About a few specification of milling cutter of head of ball of CNC Machining of 2 axes linkage

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Summary: The design that exists when the ball head milling cutter that pointed out linkage CNC Machining uses 2 axes to become point of the helix that decide part with axes and production difficult problem, gave out corresponding processing technique and relevant model, the computer is fictitious production result test and verify the validity of this method and feasibility. Milling cutter of head of 1 foreword ball is to machine complex curved surface (especially free curved surface) the main cutting tool of workpiece, the ball head milling cutter that develops high quality, low cost has important economic sense. The 2nd author is in the article " journal of Harbin Institute of Technology " 1996 the 5th period " conformal helix milling cutter plan of CNC Machining of 2 axes linkage and its geometry model " intermediary carry on the fundamental that the 2 axes linkage that with tool works brainpower collaboration studies machines circumgyrate cutting tool and corresponding model; Article author is in " tool technology " 1999 the 12nd period " the CNC Machining of begs solution and helix groove 2 axes linkage of curve of point of ball head milling cutter " medium gave out the point design of milling cutter of head of ball of treatment of 2 axes linkage and the general maths that groove machines, carried out the computer fictitious make. But because be opposite,the point design that is close to ball of ball head milling cutter to carry area on the head and made difficulty problem did not spread out development discussion, because this makes the actual application existence of this method disadvantageous. For this, be necessary to be aimed at " the CNC Machining of begs solution and helix groove 2 axes linkage of curve of point of ball head milling cutter " make a few important specifications, in order to offer reader reference and facilitating user application. The ball head milling cutter that point of the helix that decide part becomes with axes to using mainly below is in the design, difficulty in making and corresponding processing technique and mathematical model make one brief introduction, pass next fictitious the corresponding figure test and verify in making its feasibility. Hope these explain to be being become with meridian calm horn is mixed wait for pitch the congener research of the ball head milling cutter of point of two kinds of helix also can benefit somewhat. The spherical equation of milling cutter of your ball head is the design difficulty of difficulty of design of curve of point of 2 balls top and point of helix of means of settlement R= ｛ (R2-z2)½cosf, (R2-z2)½ Sinf, z ｝ (in 1) type: R -- , spherical radius Z, f -- , spherical parameter is spherical the point curve that goes up to become the Y that decide part with axes ought to satisfy differential equation (2) is become R2tan2y-z2sec2y<0, be in namely Z>Differential equation does not have real solution when Rsiny, also be in namely this part is spherical on the point curve that the design does not give to become Y part with axes. Because curve of follow-up and planar point is in on ball head Z ∈ [Rsiny, r] the point curve that the design inside partial section does not give to become Y part with axes, because this can use other point curve replace only, the simplest method is to use planar point curve to replace. The first-order derivative that if want to assure point curve,is in in join dot is successive, and before part is equal, the point curve place that takes Z=Rsiny is nodded as join and improper. By " the CNC Machining of begs solution and helix groove 2 axes linkage of curve of point of ball head milling cutter " knowable, speed of the axial of the emery wheel when grinding groove, radial feed is respectively (in 3)(4) type: R -- the W of cut round radius that groove bottom is in -- angular velocity of cutter hub circumgyrate pursues 1 feed speed-distance curve pursues of 2 point curve sectional show rate 1 times by the graph metabolic curve is knowable, when treatment is close to the groove of Z=Rsiny, feed speed Vz, Vg all tends infinity, in be being made actually, this is in cannot come true. Accordingly, when the choice connects contact, should leave Z=Rsiny to be apart from certainly, avoid the because of feed speed revulsion difficulty that brings to project implementation, choose Z=Rsin(y -y0)(y0>0) to be able to solve this one difficult problem. The problem below is to beg planar equation. Although a lot of document all allude this one problem, but all did not give out mathematical model, reason brief introduction is as follows: By " the CNC Machining of begs solution and helix groove 2 axes linkage of curve of point of ball head milling cutter " the coordinate that can beg the point that when giving Z=Rsin(y-y0) , gains to nod A (X1, y1, z0)(is shown 2 times like the graph) and the tangent vector of A point point is R1 ' =(X1 ' , y1 ' , z1 ' ) (5) nods Z axis vertical line to hand in Z axis to be nodded at B by A, criterion B dot coordinate is (0, 0, z0) , because this point is in plane to had been divided,cut vector R1 ' outside, the transversal AC on face of the knife before still needing what become G part with AB, by C=p/2 of the ∠ in right-angled triangle ABC, the horn before ∠ BAC=g() knowable, c nods coordinate (X* , y* , group of Z0) contented equation (6) begs a X* and Y* by afore-mentioned equation groups, criterion point is in planar equation to be ｛ X1 ' , y1 ' , z1 ' X*-x1 of ｝ × ｛ , y*-y1, x-x1 of ｛ of 0 ｝ × , y-y1, z-z0 ｝ =0 namely Z1(' Y1-y*)(X-x1)+z1(' X*-x1)(Y-y1)+ [X1(' Y*-y1)-y1(' X*-x1) ] (Z-z0)=0 (7) planar equation (7) and spherical equation (of 1) hand in a line to be point curve namely. Apparent, curve of this one point is in with original design point already joint is successive, g of the horn before face of the knife before correspondence has. Curve of follow-up helix point is narrated like a lot of document place, planar point goes against a bits, document puts forward to use ellipse column and spherical the tentative plan that makes a line regard point as the curve, its purpose also is to be helpful for discharging bits. To make the article is not sent too expatiatory, here is defined to using additionally two kinds only (mix into calm horn with meridian wait for pitch) point curve replaces ∈ of the Z on ball head [Rsin(y-y0) , r] the train of thought of partial point curve makes one brief introduction. In fact, " the CNC Machining of begs solution and helix groove 2 axes linkage of curve of point of ball head milling cutter " already gave out to be mixed into calm horn with meridian wait for pitch the computation of a complete set of of curve of two kinds of point is formulary, because this key is in,nod the computation of place at join. Law of this planarrer than using point more manageability, need to will nod A(X1 only, y1, the integral initial value when F=f(Z0) sets the parameter of Z0) to replace point curve to nod corresponding parameter F in this to beg can, this is equivalent to will becoming calm part with meridian (or wait for pitch) corkscrewed yarn is received repeatedly already on the corkscrewed yarn that some and axes become calm part, as a result of before horn is consistent, reason can be pressed " the CNC Machining of begs solution and helix groove 2 axes linkage of curve of point of ball head milling cutter " corresponding method undertakes machining, can get compound model point of two paragraphs of helix and groove. The treatment problem of curve of point of 3 balls top divides usable and flat curve to carry point curve on the head to undertake correction to the ball outside, the metropolis when regarding follow-up point as the curve with afore-mentioned helix point that become calm part with meridian or wait for pitch is encountered " the begs solution and helix groove 2 axes linkage of curve of point of ball head milling cutter CNC Machining " alluding treatment problem, satisfy to radius when treatment namely (R2-z2)½ CNC Milling CNC Machining