Chatter Stability Prediction Method of the Spindle-Tool Holder-Tool System with Interface Contact Characteristics

To predict chatter stability and suppress chatter vibration, a chatter stability prediction method for the spindle-tool holder-tool system with interface contact characteristics is constructed. A five-DOF model is constructed to determine the spindle-bearing interface dynamic contact stiffness considering the coupling effect of spindle and bearing. A fractal multiscale tool holder-spindle interface dynamic stiffness model is proposed considering time-varying cutting force. The fractal dimensions and cutting force coefficient parameters are identified from the power spectrum experiments and cutting force tests. The cutting force is solved according to the milling stability model. Dynamic model of the spindle-tool holder-tool system is found by the finite element method. Based on extended Floquet theory, chatter stability of the spindle system is studied. Effect of interface parameters, radial cutting depth, and feed rate on milling stability is researched. Milling force tests and milling stability tests are performed in order to verify the reliability of the method. Results find that the increase of front bearing preload and spindle-tool holder’s interference fit are effective to improve the milling stability. The optimal feed rate and the critical radial cutting depth are found. The model proposed in this paper can be used as an instruction for predicting and suppressing the chatter vibration and optimizing cutting parameters and also is helpful for designing the spindle-tool holder-tool system.

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.

Robust Chatter Stability Prediction of the Milling Process considering Uncertain Machining Positions

Milling stability is a function of the tool point frequency response functions (FRFs), which vary with the movements of the moving parts within the whole machine tool work volume. The position-dependent tool point FRFs result in uncertain prediction of the stability lobe diagram (SLD) for chatter-free machining parameter selection. Taking the variations of modal parameters to represent the variations of tool point FRFs, this paper introduces the edge theorem to predict the robust milling chatter stability. The application of the edge theorem requires the minimum and maximum modal parameters within the machining space defined by the machining position and machining allowance information. Then, radial basis function artificial neural networks (RBFANNs) are used to predict the position-dependent modal parameters in X and Y directions based on the sample information of machining positions and related modal parameters at the tool point. Moreover, sample machining spaces are determined based on the aforementioned sample positions, and the trained RBFANNs are used to obtain corresponding sample extreme modal parameters. On this basis, RBFANNs for predicting the position and machining allowance-dependent extreme modal parameters can also be trained, and they are combined with the edge theorem and zero exclusion condition to calculate robust pairs of the spindle speed (n) and limiting axial cutting depth (aplim) and then plot the robust SLD (RSLD). A case study was performed on a real three-axial vertical machining center, and the plotted RSLD considering position variations was compared with the traditional SLD. Results of the chatter tests show that the RSLD can provide more reliable (ap, n) pairs to guarantee the milling stability, validating the feasibility of the proposed robust milling chatter stability prediction method.