The rotating solid steel shaft (Fig.1 a) 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 20o . The shaft transmits a torque to point “A” of TA = 300 N.m. There is a step at point “C” as shown in Fig.1 (b), assume that D/d ratio is 1,09 and fillet radius (r) is 2,5 mm. a) Find the stress concentrations at point “C” due to bending and shear loads (Initially assume d=50mm). b) If the shaft is machined from quenched and drawn steel with Sy = 420 MPa and Sut=560 MPa and using a factor of safety of 2.5, determine the minimum allowable diameter of the shaft at “C” based on a static yield analysis using the distortion energy (DE) theory. c) If the shaft with a diameter (d) of 32 mm is made of a brittle material with Suc = 420 MPa and Sut=360 MPa, determine the factor of safety of the shaft at “C” based on a static analysis using the Brittle-Coulomb-Mohr (BCM) theory.
The rotating solid steel shaft (Fig.1 a) 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 20o
. The shaft transmits a torque to point “A” of
TA = 300 N.m. There is a step at point “C” as shown in Fig.1 (b), assume that D/d ratio is 1,09 and
fillet radius (r) is 2,5 mm.
a) Find the stress concentrations at point “C” due to bending and shear loads (Initially assume
d=50mm).
b) If the shaft is machined from quenched and drawn steel with Sy = 420 MPa and Sut=560 MPa and
using a factor of safety of 2.5, determine the minimum allowable diameter of the shaft at “C” based
on a static yield analysis using the distortion energy (DE) theory.
c) If the shaft with a diameter (d) of 32 mm is made of a brittle material with Suc = 420 MPa and
Sut=360 MPa, determine the factor of safety of the shaft at “C” based on a static analysis using the
Brittle-Coulomb-Mohr (BCM) theory.
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