Chapter 7, Problem 18P

In the figure is a proposed shaft design to be used for the input shaft a in Prob. 7–17. A ball bearing is planned for the left bearing, and a cylindrical roller bearing for the right.

(a)    Determine the minimum fatigue factor of safety by evaluating at any critical locations. Use the DE-ASME Elliptic fatigue criterion.

(b)    Check the design for adequacy with respect to deformation, according to the recommendations in Table 7–2.

Problem 7–18

Shoulder fillets at bearing seat 0.030-in radius, others $\frac{1}{8}$-in radius, except right-hand bearing seat transition, $\frac{1}{4}$ in. The material is 1030 HR. Keyways $\frac{3}{8}$ in wide by $\frac{3}{16}$ in deep. Dimensions in inches.

In the double-reduction gear train shown, shaft a is driven by a motor attached by a flexible coupling attached to the overhang. The motor provides a torque of 2500 lbf · in at a speed of 1200 rpm. The gears have 20° pressure angles, with diameters shown in the figure. Use an AISI 1020 cold-drawn steel. Design one of the shafts (as specified by the instructor) with a design factor of 1.5 by performing the following tasks.

(a)    Sketch a general shaft layout, including means to locate the gears and bearings, and to transmit the torque.

(b)    Perform a force analysis to find the bearing reaction forces, and generate shear and bending moment diagrams.

(c)    Determine potential critical locations for stress design.

(d)    Determine critical diameters of the shaft based on fatigue and static stresses at the critical locations.

(e)    Make any other dimensional decisions necessary to specify all diameters and axial dimensions. Sketch the shaft to scale, showing all proposed dimensions.

(f)    Check the deflection at the gear, and the slopes at the gear and the bearings for satisfaction of the recommended limits in Table 7–2.

(g)    If any of the deflections exceed the recommended limits, make appropriate changes to bring them all within the limits.

Problem 7–17

Dimensions in inches.