Perform free body diagram analysis to get reaction force at bearings

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Perform free body diagram analysis to get reaction force at bearings

A double reduction gearbox design has developed to the point that the general
layout and axial dimensions of the countershaft carrying two spur gears has been
proposed, as shown in Fig. 7-10. The gears and bearings are located and supported
by shoulders, and held in place by retaining rings. The gears transmit torque
through keys. Gears have been specified as shown, allowing the tangential and
radial forces transmitted through the gears to the shaft to be determined as
follows.
Bearing A
where the superscripts tand rrepresent tangential and radial directions,
respectively; and, the subscripts 23 and 54 represent the forces exerted
by gears 2 and 5 (not shown) on gears 3 and 4, respectively.
Proceed with the next phase of the design, in which a suitable material
is selected, and appropriate diameters for each section of the shaft are
estimated, based on providing sufficient fatigue and static stress capacity
for infinite life of the shaft, with minimum safety factors of 1.5.
D₁ D₂
Datum
0.25
0.75
1.25
1.75
2.0
W
480 lbf
W₂₁3 = 197 lbf
CADEF
Gear 3
d; = 12.5 in
-0
2.75
OS
G H
D₁
W$4 = 2099 lbf
W54 = 885 lbf
Figure 7-10
Shaft layout for Ex. 7-2. Dimensions in inches.
7.50
I
Gear 4
d₂ = 2.7 in
8.50
J
9.50
9.75
Bearing B
D₁ D₂
10.25
10.75
11.25
11.50
K L M B N
Transcribed Image Text:A double reduction gearbox design has developed to the point that the general layout and axial dimensions of the countershaft carrying two spur gears has been proposed, as shown in Fig. 7-10. The gears and bearings are located and supported by shoulders, and held in place by retaining rings. The gears transmit torque through keys. Gears have been specified as shown, allowing the tangential and radial forces transmitted through the gears to the shaft to be determined as follows. Bearing A where the superscripts tand rrepresent tangential and radial directions, respectively; and, the subscripts 23 and 54 represent the forces exerted by gears 2 and 5 (not shown) on gears 3 and 4, respectively. Proceed with the next phase of the design, in which a suitable material is selected, and appropriate diameters for each section of the shaft are estimated, based on providing sufficient fatigue and static stress capacity for infinite life of the shaft, with minimum safety factors of 1.5. D₁ D₂ Datum 0.25 0.75 1.25 1.75 2.0 W 480 lbf W₂₁3 = 197 lbf CADEF Gear 3 d; = 12.5 in -0 2.75 OS G H D₁ W$4 = 2099 lbf W54 = 885 lbf Figure 7-10 Shaft layout for Ex. 7-2. Dimensions in inches. 7.50 I Gear 4 d₂ = 2.7 in 8.50 J 9.50 9.75 Bearing B D₁ D₂ 10.25 10.75 11.25 11.50 K L M B N
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