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Unformatted text preview: is fixed, therefore TA
=0
TC or (500 – x) – x × 500 – x – 0.227 x = 0 or x = 500/1.227 = 407.5 r.p.m. y – x×
∴
and 34
=0
150 ...[From equation (v )] y = 500 – x = 500 – 407.5 = 92.5 r.p.m. Since the speed of the driven or output shaft Y (i.e. N Y) is equal to the speed of wheel E
(i.e. N E), therefore 34 38
TA TD
×
= 92.5 – 407.5 ×
×
120 50
TB TE
= 92.5 – 87.75 = 4.75 r.p.m. NY = NE = y – x × Assuming 100 per cent efficiency of the gear train, input power PX is equal to output power
(PY), i.e.
PY = PX = 7.5 kW = 7500 W
∴ Output torque of shaft Y , = PY × 60 7500 × 60
=
= 15 076 Nm = 15.076 kNm Ans.
2π N Y
2π × 4.75 Tangential force between wheels D and E
We know that the pitch circle radius of wheel E, m × TE 3.5 × 50
=
= 87.5 mm = 0.0875 m
2
2
∴ Tangential force between wheels D and E,
rE = = Torque on wheel E
15.076
=
= 172.3 kN Ans.
Pitch circle radius of wheel E 0.0875
...(∴ Torque on wheel E = Torque on shaft Y ) Tangential force between wheels B and C
We know that the input torque on shaft X or on wheel A = PX × 60 7500 × 60
=
= 143 Nm
2π N X
2π × 500 ∴ Fixing torque on the fixed wheel C
= Torque on wheel E – Torque on wheel A
= 15 076 – 143 = 14 933 Nm = 14.933 kNm 474 l Theory of Machines Pitch circle radius of wheel C, m × TC 3.5 × 150
=
= 262.5 mm = 0.2625 m
2
2
Tangential force between wheels B and C
rC = = Fixing torque on wheel C 14.933
=
= 57 kN Ans.
0.2625
rC EXERCISES
1. A compound train consists of six gears. The number of teeth on the gears are as follows :
Gear : A B C D E F No. of teeth : 60 40 50 25 30 24 The gears B and C are on one shaft while the gears D and E are on another shaft. The gear A drives gear
B , gear C drives gear D and gear E drives gear F. If the gear A transmits 1.5 kW at 100 r.p.m. and the gear
train has an efficiency of 80 per cent, find the torque on gear F.
[Ans. 30.55 Nm]
2. 3. 4. Two parallel shafts are to be connected by spur gearing. The approximate distance between the shafts...
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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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