Lateral Thinking on Tyre Load Variations
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TECHNOLOGY – SLIP ANGLE Lateral thinking on tyre load variations Slip Angle provides a summary A seven post rig is all well and good but when it comes to of OptimumG’s seminars lateral and longitudinal tyre loads OptimumG engineer Claude Rouelle believes there’s a need for a fresh approach Grip, balance, control and stability simulations are one of the main focuses at OptimumG. yres hate load variations. For by calculating the root mean square a given trajectory you can’t of the vertical load and dividing it Equation 1: Transmissibility Tchange the track bumps, by the average vertical load, as tyre aerodynamic, dynamic loads shown in Equation 1. Being that from lateral and longitudinal, weight the root mean squared (Equation 2) transfers or even banking on oval is the root sum of the square of all circuits. But with good springs, anti- the vertical loads applied divided roll bar and damper settings you can by the number of vertical loads limit the tyre load variation. applied during the test. Equation 2: Root mean square Four, seven or even eight post We look at this number, from rigs are used to qualify and quantify Equation 1, as a percentage load such tyre vertical load variation. variation of the mean load. Most post That could be a problem; you rig engineers will tell you that ‘lower look not only for less tyre vertical number is less tyre force variation variation but also for less lateral and hence better tyre grip’. But is it true? longitudinal tyre load variation. But a The question that we need four or seven post rig won’t give the to ask ourselves is: If using this variation. But a variation that goes The questions can also arise if lateral, longitudinal, self-alignment metric is true, by how much should from 30 per cent to 20 per cent or 40 the curve ∆ Fy Vs ∆ Fz of the front moment value or disturbance. we minimise the load variation? per cent to 30 per cent of the vertical and rear tyre is different, as shown in Do we want the same amount of load has a larger impact on the Figure 2. The same decrease of the A place in the sum load variation reduction front and lateral force consistency. vertical load variation on the front OptimumG performed a test in rear? Is this relationship linear? By Also, what if the front and rear and rear tyre won’t give the same collaboration with SovaMotion to minimising the vertical load variation tyre would have a difference ∆ Fy results of the lateral load variation. understand how the variation of the do we really increase the grip? Vs ∆ Fz? With a rig we focus on the These could create, for example, vertical load affects the variation of Imagine we would have a vertical load variations, but we have for worse or better, a different yaw the lateral force, so we could have graph of lateral load variation vs little info on lateral load variations. moment response to a steer input. a better understanding/correlation vertical load variation. Let’s look The question we must then answer We have a good understanding of the results from a rig. at a simplified and exaggerated is: How does the different vertical about the non-linearities of When a car is tested on a post numerical example (Figure 1). If we load variation affect the variation of suspension springs and dampers rig, the metric used to quantify reduce the vertical load variation the lateral force Fy and longitudinal but not always so good an how much the contact patch load from 20 per cent to 10 per cent Fx and self-alignment Mz and understanding about the stiffness variation and sprung body change is there won’t be a major lateral load camber moment Mx variations? and damping of the tyre itself. Is it true that a lower number means less tyre force variation? Figure 1: This is an example of a hypothesis where decreasing the vertical Figure 2: This example shows a hypothesis where it’s the same as Figure 1, load variation does not change the lateral force variation in the same way but here it also does not change in the same way at the front and at the rear 51 www.racecar-engineering.com NOVEMBER 2018 OptimumG_ MBGHac.indd 51 21/09/2018 15:22 TECHNOLOGY – SLIP ANGLE Figure 4: The test; the tyre is steered to a given slip angle then held there Figure 3: The two stages mass damper quarter car model. But what do we know about a tyre’s vertical stiffness and damping in real track conditions? Figure 3 shows the two stages mass force, as well as to help comprehend damper quarter car model that is how the vertical stiffness/damping used to simulate the response of the of a tyre varies with excitation car to the road input. frequency and amplitude. How non-linear are the tyre Figure 5: This shows the vertical force excitation versus the lateral force stiffnesses and damping? Are these Test limitations tyre stiffness and damping speed, We are aiming to test across the camber, vertical load, slip angle, slip complete matrix in Table 1. The ratio, pressure sensitive and even black area was not tested due to more vertical load amplitude and the limitations of the machine, at frequency sensitive? the time, since the maximum speed Table 1 summarises the test with which the machine can move conducted by OptimumG. In the vertically is 200mm/s. Five tyres test the tyre is steered to a given were tested based on this matrix in slip angle and held. We maintained one day. Serious improvements on constant static vertical average both the hardware and software of load (4000N); pressure 1.90bar; the tyre testing machine have been speed 40km/h, slip ratio 0 per made since that test, to reduce the cent, inclination angle 0deg, slip black area of this table. angle 5deg. During the procedure Figure 5 showcases the vertical the frequency of the vertical load force variation (as the input applied Figure 6: Lateral coefficient of friction versus the different vertical load is changed according to Table 1. by the machine) and the lateral excitation for the five different tyres. All the tyres lose grip with frequency Figure 4 is a picture of this test. force (as the output measured by The test was performed at a low the machine). Notice the time delay divided by the vertical force) of the The first observation is that all speed of 40km/h because at a between the vertical force being five different tyres tested at different tyres lose grip with frequency. The higher speed the tyre temperature applied in the tyre and the tyre frequency ranges. As described in other observation is that with some variation would be too big, changing generating the lateral force. Equation 1, the metric used in rig of them, like tyres A, B and D, there the tyre characteristics. The test Based on the test from Table 1 tests is only focused on getting a is a dip representing a frequency was aimed at understanding the and Figure 5, Figure 6 is possible. In lower number, which would mean where you do not want to go. And coupling between vertical load Figure 6 we are looking at the lateral a lower vertical load variation and that is often the frequency region of excitation and the generated lateral coefficient of friction (lateral force hence better lateral grip. a racecar’s suspended mass. Table 1: The frequencies of the loads that are applied to the tyre 52 www.racecar-engineering.com NOVEMBER 2018 OptimumG_ MBGHac.indd 52 21/09/2018 15:23 TECHNOLOGY – SLIP ANGLE It’s important to consider tyre stiffness when calculating your dynamic ride height In Figure 7 and Figure 8 for the same conditions applied (average Figure 7: Vertical tyre stiffness vs excitation frequency for tyre A. This has a similar vertical stiffness to D, below vertical load of 4000N; slip angle of 5deg; inclination angle of 0deg; velocity of 40km/h and a slip ratio of zero per cent) we plotted the tyre vertical stiffness for the range of different vertical load excitation, also coloured with the rolling radius for tyres A and D. Tyres A and D have a similar vertical stiffness but as the frequency increases you can see that the vertical stiffness for tyre A increases while tyre D decreases. The tyre stiffness is an important parameter to consider for the calculation of your dynamic ride height, and as the frequency changes the tyre stiffness is varying, Figure 8: Vertical stiffness vs excitation frequency for tyre D. The stiffness decreases as the frequency increases with this in mind a correction of the static ride height and/or the suspension spring stiffness would be needed. We can also see that at 0Hz (the tyre is not moving) for different pressures the tyre stiffness changes and the higher the pressure the stiffer it is, but as you start exciting the tyre the vertical stiffness is changing, in the case of tyre D at 20Hz (a bumpy track) the tyre stiffness decreases to half. Figure 9 shows the vertical load versus displacement for one of the tyres for two different frequencies but the same amplitude. In blue is a frequency of 2Hz and in red of 6Hz. We can clearly see that as the Figure 9: Frequency of 2Hz is shown in blue and 6Hz is shown in red. Note the changes in the damping of the tyre frequency changes the damping of the tyre changes a lot, and at higher From this test it has been track.