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A Milling Stability Prediction Method Based on Orthogonal Polynomials

An orthogonal polynomial, stability prediction technology, applied in special data processing applications, instruments, electrical digital data processing, etc., can solve problems such as low computational efficiency, long time, flutter stability limit, etc.

Inactive Publication Date: 2018-03-09
BEIJING INSTITUTE OF TECHNOLOGYGY
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Problems solved by technology

[0003] The article "Updated semi-discretization method for periodic delay-differential equations with discrete delay" on the volume 61 of the famous international journal "International Journal For Numerical Methods InEngineering" in 2004 discloses a milling chatter stabilization based on semi-discrete method The flutter stability limit can be obtained by using this method, but the disadvantage is that the calculation efficiency of this method is low, and it takes a long time to obtain the stability lobe map, and the calculation accuracy of this algorithm needs to be improved

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

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Embodiment Construction

[0107] The present invention comprises the following steps:

[0108] ①Establish the dynamic equation of milling cutter single degree of freedom milling process:

[0109]

[0110] in, is a constant coefficient matrix, is the coefficient matrix that changes with the time period, x(t) represents the 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;

[0111] h(t) represents the instantaneous chip thickness, which can be expressed as:

[0112]

[0113] In formula (2), N represents the number of teeth of the milling cutter, K t and K n is the tangential and normal cutting force coefficient, φ J (t) is the angular displacement of the Jth tooth, φ J (t)=(2πΩ / 60)t+(J-1)·2π / N, window function g(φ J (t)) is defined as:

[0114]

[0115] In formula (3), φ st and φ ex is the cut-in and cut-out a...

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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 orthogonal polynomials. Know the time point and its response to fit the required items, which reduces the local error of the calculation method, thereby improving the accuracy of the prediction method; at the same time, in the process of obtaining the stability lobe map, the H matrix is ​​introduced instead of directly substituting The F matrix is ​​calculated, which reduces the number of iterations in the F matrix calculation process, 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 method for predicting milling stability based on orthogonal polynomials. Background technique [0002] As our country continues to integrate into the global market, the manufacturing industry is facing more and more competitive pressures, and high-speed cutting technology has emerged as the times require, and has been widely used in the manufacture of complex parts in the fields of aviation, aerospace, ships, molds and automobiles. Cutting Chatter during the process seriously affects the surface quality of workpieces, reduces the service life of machine tools and cutting tools, 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. If the stability prediction is not carried out, many expe...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F19/00
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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