the vehicle and the decay of the coherence function and S u 0 u0ðf Þ refers to the wind spectrum for a moving point as derived in [16] from the von Kármán Fig. 4 Relative wind speed for the moving vehicle Fig. 5 A diagram of the risk analysis for vehicles running under strong crosswinds

6 According to the results, it is recommended to consider vans, trucks, cars with trailers and buses as one group and passenger cars as a separate group. Table 2 represents the dominating accident modes that lead to failure for each vehicle type in the simulation. As can be seen, different vehicle types may have different dominating accident modes. However, it should be noted that the dominating accident mode for each vehicle depends not only on the vehicle type but also on other factors (e.g. vehicle parameters, road conditions, driver operations). For instance, the dominating accident mode of the van is rotating on wet road, but overturning on dry road, cf. Table 2. Figure 6 displays the failure probability P G for a single gust event of different vehicles running under strong crosswind on wet road. The vehicle speed is v 0 ¼ 60 km/h and the wind direction is assumed to be perpendicular to the vehicle running direction (i.e. a x ¼ 0 ). As can be seen, the failure probability of each vehicle becomes larger when the mean wind speed increases. In addition, it has been found that the failure probability of the truck at a x ¼ 30 is larger than at a x ¼ 0. This implies that the worst case for a vehicle running under strong crosswind does not always occur for the wind perpendicular to the vehicle running direction. Moreover, the results also show that in comparison to the bus and the truck, the van and the car with trailer are more easily influenced by strong crosswind under the given conditions. In Fig. 7, the failure probability of vehicles running on wet road at v 0 ¼ 30 km/h is depicted. Compared to Fig. 6, it is found that the van and the car with trailer are still the most sensitive vehicles and that lower vehicle speeds will lead to smaller failure probabilities. It shows again that the vehicle speed has a great influence on the crosswind stability. Besides, it is PG v 0 =60 km/h Car with trailer 10 4 Truck (α=30 ) Truck Van Bus u 0 [m/s] Fig. 6 Failure probability of vehicles running on wet road at v 0 ¼ 60 km/h, a x ¼ 0 PG v 0 =30 km/h u 0 [m/s] Car with trailer Truck (α=30 ) Truck Van Bus Fig. 7 Failure probability of vehicles running on wet road at v 0 ¼ 30 km/h, a x ¼ 0 notable that the failure probability of the car with trailer is higher than that of the van in Fig. 7. This is different from the result shown in Fig. 6, where the failure probabilities of the two vehicles are more or less the same. The main reason for this is the destabilization of the trailer due to the reduced traction at lower vehicle speeds. Table 2 Accident modes for different road vehicles in the simulation Type of vehicle Accident mode Dry road Wet road a ¼ 0 a ¼ 60 a ¼ 0 a ¼ 60 Truck Overturning Overturning Overturning Overturning Bus Overturning Overturning Overturning Overturning Van Overturning Overturning Rotation Rotation Car Rotation Rotation Rotation Rotation Car with trailer Rotation Rotation Rotation Rotation

7 Considering the influence of road conditions on the crosswind stability of different vehicle types, vehicles running on dry road have also been studied. In general, the car with trailer running on wet road is more prone to crosswind. As is shown in Fig. 8, the failure probability of the van and the car with trailer on dry road are smaller compared to wet road conditions. However, the failure probabilities of the bus and the truck on wet and dry road are more or less the same, which is due to the large mass of the two vehicles. For heavy vehicles, the lateral friction forces of the tires are sufficient enough to resist the wind force, while for light vehicles the lateral friction forces are much smaller, which makes the vehicle much easier to shift or rotate. Figures 9 and 10 represent the failure probability of vehicles running on wet road under strong crosswind with different vehicle speeds at a x ¼ 60. Generally, the failure probability of vehicles running at a x ¼ 60 is smaller compared to that of vehicles running at a x ¼ 0 especially for low vehicle speeds. However, this is not always the case. E.g. for the van running on wet road at v 0 ¼ 60 km/h, the failure probability is nearly independent of the wind direction, cf. Figs. 6 and 10. This is due to the dominating accident mode (rotation) that is less influenced by the wind direction. Finally, a comparison for the failure probability of the passenger car running on dry road, wet road and wet road with a ¼ 60 is presented in Table 3. As can be seen, the vehicle speed still has an important influence on the failure probability. Large vehicle speeds and wet road condition lead to high failure PG v 0 =60 km/h Car with trailer 10 5 Truck (α=30 ) Truck Van Bus u 0 [m/s] Fig. 8 Failure probability of vehicles running on dry road at v 0 ¼ 60 km/h, a x ¼ 0 PG v 0 =30 km/h probability. Besides, the wind direction has also an influence on the crosswind stability. It seems that the influence of the wind direction is more pronounced for low vehicle speeds. For v 0 ¼ 60 km/h and v 0 ¼ 80 km/h, the failure probability is nearly independent of the wind direction. 5 Concluding remarks u 0 [m/s] Car with trailer Truck Van Bus Fig. 9 Failure probability of vehicles running on wet road at v 0 ¼ 30 km/h, a x ¼ 60 PG v 0 =60 km/h u 0 [m/s] Car with trailer Truck Van Bus Fig. 10 Failure probability of vehicles running on wet road at v 0 ¼ 60 km/h, a x ¼ 60 This paper studies the crosswind stability of road vehicles running with a probabilistic method. Vehicles are divided into several categories, namely buses, trucks, vans, small passenger cars and cars with trailer. For each vehicle type, a worst-case vehicle model and

8 Table 3 Failure probability of the passenger car running at u 0 ¼ 23 m=s under different conditions Vehicle speed ðkm=hþ Wind speed ðm=sþ Dry road Wet road Wet road (a ¼ 60 ) e e e e e e e e e-002 corresponding aerodynamic coefficients are identified. The gust amplitude, gust duration as well as aerodynamic coefficients are considered as random variables. Based on the proposed model, a reliability analysis has been carried out and failure probabilities for various vehicle types are computed and compared. It has been found that the influence of strong crosswind depends on the type of the road vehicle. The combined effect of aerodynamic coefficients as well as other conditions (e.g. wet/dry road) may change the vehicle accident mode or influence the failure probability. High vehicle and wind speeds lead to large failure probabilities. Besides, for a vehicle running under strong crosswind, the most dangerous case does not always occur under a wind angle a x ¼ 0. Additionally, road conditions play an important role for the crosswind stability. Vehicles with low mass (such as the van and the car with trailer) are more prone to crosswind on wet road. For passenger cars, the influence of the wind direction seems to be more pronounced at low vehicle speeds. References 1. Åström KJ, Hägglund T (1995) Pid controllers: theory, design, and tuning. Instrument Society of America, Research Triangle Park 2. Baker C (1986) A simplified analysis of various types of wind-induced road vehicle accidents. J Wind Eng Ind Aerodyn 22(1): Baker C (1987) Measures to control vehicle movement at exposed sites during windy periods. J Wind Eng Ind Aerodyn 25(2): Baker C (1988) High sided articulated road vehicles in strong cross winds. J Wind Eng Ind Aerodyn 31(1): Baker C (1994) The quantification of accident risk for road vehicles in cross winds. J Wind Eng Ind Aerodyn 52: Baker C, Reynolds S (1992) Wind-induced accidents of road vehicles. Accid Anal Prev 24(6): Bec J (2010) Influence of wind spectrum formula choice on footbridge response. In: The fifth international symposium on computational wind engineering (CWE2010). Chapel Hill, North Carolina, USA, pp Bierbooms W, Cheng P (2002) Stochastic gust model for design calculations of wind turbines. J Wind Eng Ind Aerodyn 90(11): Boada BL, Boada M, Diaz V (2005) Fuzzy-logic applied to yaw moment control for vehicle stability. Veh Syst Dyn 43(10): Cai C, Chen S (2004) Framework of vehicle bridge wind dynamic analysis. J Wind Eng Ind Aerodyn 92(7): Cheli F, Belforte P, Melzi S, Sabbioni E, Tomasini G (2006) Numerical-experimental approach for evaluating crosswind aerodynamic effects on heavy vehicles. Veh Syst Dyn 44(sup1): Cheli F, Corradi R, Sabbioni E, Tomasini G (2011) Wind tunnel tests on heavy road vehicles: cross wind induced loads part 1. J Wind Eng Ind Aerodyn 99(10): Chen S, Cai C (2004) Accident assessment of vehicles on long-span bridges in windy environments. J Wind Eng Ind Aerodyn 92(12): Chen X (2008) Analysis of alongwind tall building response to transient nonstationary winds. J Struct Eng 134(5): Cheung MS, Chan BYB (2009) Operational requirements for long-span bridges under strong wind events. J Bridge Eng 15(2): Cooper RK (1984) Atmospheric turbulence with respect to moving ground vehicles. J Wind Eng Ind Aerodyn 17(2): Dai Q, Young RK (2010) High wind warning system to prevent overturning truck crashes in Wyoming. In: Transportation research board 89th annual meeting, Deodatis G, Shinozuka M (1988) Auto-regressive model for nonstationary stochastic processes. J Eng Mech 114(11): Guo W, Xu Y (2006) Safety analysis of moving road vehicles on a long bridge under crosswind. J Eng Mech 132(4): Juhlin M (2009) Assessment of crosswind performance of buses. Ph.D. thesis. KTH 21. Manwell JF, McGowan JG, Rogers AL (2005) Wind energy explained: theory, design and application, repr. with corr. edn. Wiley, Chichester. Includes bibliographical references and index 22. Morfiadakis E, Glinou G, Koulouvari M (1996) The suitability of the von Kármán spectrum for the structure of turbulence in a complex terrain wind farm. J Wind Eng Ind Aerodyn 62(2): Proppe C, Wetzel C (2010) A probabilistic approach for assessing the crosswind stability of ground vehicles. Veh Syst Dyn 48(S1): Proppe C, Zhang X (2013) Risk analysis of railway vehicles under strong crosswinds. Int J Railw Technol 2:93 111

9 25. Proppe C, Zhang X (2015) Influence of uncertainties on crosswind stability of vehicles. In: IUTAM symposium on dynamical analysis of multibody systems with design uncertainties 26. Snæbjörnsson JT, Baker C, Sigbjörnsson R (2007) Probabilistic assessment of road vehicle safety in windy environments. J Wind Eng Ind Aerodyn 95(9): Wang J, Longoria RG (2006) Coordinated vehicle dynamics control with control distribution. In: American control conference, IEEE, pp Wetzel C, Proppe C (2010) On reliability and sensitivity methods for vehicle systems under stochastic crosswind loads. Veh Syst Dyn 48(1): Wu D (2001) A theoretical study of the yaw/roll motions of a multiple steering articulated vehicle. Proc Inst Mech Eng Part D J Automob Eng 215(12): Xu YL, Guo W (2003) Dynamic analysis of coupled road vehicle and cable-stayed bridge systems under turbulent wind. Eng Struct 25(4): Publisher s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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