Please provide working for this question, thanks The figure below represents the

Question

Please provide working for this question, thanks

The figure below represents the general layout of a compound gear train. An electric motor, rated at 1.0 kW at 2880 rpm drives gear A which has 50 teeth. Gear B has 150 teeth, gear C has 40 teeth and gear D has 160 teeth. B and C are connected to a common shaft and rotate together. All gears are spur gears with module 2 teeth and a pressure angle of 20 degree. Calculate the following: Output speed of gear D Torque transmitted to gear D Force along the pressure line between gears A and B and between gears C and D Forces tending to separate the mating gears

Explanation / Answer

angular velocity is being represented by w here

so ....

wA / wB = NB / NA ....

where NB = number of teeth in B

NA = numebr of teth in A

so 1440 / wB = 160 / 40

so wB = 1440 / 4 = 360 RPM

as B and C are directly connected ..

so wC = wB =360 RPM

again

wC / wD = ND/NC

360 / wD = 150 / 50

wD = 360 / 3 = 120 RPM

i) output speed of D = 120 RPM

ii) The power transmitted through all the gears will be same ..

so power transmitted through D = 0.75 KW = 750 Watt

angular speed = 120 rpm = 120 * 2pi / 60 rad / sec = 4*pi rad/sec

now power = torque * angular speed

so.. 750 = torque at D * 4*pi

so torque at D = 750 / (4*pi) = 59.683 N-m

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