Solution Found!
The rotating solid steel shaft is simply supported by
Chapter 7, Problem 7.3(choose chapter or problem)
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 5 340 N ? m. The shaft is machined from steel with Sy 5 420 MPa and Sut 5 560 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.
Questions & Answers
QUESTION:
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 5 340 N ? m. The shaft is machined from steel with Sy 5 420 MPa and Sut 5 560 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.
ANSWER:a. Static Yield Analysis
Using the distortion energy theory, the minimum factor of safety at yield is Fy
Fy = 2.5
From the torque at A, the required shear stress in the shaft can be found using
?_A = {TAoverJ}
where J is the polar moment of inertia of the shaft section. The smallest acceptable shaft diameter can be found by substituting the known material properties, factor of safety, and applied torque into the above equation, rearranging, and solving for d.
d = {sqrt{TAover{JFySy}}}
J = {h^3over12} , where h is th