Engineering Mechanics

(^714) „„„„„ A Textbook of Engineering Mechanics
Example 34.8. An epicyclic gear train as shown in Fig. 34.15, has a sun wheel S of 30
teeth and two planet wheels P, P of 50 teeth. The planet wheels mesh with the internal teeth of a
fixed annulus A. The driving shaft carrying the sun wheel, transmits 4 kW at 300 r.p.m. The driven
shaft is connected to an arm, which carries the planet wheels.
Fig. 34.15.
Determine speed of the driven shaft and the torque transmitted, if the overall efficiency
is 95%.
Solution. Given: No. of teeth on sun wheel (TS) = 30; No. of teeth on planet wheels (TP)
= 50; Power transmitted (P) = 4 kW = 4000 W; Speed of driving shaft = 300 r.p.m. and efficiency
(η) = 95% = 0.95.
∴ Power transmitted by the driven shaft
= 4000 × 0·95 = 3800 W
First of all prepare the table of motions as given below :
Step No. Conditions of motion
Revolution of
Arm Wheel A Wheel P Wheel S

1. Arm fixed; wheel A
   0+ 1

A

P

T

T

+ – AP

PS

TT

TT

×

rotates through + 1

revolution

• A
  s

T

T

=

2. Arm fixed; wheel A
   0+ x

A

P

T

x

T

+ – A

S

T

x

rotates through + x T

revolutions

3. Add + y revolutions + y + y + y + y
   to all elements


4. Total motion + yx + y

A

P

T

yx

T

+ – A

S

T

yx

T

Speed of the driven shaft

Let dA, dP and dS be the pitch circle diameters of the wheels A, P and S respectively. From the

geometry of Fig. 34.15, we find that

2

dA =

2

S

P

d

+d or dA = dS + 2dP