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Question 15.9: The differential gear used in an automobile is shown in Fig....

The differential gear used in an automobile is shown in Fig.15.13. The pinion A on the propeller shaft has 12 teeth and the crown gear B 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 1200 rpm and the road wheel attached to axle Q has a speed of 250 rpm while taking a turn, find the speed of road wheel attached to axle P.

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n_{B}=\left(\frac{z_{A}}{z_{B}}\right) n_{A}=\left(\frac{12}{60}\right) 1200=240 rpm .

Now    y=240 rpm .

Also    -x+y=250 .

or        x=240-250=-10 .

speed of road wheel attached to axle P = speed of gear C

= x + y.

=-10 +240 = 230 rpm.

Table 15.10 can be used to find the speed of the gears.

Table 15.10
Revolutions of Operation
Gear D Gear E Gear C Gear B

-\left(\frac{z_{C}}{z_{E}}\right)\left(\frac{z_{E}}{z_{D}}\right)=-1

\text { or } \frac{z_{C}}{z_{D}}=1

\frac{z_{C}}{z_{E}} 1 0 1. Gear B fixed, +1 revolution
to gear c, ccw.
-x x\left(\frac{z_{C}}{z_{E}}\right) x 0 2. Multiply by x
-x+y x \frac{z_{C}}{z_{E}}+y x+y y 3. Add y

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