Bifurcation and chaos analysis of mold splicing zone vibration under thermal-mechanical coupling

To improve the machining quality of the splicing area of the hardened steel mold, this paper proposes a bifurcation and chaos analysis method for the milling vibration of the splicing area of the mold under the coupled thermal-mechanical effect. First, based on the instantaneous milling force model at the splice, the milling dynamics equations of a two-degree-of-freedom rectangular spliced mold part are established. By applying the Galerkin method, the resulting nonlinear partial differential equation is reduced to a single-degree-of-freedom nonlinear system. Meanwhile, by using the Melnikov function method, the criteria for chaos motion are obtained by the Smale horseshoe mapping. Then, the fourth-order Runge-Kutta algorithm is applied to solve the bifurcation diagram, largest Lyapunov exponent diagram, displacement waveform diagram, and phase plane diagram of the nonlinear dynamic system in the mold splicing area. Subsequently, the influence of spindle speed and cutting depth on the nonlinear vibration system in the mold splice area is quantitatively analyzed. Finally, the effect of spindle speed and cutting depth on the vibration system of the workpiece is investigated through experiments. The obtained results indicate that the milling vibration amplitude in the rectangular splicing mold area can be controlled more easily and effectively by changing the cutting depth than by changing the spindle speed.