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A Milling Stability Prediction Method Based on Legendre Polynomials

A stability prediction, polynomial technology, used in prediction, instrumentation, manufacturing computing systems, etc., can solve the problem that the accuracy of the calculation method has not been improved

Inactive Publication Date: 2017-09-26
BEIJING INSTITUTE OF TECHNOLOGYGY
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Problems solved by technology

[0003] The article "A full-discretization method for prediction of milling stability" in the "International Journal of Machine Tools and Manufacture" magazine, Volume 50, 2010, published by the international publishing group ELSEVIER, discloses a milling chatter stability prediction based on the full discrete method method, this method has improved the calculation efficiency compared with the previous method, but the accuracy of the calculation method has not been improved, and the calculation efficiency and accuracy of the method can be improved

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  • A Milling Stability Prediction Method Based on Legendre Polynomials
  • A Milling Stability Prediction Method Based on Legendre Polynomials
  • A Milling Stability Prediction Method Based on Legendre Polynomials

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Embodiment Construction

[0127] The present invention comprises the following steps:

[0128] ① Establish the dynamic equation of the milling cutter in the single-degree-of-freedom milling process:

[0129]

[0130] in, is a constant coefficient matrix, is the coefficient matrix that changes with the time period, x(t) represents the state response of the tool at time t, ω n Indicates the natural frequency of the tool tip point, ζ indicates the relative damping, m t Indicates the modal quality, w indicates the axial cutting depth, and τ indicates the time lag;

[0131] h(t) represents the instantaneous chip thickness, and its expression is:

[0132]

[0133] In formula (2), N represents the number of teeth of the milling cutter, K t and K n are the cutting force coefficients in the tangential and normal directions, respectively, φ j (t) is the angular displacement of the jth tooth, the expression is φ j (t)=(2πΩ / 60)t+(j-1).2π / N, window function g(φ j (t)) is defined as:

[0134]

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Abstract

The present invention relates to the field of advanced manufacturing, in particular to a method for predicting milling stability based on Legendre polynomials. A known time point and its response are used to fit the desired term, which reduces the local error of the calculation method and thus improves the accuracy of the prediction method. At the same time, in the process of obtaining the stability lobe diagram, the H matrix is ​​introduced instead of directly substituting into the F matrix for calculation, which reduces the number of iterations in the calculation process of the F matrix, thereby saving the time of the calculation method and improving the calculation efficiency.

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 the fields of aviation, aerospace, ships, etc. Chatter during milling seriously affects the surface quality of workpieces and may cause damage to machine tools. Predicting the chatter stability of 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 significance for d...

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Application Information

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Patent Type & Authority Patents(China)
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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