Advanced Materials Research Online: 0-0- ISSN: 66-8985, Vols. 99-00, pp 89-83 doi:0.408/www.scientific.net/amr.99-00.89 0 Trans Tech Publications, Switzerland Vibration Analysis of Gear Transmission System in Electric Vehicle Bihui Xie, a, Tong Zhang and Shuguang Zuo Sino-German College for Graduate Study, Tongji University, Shanghai, 0009, China College of Automotive Engineering, Tongji University, Shanghai, 0804, China a imxiebihui@63.com Keywords: Electric Vehicle, Gear Transmission, Vibration, Contact Force. Abstract. This paper presents a systematic research on the gear transmission system of the electric vehicle. An accurate 3-D model of the gear transmission system is established in UG (Unigraphics NX) using software Gearwizard, and then imported to ADAMS/View environment. Based on the contact force of ADAMS, the vibration at 3 different test points of the model are simulated. The simulation results seem to be in good accordance with the test results, which proved the validity of the gear transmission model. Finally, the influence of helix angle on vibration at 3 different test points are also researched. The results of the total analysis can be used further to optimize the gear transmission system of the electric vehicle. Introduction Under the pressure from energy shortages and environmental contamination, the development of electric vehicles has attracted more and more attention. The vibration and noise of the electric vehicle affect greatly on the comfort of electric vehicles. However, the NVH Analysis about electric vehicles is presently still on the initial stage. The gear transmission system is one of the main resources of vibration and noise in electric vehicles. Due to the difference in power resource, the structure of gear transmission system on the electric vehicles varies substantially from traditional ones, which also causes the variation on the vibration characteristic. Most of the existing research about gear system vibration are based on the traditional vehicle. Therefore, the vibration analysis of the gear transmission system in electric vehicles is significant and original. The amplitude, direction or position of the meshing force between gears are the causes of the vibration and noise of the gear transmission system []. The current analysises of the gear system vibration are based on mathematical model or FEM software. In this paper, a vibration analysis of the gear transmission system in the electric vehicles is carried on in a different approach. In the UG/ Gearwizard software, the 3D-Model of the gear transmission system is established, which is followed by a simulation with the ADAMS software. By definition of the contact force in ADAMS, the meshing force between gears can be accurately simulated. With the PostProcessor of ADAMS, the data of vibration such as natural frequencies and accelerations of test points can be conveniently obtained. Establish 3D-Model Compared to the transmission system of the conventional vehicle, the gearbox of the electric vehicle is obviously simplified. The structure of the electric vehicle gearbox is shown in Fig., which includes pairs of speed reducing gears and a differential with 4 panel gears and differential gears. In order to establish the 3D-Model in Unigraphics NX, the parameters of the gears should be measured and calculated. The teeth number, face width, helix angle, diameters of root circle and tip circle can be directly measured. The (normal) module, (normal) pressure angle and addendum modification coefficient can be indirectly attained by calculation. After inputting the parameters into the gear design software Gearwizard, the 3D-Model of the gears is automatic modeled in UG. The All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 30.03.36.75, Pennsylvania State University, University Park, USA-06/03/6,:3:46)
80 Advances in Mechanical Design other parts of the transmission system can be also formed and assembled with UG. Fig shows the whole 3D-Model of the gear transmission system. Fig. Structure of electric vehicle gearbox Fig. 3-D Model of gear transmission system in UG Simulation and Vibration Analysis with ADAMS The 3D-Model of the gear transmission system can be saved as parasolid file and imported into ADAMS software. According to the kinematics, different joins should be set on each parts of the Model. With the function of contact force in ADAMS, the meshing force between gears can be simulated. The function of contact force in ADAMS is based on the Hertz theory [, 3]. The model of the contact force is illustrated in Fig. 3.[4] It can be assumed that, there is a stiffness-variable spring and a damping between two contact bodies. With the stiffness and the damping, the contact force can be calculated as Eq.. [4] n F n =kδ +Dδ () where F n is the contact force, k is the stiffness, δ is the penetration depth, n is force exponent, D is the damping. Rigid Body k n k n Rigid Body c c Fig. 3 Model of contact force Besides the above parameters, the other parameters such as static coefficient, dynamic coefficient, stiction transition velocity and friction transition velocity should also be input to the software to define the contact force. The stiffness k depends on the materials and the forms of the two contact bodies. The equation of the stiffness K is as below:
Advanced Materials Research Vols. 99-00 8 4 * K= ρ E () 3 * where ρ is the radius of curvature, E is the integrated elasticity modulus [5]. The stiffness and force exponent of the meshing gears can be calculated with the parameter of the gears and the E-modulus. The meshing stiffness of the spur gears K can be calculated as Eq3, and the meshing stiffness of the helical gears - ' * ud cosαtanα -ν -ν 4 4 K s = ρ E = + 3 3 (+u) E E - ' * udcosα ttanα t -ν -ν b 4 4 K h = ρ E = + 3 3 (+u)cosβ E E K can be calculated as Eq4: h where u is the gear radio, d is the reference diameter of the driving gear, v and v are the Poisson s ratios of the driving gear and driven gear, E and E are the elasticity modulus of the driving gear ' and driven gear. For spur gears, α is the pressure angle of the reference circle, α is the pressure angle ' of the pitch circle. For helical gears, α t is the transverse pressure angle of the reference circle, α t is the pressure angle of the pitch circle, β b is the helix angle of the base circle [5]. Substituting the parameters of meshing gears into the above equations leads to the following meshing stiffnesses of meshing gears:.5 first pair of speech reducing gears: K, = 3 9 4 0 N /m m,.5 the second pair of speech reducing gears: K 3,4 = 8 0 3 0 N /m m,.5 planet gear and differential gear: K 5,6 = 4 0 4 5 9 0 N /m m. The force exponent n =.5. The other parameters of the contact force are generally attained from tests. In this study, the values of these parameters are selected from the instruction literature of ADAMS as table [4]. Table Parameters of contact force in ADAMS Mat Mat c d vs vd mus mud R Steel Steel (Greasy) (Greasy) 50.000 0. 0. 0 0.08 0.05 0.5 The electric vehicle analyzed in this paper has been tested in the NVH laboratory before. During the test, the sensors are placed on the input shaft, counter shaft and output shaft. In order to compare the results of the simulation with the data of the test, the locations of the sensors on the model should be the same with the test. After all of the preparation, the gear transmission model can begin to run. The simulation results of the gear transmission system can be checked in the ADAMS/PostProcessor window, including time-domain and frequency-domain curves of the accelerations of test points. The natural frequencies of test points can be obtained from the simulation. The results comparison between the test and simulation is shown as table. The error between the simulation and test is from.% to 7.0%. The effectiveness of the simulation could be demonstrated by comparison of computed results against the test data. s (3) (4)
8 Advances in Mechanical Design Table. Results comparison between experiment and simulation: natural frequencies of test points (Hz) Counter shaft Test 76.398 0.563 99.44 399.753 Simulation 8.98 49.77 046.07 306.3 Error 3.7% 4.4% 7.0%.8% Output shaft Test 76.398 0.563 99.44 399.753 Input shaft Simulation 80.3 063.3 50. 36.75 Error.% 3.5%.%.5% Test / 0.563 96.957 399.753 Simulation / 066.5 7.08 306.3 Error / 3.% 3.%.8% Parameters Influence Analysis When the electric vehicle is running in a straight way, the influence of the differential on the vibration can be ignored. The meshing stiffness between the two pairs of speed reducing gears are the main factors of the vibration, which depends on the teeth number, module, pressure angle, helix angle and addendum modification coefficient. The modify of teeth number, module and addendum modification coefficient will impact the center distance and roof cutting of the meshing gears. During the design of the gearbox, the normal pressure angles are always set as 0 according to the GB standard. It s difficult to change the meshing stiffness through the above parameters. Therefore, the best parameter to change the contact stiffness is the helix angle. The current helix angles of two pairs of speed reducing gears are 3.4 and 30.. According to the mechanical handbook, the helix angle of gears in Vehicle gearbox should range from to 34. Keep the other gear parameters as the same value and set the helix angle of the first pair of speed reducing gears as, 5, 8, 3.4 and 34. The variation of the natural frequencies and vibration accelerations of three test points with applied helix angles are shown as Fig 4., Fig 5., and Fig 6.. From these figures it can be concluded that, when the helix angle of the first pair of gears remains 3.4, the amplitudes of three test points are relatively low. The similar analysis can be made in the term of the second helix angle. Keep the other gear parameters as the same value and set the helix angle of the second pair of speed reducing gears as, 5, 8, 30. and 34. The variation of the natural frequencies and vibration accelerations of three test points with applied helix angles are shown as Fig 7, Fig 8 and Fig 9 From these figures it can be concluded that, when the helix angle of the second pair of gears is reduces at 8, the amplitudes of three test points are relatively low. Conclusion From the comparison of computed results against test data, it is concluded that the simulation of the gear transmission system is precise. According to the Parameters Influence Analysis, the helix angles of two pair of speed reducing gears are the most important variable influence factor to improve the vibration characteristic of the gear translation system. When these two helix angle are set as 3.4 and 8, the amplitudes of three test points are relatively low. This result can be applied to optimize the gear transmission system of the electric vehicle.
Advanced Materials Research Vols. 99-00 83 References [] J. Derek Smith: Gear Noise and Vibration (Marcel Dekker, New York, 003), p.- [] K. L. Johnson: Contact mechanics (Cambridge University Press, 003), p.84-04 [3] G.G. Adams, M. Nosonovsky: Tribology International 33(000), p.43 [4] Using MSC.ADAMS/Function Builder (Version 9. MDI, 998) [5] BI Feng-rong, CUI Xin-tao, LIU Ning: Journal of Tianjin University (005) [6] Kai Long, Yin Cheng: Application of MSC. ADAMS on calculation of gear meshing force (Beijing Technological University, 009)
Advances in Mechanical Design 0.408/www.scientific.net/AMR.99-00 Vibration Analysis of Gear Transmission System in Electric Vehicle 0.408/www.scientific.net/AMR.99-00.89 DOI References [] J. Derek Smith: Gear Noise and Vibration (Marcel Dekker, New York, 003), p.- 0.07/S00447970336