Side force coefficient

Speed and Temperature Dependence of the Side Force Coefficient.712... 

In order to establish master curves of friction or side force coefficients, the speed range has to be low in order to avoid significant temperature rises in the contact area and, if the experiments are carried out on wet tracks, also lubrication effects. 

FIGURE 26.23 Side force coefficient (dimensionless quantity S/fiL) as function of the quantity c (Equation 26.17c) showing the two components due to adhesion and shding. 

FIGURE 26.27 Side force coefficient as function of c (Equation 26.17c) for a bias tire for different loads. The solid line is the function of 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, data from Nordeen, D.L. and Cortese, A.D., Trans S.A.E., 72, 325, 1964.)... 

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 26.30 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. 

FIGURE 26.35 Master curve of the side force coefficient of two tread compounds with different glass transition temperatures on wet Alumina 180 A 3,4 IR Tg = —21°C and OESBR Tg = —46°C. Two spot measurements at two different water temperatures show that the ranking if the two compounds reverses. (From Grosch, K.A., Kautschuk, Gummi, Kunststojfe, 6 m, 432, 1996.)... 

FIGURE 26.36 The side force coefficient of an OESBR black-fiUed tire tread compound on wet blunt Alumina 180 as function of log a v obtained at three speeds and five temperatures (black open squares) with a quadratic equation fitted to the data (black solid line). The red marked points were obtained at one speed for five temperatures with the dotted red line the best fitting quadratic equation, indicating the risk of extrapolation with a limited set of data. 

However, a correlation with road test ratings can often be improved if an independent term of log V is added to the transformation variable log a-jv. The friction or side force coefficient can then be written as... 

FIGURE 26.41 Side force coefficient of compound C of Table 26.4 and the rating in relation to compound A as function of temperature and log v. 

Figure 26.41 shows the side force coefficient (upper part) of compound 3 of Table 26.2 and its rating (lower) as function of temperature and log speed. The side force coefficient depends on temperature and log speed. The rating of compound 3 relative to 1 depends on temperature so strongly that a reversal in ranking occurs, the dependence on speed, however, is small. 

The latter can be estimated from the side force coefficients obtained during the abrasion experiments for a small shp angle and a high speed. They reflect directly the compound stiffness and since the dimensions are the same also the shear modulus. 

Figure 16.7 Illustration of skid resistance coefficients, (a) Braking force coefficient (BFC). (b) Side force coefficient (SFC).

The model can also be used when both slip components act simultaneously. The limiting force is still determined by the friction coefficient and pressure. The total traction at a point x in the contact area is the vector sum of the two components. This determines the point of onsetting sliding and hence the circumferential contribution is the total less the side force contribution. This is shown diagrammatically in Figure 26.25 [33]. 

Coefficients of a Quadratic Equation Representing Part of the Side Force—Log a- v Master Curve... 

Figure 26.42 compares the correlation coefficient between a road test on wet concrete and the laboratory side force measurements of the six compounds of Table 26.2 on blunt, wet Alumina 180 (a) with a log oxv-log v evaluation and (b) with a temperature-log v evaluation. It appears that the... 

FIGURE 26.42 Comparison of the correlation coefficients between laboratory side force measurements with the six compounds of Table 26.2 on wet, blunt Alumina 180 and a concrete road test track as function of log ajv and log v (left) with function of temperature and log v (right). 

In the second case, the side horizontal friction force, Fp and the vertical reaction force developed are measured (Figure 16.7b). The ratio of the two forces (Fy/F ) determines the sideway force coefficient (SFC). 

The steam-side condensing coefficient outside the tubes can be estimated using Eqs. (4.8-20H4 8-26). The resistance due to scale formation usually cannot be predicted. Increasing the velocity of the liquid in the tubes greatly decreases the rate of scale formation. This is one important advantage of forced-circulation evaporators. The scale can be salts, such as calcium sulfate and sodium sulfate, which decrease in solubility with an increase in temperature and hence tend to deposit on the hot tubes. 

Note that the exact adiabatic functions are used on the right-hand side, which in practical calculations must be evaluated by the full derivative on the left of Eq. (24) rather than the Hellmann-Feynman forces. This forai has the advantage that the R dependence of the coefficients, c, does not have to be considered. Using the relationship Eq. (78) for the off-diagonal matrix elements of the right-hand side then leads directly to... 

The pressure difference between the high and low pressure sides of the membrane is denoted as AP the osmotic pressure difference across the membrane is defined as Att the net driving force for water transport across the membrane is AP — (tAtt, where O is the Staverman reflection coefficient and a = 1 means 100% solute rejection. The standardized terminology recommended for use to describe pressure-driven membrane processes, including that for reverse osmosis, has been reviewed (24). 

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