Solution and Analysis of Chatter Stability for End Milling in the Time-domain

In this paper, the instantaneous undeformed chip thickness is modeled to include the dynamic modulation caused by the tool vibration while the dynamic regenerative effects are taken into account. The numerical method is used to solve the differential equations goveming the dynamics of the milling system. Several chatter detection criteria are applied synthetically to the simulated signals and the stability diagram is obtained in time-domain. The simulation results in time-domain show a good agreement with the analytical prediction, which is validated by the cutting experiments. By simulating the chatter stability lobes in the time-domain and analyzing the influences of different spindle speeds on the vibration amplitudes of the tool under a Fixed chip-load condition, conclusions could be drawn as follows： In rough milling, higher machining efficiency can be achieved by selecting a spindle speed corresponding to the axial depth of cut in accordance with the simulated chatter stability lobes, and in Fmish milling, lower surface roughness can be achieved by selecting a spindle speed well beyond the resonant frequency of machining system.

Prediction of Dynamic Cutting Force and Regenerative Chatter Stability in Inserted Cutters Milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.

Modelling and simulation of high-speed milling chatter regeneration based on MATLAB

Considering the deficiency in milling process parameters selection, based on the modelling of dynamic milling force and the deduction of chatter stability limits, the chatter stability lobes simulation program for milling is developed with MAT- LAB. The simulation optimization application software of dynamics was designed using engineering simulation software Visio Basic. The chatter stability lobes for milling, which can be used as an instruction guide for the selection of process parameters, are simulated with frequency response functions （FRFs） gained by hammer test. The validation and accuracy of the simulation algorithm are verified by experiments. The simulation method has been used in a factory with an excellent application effect.

Stability analysis of a thin-walled cylinder in turning operation using the semi-discretization method

In this work, the stability of a flexible thin cylindrical workpiece in turning is analyzed. A process model is derived based on a finite element representation of the workpiece flexibility and a nonlinear cutting force law. Repeated cutting of the same surface due to overlapping cuts is modeled with the help of a time delay. The stability of the so obtained system of periodic delay differential equations is then determined using an approximation as a time-discrete system and Floquet theory. The time-discrete system is obtained using the semi-discretization method. The method is implemented to analyze the stability of two different workpiece models of different thicknesses for different tool positions with respect to the jaw end. It is shown that the stability chart depends on the tool position as well as on the thickness.

Efficient and Stable Optimization of Multi‑pass End Milling Using a Cloud Drop‑Enabled Particle Swarm Optimization Algorithm

Optimization of machining parameters is of great importance for multi-pass end milling because machining parameters adversely or positively affect the time and quality of production.This paper develops a second-order fulldiscretization method(2ndFDM)-based 3-D stability prediction model for simultaneous optimization of spindle speed,axial cutting depth and radial cutting depth.The optimal machining parameters in each pass are obtained to achieve the minimum production time comprehensive considering constraints of 3-D stability,machine tool performance,tool life and machining requirements.A cloud drop-enabled particle swarm optimization(CDPSO)algorithm is proposed to solve the developed machining parameter optimization,and 13 benchmark problems are used to evaluate CDPSO algorithm.Numerical results show that CDPSO algorithm has a certain advantage in computational cost as well as comparable search quality and robustness.A demonstrative example is provided.