Explanation Write the expression for maximum interference pressure. p max = E δ max 2 R 3 [ ( r o 2 − R 2 ) ( R 2 − r i 2 ) r o 2 − r i 2 ] (I) Here, the maximum interference pressure is p max , the modulus of elasticity is E , maximum radial interference is δ max , outer diameter is r o , inside diameter is r i and nominal diameter is R . Write the expression for maximum radial interference. δ max = 1 2 ( d max − D min ) (II) Here, the maximum radial interference is δ max , the shaft maximum diameter is d max and the hole minimum diameter is D min . Calculate the tangential stress. ( σ t ) = p max ( r o 2 + R 2 ) ( r o 2 − R 2 ) (III) Here, the tangential stress is σ t . Calculate radial stress. σ r = − p max (IV) Here, the radial stress is σ r . Calculate principal stresses. σ ′ = ( σ t 2 + σ r 2 − σ t σ r ) (V) Here, the principle stress is σ ′ , the tangential stress is σ t and radial stress is σ r . Calculate the minimum factor of safety. n = S y σ ′ (VI) Here, the factor of safety is n , the shear stress is S y . Conclusion: Refer to Table A-5 “Physical Constants of Materials”; obtain the properties of modulus of elasticity for carbon steel as ( 207 ) GPa . Substitute 50.059 mm for d max and 50 mm for D min in Equation (II). δ max = 1 2 ( ( 50.059 mm ) − ( 50 mm ) ) = ( 0.059 mm ) 2 = 0.0295 mm Substitute ( 207 ) GPa for E , 0 mm for r i , 25 mm for R , 50 mm for r o and 0.0295 mm for δ max Equation (I). p max = ( ( 207 ) GPa ) ( 0

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

10th Edition

ISBN: 9780073398204

Author: Richard G Budynas, Keith J Nisbett

Publisher: McGraw-Hill Education

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Design of Shafts and Shaft Components

The shaft is basically defined as the machine element that rotates, is in circular cross-section, it is majorly used to transfer the power from one part of the system to another, or from a power generating machine to a power absorbing machine. The shaft …

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Chapter 5, Problem 78P

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The minimum factor of safety for the outer cylinder based on the distortion-energy theory.

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Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

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The minimum factor of safety for the outer cylinder based on the distortion-energy theory.

Solution Summary: The author explains the minimum factor of safety for the outer cylinder based on the distortion-energy theory. Write the expression for maximum interference pressure.

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The minimum factor of safety for the outer cylinder based on the distortion-energy theory.

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Chapter 5 Solutions