• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.1
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• pp.40-46
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• 2011

This paper is to investigate the effects of the asymmetrical support stiffness on the stability of a supercritical driveshaft with asymmetrical shaft stiffness and anisotropic bearings. The equations of motion is derived for a system including a rigid disk, a massless flexible asymmetric shaft, anisotropic bearings and a support beam. The Floquet theory is applied to perform the stability analysis with the variation of the support stiffness, the shaft asymmetry, the shaft damping and the shaft speed. The results show that the asymmetric support stiffness is closely related to the stability caused by primary resonance as well as the supercritical operation. First, the stiffness variation can stabilize the system around primary resonance by weakening the parametric resonance from the shaft asymmetry. Second, it also improve the stability characteristics at a supercritical operation when the support stiffness is not so high relative to the shaft stiffness.

• Journal of KSNVE
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• v.10 no.2
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• pp.291-298
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• 2000

This paper intends to provide an analytic vibrational model of non-circular cutting by a lathe and to investigate its stability criteria. A single degree-of-freedon model based on the orthogonal cutting theory has the characteristics of parametric excitation due to the nonlinear cutting force that changes periodically its direction as well as its magnitude. The Floquet theory has been applied to investigate the stability of the linearized system and the stability diagrams have been obtained with respect to the ovality, the cut velocity and the cut depth. Also nonlinear analysis has been performed to verify the linear analysis and compare the results with those from circular cutting. Results show that a critical cut depth is decreased as the ovality is increased while a critical cut velocity is increased as the ovality is increased. Also, a good agreement in critical conditions has been observed between the linear and nonlinear analyses for the ovality less than 2%. Accordingly, the linear analysis can be said to be applicable for most practical oval cuttings whose ovality are much less than 2%.