Homework10bsol.spring2011

Homework10bsol.spring2011 - ME 352 - Machine Design I...

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ME 352 - Machine Design I Name of Student ______________________________ Spring Semester 2011 Lab Section Number ___________________________ Homework No. 10 (30 points). Due at the beginning of lecture on Monday, April 11th. Problem 1. Solve Problem 15.26, see page 746. Problem 2. Solve Problem 15.28, see page 747.
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2 Solution to Problem 15.26. (i) Determine the first and second critical speeds of the shaft using the exact solution. The exact solutions for the first and second critical speeds of the shaft can be written as 2 11 1 22 2 11 1 22 2 11 22 12 21 1 2 22 12 (a m a m ) 4(a a a a )m m 11 , ωω 2 + = (1) From the symmetry of the loading, the influence coefficients 5 11 22 aa1 2 . 6 0 0 x 1 0c m / N == (2) From Maxwell's reciprocity theorem, the influence coefficients 5 21 12 a a 9.250 x 10 cm/N (3) The mass of the flywheels are 2 300 m m m 0.3058 N.s /cm 981 === = (4) Substituting Equations (2), (3), and (4) into Equation (1), the exact solutions can be written as 11 21 ,a m a m (5) Equation (5) can be written as 11 21 1 ω , ω amam = ± (6) Substituting the numerical values into Equation (6), the exact solutions can be written as 5 2 10 ω , ω (rad / sec) 0.3058 (12.600 9.250) = ×± (7) Using the positive sign in the denominator of Eq. (7), the first critical speed of the shaft can be obtained
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This note was uploaded on 04/23/2011 for the course ME 352 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Homework10bsol.spring2011 - ME 352 - Machine Design I...

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