Page 70 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
48

Figure E2.2 An initial design of a shaft.

Solution

Steps Computation Results Units

1. Calculate The stress at the cross section H: = 5.48 MPa
a
working stress As the shaft rotates, bending stress produced MPa
bending = 0.26
m
by constant moment M is a completely reversed = = 5.5 MPa
stress; while axial stress tension is a static stress. a m
= bending =5.48MPa
a
= =0.26MPa
m tension
Consider a unidirectional transmission, discontinuous
working condition; can be regarded as repeated
stress.

= = = 5.5MPa
m
a
2
2 − 2 × 275 − 500
2. Calculate = −1 0 = = 0.1 = 0.1
500
coefficient 0
2 −1 − 0 2 × 155 − 295 = 0.05

= = = 0.05

0 295
3. Calculate The actual number of cycles = 285.2 MPa
−1N
endurance N =8 × 60n × 300 × 2.5=7.2×10 6
strength since = 160.7 MPa
−1N
3
10 < N < N = 10 7
0
We need to calculate the strength by finite life.
√ √
m N 0 10 7
= = 275 × 9 = 285.2 MPa
−1N −1 N 7.2 × 10 6
√ √
m N 0 10 7
−1N = −1 = 155 × 9 = 160.7 MPa
N 7.2 × 10 6