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Study of braking in-a-turn stability
249
Technical Notes/JSAE Review 21 (2000) 241}263
Technical Notes
Study of braking in-a-turn stability Tamio Kano , Katsutoshi Horinouchi, Takashi Yonekawa Vehicle Evaluation & Engineering Div. I, Toyota Motor Co., Ltd., Misyuku 1200, Susono-shi, Shizuoka 410-1193, Japan Vehicle Engineering Div. Toyota Motor Co., Ltd., Misyuku 1200, Susono-shi, Shizuoka 410-1193, Japan Received 10 September 1999; received in revised form 18 October 1999
1. Introduction Generally, braking in-a-turn is likely to cause a phenomenon of pulling the vehicle to the inside of a turn under gradual braking conditions. This paper discusses braking in-a-turn stability with tests using the Vehicle Dynamics Simulator and simulation using test results, and quantitatively determines the degree of contribution of each factor } suspension, tires, brakes, etc. } in response to these phenomena.
2. Analysis of yaw moment 2.1. Analysis methods The aim of analysis is to use test results to calculate contribution to the yaw moment, and to "nd the degree of contribution of each factor (Fig. 1). 2.2. Testing In the test, data was collected from actual vehicle testing on a test course, and thereafter from driving reconstruction tests conducted using the vehicle dynamics simulator (Fig. 1). In driving reconstruction testing, a six-component axle meter and a precision steering angle meter were used as sensing devices. At spindle position the longitudinal, lateral and vertical force and self-aligning torque for four wheels were reconstructed, and therefore the same load that would occur under actual driving was dynamically applied to the suspension of the vehicle. In actual vehicle testing, vehicle states (such as yaw velocity and longitudinal acceleration) were measured, and in driving reconstruction testing suspension movement (such as changes in alignment and suspension stroke) were measured. By processing this data together, it was possible to analyze a total of 100 channels of time
series data, making it possible to acquire a large amount of information about the dynamics pertaining to the moment under the problem of pulling the vehicle to the inside of a turn. 2.3. Calculating degree of contribution The degree of each factors contribution was calculated using test data (Fig. 1). The magic formula tire model was used for tire modeling. Modeling was conducted using the method for identi"cation by means of optimal calculations using measurements from the #at belt tire test device. Four factors below were evaluated as yaw moment generation factors: B degree of contribution of change in tire side slip angle caused by steering angle changes C degree of contribution of changes in tire camber D degree of contribution of changes in vertical load E Degree of contribution of changes in longitudinal tire force Concerning the factors B}E it is assumed that each factor varies independently, and that the degree of contribution is obtained by calculating each of the yaw moments. 2.4. Analysis results Fig. 2 shows analysis results of the vehicle [Fig. 2 uses a (Greek `Aa)] used in this experiment. Looking at the analysis results, it is clear that the degree of contribution of factor D (changes in vertical load) is extremely large. In particular, the degree of contribution of the reduction of lateral force caused by a reduction of vertical load on the rear inner wheel is largest, and accounts for about 50% of overall contributions to the yaw moment. However, the degree of contribution of factor B (steering angle changes) and factor C (changes in camber angle) is small.
0389-4304/00/$ 20.00 2000 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved. PII: S 0 3 8 9 - 4 3 0 4 ( 9 9 ) 0 0 0 8 8 - 0
JSAE20004053
250
Technical Notes / JSAE Review 21 (2000) 241}263
Fig. 1. Analysis methods.
Fig. 3. Contribution to anti-OS moment of each parameter. Fig. 2. Yaw moment analysis of vehicle a.
3. Improvement investigations based on reductions in yaw moment 3.1. Estimating ewect of measures for improving load shift characteristics In order to estimate the degree of contribution of each speci"cation determining four wheel load changes, simulation by simple model was conducted. Under driving conditions from steady lateral acceleration of 7 m/s in a turn to deceleration of 3.1 m/s, the yaw moment before
and after conducting each measure was evaluated, and the anti-OS e!ect was shown by the di!erence (Fig. 3). We evaluated two types of tires, the original tire and beta tire, with modi"ed vertical load and lateral force characteristics. The beta tire has low increase in lateral force at high load ranges, so changes in the lateral force on the outer wheels during turn braking are small, and were expected to become advantageous. Also, for this study, the outer wheel pitch rigidity distribution was de"ned as outer wheel pitch rigidity divided by total pitch rigidity. Considering the relationship between vertical load and lateral force, lateral force change rate in response to changes in vertical load is large on the inner wheels. Accordingly, when the outer
Technical Notes / JSAE Review 21 (2000) 241}263
wheel pitch rigidity distribution is increased, the yaw moment is reduced. 3.2. Simulation results Fig. 3 shows the estimated anti-OS e!ect of each measure. From among the range of possible measures under the current conditions, the factor which was expected to have the largest e!ect was `(10) Improvements of tire vertical load-lateral force characteristics.a The contributions of `(9) Distribution of pitch rigiditya the suspension was signi"cant. However, `(8) Distribution of roll rigiditya had almost no e!ect. 3.3. Actual vehicle investigation An actual vehicle investigation was conducted based on the results from Section 3.2. Measures taken on the vehicle included the following: (9) Increase in the distribution of the outer wheel pitch rigidity. (10) Improvements of tire vertical load}lateral force characteristics.
251
(11) Increase in the distribution of brake force to the front. In agreement with the estimations, it was con"rmed that these improvements lowered overall yaw moment by about 30%.
4. Conclusion An analysis method in which quantitative degree of contribution of each factor is calculated from test results was developed for braking in-a-turn stability. Analysis and improvement examples using this analysis method were also discussed. For the vehicle actually used, the phenomena by which the vehicle is pulled to the inside of turns was primarily generated by imbalanced yaw moment caused by load shift. E!ective measures to reduce the yaw moment included: (a) improvements in tire vertical load}lateral load characteristics, (b) increase in outer wheel pitch rigidity distribution, and (c) increase in front brake force distribution.
Technical Notes/JSAE Review 21 (2000) 241}263
Technical Notes
Study of braking in-a-turn stability Tamio Kano , Katsutoshi Horinouchi, Takashi Yonekawa Vehicle Evaluation & Engineering Div. I, Toyota Motor Co., Ltd., Misyuku 1200, Susono-shi, Shizuoka 410-1193, Japan Vehicle Engineering Div. Toyota Motor Co., Ltd., Misyuku 1200, Susono-shi, Shizuoka 410-1193, Japan Received 10 September 1999; received in revised form 18 October 1999
1. Introduction Generally, braking in-a-turn is likely to cause a phenomenon of pulling the vehicle to the inside of a turn under gradual braking conditions. This paper discusses braking in-a-turn stability with tests using the Vehicle Dynamics Simulator and simulation using test results, and quantitatively determines the degree of contribution of each factor } suspension, tires, brakes, etc. } in response to these phenomena.
2. Analysis of yaw moment 2.1. Analysis methods The aim of analysis is to use test results to calculate contribution to the yaw moment, and to "nd the degree of contribution of each factor (Fig. 1). 2.2. Testing In the test, data was collected from actual vehicle testing on a test course, and thereafter from driving reconstruction tests conducted using the vehicle dynamics simulator (Fig. 1). In driving reconstruction testing, a six-component axle meter and a precision steering angle meter were used as sensing devices. At spindle position the longitudinal, lateral and vertical force and self-aligning torque for four wheels were reconstructed, and therefore the same load that would occur under actual driving was dynamically applied to the suspension of the vehicle. In actual vehicle testing, vehicle states (such as yaw velocity and longitudinal acceleration) were measured, and in driving reconstruction testing suspension movement (such as changes in alignment and suspension stroke) were measured. By processing this data together, it was possible to analyze a total of 100 channels of time
series data, making it possible to acquire a large amount of information about the dynamics pertaining to the moment under the problem of pulling the vehicle to the inside of a turn. 2.3. Calculating degree of contribution The degree of each factors contribution was calculated using test data (Fig. 1). The magic formula tire model was used for tire modeling. Modeling was conducted using the method for identi"cation by means of optimal calculations using measurements from the #at belt tire test device. Four factors below were evaluated as yaw moment generation factors: B degree of contribution of change in tire side slip angle caused by steering angle changes C degree of contribution of changes in tire camber D degree of contribution of changes in vertical load E Degree of contribution of changes in longitudinal tire force Concerning the factors B}E it is assumed that each factor varies independently, and that the degree of contribution is obtained by calculating each of the yaw moments. 2.4. Analysis results Fig. 2 shows analysis results of the vehicle [Fig. 2 uses a (Greek `Aa)] used in this experiment. Looking at the analysis results, it is clear that the degree of contribution of factor D (changes in vertical load) is extremely large. In particular, the degree of contribution of the reduction of lateral force caused by a reduction of vertical load on the rear inner wheel is largest, and accounts for about 50% of overall contributions to the yaw moment. However, the degree of contribution of factor B (steering angle changes) and factor C (changes in camber angle) is small.
0389-4304/00/$ 20.00 2000 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved. PII: S 0 3 8 9 - 4 3 0 4 ( 9 9 ) 0 0 0 8 8 - 0
JSAE20004053
250
Technical Notes / JSAE Review 21 (2000) 241}263
Fig. 1. Analysis methods.
Fig. 3. Contribution to anti-OS moment of each parameter. Fig. 2. Yaw moment analysis of vehicle a.
3. Improvement investigations based on reductions in yaw moment 3.1. Estimating ewect of measures for improving load shift characteristics In order to estimate the degree of contribution of each speci"cation determining four wheel load changes, simulation by simple model was conducted. Under driving conditions from steady lateral acceleration of 7 m/s in a turn to deceleration of 3.1 m/s, the yaw moment before
and after conducting each measure was evaluated, and the anti-OS e!ect was shown by the di!erence (Fig. 3). We evaluated two types of tires, the original tire and beta tire, with modi"ed vertical load and lateral force characteristics. The beta tire has low increase in lateral force at high load ranges, so changes in the lateral force on the outer wheels during turn braking are small, and were expected to become advantageous. Also, for this study, the outer wheel pitch rigidity distribution was de"ned as outer wheel pitch rigidity divided by total pitch rigidity. Considering the relationship between vertical load and lateral force, lateral force change rate in response to changes in vertical load is large on the inner wheels. Accordingly, when the outer
Technical Notes / JSAE Review 21 (2000) 241}263
wheel pitch rigidity distribution is increased, the yaw moment is reduced. 3.2. Simulation results Fig. 3 shows the estimated anti-OS e!ect of each measure. From among the range of possible measures under the current conditions, the factor which was expected to have the largest e!ect was `(10) Improvements of tire vertical load-lateral force characteristics.a The contributions of `(9) Distribution of pitch rigiditya the suspension was signi"cant. However, `(8) Distribution of roll rigiditya had almost no e!ect. 3.3. Actual vehicle investigation An actual vehicle investigation was conducted based on the results from Section 3.2. Measures taken on the vehicle included the following: (9) Increase in the distribution of the outer wheel pitch rigidity. (10) Improvements of tire vertical load}lateral force characteristics.
251
(11) Increase in the distribution of brake force to the front. In agreement with the estimations, it was con"rmed that these improvements lowered overall yaw moment by about 30%.
4. Conclusion An analysis method in which quantitative degree of contribution of each factor is calculated from test results was developed for braking in-a-turn stability. Analysis and improvement examples using this analysis method were also discussed. For the vehicle actually used, the phenomena by which the vehicle is pulled to the inside of turns was primarily generated by imbalanced yaw moment caused by load shift. E!ective measures to reduce the yaw moment included: (a) improvements in tire vertical load}lateral load characteristics, (b) increase in outer wheel pitch rigidity distribution, and (c) increase in front brake force distribution.