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1、400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 Web: www.sae.org SAE TECHNICAL PAPER SERIES 2002-01-3071 A Study on the Handling Performances of a Large-Sized Bus with the Change of Rear Suspension Geometry Kwon-Hee Suh Commercial Vehicle R&D Center,
2、Kia Motors Corp. Yoon-Ki Lee and Hae-Myun Jeong Department of Automobile, Chosun College of Science & Technology Reprinted From: Truck Modeling (SP-1729) International Truck and Bus Meeting and Exhibition Detroit, Michigan November 18-20, 2002 All rights reserved. No part of this publication may be
3、reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. For permission and licensing requests contact: SAE Permissions 400 Commonwealth Drive Warrendale, PA 1509
4、6-0001-USA Email: permissionssae.org Fax: 724-772-4028 Tel: 724-772-4891 For multiple print copies contact: SAE Customer Service Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-1615 Email: CustomerServicesae.org ISSN 0148-7191 Copyright 2002 SAE International P
5、ositions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions. Persons wishing
6、to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE. Printed in USA 2002-01-3071 A Study on the Handling Performances of a Large-Sized Bus with the Change of
7、 Rear Suspension Geometry Kwon-Hee Suh Commercial Vehicle R&D Center, Kia Motors Corp. Yoon-Ki Lee and Hae-Myun Jeong Department of Automobile, Chosun College of Science & Technology Copyright 2002 SAE International ABSTRACT Since the kinematic characteristics of a vehicle suspension are very comple
8、x and difficult to understand, CAE techniques must be applied to perform the suspension analysis. In this study, the influences of rear suspension geometry on the handling performances of a large-sized bus are investigated. The bus involved in this study has air spring type rigid axle suspensions wi
9、th four links. Quasi-static analyses are performed to evaluate the roll characteristics of the front and rear suspension. The quasi-static responses of suspensions are evaluated in terms of roll center height and roll steer. Roll center height is mainly dependent on the vertical displacement of a pa
10、nhard rod, and the vertical displacements of lower control links affect chiefly the roll steer. The parameter study with the change of rear suspension geometry is conducted to investigate the vehicle handling performance. This parameter study shows that the vertical displacement and orientation of a
11、 panhard rod have a significant influence on the handling performance of a large-sized bus. INTRODUCTION A vehicle suspension plays a role of maintaining contact between irregular road surfaces and tires as well as reducing the motion of sprung mass by adding the vertical compliance between sprung a
12、nd unsprung mass. In addition, it controls proper wheel position with respect to the vehicle and road and transfers the driving forces, braking forces, lateral forces, and torques to the chassis from the tires. Generally, the suspensions of medium and large-sized vehicles are classified into two typ
13、es: leaf spring and air spring type suspension. While the leaf spring has the hysteretic damping due to the interleaf frictions, the air spring, whose stiffness increases with load nonlinearly, maintains the wheel hop frequency constantly and shows no hysteretic damping. Hence, the high-grade medium
14、 and large-sized vehicles are usually equipped with the air spring type suspension. Since a vehicle undergoes complex interactions between suspension links through the revolution centers such as roll and pitch center, it is difficult to investigate its kinematic and dynamic behaviors. So the general
15、- purpose multibody dynamics programs such as DADS and ADAMS are used to analyze the suspension mechanism in the development of a new car. Kaminaga et al. investigate the nonlinear roll mechanism of a vehicle using DADS and show that the influence of roll center on a vehicle behavior varies with sus
16、pension types 1. Sohn et al. execute a quasi-static and dynamic analysis on vehicles whose wheel alignment characteristics are different and show that the vehicle dynamic characteristics can be changed significantly by modifying the suspension geometry 2. Xia and Willis perform the handling analysis
17、 on vehicles having four different tires and evaluate the influence of tire cornering stiffness on handling performances using the four parameter evaluation method 3. Kawagoe et al. show that for the desirable roll behavior the pitching motion of front wheel on rear wheel should be reduced by the ad
18、equate roll center characteristics, nonlinear load changes, and damper design 4. Yin et al. evaluate the roll characteristics with the change of link geometry by solving the nonlinear algebraic equations on the roll plane model of a beam-axle suspension having a panhard rod restraining link 5. Ahn i
19、nvestigates the handling performances of a medium-sized bus when the vehicles center of gravity, wheelbase, wheel tread, and tire properties are changed 6. Jones computes the forces and moments transferred to the vehicle body using the force-moment method and demonstrates the effects of load transfe
20、r and tread change not considered by roll center 7. Suh et al. optimize the bump steer characteristics of a front wheel by design of experiment and examine the vehicle dynamic characteristics with the change of front wheel alignment 8. In this paper, the handling performances of a large-sized bus wi
21、th the change of rear suspension geometry are analyzed. The front and rear suspensions are an air spring type rigid axle suspension with four links. The quasi-static models of both suspensions are constructed using DADS and their basic roll characteristics are examined. The experimental sensitivity
22、analyses are performed to study the roll center height and roll steer characteristics of the rear suspension with the change of hard points. From this sensitivity analysis the hard points sensitive to the roll center height and roll steer change are extracted. Then, the full vehicle model of a large
23、- sized bus is constructed and the reliability of the model is verified through the comparison of lane change simulation and test. Finally, a parameter study on handling performances with the changes of the selected hard points is performed, and each analysis result is evaluated using the j-turn sim
24、ulation. QUASI-STATIC ANALYSIS SUSPENSION MODELING The front and rear suspensions of a large-sized bus are the air spring type rigid axle suspensions with four links, and they are modeled using DADS as indicated in Figure 1 (a) and (b). (a) Front suspension (b) Rear suspension Figure 1. Suspension m
25、odels of a large-sized bus (A: lower link to frame mount, B: lower link to axle mount, C: upper link to frame mount, D: upper link to axle mount, E: panhard rod to axle mount, F: panhard rod to frame mount) The steering system of this bus consists of a steering column (upper and lower), gearbox, pit
26、man arm, front and rear drag links, and an idler arm, with a gear ratio of 20.5:1. Front and rear suspensions consist of an upper link and two lower links which are subject to braking and driving forces, a panhard rod which is subject to lateral forces, and an anti-roll bar to control the roll motio
27、n. Both suspensions are equipped with air spring instead of leaf spring to improve the ride quality and maintain the vehicle position constantly with the load change from curb weight to gross weight. ROLL CHARACTERISTICS The out-of phase, sine wave displacements from 100mm to +100mm are applied into
28、 the contact patches on the inner and outer wheels for the roll motion of the front and rear suspension. The roll center height and roll steer, the important roll parameters, are examined through roll analysis. Roll center height is determined by the geometry of the four links and wheel center, and
29、roll steer is defined as the ratio of yaw angle to roll angle of rigid axle 10,11. The roll characteristics of both suspensions are shown in Figures 2 and 3. (a) Roll center height (b) Roll steer Figure 2 Roll characteristics of front suspension (a) Roll center height (b) Roll steer Figure 3 Roll ch
30、aracteristics of rear suspension Table 1 Kinematic roll characteristics Suspension Roll center height (mm) Roll steer (%) Front -254.3 -7.94 Rear -156.0 -0.19 In Table 1, the front suspension shows typical toe-out characteristics with a negative roll steer, and the rear suspension has a tendency to
31、the toe-out near zero percent. The roll center height of the front suspension is positioned about 100mm lower than that of the rear suspension. Therefore, we find that the large-sized bus has a front-inclined roll axis and understeer characteristics. Generally, it is profitable to have the roll cent
32、er heights positioned as low as possible in both suspensions. In particular, the roll center height of the front suspension needs to be positioned much lower than that of the rear suspension to maintain the roadholding. The low roll center heights decrease the anti-roll moment, which induces the pha
33、se delay of roll angle and jack-up force, so that the roll response and feeling could be improved. ROLL SENSITIVITY ANALYSIS The dynamic behaviors of a large-sized bus are affected by the roll characteristics of the rear suspension when cornering. So, the experimental sensitivity analysis using the
34、perturbation method on the six hard points (point A to point F) shown in Figure 1(b) is performed to investigate the change of roll motion in the rear suspension. The results are indicated in Table 2. Table 2 Kinematic roll sensitivity in rear suspension Hard points Roll center height (mm) Roll stee
35、r (%) Original -156.0 -0.19 Ax -156.0 -0.19 Ay -156.0 -0.05 Az -156.2 -0.37 Bx -156.0 -0.19 By -156.0 -0.32 Bz -155.8 -0.01 Cx -156.0 -0.19 Cy -156.0 -0.19 Cz -156.0 -0.19 Dx -156.0 -0.19 Dy -156.0 -0.19 Dz -156.0 -0.19 Ex -156.0 -0.19 Ey -156.0 -0.19 Ez -156.5 -0.18 Fx -156.0 -0.19 Fy -156.0 -0.19
36、Fz -156.5 -0.18 In Table 2, the roll center height is dependent on the vertical locations of points E and F, the height and rotation of panhard rod, and the roll steer depends on the vertical location of point A and the lateral location of point B in the lower link. So we select the vertical locatio
37、ns of points A, E, and F as the design parameters for evaluating the vehicle dynamic characteristics except for the lateral location of point B because the design change on the lateral location of point B is actually impossible on the basis of chassis layout. FULL VEHICLE DYNAMIC ANALYSIS FULL VEHIC
38、LE MODEL The full vehicle model to simulate the actual motions of a large-sized bus is shown in Figure 4. It consists of 45 rigid bodies, 7 cylindrical joints, 9 revolute joints, 3 spherical joints, 7 universal joints, 39 bushings, 6 springs and dampers, 26 initial velocity conditions, 1 steering dr
39、iver condition, and 1 relative driver condition for gear ratio. So the full vehicle model has a total of 126 degrees of freedom. Also, the tire complex module of DADS is used to model the real tires. The vertical stiffness and carpet plot data are referenced from the test results of the tire manufac
40、turer. Figure 4 Full vehicle model of a large-sized bus LANE CHANGE ANALYSIS AND TEST The lane change analysis and test are implemented with a transition length 30m and a width of 3.5m at the speed of 80km/hr for 4 seconds. The evaluation terms of the analysis and test are roll angle, roll rate, yaw
41、 rate, and lateral acceleration. The analysis and test results are shown in Figures 5 through 8 where a dotted line and a solid line represent the test result and analysis, respectively. Comparing the analysis results with the test results, the maximum values of each evaluation term show relatively
42、small differences, and both results seem to have similar waveforms especially in terms of damping. As a result, we can verify the reliability of full vehicle model through this process. Figure 5 Roll angle change during lane change maneuver Figure 6 Roll rate change during lane change maneuver Figur
43、e 7 Yaw rate change during lane change maneuver Figure 8 Lateral acceleration change during lane change maneuver PARAMETER STUDY ON VEHICLE HANDLING From the roll sensitivity analysis on the rear suspension, the design parameters such as the vertical locations of points A, E, and F are selected. Sin
44、ce air springs and shock absorbers have possible influences on the vehicle motion, the lateral locations of air springs and shock absorbers need to be considered as the additional design parameters. Each analysis condition for the parameter study is indicated in Table 3. In cases 9 and 10, the sprin
45、g tread and shock absorber tread are so wide that only the narrow spring and shock absorber treads are considered. Table 3 Analysis conditions for parameter study Cases Hard points Variations (mm) Case 1 Az +50 Case 2 Az -50 Case 3 Ez +50 Case 4 Ez -50 Case 5 Fz +50 Case 6 Fz -50 Case 7 Ez, Fz +50 C
46、ase 8 Ez, Fz -50 Case 9 SPRGy -50 Case 10 SABSy -50 To investigate the dynamic behaviors of a full vehicle with the change of rear suspension geometry, the j-turn analyses are implemented on the 10 cases in Table 3 2. As shown in Figure 9, the step steer input of 54 degrees is applied into the steer
47、ing wheel for 0.2 second from 3 second at the speed of 80km/hr for this j-turn simulation. Figure 9 Steering wheel angle for j-turn simulation The four terms for evaluating handling performances in j-turn simulation are steering sensitivity, understeer gradient, roll gain, and lateral acceleration r
48、esponse time. Steering sensitivity means the change of lateral acceleration on the change of steer angle at the lateral acceleration of 0.15g, and it is generally expressed in Equation (1). sw y d da 100SS = = = = (1) Understeer gradient indicates the turning response at the lateral acceleration of
49、0.15g, and it is defined as Equation (2). 2 y sw V Lg da d G 1 K = = = = (2) where G is a steering gear ratio, sw is a steer angle, y a is a lateral acceleration, L is wheelbase, and V is a vehicle speed. The positive understeer gradient means that a vehicle has the understeer tendency, and the negative understeer gradient indicates that a vehicle has the oversteer characteristics. Roll gain is the magnitude of roll angle generated by the lateral acceleration of 0.15g when cornering. As the roll gain becomes smaller, passengers feel a
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