b The fatigue data for a brass alloy are given as follows St

b) The fatigue data for a brass alloy are given as follows:

Stress Amplitude (MPa)    Cycles to Failure

310                                  2 x 10^5

223                                   1 x 10^6

191                                  3 x 10^6

168                                  1 x 10^7

153                                 3 x 10^7

143                                   1 x 10^8

134                                   3 x 10^8

127                                      1 x 10^9

Suppose that the fatigue e data were taken from torsional tests, and that a shaft of this alloy is to be used for a coupling that is attached to an electric motor operating at 1500 rpm. Give the maximum torsional stress amplitude possible for each of the following lifetimes of the coupling: (a) 1 year, (b) 1 month, (1) 1 day, and (d) 2 hours.

Solution

For each lifetime, first compute the number of cycles, and then read the corresponding fatigue strength from the above plot.

                (a) Fatigue lifetime = (1 yr)(365 days/yr)(24 h/day)(60 min/h)(1500 cycles/min)

= 7.9*10^8 cycles.

The stress amplitude corresponding to this lifetime is about 130 MPa.

                (b) Fatigue lifetime = (30 days)(24 h/day)(60 min/h)(1500 cycles/min)

= 6.5*10^7 cycles.

The stress amplitude corresponding to this lifetime is about 145 MPa.

                (c) Fatigue lifetime = (24 h)(60 min/h)(1500 cycles/min)

= 2.2*10^6 cycles.

The stress amplitude corresponding to this lifetime is about 195 MPa.

            (d) Fatigue lifetime = (2 h)(60 min/h)(1500 cycles/min)

= 1.8*10^5 cycles.

The stress amplitude corresponding to this lifetime is about 315 MPa