Fig. 13.24 shows a differential gear used in a motor car. The pinion A on the propeller shaft has 12 teeth and gears with the crown gear B which has 60 teeth. The shafts P and Q form the rear axles to which the road wheels are attached. If the propeller shaft rotates at 1000 r.p.m. and the road wheel attached to axle Q has a speed of 210 r.p.m. while taking a turn, find the speed of road wheel attached to axle P.
Question : Fig. 13.24 shows a differential gear used in a motor car. Th...
Given : T_{ A }=12 ; T_{ B }=60 ; N_{ A }=1000 \text { r.p.m.; } N_{ Q }=N_{ D }=210 \text { r.p.m. }
Since the propeller shaft or the pinion A rotates at 1000 r.p.m., therefore speed of crown gear B,
N_{ B }=N_{ A } \times \frac{T_{ A }}{T_{ B }}=1000 \times \frac{12}{60}= 200 r.p.m.
The table of motions is given below :
| Revolutions of elements | |||||
| Step No. | Conditions of motion | Gear B | Gear C | Gear E | Gear D |
| 1 | Gear B fixed-Gear C rotated through + 1 revolution (i.e. 1 revolution anticlockwise) | 0 | +1 | +\frac{T_{ C }}{T_{ E }} | -\frac{T_{ C }}{T_{ E }} \times \frac{T_{ E }}{T_{ D }}=-1\left(\because T_{ C }=T_{ D }\right) |
| 2 | Gear B fixed-Gear C rotated through + x revolutions | 0 | +x | +x \times \frac{T_{ C }}{T_{ E }} | -x |
| 3 | Add + y revolutions to all elements | +y | +y | +y | +y |
| 4 | Total motion | +y | x+y | y+x \times \frac{T_{ C }}{T_{ E }} | y-x |
Since the speed of gear B is 200 r.p.m., therefore from the fourth row of the table,
y = 200 …(i)
Also, the speed of road wheel attached to axle Q or the speed of gear D is 210 r.p.m., therefore from the fourth row of the table,
y – x = 210 or x = y – 210 = 200 – 210 = – 10
\therefore Speed of road wheel attached to axle P
= Speed of gear C = x + y
= – 10 + 200 = 190 r.p.m.