SAE-TPS-522009-01-2107.pdf
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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 Prediction 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 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 50 100 150 200 250 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, 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. This 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 forces 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 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: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 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, this 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 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 with 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 of 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, resulting 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 motion in term of the modal coordinates is single degree of freedom system in damping. Transient response has free vibration and forced vibration. Transient responses are calculated using the solution of free vibration and that of forced vibration. To proceed, transient responses in term of physical coordinates are obtained using the equation (2) ROAD FORCES The tire runs over the cleat on flat road surface. As a first step, linear spring elements are adjusted to express contact pressure distribution for the tire rolling on flat road surface. Road forces to input the FE tire model are the result of subtracting road forces when the cleat is a height of 2 mm from when the cleat is a height of 0 mm. Figure 10 shows road forces (longitudinal (x), lateral (y), and vertical) under the condition of the tire inflated to 230 kPa, loading to 4000 N at the spindle, rolling velocity 50km/h. Figure 11 shows contact area of the FE tire model. To express rolling condition, node points to input the static tire model are shifted leading edge from trailing edge. Therefore, it is necessity of a decision of input to each node. A decision method of input to each node for simulation was shown in Figure 12.The times of road forces in figure 12 were divided into the number of nodes to input. Then, the equally time is duration of activity, t. The amplitudes of input to each node i F are obtained by dividing each sectional value of integral by t. i Fis assumed to be pulse input, and worked the FE tire model by t. Fig.10 Measured road forces at shoulder tread block Author:Gilligan-SID:1178-GUID:20758466-141.213.232.87 Fig.11 Contact plane view Fig.12 decision method of input to each node ANALYTICAL RESULT OF RESPONSIVE SPINDLE FORCES Time history forces were predicted using by NX-Nastran. Additionally, Road forces of shoulder rib were measured when the tire was rolling over the cleat. And, during testing of the tire rolling over the cylinder on the shoulder rib, vertical spindle forces were measured. Comparison of vertical spindle forces between experiment and analysis is shown in Figure 13. The analytical results of vertical spindle forces were in reasonable agreement with the experimental results of these. From above, the spindle forces when the tire was rolling can be predicted by using the FE tire model and the distribution of the dynamic road forces which measured experimentally. Fig.13 Comparison of vertical spindle force between experiment and analysis CONCLUSION The dynamic road forces of the rolling tire at the contact patch were measured directly using a tri-axial force sensor. Using linear spring elements to express road contact and the equivalent of the stiffness on the rolling tire, the FE tire model on the static analysis expressed vibration characteristic on the tire rolling. Using the FE tire model and the distribution of the dynamic road forces which measured experimentally, the spindle force during the operation can be predicted. REFERENCE 1. Y. Kamada, U. Umakoshi?” Trend of the Study on Road Noise (A New Integrated Technique in Road Noise Analysis)”, Journal of Society of Automotive Engineers of Japan, Vol.49, No.1, pp88-92(1995) 2. M.Constant, J.Leyssens, F.Penne, R.Freymann, “Tire and Car Contribution and Interaction to Low Frequency Interior Noise”, Noise and Vibration Conference Proceedings, SAE Paper No.2001-01- 1528, (2001) 3. H. Nakagawa, T. Koizumi, N. Tsujiuchi, K. Moriguchi, “Analysis of Road Force on Rolling Tire Using Triaxial Force Sensor”, 2007 JSAE Annual Congress (Fall), No.123-07, pp25-28(2007) 4. H. Yamada, ” Simulation of Tire Spindle Forces Caused by Road Roughness”?inter- noise2003?866-871(2003) 5. A. Nishi, N. Tanaka, N. Tsujiuchi, T. Koizumi, H. Oshima, K. Minato, M. Yoshida, Y Tsuchiya, “Development of Measuring System to Measure Standing Pose of the Foot Using Distributed Triaxial Force Sensor”, Proc. of the 28th IEEE EMBC Annual International Conference (2006) 6. T. Nakagawa, N. Sugiura, Y. Tsurumi, N. Mori, M. Asai, I. Kido, “An Analyzing Method of the Exciting Force on Tire for Road Noise”, 1998 JSAE Annual Congress, No.78-98, pp13-16(1998) 7. H. Yamada, O. ishiyama, J. Namaizawa, H. Ogawa, “Development of road noise prediction method”, 2000 JSAE Annual Congress, No.65-00, pp1-4(2000) 8. M.Chargin, D.Bella, Tire Models for Use in Dynamic Analyses, Noise and Vibration Conference Proceedings, SAE Paper No.2005-01-2382, (2005) Contact area Author:Gilligan-SID:1178-GUID:20758466-141.213.232.87 9. T. Sagushi, T. Tomida, S. Urata, K. Kato, “Tire Radiation-Noise Using FEM”, Proc. of Inter-noise, 2006 10. T. Sagushi, “Influence of the Rolling Condition Given to the Natural Frequency of a Tire”, 1998 JSME Annual Congress, pp1-4(1998) CONTACT If you would like to get some further information, please contact: Professor Nobutaka Tsujiuchi Department of Mechanical Engineering Doshisha University Email: ntsujiucmail.doshisha.ac.jp Professor Takayuki Koizumi Department of Mechanical Engineering Doshisha University Email: tkoizumimail.doshisha.ac.jp Term: mass matrix stiffness matrix physical coordinates force vector coordinate transformation matrix modal coordinates i th modal mass i th modal damping i th modal stiffness i th modal force i m i c F x M K i k i Author:Gilligan-SID:1178-GUID:20758466-141.213.232.87
