Tire Transient Lateral Force Generation: Characterization and Contribution to Vehicle Handling Performance
Tire force generation is often described in terms of a steady-state force response, which is considered independent of time and a function of the kinematic roll conditions such as slip angle. In addition to the steady-state response, the tire also exhibits a time-dependent transient force response, which in the lateral direction is a delay in the buildup of the cornering force. This delay is often characterized by the so-called tire relaxation length (RL) (Ly), a tire performance characteristic often thought to have a strong effect on handling performance. The definition and mechanistic interpretation of tire lateral RL is discussed, and different methods for measuring and interpreting lateral RL are compared. The measurement methods include different types of flat belt as well as static stiffness measurements. Because of different levels of measurement uncertainty, the repeatability and benefits of the different measurement methods are demonstrated. To determine the effect of including tire transient response in tire/vehicle system models, a handling study was performed. The study included a series of CarSim handling simulations with tires of different transient force and moment characteristics as well as an analysis of outdoor subjective handling ratings. The results show the relatively small contribution of tire transient characteristics to vehicle handling performance compared with the tire steady-state force response.ABSTRACT
Sequence of pictures taken of a tire running on a flat belt testing machine at 7 km/h. The tire rolling direction is toward the camera. After the slip angle is changed (at T = 0.000 s), the conditions, such as slip angle, inclination angle, and vertical load, are held constant. An arrow pointing to the same sidewall location in each frame shows the deflection of the sidewall as the cornering force increases to a steady-state value. The rolling distance required by the tire to reach a steady-state cornering force value is the same distance required for the sidewall deflection to occur.
Procedure for the step steer test. (a) The tire is first rolled forward under the test load and at zero steer angle. (b) The motion is stopped, and the steer angle is changed. (c) The tire is rolled forward, causing the cornering force and aligning torque to approach steady-state values over a rolling distance that is a function of the tire and conditions.
The lateral position of the belt of a flat belt testing machine was recorded during a step steer test. The belt always shifts to the left (positive direction) when the belt begins to move, regardless of the slip angle direction. The belt shifting changes the effective slip angle seen by the tire, reducing the accuracy of the measurement.
Lateral RLs are calculated from the step steer test data by measuring how quickly cornering force increases. Lateral RLs are significantly shorter in the tests with negative slip angles (as compared with the identical test with positive slip angles). Lateral RLs are expected to be about the same for positive and negative slip angles, and the bias is likely due to the change in effective slip angle caused by undesired lateral belt movement. Lateral RL has previously been shown to be dependent on vertical load. However, no load sensitivity is seen in the data because the measurement uncertainty is so large.
Shown above are lateral force (Fy) measurements from a step steer test (step steer occurs at distance 0). An exponential curve fit has also been applied. The primary difference between the measured data and the curve fit is a once-per-revolution oscillation in the measurement. The oscillation is caused by lateral nonuniformities in the tire. Lateral RLs are typically a fraction of the circumference of the tire, allowing the lateral nonuniformity to significantly increase measurement uncertainty.
Step steer tests were performed multiple times on each tire (step steer occurs at distance 0). Ideally, the measurement uncertainty would be low, and the results from each test would be similar. The oscillation in Fy caused by lateral nonuniformity can cause Fy to appear to rise slightly faster or slower, contributing to measurement uncertainty and decreasing the repeatability of the result. In this example, the second test resulted in a lateral RL that was 22% lower than the results on the first test on the same tire.
One method that can be used to minimize the effect of lateral nonuniformity is to perform the step steer test multiple times. Four tests can be conducted such that the tire rotation is 90° out of phase from the previous test. All of the tests can be averaged together to minimize measurement uncertainty and maximize the repeatability of the result.
In the RL test, the steering angle of the unloaded tire is changed to a nonzero value. The tire is then loaded and rolled forward.
Measurements of aligning torque (Mz) in the RL test look very similar to the measurements of Fy in the step steer test. Once the tire begins to roll, the F&M increase asymptotically toward a steady-state value. The data are fit to an exponential function.
In the PT test, a nonzero steering angle is applied to the unloaded tire. The tire is then loaded against the ground, followed by a steering angle change back to zero. The tire is then rolled forward.
In the PT test, the measurement of Mz starts at a relatively large magnitude. As the torsional deflection of the tire carcass (caused by the steering angle change to the nonrolling tire) is unwound, Mz quickly drops. The data are fit to an exponential function.
Measurements of Mz during the step steer test can be reproduced by adding the results of the RL test and the PT test. The curve fits that were created in the RL and PT tests are shown in the dashed and dotted lines, respectively. The sum of those two curve fits closely approximates the measured data during the step steer test.
In the lateral stiffness test, the force required to produce a lateral displacement at the spindle is measured on a nonrolling tire. The deflection for small displacements is linearly curve fit (dashed line), and the lateral stiffness is the slope of the curve fit.
Lateral RLs measured using all three methods and all four tire constructions are shown. Note that values for the step steer method are an average of tests performed at ±0.5° and ±1.0° steering angles. Tires A and B were tested twice at each steering angle (eight total step steer tests). Tires C and D were tested once at each steering angle (four total step steer tests).
Linear regression of the lateral RLs from the sinusoidal steer and stiffness ratio methods show high correlation between them.
The LatAccGain/1.0 objective handling metric has been measured from simulations. Changes to the lateral RL parameter in the tire model result in changes to handling performance (as evidenced by the objective handling metric shown on the vertical axis). The range for the objective metric seen in the Chen investigation [22] is also plotted for comparison. In this particular example, changes to lateral RL produce changes in the objective handling metric that are much smaller than the range seen in [22].
The LatAccGain/1.0 objective handling metric has been measured from simulations. Changes to the cornering stiffness in the tire model result in changes to handling performance (as evidenced by the objective handling metric shown on the vertical axis). The range for the objective metric seen in the Chen investigation [22] is also plotted for comparison. In this particular example, changes to cornering stiffness produce changes in the objective handling metric that are of similar magnitude to those seen in [22].
A linear regression study has been performed between subjective on-center response ratings and measurements of lateral RL. Lateral RL was measured at the vehicle's front tire nominal load. No correlation was seen between these two quantities.
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