The figure shows a proposed design for the industrial roll shaft of Prob. 7–4. Hydrodynamic film bearings are to be used. All surfaces are machined except the journals, which are ground and polished. The material is 1035 HR steel. Perform a design assessment. Is the design satisfactory?
Problem 7–6
Bearing shoulder fillets 0.030 in, others
Weather the design is satisfactory or not.
Answer to Problem 6P
The design is satisfactory for crown gear.
Explanation of Solution
Write the expression for force acting on roller.
Here, normal force is
Write the expression for force acting on C along z axis.
Here, force on C in z axis is
Write the expression for torque.
Here, torque is
Write the expression for force at B along z axis.
Here, force at B along z axis is
Write the expression for force at B along y-axis
Here, force at B along y-axis is
Write the expression for moment about O.
Write the expression for moment about A.
Write the expression for moment at point C.
Write the expression for moment at A.
Write the expression for moment about O.
Write the expression for moment about A.
Write the expression for moment at point C along z-axis.
Write the expression for moment at A along z-axis.
Write the expression for total moment.
Here, bending moment in x-y plane is
Write the expression for total moment at D.
Here, moment on x-y plane at D is
Write the moment equation in x-y plane.
Integrate Equation (XVI).
Integrate Equation (XVII).
Apply boundary Equation, substitute
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Write the moment equation in x-z plane.
Integrate Equation (XVIII).
Integrate Equation (XIX).
Substitute
Substitute
Substitute
Substitute
Write the expression for flexural rigidity.
Here, flexural rigidity is
Write the expression for deflection at A.
Here, speed is
Write the expression for relative deflection.
Here, force is
Write the expression for deflection at B.
Write the expression for deflection at z.
Here, deflection at A is
Write the expression for relative deflection.
Here, force is
Write the expression for deflection at B.
Here, deflection at B is
Write the expression for gear mesh.
Here, gear mesh at B is
Write the expression for concentration factor for bending.
Here, concentration factor for bending is
Write the expression for concentration factor torsion.
Here, concentration factor for torsion is
Write the expression for endurance limit.
Here, endurance limit is
Write the expression for surface factor.
Here, surface factor is
Write the expression for size factor.
Here, size factor is
Write the expression for endurance limit at critical path.
Here, surface modification factor is
Conclusion:
The following figure shows roller forces.
Figure-(1)
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The figure below shows the free body diagram and bending moment diagram.
Figure-(2)
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The figure below shows the bending moment diagram for x-y plane.
Figure-(3)
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The figure below shows free body diagram and the bending moment diagram in x-z plane.
Figure-(4)
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The figure below shows the bending moment diagram.
Figure-(5)
The figure below shows the forces in x-z plane.
Figure-(6)
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The figure below shows the bending moment diagram.
Figure-(7)
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Calculate factor of safety.
The figure below shows forces in x-y plane.
Figure-(8)
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The figure below shows the forces on the system.
Figure-(9)
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Refer to table A-20, “Deterministic ASTM minimum tensile and yield strength for some hot rolled and cold drawn steels” to obtain tensile strength as
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Refer to table 7-1, “First iteration estimated for stress concentration factors” to obtain concentration factor for bending stress as
Refer to figure6-20, to obtain notch sensitivity as
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Refer to table 6-2, “Parameters for main surface condition factor” to obtain
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Refer to table 7-1, “First iteration estimated for stress concentration factors” to obtain concentration factor for bending stress as
Refer to figure6-20, to obtain notch sensitivity as
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Refer to table 6-2, “Parameters for main surface condition factor” to obtain
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The factor of safety is acceptable for crowned gear.
Thus, crowned gear is more reliable.
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Chapter 7 Solutions
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