Face CNC Machining to combine free curved surface to transfer technology

Often use assorted curved surface in real products plan. Alleged combination curved surface, the curved surface that will differ namely piece with certain kind join rises compositive curved surface. Although assorted curved surface can convey complex form conveniently, but bring another issue however, this combines the curved surface in curved surface namely between transfer problem. If think the contented and specific requirement between face of Zhang Qu letting sheet joins directly, this will be extremely difficult, it is impossible even. Then. People is used join between assorted curved surface transfer the face will handle the transition between curved surface problem. Because transfer main effect that waits for a respect in the function of the product, exterior, treatment, the research of this respect is accordingly more. Although transfer to curved surface at present problem research is more, and algorithm becomes better day by day, but they are mere to transferring from mathematical angle the problem undertakes study, and the requirement that machines without the consideration, the loss of efficiency that when come out or the likelihood cannot machine the face, the transition that such building must increase the number that change a knife and makes machine. For this, the article plans to transfer to curved surface from the angle of CNC Machining the technology undertakes study. 1.

When free curved surface transfers to use curved surface to undertake joining interim to combining curved surface theoretically glossily, transfer it is contented and certain to need between face and assorted curved surface spend glossily (also weigh smooth compliance) requirement. Current, the about join smooth compliance tolerance that two kinds differ: A kind of parameter that is a tradition is successional, another kind is geometry successional. The definition with successional parameter is: When and become only P(s of two curved surface, t) and Q(u, v) edge their P(g)=Q(g) of communal jumper is had everywhere until of N rank slant guide arrow, say they have N rank parameter along this jumper successional or be Cn is successional. And the definition with successional geometry is: P(s of two curved surface, t) and Q(u, v) edge their P(g)=Q(g) of communal jumper has N rank geometry successional or be Gn is successional. When and should be among them only can be changed by new parameter in order to make they along this communal jumper has N parameter successional or be Cn is successional. People realises stage by stage in practice, traditional parameter is successional be appropriate when the smooth compliance of the curved surface of magnanimity nonparametric form, but suitable to light needless excessive limitation is when the smooth compliance of the curved surface that is used at parameter form, accordingly, what it cannot cut magnanimity parameter curved surface truly is smooth degree. Geometry is successional it is successional to parameter slacken necessarily, also be what change to parameter is necessary and flabby, but it is smooth anything but those who spend is lax, such, it can think appearance definition and appearance control offer additional freedom to spend. Accordingly, geometry is successional it is the magnanimity with smooth to parameter curved surface idealer compliance. The level that considers parameter curved surface already became free curved surface now conveys a form, the article also uses geometry successional processing transfers connective is smooth between face and assorted curved surface sexual problem. And integrated consideration precision and benefit principle, the article uses G1 and first-order geometry only successional. This are successional can convey for: P(s of two curved surface, t) and Q(u, v) edge their P(g)=Q(g) of communal jumper has first-order geometry successional or the successional " that is G1 is become and become them only along this communal jumper has common to cut plane or normal of common curved surface everywhere. 2.

The curved surface that faces CNC Machining transfers the place before the technology is like is narrated, at present the curved surface in geometrical model system transfers to do not have the requirement that considers CNC Machining from mathematical angle only. The faces CNC Machining combines free curved surface transition that the article puts forward the smooth compliance requirement that the technology satisfies maths to go up not only, more important is its characteristic considering CNC Machining. This curved surface transfers the technology basically includes the following steps. Combine the disperse of curved surface and beg those who give assorted curved surface to cross a line current to the disperse of free curved surface research is more, its algorithm is more mature also, do not do thorough analysis here. This literary grace changes a method to undertake disperse to combining curved surface with triangular disperse, the specific implementation of this method consults please relevant document. After assorted curved surface passes disperse, beg those who solve them to cross a line (express approximately with small line segment) also be very easy, here also no longer give uncecessary details. With cut plane cut combines curved surface and reach cut crosses a line substantially of current CNC Machining of assorted curved surface has law of operation accord with, area to machine law and sectional law 3 kinds. Among them sectional law is the knife orbit plans to be on the plane of a group of mutual parallel, and it is normally a group perpendicular the plane at XY face. This method is the most commonly used method in combining curved surface to machine, it can regard assorted curved surface as a whole to undertake machining, cutting tool contrail spans whole combination curved surface, treatment efficiency is taller. The article also is aimed at reason the transition that this treatment method puts forward to combine curved surface method. Should use perpendicular when the assorted curved surface that already passed disperse at the planar cut of XY face, can reach with small line segment denotive cut crosses a line conveniently likewise. After the curvature that begs an assorted curved surface to hand in a line to be in in cut should beg those who give assorted curved surface and plane to cross a line, can beg plane giving check and triangle piece each edge is nodical (each end points of small line segment) the curvature of the curved surface of place. The curved surface of ─ of ─ of law curvature F1 that its beg curved surface of ─ of ─ of the Kn in solving a process to be Kn=f2=Ldu²+2Mdudv+Ndv²f1Edu²+2Fdudv+Gdv²(1) type the first invariant, curved surface of ─ of ─ of Pvf2 of · of Pv;G=Pv of · of E=Pu · Pu;F=Pu the 2nd invariant, pvv of Puv; N=n · of L=n · Puu; M=n · reachs after law curvature, see its extreme value through begging, can beg give the biggest curvature this a little bit. Formula of the extreme value that seek solution is: After KnE-LKnF-MKnF-MKnG-N(2) hands in a line to be in the curvature of curved surface to be begged to go out when assorted curved surface and cut plane, ─ of ─ of the L in can using the formula below to calculate next stop plane and the span with current planar cut to be L={4(R+r)²(h+r)²-[r²+2Rr+(h+r)²]²}½(R+r)(h+r)(3) type the biggest span of plane of cut of two photographs adjacent, the radius of the smallest curvature of plane of cut of the edge on curved surface of combination of Mmr ─ ─ , the ball head radius of cutting tool of head of ball of MmR ─ ─ , the leftover height that Mmh ─ ─ allows, mm at the same time, write down next current cut plane and assorted curved surface to pay the cost with the biggest curvature of the curved surface on the line. Such, can reach each cut plane hand in a line to be in the maximum of the curvature of curved surface with what combine curved surface. The maximum of the curvature that the radius blend of assorted curved surface with affirmatory and reasonable analysis is in when each cut plane is begged after going out, can analyse judgement to combine the radius blend of curved surface. In CNC Machining, knife of experience of have nothing to do with of orbit generate, especially the interference of among them contrail examines with processing it is the most complex link. And cutting tool radius (point to ball head cutting tool here) two the time that choose and the knife changes in treatment is influence treatment efficiency the mainest factors. If consider alone, cutting tool radius is bigger, treatment efficiency is taller; And the time that change a knife is less, treatment efficiency is taller. But to given curved surface, the cutting tool radius of the choice is bigger, often mean the increase of the frequency that change a knife. The target of the article is to make combine curved surface to because increase,do not transfer as far as possible face and reduce efficiency. Be based on this, the transition that we put forward curvature radius criterion is as follows: If combine curved surface opposite to cross curvature radius to have clear numeric demand, criterion the numerical value that the radius blend with each cut corresponding plane is a requirement; In the biggest curvature that if all cut plane is right,answers otherwise the biggest person the ball head curvature that is less than economic cutting tool, economic cutting tool is most economic cutting tool, this cutting tool makes treatment efficiency highest, criterion the ball head radius that the radius blend with each cut corresponding plane is this cutting tool; The radius blend that combines curved surface to make the same score face correspondence in every cut otherwise is the reciprocal of the biggest curvature with this cut corresponding plane. Use B batten curved surface 3 times to undertake the face reachs planning to close reaching interim after the radius blend with the each cut corresponding plane that assembles curved surface, the section that the circular arc that we use this curvature radius above all assembles same section plane correspondingly curved surface hands in a line to undertake G1 smooth circle horn transfers, such, we get a series of circular arc, write down each to transfer circular arc paragraph start and terminus, also transfer namely circular arc and the node that combine curved surface cut to cross a line, these start and connect a line terminally to be combination namely curved surface and transfer the communal jumper of the face. We use curved surface to draft what to this a series of circular arc undertake planning to close reaching asking to combine a technology later transfer face. The article uses curved surface of batten of accurate even B 3 times to serve as the form that plans to combine an aspect. The place before be like is narrated, the article uses G1 successional as combination curved surface is mixed transfer the light of the face arranges criterion. This criterion conveys as follows: P(s of two curved surface, t) and Q(u, v) edge their P(g)=Q(g) of communal jumper has first-order geometry successional or be G1 is successional, when and become them only along this communal jumper is in not 4 of photograph coincide Ps(g) that cut arrow, pt(g) , qu(g) and Qv(g) ought to in all face, this in all face condition can be conveyed on maths for (× of Ps × Pt) (Qs × Qt)=(Ps, pt, qv)Qu(Ps, pt, qv)Qu=0. As a result of B batten curved surface local modification sex, so but will transfer alone each faces of face and assorted curved surface undertake G transfers glossily respectively. When transferring, be in above all every paragraphs of circular arc paragraph on take a certain number of places, and to go to the lavatory, answer in the check the number on each circular arc identical; Next with circular arc paragraph direction is U direction, with each circular arc paragraph on bit more corresponding it is even the line V direction; B batten is used to beg algorithm to beg the reference point that gives correspondence instead later. Finally, the $ of G1 smooth condition that alludes above the basis is made a bit to reference point fluctuant the transition that can plan to add up to contented condition face. 3.

The faces CNC Machining curved surface that the article puts forward epilogue transfers the research that to combining the transition of curved surface from the angle of CNC Machining the technology had thorough system offerred the technology corresponding algorithm. The curved surface that it shunned a convention transfers the defect that the technology does not have the feasibility that considers treatment and efficiency from mathematical angle purely, not only the transition that makes generate the basic requirement that the face can satisfy smooth compliance, and the number that when making undertaking machining to its, reduced to change a knife as far as possible, improved the efficiency of treatment. This transfers for curved surface the technology offerred new thinking, be helpful for the process of CAD/CAM unifinication at the same time. CNC Milling