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Unformatted text preview: that the speed of the motor or the speed of the pinion A i s 1000 r.p.m.
Therefore
x + y = 1000 ...(i) Also, the annular wheel E is fixed, therefore y –x× TA
=0
TE y = x× or 15
TA
=x×
= 0.273 x
55
TE ...(ii) From equations (i) and (ii),
x = 786 and y = 214 ∴ Speed of machine shaft = Speed of wheel D, ND = y – x × TA TC
15 15
×
= 214 – 786 ×
×
= + 37.15 r.p.m.
20 50
TB TD = 37.15 r.p.m. (anticlockwise) Ans.
Torque exerted on the machine shaft
We know that
Torque developed by motor × Angular speed of motor
= Torque exerted on machine shaft
× Angular speed of machine shaft
or 100 × ωA = Torque exerted on machine shaft × ωD ∴ Torque exerted on machine shaft = 100 × 1000
ωA
N
= 100 × A = 100 ×
= 2692 Nm Ans.
37.15
ωD
ND l Chapter 13 : Gear Trains 465 Example 13.20. An epicyclic gear train consists of a sun wheel
S, a stationary internal gear E and three identical planet wheels P
carried on a star shaped planet carrier C. The size of different toothed
wheels are such that the planet carrier C rotates at 1/5th of the speed
of the sunwheel S. The minimum number of teeth on any wheel is 16.
The driving torque on the sun wheel is 100 Nm. Determine : 1. number of teeth on different wheels of the train, and 2. torque necessary to
keep the internal gear stationary.
Solution. Given : NC = NS
5 Fig. 13.27 1. Number of teeth on different wheels
The arrangement of the epicyclic gear train is shown in Fig. 13.27. Let T S and T E be the
number of teeth on the sun wheel S and the internal gear E respectively. The table of motions is
given below :
Table 13.22. Table of motions.
Revolutions of elements
Step
No. Conditions of motion Planet
carrier C Sun
wheel S Planet
wheel P TS
TP 1. Planet carrier C fixed, sunwheel S
rotates through + 1 revolution (i.e.
1 rev. anticlockwise) 0 +1 – 2. Planet carrier C fixed, sunwheel S
rotates through + x revolutions 0 +x – x× 3. Add + y revolutions to all elements +y +y Total motion +y x +y y –x× – TS TP
T
×
=– S
TP TE
TE +y 4. Internal gear E TS
TP – x× TS
TE +y TS
TP y –x× TS
TE We know that when the sunwheel S makes 5 revolutions, the planet carrier C makes...
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This note was uploaded on 02/13/2014 for the course MIE 301 taught by Professor Celghorn during the Fall '08 term at University of Toronto Toronto.
 Fall '08
 CELGHORN

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