Question

PROBLEM 2 A part of a machine is subject to the following fluctuating stress of σmax = 55 kpsi and σmin = 20 kpsi applied for 7 (104 ) cycles. If the load changes to σmax = 48 kpsi and σmin = -30 kpsi, how many cycles should the spring survive, using the Gerber criterion? The material is AISI 1040 CD and has a fully corrected endurance strength of Se = 27 kpsi. Assume that f = 0.9. Use Miner’s method.

Answer 1

ANSWER ;

The ultimate tensile stress for this steel is:

Sut =85 kpsi

We have to find the maximum number of cycles for each load state,using the equation:

Where "a" and "b" are constants given by:

  

  

From Gerber's criteria equation, replacing Sf for Se and clearing:

  

For the first load state:

The maximum number of cycle is then :

For the second load state :

The maximum number of cycles is then:

  Using Miner's method :

Where n is the number of cycles applied and N is the maximum number of cycle .D is the total damage accumation of the piece .For D=1 (failure):