Tire Tests and Tire Testing Machine

Many methods exist to measure and determine the parameters that characterize a vehicle. Some of these methods are much better suited for measuring scaled vehicle properties. For this project, a high resolution SolidWorks model was developed. The SolidWorks model permits estimation of the vehicle’s mass and geometric properties.

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Additional tests were performed in order to determine the tire’s properties. A summary of the values used to simulate the scaled vehicle are shown below in Table 3.

Table 3. Parameters of Traxxas RC truck

Parameter Symbol Value

Sideslip Coefficient of Front Tire Sideslip Coefficient of Rear Tire Vehicle mass

Moment of Inertia

Distance from C.G. to Front Tire Distance from C.G. to Rear Tire Pacejka tire model peak factor Pacejka tire model shape factor Pacejka tire model stiffness factor Pacejka tire model curvature factor

C_αf C_αr m I_z a b D C B E 63.2 N/rad 63.2 N/rad 3.117 kg 0.0452 kg*m² 0.212 m 0.126 m 70 N 0.09 82 0.65

As discussed in chapter 2, the tires play a central role in determining the dynamic behavior of a vehicle and its motions. Tests were conducted to determine the tire

parameters for the Magic Formula. In order to use an empirical tire model to estimate the forces developed by the tires, data must be obtained and reduced to find the value of each parameter in the model. The parameters that appear in the formula represent the physical characteristics of the tire. A skid-pad test was performed as a simple means of relating the sideslip angle to the amount of force generated by the tires. This test was conducted by driving at a constant speed in a circular motion with a constant steer angle while monitoring the speed and radius of the circle circumscribed by the vehicle. The wheel speeds were monitored with wheel encoders and the radius was measured in the field with a tape measure while the vehicle performed the test. The side slip angle was estimated by subtracting the measured steer angle by the ideal no-slip Ackermann steer angle for the observed radius at the measured speed. The lateral force was estimated with the measured steady-state velocity, radius, and the vehicle’s mass. To estimate the lateral

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force provided by each tire during the skid-pad test, the total lateral force was averaged over the four tires by imposing a neutral steer assumption, which means the slip angle was assumed to be equal for the front and rear tires. Further tests were performed by creating a tire dynamometer. A tire dynamometer was assembled by retrofitting a small wood lathe for the purpose of testing small tires in order to characterize the tire’s ability to grip and generate lateral cornering forces. This also provided an estimation of the tire’s cornering stiffness and helped to validate the skid-pad test results. Various springs were used to measure the force generated by the tire that was affixed to a carriage. First, the springs used to measure the force were characterized to find their respective stiffness’s. Different springs offered different resolutions and capacities when measuring the lateral force generated by the tire. The tire was set and locked at different angles. The lathe was then started and the carriage holding the tire was allowed to travel down the ways until steady-state was observed, which occurred when the tire’s lateral force and the spring force came into equilibrium. Once steady-state was achieved, the spring’s deflection was recorded and the corresponding force was calculated. This test was performed at a variety of slip angles with varying vertical loads in order to generate the characteristic tire

curves. These tests facilitated estimation of the tire’s cornering stiffness. The tire dynamometer and skid-pad tests are shown in Figure 56.

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Figure 56. Skid-pad (upper right) and tire dynamometer tests (upper left, lower left, lower right)

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Figure 57. Tire dynamometer and skid-pad test results performed with varying vertical loads (Fz)

The plot in Figure 57 shows the force generated per tire at a given sideslip angle. The Pacejka Magic Formula tire model curve was fit to each data set. The effect of different vertical loads was observed by altering the load and observing the change in the shape of the curve. The greater the vertical load the greater the adhesion between the tire and the road surface. Increasing the vertical load increased the peak lateral force and retarded its occurrence with respect to the slip angle. The effect of different coefficients of friction was also observed by comparing the smooth, polished concrete skid-pad test results to the tire dynamometer test results performed on a roughened PVC surface. A higher coefficient of friction also increased the peak lateral force and retarded its occurrence with respect to the slip angle. A tire’s cornering stiffness is determined by evaluating the slope of the characteristic curve at the origin, as expressed in Equation 35.

F = 0.25*𝜶 0 0.5 1 1.5 2 2.5 3 3.5 4 0 5 10 15 20 25 30 Late ral Fo rc e ( lb f)

Side Slip Angle (deg)

Tyre Tester on PVC ( Fz ~ 6.3 lb @ 8mph ) Skid Pad Test on Concrete (Fz ~ 2.5 lb @ 6mph)

127 𝑪_𝜶= (𝝏𝑭𝒚

𝝏𝜶)_𝜶=𝟎 ( 35 )

The tire’s cornering stiffness was estimated by evaluating the slope in the linear region of each curve nearest to the origin. In accordance with Equation 35, the slope of the linear region for each curve was estimated using the origin and the first data point. This yielded similar estimates of the cornering stiffness for each trial. The tire’s cornering stiffness was estimated to be 0.25±0.05 lbf/deg. These tests only provided a rough

estimate of the non-pneumatic tire’s cornering stiffness, largely due to the small sample size and the propagated measurement errors. However, performing these tests was more favorable than basing a value on scaled pneumatic tire research alone, creating a more intricate tire dynamometer, or performing a very complex finite element analysis of the tire. For comparison, typical tire dynamometer tests measure around 15 parameters to fully characterize the lateral tire dynamics and to evaluate the lateral Pacejka tire model parameters. In the next section, the dynamometer that may be used with the simulation is described.