A wormgear is mounted at the right end of the shaft (location D) as shown in the

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Question:

A wormgear is mounted at the right end of the shaft (location D) as shown in the figure below. The magnitudes and directions of the three forces acting on the gear are given in the figure. The bearing at C transfers the axial thrust force from the gear to the housing. The power istransmitted by a chain sprocket at B to drive a conveyor removing cast iron chips from a machining system. The shaft is along the x-axis, from left to right; the z-axis is vertical going upward; the y-axis forms a right-handed coordinate system with x and z.

(please answer questions in order and with all the details)

FBD and load diagrams (6 marks) (a) Draw free-body diagrams in the vertical (x-z) and horizontal (x-y) planes for the shaft and

determine the components of reaction forces at bearings A and C, and chain tension Fc (3 marks).

(b) For this question, the diagrams do not need to be to scale, but you need to indicate numerical values. Draw diagrams of the axial force and torque along the shaft. Determine the equations for the shear forces and bending moments for the shaft, and draw their diagrams in the vertical (x- z) and horizontal (x-y) planes (3 marks).

Shaft diameter at location C (13 marks)

(c) Verify that the total bending moment and torque at location C are 4,854 lb.in and 4,168 lb.in, respectively (1 mark). If your values do not match these, use the given values here. Determine Mm, Ma, Tm and Ta at location C (3.5 marks).

(d) The shaft is made of 1040 cold-drawn steel with Su = 80 ksi and Sy = 71 ksi. Assume that the shaft diameter is between 2 and 4 inches, and that the reliability of the shaft is 99%. All important surfaces are machined. Determine the endurance limit of this steel for the shaft (2.5 marks).

(e) For the step radius (r = 0.06 in) to the right of the bearing at location C, take Kt = 2.6 in bending, and Kts = 2.3 in torsion. Determine q, qs, Kf and Kfs (2 marks). Assume a design safety factor of 2.5. Determine the shaft diameter D3 at location C based on strength analysis in fatigue, and ignoring the thrust load on the shaft (4 marks) (see Useful equations at the end of document).

Bearing selection (6 marks)

(f) At location C, based on a bore diameter of 55 mm, a radial load of 1,742 lb and a thrust load of 265 lb, select a suitable radial contact bearing for 8,000 hr of use at 100 rpm with 96% reliability under light to moderate impact loading .