03-03ChapGere.0009 - K.E . 5 (length)(force) S TRAIN ENERGY...

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Problem 3.9-11 A heavy flywheel rotating at n revolutions per minute is rigidly attached to the end of a shaft of diameter d (see figure). If the bearing at A suddenly freezes, what will be the maximum angle of twist f of the shaft? What is the corresponding maximum shear stress in the shaft? (Let L 5 length of the shaft, G 5 shear modulus of elasticity, and I m 5 mass moment of inertia of the flywheel about the axis of the shaft. Also, disregard friction in the bearings at B and C and disregard the mass of the shaft.) Hint: Equate the kinetic energy of the rotating flywheel to the strain energy of the shaft. Solution 3.9-11 Rotating flywheel 244 CHAPTER 3 Torsion n (rpm) C B d A d 5 diameter n 5 rpm K INETIC ENERGY OF FLYWHEEL n 5 rpm U NITS : I m 5 (force)(length)(second) 2 v 5 radians per second
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Unformatted text preview: K.E . 5 (length)(force) S TRAIN ENERGY OF SHAFT ( FROM E Q . 3-51b) I P 5 p 32 d 4 U 5 GI P f 2 2 L 5 p 2 n 2 I m 1800 K.E. 5 1 2 I m 2 p n 60 2 v 5 2 p n 60 K.E. 5 1 2 I m v 2 d 5 diameter of shaft U NITS : G 5 (force)/(length) 2 I P 5 (length) 4 f 5 radians L 5 length U 5 (length)(force) E QUATE KINETIC ENERGY AND STRAIN ENERGY Solve for f : M AXIMUM SHEAR STRESS Eliminate T : t max 5 n 15 d B 2 p GI m L t max 5 Gd 2 L ? 2 n 15 d 2 B 2 p I m L G t 5 Gd f 2 L t 5 T ( d / 2) I P f 5 TL GI P f 5 2 n 15 d 2 B 2 p I m L G K.E. 5 U p 2 n 2 I m 1800 5 p Gd 4 f 2 64 L U 5 p Gd 4 f 2 64 L Shaft Flywheel A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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