Study on frequency response and bifurcation analyses under primary resonance conditions of micro-milling operations

Avoidance of resonance in fluctuation of milling tool is vital for reaching excellence quality and performance of the cutting operation. The cutting tool in resonance condition vibrates with considerable magnitude that causes to increase milling tool wear and manufacturing prices. Analytical study of primary resonances and bifurcation behavior of a micro-milling process, including structural nonlinearities, gyroscopic moment, rotary inertia, velocity-dependent process damping, static and dynamic chip thickness, is chief aim of this article. The milling tool is modeled as a 3-D spinning cantilever beam that is motivated by cutting forces. To get the analytical solution for frequency response function and bifurcation behavior of the system under primary resonances, the method of multiple scales is operated on converted ordinary differential equations that are obtained by applying assumed modes method on nonlinear partial differential equations of tool vibration. The effects of different process parameters and nonlinear terms on the frequency response of the tool tip oscillations are examined. In addition, the effects of detuning parameter and damping ratio on the bifurcation and behavior of the limit cycle under primary resonances are examined. The results shows that these parameters are the bifurcation parameters and Neimark, symmetry breaking, flip, and period-3 bifurcations occur when the detuning parameter is varied. (C) 2020 Elsevier Inc. All rights reserved.