SAE-TPS-522009-01-2107.pdf
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1、 The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAEs peer review process under the supervision of the session organizer. This process requires a minimum of three (3) reviews by industry experts. All rights reserved. No part of this publication m
2、ay be 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. ISSN 0148-7191 Positions and opinions advanced in this paper are those of the author(s) and not nec
3、essarily those of SAE. The author is solely responsible for the content of the paper. SAE Customer Service: Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-0790 Email: CustomerServicesae.org SAE Web Address: http:/www.sae.org Printed in USA 2009-01-2107 Predict
4、ion of Spindle Force Using Measured Road Forces on Rolling Tire Nobutaka Tsujiuchi, Takayuki Koizumi and Masami Matsubara Doshisha University Kinya Moriguchi and Ichiro Shima Toyo Tire inflation 230kPa Contact patch width mm Contact patch length mm ? ? -60-40-200 80 100 120 140 160 180 200 220 Fz N
5、0 50 100 150 200 250 Contact patch width mm Contact patch length mm ? ? -60-40-200 80 100 120 140 160 180 200 220 Fz N 0 50 100 150 200 250 Inflation pressure 200kPa Inflation pressure 230kPa Contact patch width mm Contact patch length mm ? ? -60-40-200 80 100 120 140 160 180 200 220 Fz N 0 50 100 1
6、50 200 250 Inflation pressure 260kPa Fig.6 Comparison of road forces distribution at different inflation pressures; rolling velocity 50km/h Figure 5, 6 shows that the distribution of the dynamic road forces in the vertical direction is not influenced on rolling velocity and inflation pressure. And,
7、the resultant vector indicates the same direction without the influence of different rolling velocities and different inflation pressures. Figure 5, 6 shows that the distribution of the dynamic road forces on the rolling tire in the vertical direction is highest at the shoulder of the tire tread. Th
8、is result reveals the influence of centrifugal forces when the tire is running has a very big effect at the shoulder among the tread blocks. Road forces of leading edge are higher than these of trailing edge without any rolling velocity and inflation pressure. The shear vectors of the two road force
9、s on identical tread block at the shoulder or center are different. When the tire contacts with roads, the tread rubber easily gets the shear direction for the shear deformation. This phenomenon made the shear vectors of the two road forces different. From described above, the method of measurement
10、of road forces can be applied. RESPONSE ANALYSIS OF SPINDLE FORCES The spindle forces were predicted using road forces experimentally and mode transient response analysis. Comparison of spindle forces between prediction and experiment show the proposed method validity. Author:Gilligan-SID:1178-GUID:
11、20758466-141.213.232.87 Additionally, this paper focuses on vertical spindle vibration to be more dominant than the others direction vibration in road noise 5. And, the conditions of test were the tire inflated to 230 kPa at velocity of 50 km/h. FE TIRE MODEL Tire is made of rubber, fibrous material
12、 and others in turn complex material. Therefore, model size being able to express tire design variable is very big. So, we built a simple model which has good vibration characteristic of the test tire. Analysis software I-deas and NX-Nastran was used. The built model was shown in Figure 7. Also, thi
13、s FE tire model was provided by TOYO TIRE mass and stiffness. The mass of the tire is constant on the rolling tire. Therefore the decrease of natural frequencies was by the decrease of the stiffness. In this study, the equivalent of the stiffness on the rolling tire was applied. Using the eigenvalue
14、 analysis under the condition of the tire inflated to 230 kPa, unrolling, the spindle fixed, and no road contact in the tire model, natural frequencies on the static case were identified. Under the same condition, the stiffness of the tire model was reduced which its first natural frequency agree wi
15、th experiment on the rolling tire. Comparison of natural frequencies (1- 5th mode) of the tire model between unrolling and rolling showed the decrease of natural frequencies on rolling by red lines in Figure 9. Additionally, the decreasing value of natural frequencies between unrolling and rolling o
16、f experiment was good agreement with that of analysis. Fig.9 Comparison of mode number between experiment and analysis MODE TRANSIENT RESPONSE ANALYSIS When the spindle forces were predicted, mode transient response analysis was performed. In physical coordinates, temporarily ignore the damping, res
17、ulting in the equation FxKxM=+? ? (1) Transform the variables from physical coordinates x to modal coordinates by =x (2) If the physical coordinates in terms of the modal coordinates and modal damping is used, the following equation is obtained )()()()(tftktctm iiiiiii =+ ? ? (3) This equation of mo
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