ABSTRACT
The objective conditions of vehicle travel require that its wheels move at different velocities. This is caused by the fact that the paths traveled by each of the wheels are not the same. The paths of travel of the different wheels both in the horizontal and vertical directions have different curvatures. Moreover, a slight inequality in the radii of the wheels stemming from allowances in tire manufacture and differences in the degree of wear of the individual tire treads, and differences in tire inflation pressure, loads on the wheels, and other factors cause the difference in velocities. Inequality in the velocities of driven wheels is accommodated by seating them individu-
ally on the axle of rotation, whereas that of driving wheels, by the use of open differentials (further referred to as differentials). The differential as a power-dividing unit in general form is a mechanism with a single input link and two output links (Figure 2.1). These links rotate about the principal axis of the differential. A torque, T0, is supplied to
the input link that rotates at velocity v0; the input power is hence Pin¼T0v0. The output links rotate at angular velocities v0 and v00 and are subjected to torques T0 and T00; accordingly, the output powers at the differential’s output shafts are T0v0 and T00v00. Depending on the type of gears that are used, differentials are known as bevel-gear
(Figure 2.2a and c) and spur-gear differentials (Figure 2.2b and d). If the output torques are the same, T0 ¼T00, then the differentials are known as symmetrical
(Figure 2.2a and b), whereas when T0 6¼ T00, the differentials are known as asymmetrical (Figure 2.2c and d). Unlike the bevel-gear differential, in the spur-gear differential the coupling between the
side gears is attained by a pair of double planetary gears or pinions (Figure 2.2b). Each pinion is coupled by one of its rings to an output side gear that sits on an output shaft (or a half axle), whereas by its other ring-to its twin pinion. There may be two to four such pinions, sitting of pins, or spiders. Bevel-gear differentials have two or four pinions; three pinions are used very rarely. It is seen by comparing the open-type bevel-gear and spur-gear differentials that the
bevel-gear differential has the advantage of using fewer gears (there are no paired pinions) and of the smaller overall dimensions of the housing in the plane perpendicular to the principal axis, whereas the spur-gear differential, while being somewhat more complex, has the advantage of greater ease in manufacturing the gears, the absence of axial loads in the gearing, and smaller overall dimension in the direction of the principal axis (Figure 2.2).
