Assignment Shaft DesignDue date/ time: Wednesday, 2nd April, 2014 at the Start of the Class (first lecture) A shaft is loaded in bending and torsion such that Ma = 70 N · m, Ta = 45 N · m, Mm = 55 N · m, and Tm = 35 N · m. For the shaft, Su = 700 MPa and Sy = 560 MPa, and a fully corrected endurance limit of Se = 210 MPa is assumed. Let Kf = 2.2 and Kf s = 1.8. With a design factor of 2.0 determine the minimum acceptable diameter of the shaft using the (a) DE-Gerber criterion. (b) DE-elliptic criterion. (c) DE-Soderberg criterion. (d) DE-Goodman criterion. Discuss and compare the results. The section of shaft shown in the figure is to be designed to approximate relative sizes of d = 0.75D and r = D/20 with diameter d conforming to that of standard metric rolling-bearing bore sizes. The shaft is to be made of SAE 2340 steel, heat-treated to obtain minimum strengths in the shoulder area of 175 kpsi ultimate tensile strength and 160 kpsi yield strength with a Brinell hardness not less than 370. At the shoulder the shaft is subjected to a completely reversed bending moment of 600 lbf · in, accompanied by a steady torsion of 400 lbf · in. Use a design factor of 2.5 and size the shaft for an infinite life. The rotating solid steel shaft is simply supported by bearings at points B and C and is driven by a gear (not shown) which meshes with the spur gear at D, which has a 150-mm pitch diameter. The force F from the drive gear acts at a pressure angle of 20°. The shaft transmits a torque to point A of TA = 340 N · m. The shaft is machined from steel with Sy = 420 MPa and Sut = 560 MPa. Using a factor of safety of 2.5, determine the minimum allowable diameter of the 250-mm section of the shaft based on (a) a static yield analysis using the distortion energy theory and (b) a fatigue-failure analysis. Assume sharp fillet radii at the bearing shoulders for estimating stress-concentration factors. The motor provides a torque of 2500 lbf · in at a speed of 1200 rpm. including means to locate the gears and bearings. shaft a is driven by a motor attached by a flexible coupling attached to the overhang. and to transmit the torque. Develop the moment and shear diagrams for the shaft modeling the roll force as (a) a concentrated force at the center of the roll. Use an AISI 1020 cold-drawn steel. (d) Determine critical diameters of the shaft based on fatigue and static . In the double-reduction gear train shown. and generate shear and bending moment diagrams. with diameters shown on the figure. The material passes under the roll.5 by performing the following tasks. The gears have 20° pressure angles. Design one of the shafts (as specified by the instructor) with a design factor of 1.A geared industrial roll shown in the figure is driven at 300 rev/min by a force F acting on a 3-in-diameter pitch circle as shown. and (b) a uniformly distributed force along the roll. The coefficient of friction is 0. (c) Determine potential critical locations for stress design. (a) Sketch a general shaft layout.40. The roll exerts a normal force of 30 lbf/in of roll length on the material being pulled through. These diagrams will appear on two orthogonal planes. (b) Perform a force analysis to find the bearing reaction forces. and the slopes at the gear and the bearings for satisfaction of the recommended limits in Table 7–2. and the critical speed of the combination. Also ensure that the shaft does not yield in the first load cycle. 7–17. Estimate the first critical speed due to the loads. (a) Determine the minimum fatigue factor of safety by evaluating at any critical locations. according to the recommendations in Table 7–2.stresses at the critical locations. make appropriate changes to bring them all within the limits. The shaft shown in the figure carries a 18-lbf gear on the left and a 32-lbf gear on the right. (g) If any of the deflections exceed the recommended limits. rather than one that is considered conservative. In the figure is a proposed shaft design to be used for the input shaft a in Prob. showing all proposed dimensions. Use a fatigue failure criteria that is considered to be typical of the failure data. A ball bearing is planned for the left bearing. and a cylindrical roller bearing for the right. the shaft’s critical speed without the loads. ( f ) Check the deflection at the gear. Sketch the shaft to scale. (b) Check the design for adequacy with respect to deformation. (e) Make any other dimensional decisions necessary to specify all diameters and axial dimensions. . . (b) If the goal is to double the critical speed. (a) Find the lowest critical speed of the shaft.A 25-mm-diameter uniform steel shaft is 600 mm long between bearings. find the new diameter. (c) A half-size model of the original shaft has what critical speed? The shaft shown in the figure carries a 18-lbf gear on the left and a 32-lbf gear on the right. and the critical speed of the combination. the shaft’s critical speed without the loads. Estimate the first critical speed due to the loads.