Chatter stability prediction of milling considering nonlinearities

Nonlinearities have been evidenced during the chatter vibration of milling. Machinability of the thin-walled part is feed rate and position-dependent, and is subject to process damping at low cutting speed. Therefore, chatter stability prediction of milling considering nonlinear cutting force, nonlinear structural stiffness and process damping is investigated. The cutting force and stiffness are established based on the polynomial model and the process damping is investigated based on the dissipated energy. The dynamic cutting force and stability lobes are solved in the time domain with coefficients updated at each iteration. By formulating the displacement as an expanded form via the perturbation method, the time-consuming solution of delay differential equations is avoided. After formulating the identification of the nonlinear model via cutting tests and modal tests, numerical simulations considering nonlinearities are carried out and compared with the analytical method. The proposed method attains high accuracy of classic time-domain solution, but with an improved computational efficiency. Finally, cutting tests are conducted to verify the prediction of cutting force and stability lobes.

Chatter Stability Prediction of Cutting Process With Process Damping Utilizing Finite Element Analysis

This paper presents a new approach to predict chatter stability in cutting considering process damping. Traditional chatter stability analysis methods enable to predict stable or unstable conditions. Under unstable conditions, the chatter vibration can increase theoretically infinitely. However, chatter vibration is damped at a certain amplitude in real process due to process damping, i.e., the cutting process is stabilized by means of tool flank face contact to the machined surface. In order to consider the influence of the process damping, a simple process damping force model is introduced. The process damping force is assumed to be proportional to the structural displacement. The process damping coefficient is a function of the vibration amplitude and the wavelength. In order to identify the coefficients, a series of finite element analysis is conducted in the present study. Identified coefficients are introduced into the conventional zero-order-solution in frequency domain. The proposed model calculates chatter stability limit assuming process damping with finite amplitude. Hence, this analysis enables to estimate the amplitude-dependent quasi-stable conditions. Analytical results for thee face turning operation demonstrated influence of process damping effect on resultant vibration amplitude quantitatively.