Chatter in milling is still a main obstacle in surface finish,machining accuracy and tool life.Its prediction and avoidance are challenging subjects in the machining field.In this paper,an improved semi-discretization method is proposed to predict variable spindle speed milling with helix angle.Based on tool geometry and machining theory,the cutting region is divided into five different cases to calculate the cutting force.The influences of radial immersion rate and modulation parameters relative to variable spindle speed milling are explored.By comparison with constant spindle speed,the simulation results show that the variable spindle speed scheme can obtain a larger range of stability.In short,the helix angle and variable spindle speed play an important role in the stability of milling process.
The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.
