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Homework10bsol.spring2011

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

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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 2 2 1 2 ( a m a m ) ( a m a m ) 4 ( a a a a ) m m 1 1 , ω ω 2 + ± + = (1) From the symmetry of the loading, the influence coefficients 5 11 22 a a 12.600 x10 cm/N = = (2) From Maxwell's reciprocity theorem, the influence coefficients 5 21 12 a a 9.250 x10 cm/N = = (3) The mass of the flywheels are 2 1 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 2 2 1 2 1 1 , a m a m ω ω = ± (5) Equation (5) can be written as 2 2 1 2 11 21 1 ω , ω a m a m = ± (6) Substituting the numerical values into Equation (6), the exact solutions can be written as 5 2 2 2 1 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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Homework10bsol.spring2011 - ME 352 Machine Design I Spring...

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