Dynamics of a Rotating Shaft Subject to Moving Loads, and Its Possible Application in Machining.

Abstract

The dynamic behavior of a rotating shaft subject to axially moving loads, and its possible application in machining is studied in four independent but closely related studies. The first study treats the dynamic response of a rotating, simply-supported shaft, subject to a moving load. This shaft is modeled by Euler-Bernoulli, Rayleigh and Timoshenko beam theories. Modal Analysis and Integral-Tranformation solution methods are applied. The chapter includes a parametric study which yields recommendations for proper modeling of the shaft for various ranges of parameters. The second study advances two methods for solving the dynamic reponse of a rotating, uniform shaft with various boundary conditions subject to arbitrary loads. Modal analysis gives accurate numerical results and a good physical insight into this problem; Galerkin's method is easy to implement and gives an excellent approximation to the exact solution. An illustrative example treats the axially moving load case using both methods. For third study introduces a dynamic cutting force model for a slender workpiece in a turning operation. The workpiece is modeled as a distributed parameter system. Using this model results in a new dynamic problem of a beam subject to a deflection-dependent moving load. Galerkin's method is used to reduce the partial differential equations of the beams motion to a coupled set of ordinary differential equations with periodic coefficients. The determination of the instability regions of this system and its forced response are presented and discussed. In the last study, the proposed dynamic cutting force model is studied both analytically and experimentally for a stable (chatter free) turning process. In the experimental study, where the natural frequencies of the workpiece with and without cutting were measured; the results are found to be in good agreement with a unidirectional model over a reasonable range of damping coefficients. The experimental procedure is advanced as a means of estimating the overall damping coefficient associated with turning operations.