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Unformatted text preview: 5- 80Problems and Solution Section 5.7 (5.74 through 5.80) 5.74A 100-kg compressor rotor has a shaft stiffness of 1.4 ×107N/m. The compressor is designed to operate at a speed of 6000 rpm. The internal damping of the rotor shaft system is measured to be ζ= 0.01. (a) If the rotor has an eccentric radius of 1 cm, what is the rotor system's critical speed? (b) Calculate the whirl amplitude at critical speed. Compare your results to those of Example 5.7.1. Solution:(a) The critical speed is the rotor's natural frequency, so !c=km=1.4"107100=374.2 rad/s =3573 rpm(b) At critical speed, r= 1, so from Equation (5.81), X=!2"=0.012 0.01( )=0.5 mSo a system with higher eccentricity and lower damping has a greater whirl amplitude (see Example 5.7.1). 5.75Redesign the rotor system of Problem 5.74 such that the whirl amplitude at critical speed is less than 1 cm by changing the mass of the rotor....
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- Fall '09