Stability for multiple delays machining system with variable pitch tools considering nonlinear cutting force coefficients

• Published in: International journal of advanced manufacturing technology Vol. 130; no. 7-8; pp. 3905 - 3916
• Main Authors: Nie, Wanying, He, Chunsheng, Zheng, Minli
• Format: Journal Article
• Language: English
• Published: London Springer London 01.02.2024; Springer Nature B.V
• Subjects: Aluminum base alloys; CAE) and Design; Coefficients; Computer-Aided Engineering (CAD; Cutting force; Cutting parameters; Differential equations; Dimensional stability; Dynamic models; Dynamic stability; Dynamical systems; Eigenvalues; Engineering; Industrial and Production Engineering; Low speed; Mechanical Engineering; Media Management; Milling (machining); Nonlinear dynamics; Original Article; Size effects; Stability analysis; Stability lobes; Vibration control; Vibration response; Workpieces; Variable pitch tool; Multiple delays; Full discrete method; Cutting force coefficients; Cutting stability
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-024-12977-2

    Different pitch parameters of the tool can lead to the changes in the delay of the machining system. A mechanical model of the variable pitch tool is developed by taking the regenerative chatter into account in the machining system with multiple delays. The dynamic differential equations with multiple delays are studied based on the fully discrete method; the Gaussian integral method is used to approximate the state item of the vibration response in the discrete interval, and the periodic and the delay items are linearly approximated to determine the transition matrix of the discrete state in the multiple delays period. The relationship between cutting force coefficients and cutting parameters is defined based on the size effect of the tool-workpiece contact area; a nonlinear model of the cutting force coefficients is presented by the cutting force detection experiment of aluminum alloy milling with the variable pitch tool. The state transition matrix of the multiple delays system is obtained by combining the Gauss full discrete method with the nonlinear cutting force coefficients, and then the effectiveness of the proposed method is verified by analyzing the convergence degree of the eigenvalue of state transition matrix. At the same time, the relationship between cutting parameters and the stability critical of the machining system is analyzed to draw the three-dimensional stability lobe diagram, which makes it clear that the limiting cutting depth of the tool increases about 2–3 times as the cutting width decreases. Combining with a cutting stability experiment of the variable pitch tool, it is verified that the dynamic model with the nonlinear dynamic parameters has higher prediction accuracy of the cutting stability than others. And it is observed that the eigenvalue of changes of the dynamic model is more violently in the low speed region (2000–4000 rpm), which indicates that the stability of the processing system is more sensitive to the cutting depth under the low speed condition, and the vibration reduction performance of variable pitch tools is more significant.