Dynamic analysis and optimal design of lathe spindles using finite element method

Reddy, Velagala Ramakanta (1984) Dynamic analysis and optimal design of lathe spindles using finite element method. Masters thesis, Memorial University of Newfoundland.

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Abstract

This thesis presents the free vibration response, transient response and optimal design of a lathe under transient conditions. The optimal design is based on minimizing the maximum dynamic displacement response of the system. -- The differential equation of motion characterizing the behaviour of a lathe spindle-workpiece system is formulated based on the Euler-Bernoulli's equation. The matrix differential equation of motion is obtained using finite element technique. The boundary condition at the live center is taken as hinged connection. In order to economize on CPU time and memory, the system matrices are condensed by using the dynamic condensation technique. -- The free vibration response of the system is studied by varying parameters such as the bearing spacing, the bearing stiffness etc. The effects of these variations on the static deflection, the natural frequencies and the rate of decay of free oscillations of the system are analyzed. The condensation of the system matrices is done by selecting the appropriate number of masters by comparing the natural frequencies of the condensed and uncondensed systems. The free vibration response of the system is studied by assuming the initial velocity vector to be equal to zero. -- A method comprising of the finite element technique and modal analysis is used for studying the system behaviour under transient cutting conditions. The response of the system due to an impulse and exponentially decaying pulse excitations is obtained. The effect of the variations of system design variables on the maximum dynamic displacement response is presented. Based on these variations the optimal values of the variables are obtained. -- An optimal design of the lithe spindle-workpiece system using a nonlinear programming technique with bearing spacing, bearing stiffness and location of an external damper is obtained. The minimization of the maximum dynamic displacement response of the system is chosen as the objective for this optimization scheme. The optimal values of the design variables obtained by single parameter optimization are then compared with those obtained by multi-parameter optimization.

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