A transmission, shown below, is used to reduce the angular velocity of a motorcy

Question

A transmission, shown below, is used to reduce the angular velocity of a motorcycle engine to a slower, higher torque outpout that can be used to power the rear wheel of the motorcycle. The crank shaft is first connected to a gear (2) which reduces the angular velocity of the output shaft and amplifies torque. The output is then sent to the rear wheel of the motorcycle through a sprocket/chain drive (elements 3,4) and finally to the rear wheel of the motorcycle (element 5). Given tooth number and diameter data in the table, determine the angular velocities and rotational directions of all gear components (fill in the table below) if the motorcycle is moving at 70 mph. Note rotational direction on your angular velocity answer or on the diagram below. Determine the input angular velocity of the motor crank shaft in rev/min required to sustain 70 mph linear velocity at the rear wheel. To minimize noise, vibration, and wear, the manufacturer of the motorcycle wants to use helical gears instead of less expensive spur gears if any of the linear velocities at gear surfaces exceed 4,000 cm/s. Which type of gear should be used for the gear elements 1 & 2.

Explanation / Answer

v = 70 mph = 31.2928 m/s = pi*0.7*w
w = 14.23 rad/s [ w for gear 5 ]
V for gear 5 = 31.3 m/s

w for gear 4 = 14.23 rad/s
v for gear 4 = w*r = ?

Now, gear ratio of gear 4 and gear 3 = 2 : 1
so, but, wr = w'*r'
and 2*pi*r / 2*pi *r' = 2:1 = r/r'
w' = w*2 = 28.47 rad /s
dia of gear 4 = 8 cm

V of gear 4 = 0.5692 m/s
v of gear 3 = 0.5692 m/s
w of gear 3 = w' = 28.47 rad/s
w of gear 2 = 28.47 rad/s
r for gear 2 = r"
75/15 = r"/4
r" = 6cm
v for gear 2 = 1.7082 m/s

now, w*6 = w"*4
w" = 42.705 rad/s
v for 1 = 0.8541 m/s

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