In the epicyclic gear train shown in fig. 1 a gear C which has teeth cut internally and externally is free to rotate on an arm driven by the shaft S1. It meshes externally with the casing D and internally with the pinion B. The gears have following number of teeth: T = 24, T = 32 and Td= 48, Find the velocity ratio between (i) S1 and S2 when D is fixed. (ii) S1 and D when S2 is fixed. What will be the torque required t5o fix the casing D if a torque of 300Nm is applied to shaft S1? -

Mumbai University > MECH > Sem 5 > Theory Of Machines 2

Marks: 12 M

Year: May 2015

Assume N = 60rpm

Case 1) D fixed

mTc/Td + N = 0

m 32/48 + 60 = 0

M = 90

So, Ns1/Ns2 = Na/Nb = N / (mTc/Tb + N) from table

Ns1/Ns2 = 60 / (90 x 32/24 + 60) = 0.33

Case 2) S2 fixed or B fixed

mTc/Tb + N = 0

m x 32/24 + 60 = 0

m = -45

so, Ns1/Nd = N / (-mTc/Td + N) = 60 / (45 x 32/48 + 60)

Ns1/Nd = 0.67

Also, assuming no power loss

Ps1 = Pd

Ts1 x Ns1 = Td x Nd

Td = Ts1x Ns1/ Nd = 300 x 0.67 = 200 Nm