Gyuláné Vincze, Gergely György Balázs
Budapest University of Technology and Economics Department of Electric Power Engineering
Force that can be transferred on the surface of the wheels depends on force pressing the wheel to the road and the gripping coefficient, according to equation (1.2). There is a nonlinear relation between the motive force required for traction and force transferable with wheels, as can be seen in Figure 1.8.a.
As the figure shows, transferable force follows the required value, indicated with dashed line, but curves separate sooner or later, depending on weather conditions. Until transferred force can follow the required force, the vehicle is in normal rolling mode (with small slip). In this case the difference of the two forces is the rolling resistance, which depends on wheel deformation, wheel and road conditions and speed of the vehicle. Increasing the required force (engine torque, brake force), rolling friction becomes slipping friction, and transferable force becomes smaller than required, and it has limit value. Momentary limit Ftmax, indicated in Figure 1.8.a, highly depends on weather and other conditions. The biggest from these limits is the gripping limit F μ indicated in equation (1.3).
Gripping limit depends on vehicle speed, decreases when velocity increases, as can be seen in Figure 1.8.b. It has two reasons. One is that lifting force, ignored in equation (1.3), increases with higher speed, so force pressing the wheels on the road decreases. Another is that the effect of road rugosity becomes more and more higher when speed increases, wheels often move off the road. As gripping ability decrease with speed, and rolling resistance increases, a speed limit (300-350 km/h) has to be used for traditional trains.
In traction mode, force higher than transferable (shaft torque/radius) spins the wheels, and blocks the wheel in brake mode. Both effects are harmful, so control of traction and brake force has to be used. To characterize spinning and blocking, relative slip of a wheel is defined as follows:
where v circ is circumferential speed of the wheel (Figure 1.9.b). To calculate slip precisely, we should know the speed of the vehicle even if spinning has already started. In practice, angular velocity ω w is measured and circumferential speed can be calculated as v circ =r w ω w. Speed of the vehicle can be calculated with average angular speed (ω av ):
where r w is radius of wheel, k m is number of measured wheels. Calculation is less accurate if more than one wheel slides and another uncertainty is the radiussince wheel can deform during wear and load. v circ >v road (see Figure 1.9.b) and s>0 during sliding, and v circ <v road and s<0 during blocking, where v road =-v vehicle. Figure 1.9.a shows the relation between the absolute value of relative slip and gripping coefficient. This relation is similar to all vehicles running on wheels, but μ and s values can change significantly, for example for vehicles running on rail or road. A short slip range can be determined for a vehicle type where there is a linear relation between gripping coefficient and slip. This range is the range of normal rolling. If gripping worsens, relative slip goes outside of this range (as an indicator) in case of spinning or blocking.
Anti-spin of wheels operate in tractive mode and the torque of traction motor(s) is controlled (limited). Anti-spin system limits the torque so that relative slip is inside the narrow range shown in Figure 1.9.a, i.e. wheels can roll and transfer force to the road. The role of anti-spin is to prevent spin of wheels and, in case of rails, to protect rails and wheels. Wear of rails in case of spinning or blocking is a problem in high-speed trains at stations and places where stop and start happen often. To increase grip, sand technique is often used for vehicles running on rail.
Anti-blockin g of vehicles running on wheels operates in brake mode and (total) brake force is limited in case of using several brake systems. There are two goals of anti-blocking. In case of rails anti-blocking is designed to prevent slipping to protect rail and wheels and to ensure rolling of wheels. In case of tyres, anti-blocking system limits brake force so that transferrable brake force on wheels should be maximal. This goal can be reached with about 5% relative slip where gripping is maximal. Such a brake force control is called ABS.
(References used in this section are: …)