The influence of spatially nonuniform temperature fields on the vibration and stability characteristics of EDM wires

This is an investigation into the effect of spatially nonuniform temperature fields on the free vibration and stability 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 equilibrium and eigenvalue analysis is performed to examine the behavior of the small amplitude natural frequencies as a function of the transport speed under normal cutting conditions. It is shown that both divergence and Hopf bifurcations may occur in this system. Specifically, at low transport speeds the straight wire configuration is unstable due to a thermal buckling instability. At intermediate speeds, the straight configuration is restabilized by the reduced residency time of the wire in the kerf. At high speeds the straight configuration is again unstable; this is due to a series of transport instabilities. The influence of the input discharge energy and the applied axial wire tension on the size of the restabilized zone is determined and the implications for cutting accuracy are discussed.