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Method for forecasting milling stability based on Legendre polynomial expansion

A stability prediction and polynomial technology, which is applied in prediction, instruments, manufacturing computing systems, etc., can solve the problem that the accuracy of calculation methods has not been improved.

Inactive Publication Date: 2015-06-03
BEIJING INSTITUTE OF TECHNOLOGYGY
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Problems solved by technology

[0003]"A full-discretization method for prediction of milling stability" on Volume 50 of "International Journal of Machine Tools and Manufacture" published by International Publishing Group ELSEVIER, 2010 This article discloses a milling chatter stability prediction method based on the full discrete method. Compared with previous methods, this method has improved computational efficiency, but the accuracy of the computational method has not been improved. The computational efficiency and Accuracy can be improved

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  • Method for forecasting milling stability based on Legendre polynomial expansion
  • Method for forecasting milling stability based on Legendre polynomial expansion
  • Method for forecasting milling stability based on Legendre polynomial expansion

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Embodiment Construction

[0128] The present invention comprises the following steps:

[0129] ① Establish the dynamic equation of the milling cutter in the single-degree-of-freedom milling process:

[0130] (1)

[0131] in, is a constant coefficient matrix, is the coefficient matrix that changes with time period, Indicates that the tool is momentary status response, Indicates the natural frequency of the tip point, represents the relative damping, represents the modal mass, is the axial depth of cut, Indicates time lag;

[0132] Indicates the instantaneous chip thickness, and its expression is:

[0133] (2) In formula (2), Indicates the number of teeth of the milling cutter, with are the cutting force coefficients in the tangential and normal directions, respectively, for the first The angular displacement of the cutter tooth, the expression is , the window function The definition formula is:

[0134] (3)

[0135] In formula (3), with respectively The e...

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Abstract

The invention relates to the advanced manufacturing field, particularly to a method for forecasting milling stability based on Legendre polynomial expansion. According to the method, the Legendre polynomial expansion is adopted to approximate a state item, a time-lag term and a periodic coefficient item in a kinetic equation, and a plurality of known time points and responses thereof are used for fitting the items required, so that the partial error of the calculation method is reduced, thus the precision of the forecast method is improved. Meanwhile, in the process of obtaining a stable lobe graph, an H matrix is introduced rather than being directly put into an F matrix to calculate, so that iterative times in the calculation process of the F matrix are reduced, thus the time of the calculation method is saved, and the calculation efficiency is improved.

Description

technical field [0001] The invention relates to the field of advanced manufacturing, in particular to a milling stability prediction method based on Legendre polynomials. Background technique [0002] As the manufacturing industry accounts for an increasing proportion of my country's national economy, the requirements for the level of mechanical processing are also getting higher and higher. High-speed cutting technology emerged as the times require, and has been widely used in the manufacture of complex parts in aviation, aerospace, ships and other fields. The chatter in the milling process seriously affects the surface quality of the workpiece and may cause damage to the machine tool. Predicting the chatter stability in the milling process and selecting appropriate processing conditions can control the occurrence of chatter, improve processing efficiency, and reduce processing costs. The accuracy and computational efficiency of stability prediction methods are of great si...

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Application Information

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IPC IPC(8): G06Q10/04G06Q50/04
CPCY02P90/30
Inventor 刘志兵闫正虎王西彬吕维维刘彪赵倩王东前
Owner BEIJING INSTITUTE OF TECHNOLOGYGY
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