Abstract
This article focuses on the computing efficiency of the instantaneous cutter position error curve in computer numerical control cutter positioning, which reflects the positional relationship between the cutter and the desired surface and leads to the strip width of current positioning. The directed projection is proposed to measure the distance of a discrete point to the cutter surface. Two models using fitting techniques are established to compute the instantaneous cutter position error curve. The fitting technique used in this article is based on the quartic polynomial model. In addition, to enhance the accuracy in the nonsymmetric case, the nonsymmetric quartic polynomial model is established, and it induces a more adaptable method. Illustrated experiments show good performance of the proposed methods.
Highlights
The optimization of cutter positioning has been a great interest for scientists in computer numerical control (CNC) machining, especially in five-axis machining.[1,2]
In the initial positioning of a cutter in CNC machining, x1 can be determined since it is connected to the given driving point on the desired surface, one could obtain (Xi, Yi)[0] i n by searching from X0 = x1 or Xn = x1
As we can see, when the driving point P is given and the cutter positioning CP is fixed, a determined step leads to a determined estimated strip width according to section ‘‘Calculation of strip width.’’ strip width can be denoted by width(step, P, CP)
Summary
The optimization of cutter positioning has been a great interest for scientists in computer numerical control (CNC) machining, especially in five-axis machining.[1,2] In order to estimate the adjustment, it needs to compute the envelope at current cutter positioning. In the optimization of the cutter positioning, one needs to determine the actual effective cutting area by measuring the relationship between the desired surface and the envelope of the cutter. The above expression of the ICPEC indicates the instantaneous positioning deviation of the cutter from the desired surface, but it is not so evident for computing the cutting strip width. In the initial positioning of a cutter in CNC machining, x1 can be determined since it is connected to the given driving point on the desired surface, one could obtain (Xi, Yi)[0] i n by searching from X0 = x1 or Xn = x1. As we can see, when the driving point P is given and the cutter positioning CP is fixed, a determined step leads to a determined estimated strip width according to section ‘‘Calculation of strip width.’’ strip width can be denoted by width(step, P, CP).
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