IMPACT OF ROAD SURFACE ROUGHNESS AND ENGINE TORQUE ON THE LOAD OF AUTOMOTIVE TRANSMISSION SYSTEM

International Journal of echanical Engineering and Technology (IJET) Volume 10, Issue 02, February 2019, pp. 1752 1761, Article ID: IJET_10_02_181 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijet&vtype=10&itype=2 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 IAEE Publication Scopus Indexed IPAT OF ROAD SURFAE ROUGHNESS AND ENGINE TORQUE ON THE LOAD OF AUTOOTIVE TRANSISSION SYSTE Thai Nguyen University of Technology, Thai Nguyen city, Vietnam Email: tuannkcn@tnut.edu.vn ABSTRAT The purpose of this paper is to evaluate the effect of the engine torque and the road surface roughness on the load of the automotive transmission system. In the study, a dynamic model for the automobile with 4x4 wheel formula is created. The model includes the transmission system itself, the suspension system and the automotive body. Also, the excitation sources from the oscillation of the engine torque and the road surface roughness are analyzed. Based on the created model, the mathematical model is built. Some calculated simulation results of the impact of road surface roughness and engine torque on the load of automotive transmission are shown for illustration. Key words: engine torque, road excitation, dynamic load, transmission system, suspension ite this Article:, Impact of Road Surface Roughness and Engine Torque on the Load of Automotive Transmission System, International Journal of echanical Engineering and Technology 10(2), 2019, pp. 1752 1761. http://www.iaeme.com/ijet/issues.asp?jtype=ijet&vtype=10&itype=2 1. INTRODUTION The transmission system plays an important role in the overall performance of vehicle. Especially, it has a significant influence on the dynamical characteristic, fuel consumption and stability of the vehicle [1,14,18]. The literatures [2,6,7,14,18,19] shows that automotive transmission system is a very complex oscillating system affected by various excitation sources such as the oscillation of internal combustion engines, the road surface roughness or by driving skill of driver, etc. There have been a number of studies on the dynamic loads acting on the automobile transmission system [2,4,6,17,18]. These works mainly focus on studying the effect of structural parameters, the impact of suddenly engage clutch, etc. on the load of transmission components. In addition, there are quite a lot of published researches on the appearance of loads in the automobile transmission system when starting vehicle from the rest or during gearshift [6, 19] etc. in which the excitation from engines has been described in the simple form. http://www.iaeme.com/ijet/index.asp 1752 editor@iaeme.com

The analysis of reference documents [1-19] above shows that there exist a number of published works related to the load acting on the transmission system. However, these studies often focus on analyzing the effect of independent factors. Up to now, there has not been any research on the effect of engine and road excitation on the dynamic load of automobile transmission system. Therefore, the main purpose of this study is to investigate the influence of the road surface roughness and oscillation of engine torque on the load of transmission components of automobile with 4x4 wheel formula. 2. ATERIAL AND ETHOD 2.1. Dynamical model To analyze the influence of road surface roughness and IE torque oscillations on dynamic loads of automotive transmission system, this study uses the equivalent dynamic model of automobile with 4x4 wheel formula as shown in Figure 1. Figure 1. Dynamic model of vehicle with 4x4 wheel formula where: m s m s1, m s2 are the sprung mass of the vehicle, the front axle and the rear axle, respectively m u1 and m u2 are the unsprung masses of the front axle and the rear axle k t1 and k t2 are the stiffness coefficients of tires s1 and s2 are the suspension stiffness coefficients K t1, K t2 are the damping coefficients of tires and the suspension damping coefficients L is the wheelbase of vehicle a and b are coordinates of the vehicle's center of gravity I 8 is the moment of inertia of vehicle body about the horizontal axis, I e is the moment of inertia of the part rotation of engine, I 1 is the moment of inertia of the part rotation of clutch I 2 is the moment of inertia of gearbox and the distribution box I 3, I 4 are the moments of inertia of the front wheels and the rear wheels I 5 is the moment of inertia of the flywheel equivalent to the mass of the forward motion of the vehicle I 6 and I 7 are the moments of inertia of the front axle and the rear axle, respectively I 8 is the moment of inertia of vehicle body about the http://www.iaeme.com/ijet/index.asp 1753 editor@iaeme.com

Impact of Road Surface Roughness and Engine Torque on the Load of Automotive Transmission System horizontal axis z 0, z 1, z 2, ζ 1 and ζ 2 are the vertical displacements of sprung and unsprung masses φ i are the angle displacement of the masses I i, c ij and k ij are the damping coefficient and the stiffness coefficient of the part of transmission (i, j=1-6) k 68 and k 78 are the torsional roll stiffness of springs of front and rear axles. In order to develop the mathematical model of the systems in figure 1, Lagrange method has been applied. The equations of motion are as follows: I T ( t) T ( t) e e e c K Tc (t) 0 F a F b I 1 1 12 1 2 12 1 2 I K K 2 2 12 1 2 12 1 2 23 2 3 6 23 2 3 6 K 0 24 2 4 7 24 2 4 7 I K K (t) 3 3 23 2 3 6 23 2 3 6 35 3 5 35 3 5 1 I K K (t) 4 4 24 2 4 7 24 2 4 7 45 4 5 45 4 5 2 I K - -K - 0 5 5 35 3 5 35 3 5 45 5 4 45 5 4 I +K 0 6 6 23 2 3 6 23 2 3 6 68 6 8 I +K 7 7 24 2 4 7 24 2 4 7 78 7 8 I +.. 0 8 8 68 6 8 78 7 8 s1 s2 m z F F 0 8 0 s1 s2 m F F 0 u1 1 s1 t1 m F F 0 u 2 2 s2 t 2 F c z k z s1 s1 1 1 s1 1 1 F c z k z s2 s2 2 2 s2 2 2 F c q k q t1 t1 1 1 t1 1 1 Ft 2 ct 2 2 q2 kt 2 2 q 2. Where: z 1 and z 2 are the displacements of the sprung masses of the front and rear axles and at the center in the vertical direction. The relationship between z 0, z 1 and z 2 has the following form: z z a. 1 0 8 z z b. 2 0 8 According to [2,4,5,6], the moment in the components of transmission system can be expressed by the relative stiffness of the components and the relative displacement of the masses of transmission system as: М С М С М С 12 12 2 1 23 23 3 2 6 24 24 3 2 7 М С М С М С М С 35 35 5 3 45 45 5 4 68 68 6 8 78 78 7 8 Differentiating equations (3) with respect to t yields: (1) (2) (3) http://www.iaeme.com/ijet/index.asp 1754 editor@iaeme.com

8 6 8 68 68 6 8. 12 12 1 2 12 12 1 2 23 23 2 3 6 23 23 2 3 6 24 24 3 4 7 24 24 2 4 7 35 35 3 5 35 35 3 5 45 45 4 5 45 45 4 5 68 6 78 78 7 8 78 78 7 8 (4) After some transformations we get: I T ( t) T ( t) e e e c K K K K T (t) I I I I I I I I I 12 12 12 12 23 12 12 24 12 12 c 12 12 12 23 23 24 24 12 1 2 1 2 2 23 2 2 24 2 1 K K K K K 23 23 23 23 23 23 12 23 23 24 23 23 12 12 24 24 I I I I 23 23 23 I I I 2 3 6 I I I 2 3 8 K ( ) F a. 0 I. I I I 35 23 23 23 s1 23 t 35 35 1 3 35 3 6 6 2 12 2 2 24 2 K K K K K I I I I I I I I I 24 24 24 24 24 24 12 24 24 24 24 24 12 12 2 4 7 2 4 7 2 12 2 2 K ( ) F b. 0 I. I I I 45 24 24 24 s 2 24 t 45 45 2 4 45 4 7 7 23 24 24 23 23 23 2 35 35 35 35 23 35 35 45 35 35 35 35 35 35 23 23 45 45 1 45 K K K K (t) 0 I I I I I I I I I 3 5 3 5 3 23 3 5 45 5 3 K K K K (t) 0 45 45 45 45 24 45 45 35 45 45 45 45 45 24 24 35 35 2 I I 4 5 I I I I I I I I 4 5 4 24 4 5 35 5 4 K F b. F a. I I I I I I I 68 68 68 23 68 68 s2 68 s1 68 68 78 23 23 68 78 I 6 8 8 6 23 6 8 8 78 78 7 I s s s 0 1 2 u s t 1 1 1 1 u s t 2 2 2 2 m z F F 0 m F F 0 m F F 0 q k q F c z k z 78 24 78 78 s2 78 s1 78 68 24 24 78 8 8 7 24 7 8 8 s s s 1 1 1 1 1 1 1 F c z k z s s s 2 2 2 2 2 2 2 F c q k q F t t t 1 1 1 1 1 1 1 t 2 c t (6) K F a. F a. I I I I I. 2 2 2 t 2 2 2 0 0 I 0 http://www.iaeme.com/ijet/index.asp 1755 editor@iaeme.com

Impact of Road Surface Roughness and Engine Torque on the Load of Automotive Transmission System Solving the system equations (6) allows us to determine the effect of excitation from the road surface roughness and the torque of internal combustion engine on the elastic moments ij in the components of transmission system. 2.2. Excitation resources Excitation from road surface roughness. In the International Road Roughness Test [14], the roughness of the road is defined as the deviation of the road from the ideal plane along the running direction of the vehicle. The power spectral density function of road can represent the distribution of road roughness energy in the spatial frequency domain, using the following formula as the fitting expression: q S n S n n q 0 n0 W In this formula: n is the spatial frequency (m -1 ) n 0 is the reference spatial frequency, n 0 =0.1(m -1 ) S q (n 0 ) is the road power spectral density at the reference spatial frequency and called the road roughness coefficient. Its value depends on the road grade W is the frequency index, the frequency of the slope of the double logarithmic coordinates, which determines the frequency structure of the road power density. The road surface roughness is assumed to be a zero-mean stationary Gaussian random process. It can be generated through an inverse Fourier transformation: q N t 2S n n cos2n t i1 q i k where i is random phase uniformly distributed from 0 to 2. Thus, based on the above equation, a simulation road model is built in Simulink. The curve of road excitation lass- according to ISO 8068 is shown in Figure 3. i (2) (3) Figure 2. Simulink model for road profile Figure 3. The curve of road profile according to ISO 8068 standard [15] Engine excitation. There are various methods to determine the torque of the internal combustion engine such as harmonic analysis method, method of using experimental formula, graphical method, simulation method [7,8,18] etc. This article uses simulation method with the help of the Simscape tool in atlab software [9]. Figure 4 shows a block diagram of the engine model used to determine the engine torque. The input parameters of the engine model include the number of cycles, cylinders, cylinder diameter and piston stroke. The output variables of the model are engine speed w e and engine torque T e. Physical signal port Th is the engine throttle level as a fraction between 0 and 1. This fraction corresponds to the percentage of full power generated. The block uses the physical signal input whenever the pressure lookup table in the block dialog box is parameterized only in terms of the crank angle. http://www.iaeme.com/ijet/index.asp 1756 editor@iaeme.com

Using the model shown in Fig. 4, it is possible to determine the engine torque according to the variation of structural parameters of engine and throttle level [9]. Figure 4. Simscape model for IE Figure 5. Engine torque vs time with difference throttle level and number of cylinder 3. RESULTS AND DISUSSIONS In order to study the impact of road surface roughness and engine torque on the load of transmission system, a simulation of this system was carried out in atlab Simulink. The parameters for the model are shown in Table 1 and Table 2. Table 1. The parameters of transmission system [3] Gears Parameters No.1 No.2 No.3 No.4 No.5 I 1 (kg.m 2 ) 0.11530 0.11530 0.11530 0.11530 0.11530 I 2 (kg.m 2 ) 0.01114 0.01429 0.02079 0.03030 0.04039 I 3 (kg.m 2 ) 0.02010 0.06138 0.14635 0.27069 0.40258 I 4 (kg.m 2 ) 0.02073 0.06332 0.15098 0.27925 0.41530 I 5 (kg.m 2 ) 5.60347 17.114 40.8048 75.4726 112.244 I 6 (kg.m 2 ) 0.00055 0.00168 0.00402 0.00743 0.01105 I 7 (kg.m 2 ) 0.00053 0.00162 0.00387 0.00715 0.01064 12 (N.m.rad -1 ) 440.277 572.182 606.884 636.148 612.964 23 (N.m.rad -1 ) 231.397 706.727 1 685.05 3 116.67 4 635.14 24 (N.m.rad -1 ) 231.397 706.727 1 685.05 3 116.67 4 635.14 35 (N.m.rad -1 ) 45.946 140.326 334.578 618.836 920.340 45 (N.m.rad -1 ) 30.285 92.494 220.534 407.901 606.634 68 (N.m.rad -1 ) 190.270 581.119 1 385.56 2 562.73 3 811.32 78 (N.m.rad -1 ) 190.270 581.119 1 385.56 2 562.73 3 811.32 Table 2. The parameters of vehicle [3] Parameters Values Parameters Values I 8 (kg.m 2 ) 868.7 t1 (N.m -1 ) 57300 m 8 (kg) 1200 t2 (N.m -1 ) 63600 K s1 (N.s.m -1 ) 4359 m u1 (kg) 60 K s2 (N.s.m -1 ) 4350 m u2 (kg) 50 K t1 (N.s.m -1 ) 1250 m s (kg) 686 K t2 (N.s.m -1 ) 1250 a(m) 0.9 s 1 (N.m -1 ) 450000 b(m) 1.2 s 2 (N.m -1 ) 450000 f 0.002 r w (m) 0.28 http://www.iaeme.com/ijet/index.asp 1757 editor@iaeme.com

Impact of Road Surface Roughness and Engine Torque on the Load of Automotive Transmission System The results of calculating transmission moments with difference road condition and engine torque values are presented in Figures 6-8. Impact of engine torque. Figure 6 shows the calculation results of moment on the front axle when the automobile is moving at 2-nd gear. As it can be observed in Figure 6, the throttle level of internal combustion engine has a great influence on the value of the moment at the front axle. When changing the throttle level of engine Th=0.5 Th=0,8 Th=1, the maximum moments generated in the front axle are 821(N.m), 1059.6(Nm) and 1179.3(N.m), respectively. Figure 6. Influence of throttle level on the moment 23 at the front axle Figure 7 illustrates the calculation results of torque at the rear wheel depending on the cylinder number of the engine. It is noticed in Figure 7 that with the same engine power, the more numbers the cylinders have, the smaller the maximum torque value is at the rear axle. omparing the calculation results of moment at the rear wheel of automobile corresponding with using 4 cylinder and using 6 cylinder engines shows that the difference between maximum torque at the rear axle of these two cases is about 10,2%. Figure 7. Influence of cylinder number on the moment 35 of front axle Impact of road surface roughness. To see more clearly the effect of excitation from the road surface roughness on the load at the components of automotive transmission system, the author conducted a calculation simulation when the car moved on two different road conditions (Figure 8) at 4-th gear at the speed of 30 km/h. http://www.iaeme.com/ijet/index.asp 1758 editor@iaeme.com

Figure 8a is the resulting torque at the driving wheel when the automobile moves at gear 2nd on the ISO class road in two cases: with and without the influence of the road excitation. From the calculation results, we can see that with the influence of excitation from road surface, the torque on the front axle 23 increases about 0.9% in comparison with the case where the influence of excitation from road surface is ignored. a) 23 vs time with and without excitation from road surface roughness b) 24 vs time with the abrupt of bad road Figure 8. Influence road excitation on the moment 24 of front axle The resulting moment at front axle when the vehicle is moving suddenly from ISO class road to a very bad road with surface roughness 3 times greater than surface roughness of ISO class road (the period corresponding to Time=5-10s) is depicted in Figure 8b. The simulation result shows that the maximum moment at the rear axle 24max in this period increases but not significantly. In the period of automobile moving on the road ISO class road (corresponding to Time=0-5 seconds), the value 24max is equal to 1157.1 Nm. When the vehicle suddenly moves to a bad road (Time = 5-10 seconds), the value of 24max is 1168.6 N.m, i.e. only about 1% larger than when the vehicle moves on the road ISO class road. 4. ONLUSIONS In this paper, the simulation of the influence of engine torque oscillation and excitation from road surface roughness on the load of automotive transmission system was conducted. For this purpose, the dynamic and mathematical models of system were developed, and the simulations were carried out with the help of atlab/simulink R2018a. The main conclusions are as follows: http://www.iaeme.com/ijet/index.asp 1759 editor@iaeme.com

Impact of Road Surface Roughness and Engine Torque on the Load of Automotive Transmission System (i) The load of the automotive transmission system depends on many factors such as the oscillation of engine torque, the speed of clutch engagement, the excitation from road surface roughness, etc. (ii) When traveling on the road, the dynamic loads at the transmission components depend on the engine torque oscillation and excitation from road surface. However, the main factor affecting the load of transmission components is the engine torque oscillation. The calculation results show that when the vehicle moves on ISO road type, at 3-rd gear and at the speed of 30 km/h, the maximum moment generated in the axles in case of considering the excitation from the road surface is about 0.9% larger than that in the case where it is not taken into consideration. (iii) With the same working conditions and the same transmission system structure, the more numbers the cylinders have, the smaller the maximum moment value is at the transmission component. The calculation results in using 4 cylinder and using 6 cylinder engines show that the difference between maximum moment at the rear axle of these two cases is about 10,2%. AKNOWLEDGEENTS The work described in this paper was supported by Thai Nguyen University of Technology for a scientific project. REFERENES [1] J.Y. Wong, Theory of ground vehicles, 4th ed., (John Wiley and Sons, Inc., New York, 2008) [2] Tsitovich I.S., Algin V. B.: Vehicle dynamics: Science and Technology, insk (1981). - 191 pp. (in Russian). [3], Le Van Quynh: odeling and simulation of vehicle vertical vibration from powertrain and road excitation.: International Symposium on Technology for Sustainability, pp. 512 515. Bangkok, Thailand (2012). [4] Lomankin V. V.: Research interaction vibration of transmission and suspension system of three axles vehicle, oscow, Abstract diss. 1971 (in Russian). [5] Afanasev B. A., Belousov B. N et al: Design AWD wheeled vehicle, vol 2 (in Russian), GTU Bayman Publisher, oscow (2008). [6] Blinov E.I.: Dynamic and energy wheeled vehicle (in Russian), echanical engineering Publisher, oscow (2005). [7] Stotsky A.A.: Automotive Engines. ontrol, Estimation, Statistical Detection, Springer- Verlag Berlin Heidelberg, 2009. 215 р. [8] histyakov V. K., The dynamic of piston and combined engine, (in Russian), Engineering Publishing house, oscow (1989). [9] https://www.mathworks.com [10] Pavlov Š., Droppa P., Štiavnický., Vibration analysis of resources in mobile technics, achines, Technologies, materials, International virtual journal for science, technics and innovations for the industry, YEAR II, ISSUE 10-11/2008, pp. 41-43, Sofia, 2008 http://www.iaeme.com/ijet/index.asp 1760 editor@iaeme.com

[11] Hamid Reza Karimi: Optimal Vibration ontrol of Vehicle Engine-Body System using Haar Functions, International Journal of ontrol, Automation, and Systems, vol. 4, no. 6, pp. 714-724, December 2006. [12] Zhengchao Xie, Pak-Kin Wong, Yucong ao: A numerical investigation on active engine mounting systems and its optimization, Journal of Vibro-engineering, Nov 2014, Vol 16. [13] Y. Nakaji, S. Satoh, T. Kimura, T. Hamabe, Y. Akatsu, and H. Kawazoe, Development of an active control engine mount system, Vehicle System Dynamics, Vol. 32, pp.185 198, 1999. [14] Guzzella L., Sciarretta A. Vehicle Propulsion Systems: Introduction to odeling and Optimization, 2nd ed. Springer-Verlag Berlin Heidelberg, 2007. [15] International Organization for Standardization (ISO), echanical vibration road surface profiles reporting of measured data, ISO 8068: 1995 (E), ISO, Geneva. [16] Giuseppe antisani, Giuseppe Loprencipe: Road Roughness and Whole Body Vibration: Evaluation Tools and omfort Limits, Journal of Transportation Engineering, September 2010. [17] Nguyen Trong Hoan,, "odeling and calculation the dynamics load of hydro dynamical transmission system of vehicle drivetrain", Vietnam echanical Journal, 2005 [18] Nguyen Trong Hoan and, Automotive transmission system, (Vietnam educational Publishing house 2018). [19] Shuplyakov V.S. Oscillations and loading of the vehicle transmission,.: Transport, 1974. - 328 p. http://www.iaeme.com/ijet/index.asp 1761 editor@iaeme.com