Compensation of cutting tool radius interferes examining vector algorithm
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source:CLAREY CNC Machining
Because the generation of 1 interference is machined the uncertainty of spare parts outline and complexity, perhaps encounter outline greatly too when the radius of cutting tool inside when pointed horn, the contrail that if handle bad cutting tool to transfer in outline,is in, the phenomenon that cuts outline too with respect to meeting occurrence cutting tool (graph 1) , this is the interference of cutting tool. Cutting tool interference can cause the attaint of the spare parts to must try to overcome. The interference of outline examines cent is two kinds of circumstances, one kind is two paragraphs of outline interference examines, another kind is multistage outline interference examines. Two paragraphs of outline have the photograph neighbour that interference of two paragraphs of outline examines to fill to attending a knife only interference examines, take no account of other outline paragraph interference circumstance. Consideration other outline paragraph examine, call multistage the interference of outline examines (graph 1b) . Be in usually, undertake to two paragraphs of outline good interference examines to already can satisfy the requirement that interference examines. Accordingly, the article considers the interference of two paragraphs of outline to examine only. Graph 1 outline cuts a phenomenon too at present, already a few methods can undertake examining to the interference of cutting tool, but judgement condition is too trival. The article accepts the judgement of the type through turning to outline and combinative outline compensates the change of around direction vector, reached one kind judges the effective algorithm that cutting tool interferes. 2 turn in receiving the judgement of the type to examine in interference of compensatory of cutting tool radius, want those who judge outline to turn above all receive a kind. Of outline turn receive a type to divide kind of case in all: Shorten model, stretchy model and insert model. The tangent of two paragraphs of outline is in photograph adjacent the included angle of side of nodical department work, the included angle that calls two paragraphs of outline (graph 2 medium α horn) . 1) is more than when the included angle of two paragraphs of outline when 180 ° are less than 360 ° , the length of the contrail that cutting tool place walks along is less than the length of real profile, this kind of circumstance is called shorten model (graph 2a) . Graph of 2 outline turn receive type 2) to be less than when the included angle of two paragraphs of outline be equal to 180 ° to be more than when be equal to 90 ° , the contrail that cutting tool place walks along should is more than or be equal to the length of real profile, this kind of circumstance is called stretchy model (graph 2b) . 3) is less than when the included angle of two paragraphs of outline when 90 ° are more than 0 ° , not only the length that the contrail that cutting tool place walks along wants to be more than real profile, and should insert one Duan Zhi line or circular arc, this kind of circumstance is called insert model (graph 2c) . Turn in 3 kinds of outline in receiving a kind, shorten only model meeting generation interferes a circumstance, and stretchy model and insert model the interference that won't cause outline. Accordingly, receive a type to undertake reasonable judgement can decrease effectively to turning above all examine the computational quantity that cutting tool interferes. Hypothesis photograph adjacent of two paragraphs of outline cut vector to be 3) of graph of L1, L2(. The fork of L1, L2 is accumulated what be in planar normal K to go up in them is umbriferous for K of · of S=(L1 × L2) , turn the judgement condition that accepts a type is: (1) Zun Dao fills: When S>0, to shorten model;s ≤ 0 when, shorten to be not model;(2) right knife fills: When S<0, to shorten model;s ≥ 0 when, shorten to be not model. Graph 3 turn the radius that receives the judgement of the type to set cutting tool is R, and when Zun Dao fills, when R>0; right knife fills, r<0. Criterion above condition is OK and amalgamative become for K] of · of L2) of C= Sign(r)[(L1 × when C>0, turn receive a type to be shorten model, should undertake interfering examining;c ≤ 0 when shorten to be not model, do not need to undertake interfering examining. Of 3 interference examine judgement outline turns after receiving a kind, can undertake interfering examining according to outline further. Below it is with two paragraphs of outline that connect with circular arc point-blank exemple will explain how to undertake interfering examining. If the graph is shown 4 times, outline is comprised by a paragraph of linear AO and OB of a paragraph of circular arc. Start is A, terminus is B, AO and OB are handed in at O dot. Cutting tool radius is R, edge outline is left treatment. Graph 4 examine with what circular arc interferes point-blank in normal compensation, when producing interference namely, the cutting tool course after compensation pursues to O1B1(for A1O1 4) , o1 nods the orbit node after be being compensated for cutting tool radius. The directional vector that sets linear AO is L= Xu1i+ Yu1j (1) criterion, the equation of linear A1O1 is - the coordinate that Yu1x+ Xu1y= R (2) sets OB to be in C of round the centre of a circle is (Xc, yc) , round radius is R, criterion the equation with O1B1 round place is (X- Xc)2+ (y- Yc)2= (R+ R)2 (3) by type (2) , (the coordinate that 3) can get O1 to nod (X01, y01) is below discuss the case that produces interference: 1) to linear AO by the graph 4 in be shown knowable, a1 is the position that cutting tool center manages compensation hind in outline start A. Vector AA1 is perpendicular at linear AO, direction points to A1 of cutting tool center, and its length is equal to R, call the cutting tool radius that AA1 nods in A for outline vector, write down for TA. The coordinate that O dot sets to be nodded at A relatively in type is (X1, y1) , the coordinate that can get O1 be nodded at A1 relatively undertakes machining for A1O1 of cutting tool edge, when advancement arrives on the extension line of A1O1, meet a circular arc cut away from the back, had happened to cut. We notice hypothesis new outline arrives for A ＇ O OB, start is A ＇ , the position after countervail of A ＇ have a snack to stave off hunger is A ＇ 1, so the treatment contrail after cutting tool is compensated begins to be nodded from A, 1O1 of classics A ＇ arrives O1B1. Produced interference namely at this moment, because be in when cutting tool A ＇ when 1 o'clock already the circular arc cut away from the back. The direction of 1 concerns the generation that cuts too and O of vector A ＇ and ＇ of 1O of vector A ＇ . The vector that sets them is L1, L2 respectively, the judgement condition that interferes is: L1 and L2 way are opposite, namely L1+ L2= 0 (4) 2) sets photograph of C of the centre of a circle to be I, J to the coordinate of start O to circular arc OB, terminal B photograph is Xe, Ye to the coordinate of start O. The vector that sets O of circular arc start to C of the centre of a circle is OC, b of circular arc terminus is BC to the vector of C of the centre of a circle, the vector that sets nodical O1 to dot C is O1C, the dot B1 after B compensates circular arc terminus is B1C to the vector that nods C, the vector of cutting tool radius that B nods is TB=Xtbi+Ytbj, criterion the fork that the condition that circular arc interferes is vector OC and BC is accumulated what be in planar normal K to go up in them is umbriferous accumulate the umbriferous direction on K with the fork of vector O1C and B1C contrary, namely [(what K]<0 (5) above of · of B1C) of × of K][(O1C of · of OC × BC) analyses is the case that accepts circular arc point-blank, the case that accepts circular arc with circular arc point-blank to receiving point-blank can undertake similar analysis: To linear, press type (4) , if the vector way of compensation around is opposite, generate interference, do not produce interference Z otherwise to circular arc, press type (5) , if the circular arc way of compensation around is same, do not generate interference, interfere otherwise. The numerical control that the way of interference check checking computations that the article offers 4 last words has developed in this place is used in the system, examine through long application and production, be confirmed to be practical, it is fast and effective. It can examine the whole situation that two paragraphs of outline interfere, satisfy the basic requirement that interference examines. CNC Milling