Unformatted text preview: — TB
TC â€“ xÃ— +y TB
TD y â€“ xÃ— TB TE
Ã—
TD TF +y TB
TC y â€“ xÃ— TB TE
Ã—
TD TF Chapter 13 : Gear Trains l 461 1. Speed of the output shaft when gear C is fixed
Since the gear C is fixed, therefore from the fourth row of the table, y â€“xÃ— TB
=0
TC or y â€“ xÃ— 20
=0
80 âˆ´
y â€“ 0.25 x = 0
...(i)
We know that the input speed (or the speed of gear B ) is 1000 r.p.m. counter clockwise,
therefore from the fourth row of the table,
x + y = + 1000
...(ii)
From equations (i) and (ii), x = + 800, and y = + 200
âˆ´ Speed of output shaft = Speed of gear F = y â€“ x Ã— TB TE
Ã—
TD TF 20 30
Ã—
= 200 â€“ 187.5 = 12.5 r.p.m.
80 32
= 12.5 r.p.m. (counter clockwise) Ans.
= 200 â€“ 800 Ã— 2. Speed of the output shaft when gear C is rotated at 10 r.p.m. counter clockwise
Since the gear C is rotated at 10 r.p.m. counter clockwise, therefore from the fourth row of the table, y â€“ xÃ— TB
= + 10
TC âˆ´
y â€“ 0.25 x = 10
From equations (ii) and (iii),
x = 792,
âˆ´ Speed of output shaft or y â€“ xÃ— 20
= 10
80 ...(iii)
and y = 208 = Speed of gear F = y â€“ x Ã— 20 30
TB TE
Ã—
= 208 â€“ 792 Ã—
Ã—
80 32
TD TF = 208 â€“ 185.6 = 22.4 r.p.m. = 22.4 r.p.m. (counter clockwise) Ans.
Example 13.18. Fig. 13.24 shows a differential
gear used in a motor car. The pinion A on the propeller
shaft has 12 teeth and gears with the crown gear B which
has 60 teeth. The shafts P and Q form the rear axles to
which the road wheels are attached. If the propeller
shaft rotates at 1000 r.p.m. and the road wheel attached
to axle Q has a speed of 210 r.p.m. while taking a turn,
find the speed of road wheel attached to axle P.
Solution. Given : T A = 12 ; T B = 60 ; N A = 1000
r.p.m. ; N Q = N D = 210 r.p.m.
Since the propeller shaft or the pinion A rotates at
1000 r.p.m., therefore speed of crown gear B , 12
TA
= 1000 Ã—
60
TB
= 200 r.p.m.
The table of motions is given below :
NB = NA Ã— Fig. 13.24 462 l Theory of Machines
Table 13.20. Table of motions.
Revolutions of elements Step No. Conditions of motion Gear B Gear C Gear E + TC
TE Gear B fixedGear C rotated
thro...
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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.
 Fall '08
 CELGHORN

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