Fatigue Design – Assignment 1 Stress-based approach: Redesign of a shear pin under cyclic bending loads

• Responsible teacher: Lennart Josefson • Supervisor: Anders Ekberg

Time to finish and hand over to supervisor: 2007-01-31 Note: To pass the assignment you must print out your program code (Matlab, Fortran, Mahematica, Maple, Excel working sheet) and include it in your report The paper below discusses the failure of a flocculator train at a water filtration plant, see Figures 1 and 2. The 4-20 rpm output shaft turns the flocculators at 1-5 rpm. Mounted on this shaft is a torque limiting coupling , utilizing a SAE 1040 steel shear pin. This shear pin fails if the flocculator paddles jam, thus protecting the equipment from overload. With the current design, a shear pin only lasts about one week. Analysis suggests that cyclic fatigue, caused by misalignment between the driving and driven coupling elements, causes premature pin failure. The cost of frequently changing shear pins is believed to be too high, therefore a redesign of the shear pin is needed The torque limiting coupling is shown in Figure 3 and the shear pin is shown in Figure 4 (the radius in the notch ρ = 1.2 mm). Figure 5 explains the wobbling mechanism which is believed to create the additional bending load that enhances the failure of the pin. Mechanical properties for SAE 1040 and the proposed new material are shown in Table 1. Tasks:

• Calculate the shear stress in the shear pin at the maximum rotational speed of the coupling based on the power of the drive motor. The radius from the center of rotation r is given in Figure 6 below. Compare with the the ultimate strength for the pin material.

• Derive an expression for the angular rotation at the shear pin end due to the

applied moment M from the wobbling action assuming that the shear pin can be assumed to be a cantilever beam with varying cross sectional area, see Figure 6.

• Calculate the fatigue strength at 105 cycles (the estimated number of cycles to

failure) based on the text book (Dowling Ch 10.7) with corrections factors applied and with an additional environmental parameter menv included. For the SAE steel menv = 0.45.

• Estimate the bending stress amplitude (and bending moment M amplitude) assuming that the pin undergoes a fully reversed bending moment due to the wobbling with the bending stress amplitude equal to the fatigue strength at 105 cycles.

• Calculate the rotation of the tip of the shear pin corresponding to the bending

moment amplitude above.

• In the new design, the pin material is chosen as PH 13-8 Mo. This steel has a much higher corrosive resistance menv = 1.0. Calculate the diameter of the notch D2 for the new pin based on the difference in ultimate shear strengths for the two materials. You may assume that the shear strength is 0.5 * the yield strength. Verify that the new pin will fail in shear.

• The new design shall have a design life of at least 107 cycles. Calculate the

bending stress amplitude for the new shear pin based on the new diameter above. Verify that this stress amplitude is less than the fatigue strength at 107 cycles for the PH13-8 Mo steel. The fatigue strength at 107 cycles for the new material can be estimated to be 0.29*the ultimate strength.