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Solution – shaft problem
Question 1
The tangential force on the gear is 15000*cos(20
0
) = 14095 N
The radial force is 15000*sin(20
0
) = 5130.3 N
The other gear has half the diameter, so the loads are twice (28190 N and 10260.6 N)
Summing moments and forces the bearing reactions are as shown below, leading to the
bending diagrams for each plane below.
xy plane
zx plane
The worst bending moment is the vector sum at the righthand gear giving 4718.6 Nm.
The torque = tangential force by pitch radius = 14095 x 0.375 = 5285.6 Nm
3979.8Nm
2535.0 Nm
2082.3 Nm
28190 N
5130.3 N
10260.6 N
6941 N
8449.9 N
829.1 N
14095 N
13265.88 N
248.7
Nm
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View Full Document Maximum bending stress = 32 x 4718.6/(
π
x 0.075
3
) = 113.9 MPa
Maximum torsional shear stress = 16 x 5285.6/(
π
x 0.075
3
) = 63.81 MPa
Von Mises stress (max. distortion energy measure)
=
√
(113.9
2
+ 3 x 63.81
2
) = 158.7 MPa
Consider the xy plane, I =
π
x 75
4
/64 = 1.553E6 mm
4
,
EI = 3.106E11 N mm
2
300 mm
250 mm
300 mm
x
2082.3 Nm
2535.0 Nm
Regarding the bending moment diagram as 4 triangles,
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This note was uploaded on 11/26/2011 for the course MECH 2100 taught by Professor Billdaniel during the Three '11 term at Queensland.
 Three '11
 BillDaniel

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