Question

Problem 1 (20 points) A gear reduction unit uses the countershaft shown in Fig. 1. Gear A receives power from another gear with the transmitted force FA = 30 kN applied at the pressure angle ?A = 20°. The power is transmitted through the shaft and delivered through gear B at the pressure angle ?B = 25°. The shaft design proposed for this application is shown in Fig. 2. The material is AISI 1040 cold-drawn steel. The keyseats are cut with standard endmills. The effective centers of the gears for force transmission are also shown in Fig. 2. a. Examine the shaft for strength at the critical locations and determine the minimum fatigue factor of safety using the DE-Goodman failure criterion. You may assume that the torque is steady, and the bending moment is fully reversed. y 400 mm FB 350 mm O 300 mm 25° FA 20° z 50-mm dia. A Gear A, 600-mm dia. B C Gear B, 300-mm dia. x Figure 1 b. The shaft is simply supported in cylindrical roller bearings at O and C. Calculate the slope at points O, A, B, and C using singularity functions (you may use the MATLAB® script provided in Blackboard). Check that the slopes do not exceed the recommended values listed in Table 7-2. If any of the slopes exceed the recommended limits, make appropriate changes to bring them all within the limits.

          Problem 1 (20 points)

A gear reduction unit uses the countershaft shown in Fig. 1. Gear A receives power from another gear with the transmitted force FA = 30 kN applied at the pressure angle ?A = 20°. The power is transmitted through the shaft and delivered through gear B at the pressure angle ?B = 25°.

The shaft design proposed for this application is shown in Fig. 2. The material is AISI 1040 cold-drawn steel. The keyseats are cut with standard endmills. The effective centers of the gears for force transmission are also shown in Fig. 2.

a. Examine the shaft for strength at the critical locations and determine the minimum fatigue factor of safety using the DE-Goodman failure criterion. You may assume that the torque is steady, and the bending moment is fully reversed.

y
400 mm
FB
350 mm
O
300 mm
25°
FA
20°
z
50-mm dia.
A
Gear A, 600-mm dia.
B
C
Gear B, 300-mm dia.
x
Figure 1

b. The shaft is simply supported in cylindrical roller bearings at O and C. Calculate the slope at points O, A, B, and C using singularity functions (you may use the MATLAB® script provided in Blackboard). Check that the slopes do not exceed the recommended values listed in Table 7-2. If any of the slopes exceed the recommended limits, make appropriate changes to bring them all within the limits.

Problem 1 (20 points)

A gear reduction unit uses the countershaft shown in Fig. 1. Gear A receives power from another gear with the transmitted force FA = 30 kN applied at the pressure angle ?A = 20°. The power is transmitted through the shaft and delivered through gear B at the pressure angle ?B = 25°.

The shaft design proposed for this application is shown in Fig. 2. The material is AISI 1040 cold-drawn steel. The keyseats are cut with standard endmills. The effective centers of the gears for force transmission are also shown in Fig. 2.

a. Examine the shaft for strength at the critical locations and determine the minimum fatigue factor of safety using the DE-Goodman failure criterion. You may assume that the torque is steady, and the bending moment is fully reversed.

y
400 mm
FB
350 mm
O
300 mm
25°
FA
20°
z
50-mm dia.
A
Gear A, 600-mm dia.
B
C
Gear B, 300-mm dia.
x
Figure 1

b. The shaft is simply supported in cylindrical roller bearings at O and C. Calculate the slope at points O, A, B, and C using singularity functions (you may use the MATLAB® script provided in Blackboard). Check that the slopes do not exceed the recommended values listed in Table 7-2. If any of the slopes exceed the recommended limits, make appropriate changes to bring them all within the limits.

Added by Julia G.

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