This is an investigation into the effect of spatially nonuniform temperature fields on the undamped, free vibration characteristics of the wire electrode in the wire electro-discharge machining (EDM) process. In particular, a nonlinear multi-mode structural model is developed for the translating wire along with a thermal model which accounts for heat input (from sparking), axial conduction, radial convection, and energy storage. The two models are then coupled through the internal thermal stress terms of the structural model.
Using these combined models, an eigenvalue analysis is performed to examine the behavior of the natural frequencies (Im(λ)) as a function of the transport speed. It is shown that both divergence and Hopf bifurcations occur in this system. Specifically, the system is unstable at low transport speeds due to thermal buckling, stable at intermediate speeds, and unstable at high speeds due to a series of transport instabilities. Furthermore, it is shown that the frequency loci for a given mode decreases as the input discharge energy and, hence, the mean wire temperature are increased. This lowers the critical transport speed associated with the transport instability.