Slip angle

At small shp angles the force-slip angle relation reduces to... 

This means that at small slip angles the force is independent of load and friction coefficient and at zero slip angle the slope of the curve is given by... 

FIGURE 26.26 Braking force as function of the slip on a wet surface in the presence of side forces at different set slip angles (calculated with the brush model). 

FIGURE 26.28 Side force coefficient and self-aligning torque of a radial ply tire 175 R 14 on two wet road surfaces of different friction coefficient, at three slip angles and loads as function of the quantity c (Equation 26.17c) aU on log scales. The sohd hnes correspond to the brush model. (From Schallamach, A. and Grosch, K.A., Mechanics of Pneumatic Tires, S.K. Clark (ed.). The US Department of Transportation, National Highway Safety Administration, Washington DV.)... 

Figure 26.33 shows the side force coefficient as function of log speed for different temperatures at a constant load and slip angle for a tire tread compound based on 3,4 cw-poly-isoprene, a polymer... 

FIGURE 26.29 Side force as function of slip angle measured on the LAT 100 laboratory test equipment. Load 75 N, speed 2 km/h. 

FIGURE 26.30 Side force coefficient S/L as function of slip angle for different loads. To fit the brush model curve, the friction coefficient had to be adjusted for load dependence according to /a = /lIo(T/To) (surface Alumina 180, speed 2 km/h). 

FIGURE 26.32 Braking and side force coefficient as function of the longitudinal slip for a set slip angle of 8° on wet asphalt at a constant speed of 30 mph, obtained with the Mobile Traction Laboratory (MIL) of the NHTSA. The curves were fitted using the brush model for composite shp with a variable friction coefficient. 

The basis of comparison is Similar log a v values and track surface stmctures for laboratory and road test conditions. As discussed under Section 26.3.6 side force measurements at constant slip angle and load over a suitable range of speeds and temperatures form a very good basis for comparison with road data. 

Abrasion under limited slip used to be, and to some extent still is, measured either with the standard Akron abrader or the Lamboum abrader. In case of the Akron abrader the sample runs under a slip angle at a constant load against the abrasive surface of an alumina grind stone. Speed and load are fixed the side force is not measured. 

Varying the slip angle over a wide range from 40° to +40°... 

Figure 26.61 shows the abrasion of an OESBR tread compound as function of load for different slip angles on a sharp Alumina 60 surface. Because of the wide range of abrasion rates for different slip angles the abrasion data were plotted on a log scale. It is seen that at the small slip angle the dependence on load is small and becomes more pronounced as the slip angle is increased. This is expected from the bmsh model. At small slip angle the side force is independent of the load and hence it is expected that the abrasion behave in a similar way. 

FIGURE 26.61 Log (abrasion) of an OESBR and a natural rubber (NR) tire tread compound as function of load at different slip angles at a speed of 19.2 km/h. left Abrasion loss of the OESBR compound as function of load. Right the relative wear resistance rating of natural rubber (NR) to the OESBR as function of load for different slip angles. 

FIGURE 26.62 Abrasion of OESBR and an 80 natural rubber (NR)/20 butadiene rubber (BR) blend tire compound as function of slip angle at a load of 76 N and a speed of 19.2 km/h. 

Also shown is the relative rating between the OESBR compound and an NR + black tire tread compound. At the smallest slip angle the rating of the NR is better than the OEBR but decreases with the load. As the slip angle is increased the rating reverses. 

Both load and slip angle can be combined if the abrasion is considered to be a function of the energy dissipation. If the side force is measured and the slip angle is known the data can be evaluated directly as function of energy. This is the case with the LATIOO and is shown in Figure... 

FIGURE 26.63 The abrasion data of figure 61 plotted on logarithmic scales and the relative rating of the natural rubber (NR)/BR blend in relation to the OESBR as function of log slip angle. 

FIGURE 26.66 Log (abrasion) as function of log speed for three different tire tread compounds. Load 76 N, slip angle 14.6°. Surface Alumina 60. (From Grosch, K.A. and Heinz, M., Proc. IRC 2000, Helsinki, 2000, paper 48.)... 

FIGURE 26.72 Log tire wear as function of log slip angle obtained with the MRPRA trailer for three tire tread compounds. 

FIGURE 26.74 Abrasion of a natural rubber (NR) and a styrene-butadiene rubber (SBR) tread compound as function of tbe tire surface temperature brought about by ambient temperature changes at a constant slip angle measured with the MRPRA test trailer. 

The effect can be seen in Figure 26.75 which shows the results obtained with the two-wheeled trailer discussed above. Tire group A was a re-treaded bias tire group B a commercial steel-belted radial ply tire. When one tire of each group was mounted on the axle of the trailer for equal set slip angles, the direction of the tow bar adjusted itself in such a way that the tires run under the same... 

With an apparatus which allows tests to be readily made over a range of test conditions, such as pressure and slip angle, it may be possible to establish empirical relationships. 

The Laboratory Abrasion Tester 100 (LAT 100)65 uses a wheel test piece on an abrasive disk geometry so is the type (d) of Figure 11.4. The abrasive disk is driven and the speed, contact force and the slip angle of the test piece can all be varied. What makes this apparatus so different from all the others is not only the versatility but the sophistication of the instrumentation and the computer control. This means that it can be used to obtain data as a function of several parameters and combine results to make predictions of wear for the extremely complicated service conditions of tyres. Not surprisingly, it is very expensive and unlikely to be used on a routine basis outside of tyre companies. Nevertheless, is has now been proposed for standardization in ISO TC 45. 

Akron and the improved Lamboume are distinctive for the ability to vary slip angle in a simple manner and the Schiefer for giving uniform multidirectional abrasion. Probably the most versatile commonly used apparatus is the Taber because of the very wide range of abradants readily available and its ability to operate with lubricants. The LAT 100 is in a class of its own as regards sophistication and features. 

Silicone haptics enhancement of slip and slip angle release effects low friction soil, dirt, and water repellency weatherability UV stability... 

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