Apply a least square method to optimize blade machine program

The athletic function of 1 columnar spiral is well-known, general the athletic function that 3 coordinate CNC Milling has columnar spiral. Graph 2 denotive it is the columnar spiral motion that is bottom plane with Xy. Hypothesis M is the athletic dot of heart of ball of ball head knife, it rises horn to be made in Z axis direction by certain helix on one hand rise (drop) motion; Other side, motion nods the umbriferous contrail on Xy plane to form a circular arc that decides a diameter. The equation expression of Nextpage columnar spiral is: Among them A is circular arc radius, t is circular arc horn (radian is an unit) , k is spiral slope. According to this one principle, can draft dot of countless spaces disperse to synthesize a certain number of the columnar snail line segment that photograph of from beginning to end holds, narrow greatly thereby paragraph of number of CNC Machining program. Specific course of action is the much space that gets interpolation is nodded in order (X1, y1, z1) , (X2, y2, z2) , (X3, y3, z3) , ... , (Xn, yn, zn) undertakes so called " two-way plan to close " . To in an attempt to 2 for exemple, on Xy plane, use a least square method to regard maths as the model, what will plan to add up to dimensional disperse dot to go up in Xy plane with circular arc is umbriferous (X1, y1) , (X2, y2) , (X3, y3) ... , (Xn, yn) dot. Graph 2 columnar spiral reach his to develop a plan 2.

A large number of finer orderly points that the fundamental of 2 least square methods gains contrail of dimensional cutting tool through computational interpolation are listed, get on these dots in Xy plane umbriferous, bit more umbriferous to these, if had used a dot to make round way, criterion although each paragraphs of circular arc is nodded through giving, but in did not give a dot to manage circular arc and disperse site the error is bigger between umbriferous curve. Plan to close these points with the least square method, if the graph is shown 3 times, approximate circular arc does not give a point through every certainly, but approximate circular arc and every the sum of squares of absolutely error is between the dot the smallest. Circular arc and the error that nod academic and exact value each can be used artificially " tolerance " come demarcate. "Tolerance " not be spare parts treatment allow common difference, ask according to spare parts precision however given the curve assumes office of a bit allow computation absolutely error. "Tolerance " smaller, approach precision taller, but approximate circular arc paragraph number is more. Nextpage pursues 3 least square methods plan to add up to circular arc 2.

The coordinate of the centre of a circle that the computational method of 3 least square methods sets approximate circular arc is (A, b) , radius is R, (Xi, yi) assumes office for the curve the coordinate of a bit, can get: If set " tolerance " the value is Ta, all drafting that add up to a dot to all be in of R ± Ta " tolerance " belt inside limits, if the graph is shown 3 times, think circular arc plans to combine a success. While to Xy plane undertakes circular arc plans to close, still must be opposite by equation group formula Z1, z2, z3... Zn undertakes pointwise is checked. The radius that knows to plan to add up to circular arc is A, initiative horn is T1, stop horn to be Tn, start Z value is Z1, terminus is Zn, slope of that end spiral. Know spiral slope K, can be opposite by formula case, the Z value that either drafts to close a point between terminus undertakes checking, if the Z value of these dots all is in of set " tolerance " in Tb limits, think spiral of this paragraph of circular arc drafts synthetic result. Of course, go up to Xz or Yz plane according to needing to also can nod dimensional disperse umbriferous, it is the dimensional spiral of bottom plane in order to generate with Xz or Yz, its principle and methodological ibid. The work out of 3 software 3.

1 flow describes Nextpage to be in software of CNC Machining process designing, by afore-mentioned plan to add up to principle and method, use advanced programming language to design its independence " pretreatment " module, this module uprights at " interpolation is calculated " module and " postposition is handled " between module. "Pretreatment " the flow thick block diagram of module describes as follows: Columnar spiral plans to add up to block diagram 3.

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1 " affirmatory Xy, xz, yz is planar " the end that chooses columnar spiral namely is planar, the coordinate system place of the requirement that it machines by the spare parts and numerical control machine tool decides. For example, the treatment that the graph shows 1 times is the bottom plane that plans to add up to columnar spiral with respect to choice Yz. 3.

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2 " tolerance " Ta and Tb value but according to the treatment of the spare parts precision asks to part set, size can differ. Generally speaking, "Tolerance " the value is less than the tolerancepublic errand value of the spare parts much. 3.

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3 " occupy array A from Sf file reading " , the initial phase that close drafts in first paragraphs of spiral, must read in the ability after data of 3 groups of coordinate to undertake first in array A the following " two-way plan to close " circularly. 3.

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4 " array B reads in Ef file " , right now data file format is accorded with completely " postposition is handled " the requirement of module. Ef file serves as " postposition is handled " the original document of module. 4 last words this method turns at blade circular arc except application outside receiving the CNC Machining of place, still apply at the treatment of the place such as blade protruding stage, lamina face and edge of steam of blade pass in and out. Carry out a proof, using afore-mentioned principles and method to plan to add up to dimensional disperse check the number to occupy is method of a kind of very good process designing pretreatment. It is like next advantages: (1) process designing reachs versatility neatly strong. When process designing, can choose according to the public errand of the spare parts " tolerance " , accomplish process designing precision adjustable. Can choose umbriferous face of Xy, Xz or Yz to plan to add up to columnar spiral arbitrarily, satisfy the process designing requirement of different spare parts and machine tool thereby. When primitive data Z=0 or Z value are same, yi Ke work out gives the CNC Machining order that planar circular arc comprises, because this also can satisfy the treatment requirement of cut of numerical control line and mill of planar numerical control. (2) machines the premise of precision to fall in contented spare parts, weaves machine program paragraph least, it is the 1/3 ― 1/10 of method of other process designing commonly. With similar plan the blade circular arc of 1 turns receive treatment to be exemple, after be being handled via planning to close, weaves numerical control mill machine program is only 6 ― 8. Through using a proof in great quantities, this kind of method simplified greatly the input of data, saved the memory that machine tool computer installs, improved work efficiency and exterior treatment quality, because this gets the welcome of machine tool handlers. CNC Milling