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Interpolation method of spline curve based on chord intercept method

A technology of spline curve interpolation and chord interception, which is applied in the direction of instruments, computer control, simulators, etc., can solve problems such as complex convergence conditions, influence on applications, and large amount of calculation, so as to avoid derivation calculations and achieve high machining accuracy , the effect of small amount of computation

Active Publication Date: 2016-08-17
中国科学院沈阳计算技术研究所有限公司
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Problems solved by technology

However, due to the complex convergence conditions of this method, the application of this method is affected.
The "parameter-arc length" fitting method aims to establish the nonlinear functional relationship between the "parameter-arc length" of the spline curve. However, this method has a large number of integral operations, which is relatively complicated and requires a large amount of calculation. It has great potential in practical engineering applications. certain limitations

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  • Interpolation method of spline curve based on chord intercept method
  • Interpolation method of spline curve based on chord intercept method
  • Interpolation method of spline curve based on chord intercept method

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Embodiment Construction

[0031] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

[0032] The technical scheme adopted in the present invention is:

[0033] The present invention is based on the spline interpolation algorithm of chord intercept method, has the following steps:

[0034] According to the machining accuracy requirements, determine the feed speed during machining;

[0035] Create a construction equation based on the feed rate obtained above, as well as the known spline curve equation and interpolation period, to calculate the interpolation parameters;

[0036] Apply Taylor prediction equation and Adams prediction equation to predict the two initial values ​​of the interpolation parameters; then according to the construction equation and the initial value of the parameters, the interpolation parameters are obtained by the chord-intersection iteration method, and then substituted into the parametric spline equati...

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Abstract

The invention relates to a spline curve interpolation method based on a secant method. The spline curve interpolation method is applied to spline curve interpolation of a numerical control system. The spline curve interpolation method comprises the steps of establishing a structure equation according to the cutter feeding speed during processing, a spline curve equation and an interpolation cycle, and enabling the equation root to be an interpolation parameter; utilizing the structure equation and applying a secant iteration method to solve the interpolation parameter, and predicting an initial value of the interpolation parameter by adopting a Taylor prediction equation and a Bill Adams prediction equation; substituting the solved interpolation parameter into the spline curve equation, and obtaining the actual cutter feeding amount of every movement axis. The method is small in calculation amount, and execution efficiency of a numerical control machine tool is high; limitation of chord height errors is considered, and processing contour precision is guaranteed; the secant method has superlinear convergence, so that when the method is utilized to calculate the interpolation parameter, the convergence rate is high, the calculation amount is small, and the stability is good.

Description

technical field [0001] The invention relates to a spline curve interpolation method for numerical control machining, in particular to a method for calculating interpolation parameters by using a chord cut method according to the spline curve interpolation principle. Background technique [0002] The traditional CNC machining system can only realize circular arc and linear interpolation. When machining complex surface parts, it is necessary to discretize the curve with the help of the CAM offline programming system after CAD modeling to generate a large number of small circular arcs or straight lines. for processing. The problem with this processing method is firstly that the amount of program is large, which increases the communication burden between CAD / CAM and CNC, and at the same time increases the preprocessing workload of CNC; in addition, the small line segment as the tool track destroys the surface smoothness, frequently Acceleration and deceleration are likely to ca...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G05B19/41
Inventor 孙一兰杨东升王允森盖荣丽邵新龙
Owner 中国科学院沈阳计算技术研究所有限公司
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