Effect of machining parameters on the stability of separated and unseparated ultrasonic vibration of feed direction assisted milling

A dynamic model is established to study the effect of ultrasonic amplitude, ultrasonic frequency, feed per tooth, and spindle speed trends on separated and unseparated feed ultrasonic milling. This model applied both theory and method, such as linear theory of nonlinear periodic function, as well as the trajectory and full-discretization methods. First, the characteristic of cutter tooth trajectory is articulated, and the differences in the instantaneous chip thickness are analyzed for two types of milling systems. Second, a judging function is proposed, and the model of instantaneous chip thickness is constructed. Third, the time delay differential equations of separated and unseparated feed ultrasonic milling systems are uniformly established using linear theory of nonlinear periodic function. Finally, the time delay differential equations are solved by the full-discretization method. Stability prediction lobe diagrams of the two kinds of feed ultrasonic milling systems are drawn by MATLAB7.1 software. Experimental results indicate that the influence of the processing parameters on the system stability is more sensitive for the separated system than that of the unseparated system. The effect of feed per tooth on stability of two types of systems is the most significant. At approximately 5000 rpm, the feed ultrasonic milling system appears to have a bifurcation flip, which causes a sharp decline in the stability. Therefore, the two types of systems are unsuitable for machining under high speeds. Experimental results confirm the correct effect of these parameter trends on the stability of lobe diagrams.