Answer to Question #208127 in Mechanical Engineering for Sanajit

Question #208127

An epicyclic gear consists of bevel wheels as shown in Fig. 13.49. The driving pinion A has 20 teeth

and meshes with the wheel B which has 25 teeth. The wheels B and C are fixed together and turn freely

on the shaft F. The shaft F can rotate freely about the main axis X X. The wheel C has 50 teeth and

meshes with wheels D and E, each of which has 60 teeth. Find the speed and direction of E when A

rotates at 200 r.p.m., if

1. D is fixed, and 2. D rotates at 100 r.p.m., in the same direction as A.

In both the cases, find the ratio of the torques transmitted by the shafts of the wheels A and E, the

friction being neglected


1
Expert's answer
2021-06-18T07:54:33-0400


The speed of A

"x+y=200 \\implies y=200-x"

Part a

D is fixed

"y+x \\frac{T_A*T_C}{T_B*T_D}=0 \\implies 200-x+x \\frac{20*50}{25*60}=0"

"x=600 ; y= 200-600= -400"

Speed of E, "y-x \\frac{T_A*T_C}{T_B*T_E}=0 \\implies -400-600 \\frac{20*50}{25*60}=-800 rpm"

E rotates at 800 rpm in the direction opposite to A

Part b

D rotates at 100 rpm in the same direction of A

"y+x \\frac{T_A*T_C}{T_B*T_D}=-100 \\implies -x+ \\frac{2}{3}x=-100 rpm \\implies x= 300"

"y=200-x=-100"

Speed of E

"y-x \\frac{T_A*T_C}{T_B*T_E}=-100 -300* \\frac{2}{3}= 300"

E rotates at 300 rpm in the direction to A

"T_1 \\omega _A=T_0\\omega _E \\implies \\frac{T_1}{T_0}=\\frac{\\omega _E}{\\omega _A}"

Case A

"\\frac{T_1}{T_0}=\\frac{800}{200}=4"

The ratio of torque transmitted by the shaft of wheel A and E is 4


Case B

"\\frac{T_1}{T_0}=\\frac{300}{200}=1.5"

The ratio of torque transmitted by the shaft of wheel A and E is 1.5


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