2 The stick diagram of a six-speed FWD MT is shown in Figure 2.9a. The tire radius

of the vehicle is R (ft). The numbers of teeth are labeled in the drawing for clarity.

The gear ratios from the 1st to the 4th gears are: 1st gear (3.92), 2nd gear (2.76),

3rd gear (1.85), 4th gear (1.35). The numbers of teeth of the final drive gears are:

NFi = 21, NFo = 66.

a) Determine the equivalent mass moment of inertia to be synchronized in a 1-2

upshift and a 4-3 downshift respectively, in terms of the mass moments of inertia

of the involved parts.

b) A 2-3 upshift is to be made at a vehicle speed of V (mph). Assuming the synchro-

nization time is At and the angular velocity change is uniform during synchro-

nization, determine the friction torque to be generated by the synchronizer

friction cones.

c) Determine the work done by the friction and the angle of rotation of gear N4; in

the process of synchronization for the shift in (b).

d) The synchronizers used in the transmission are the same and the angular velocity

change during synchronization is assumed to be uniform. If the shift force in a

2-3 upshift, F23, is 10 N, determine the shift force in a 1-2 shift, F12. Both shifts

are made at the same engine speed and within the same synchronization time.

Note: Your answers must not contain the gear tooth labels.