Size dependent vibration analysis of micro-milling operations with process damping and structural nonlinearities

Abstract

Micro-milling is one of the micro-manufacturing techniques used for creating micro-scale features. In this article, a size-dependent formulation based on the strain gradient elasticity theory is developed to analyze the micro milling tool vibration. A new cutting forces formulation in rotating frame is presented in this paper. Considering structural nonlinearities, gyroscopic moment, rotary inertia, process damping and size effect, nonlinear equations of tool motion are derived using non-classical Timoshenko beam theory and Hamilton's principal. Partial differential governing equations of the tool are converted to ordinkary differential equations by using assumed modes method. Then the method of multiple scales is used to obtain the analytical solution for tool vibrations. The proposed approach is applied to investigate the chatter instability observed in micro-milling operations. To verify the presented model, simulated stability lobe diagrams are compared with the results obtained from experimental tests and literature. According to the results, neglecting size effect, gyroscopic and rotary terms in the tool model causes significant errors in prediction of the chatter in micro-milling process.