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Solution tutorial 10_2011

# Solution tutorial 10_2011 - Solution shaft problem Question...

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Solution – shaft problem Question 1 The tangential force on the gear is 15000*cos(20 0 ) = 14095 N The radial force is 15000*sin(20 0 ) = 5130.3 N The other gear has half the diameter, so the loads are twice (28190 N and 10260.6 N) Summing moments and forces the bearing reactions are as shown below, leading to the bending diagrams for each plane below. xy plane zx plane The worst bending moment is the vector sum at the right-hand gear giving 4718.6 Nm. The torque = tangential force by pitch radius = 14095 x 0.375 = 5285.6 Nm 3979.8Nm 2535.0 Nm 2082.3 Nm 28190 N 5130.3 N 10260.6 N 6941 N 8449.9 N 829.1 N 14095 N 13265.88 N 248.7 Nm

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Maximum bending stress = 32 x 4718.6/( π x 0.075 3 ) = 113.9 MPa Maximum torsional shear stress = 16 x 5285.6/( π x 0.075 3 ) = 63.81 MPa Von Mises stress (max. distortion energy measure) = (113.9 2 + 3 x 63.81 2 ) = 158.7 MPa Consider the xy plane, I = π x 75 4 /64 = 1.553E6 mm 4 , EI = 3.106E11 N mm 2 300 mm 250 mm 300 mm x 2082.3 Nm 2535.0 Nm Regarding the bending moment diagram as 4 triangles,
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Solution tutorial 10_2011 - Solution shaft problem Question...

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