Be not the trunk maths model of milling cutter of head of CNC Machining ball

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Summary: Before collect introduced milling cutter of head of ball of blame CNC Machining, hind the fundamental of knife face and trunk maths model, for low cost batch milling cutter of manufacturing ball head provided academic basis. Milling cutter of head of 1 foreword ball is CNC Machining complex curved surface (especially free curved surface) main cutting tool, market demand is very big. Because form of blade of ball head milling cutter is complex, be opposite domestic and internationally at present the treatment of ball head milling cutter needs to come true on machine tool of numerical control of much axis linkage mostly, because equipment is costly (can amount to) of about a hundred 10 thousand dollars, the sheet because of this cutting tool finished cost is higher. To reduce cutting tool finished cost, the method of blame CNC Machining that the author begins to study ball head milling cutter from 1991, face of the knife before putting forward to grind milling cutter of the head that make a ball early or late together with cooperative investigator, hind the mathematical model of knife face, the alignment of the relevant treatment model that discussed milling cutter of head of hard alloy ball and ball head milling cutter produces a problem. Study in the development to ball head milling cutter development is medium, to solve the problem with more complex orgnaization of grinding of face of the knife after primary treatment program is medium, convert flat curve profiling replaces dimensional curve to profiling undertakes machining and score a success, reduced milling cutter finished cost further. To make a person of the same trade right ball head milling cutter is not the principle of CNC Machining and method to have an overall idea, the article machines principle and the model of maths of relevant main force that are used at fashioning a product finally to make one collect introduction to what elaborate in a few document. Graph 1 before knife face machines a principle 2 before principle of knife face treatment and trunk model are be helpful for cutting, the point curve of ball head milling cutter should is " S " form is spherical curve, machine namely form before knife face and hand in a line spherically to should be " S " form curve. If principle of treatment of face of the knife before the ball head milling cutter that designs for this pursues 1 is shown. When treatment, cone emery wheel circles circumgyrate of the O1 that decide an axis, at the same time workpiece (by treatment milling cutter) circle circumgyrate of its axes Oz, face of the knife before the face including sth resembling a net of face a group of things with common features is the arenaceous outline that cone emery wheel forms relative to workpiece motion namely. It is the trunk maths model that face of the knife before building machines, choose originally respectively the right hand rectangular coordinates on workpiece and emery wheel is couplet S=[O; X, y, z] and S1=[O1; X1, y1, z1](sees graph 1) , among them Y and Y1 axis parallel and point to upper part. If write down radius of emery wheel main aspects to be R2, half vertex angle is cone emery wheel G, emery wheel main aspects is P to the distance of O1, the included angle of Z and Z1 axis is F, it is R when ball head radius when, the commutation style that changes coordinate to fasten S by coordinate department S1 is R={x, y, z}={x1cosf+z1sinf-psinf, y1+R2, x1sinf+z1cosf+R-pcosf} (1) fastens the equation of face of emery wheel outline in S1 to be R1={x1 in coordinate, y1, z1}={ucosv, usinv, face of outline of P+(R2-u)cotg}(2) your emery wheel circles Y1 axis with circumgyrate of angular velocity W1, the in T hour instantaneous equation that will get is changed in coordinate department S, make its opposite again Oz axis with circumgyrate of angular velocity W2, can get athletic relatively issueing emery wheel outline the face including sth resembling a net of face a group of things with common features (namely before knife face) equation is (3)3 point curve and parameter optimize type (of correspondence of the first type in 3) equation group spherical it is X*2+y*2+z*2=R2(4) pushball face and before. To make point curve is ideal " S " form curve, answer design variable to undertake actorring or actress choosing. Design variable is X=[X1, x2, x3]=[p, q, r2](5) among them Q=w2/w1. Particular actor chooses mathematical model to be able to consult of write in collaboration with of Shi Peilin, Wang Wei, Tang Yuyong " model of the maths in be being made about spherical milling cutter studies " (print at " machinist Cheng journal " 1994 the 5th period) , be omitted here. Graph 2 hind knife face machines a principle 4 hind principle of knife face treatment and trunk model are set by type (3) , (the spherical point curve that 4) interprets is R2={x2, y2, z2} (6) is ground make hind knife face must cross this point curve, and have enough hind horn. If the graph is shown 2 times,face of the knife after be what this designs machines a principle. In the graph, the calm dot that P0 is Y axis to go up (0, y0, 0) , p2 is either of point music on-line to nod, p is correspondence of on-line of planar profiling music to nod, by P dot contrail assures face of emery wheel outline to undertake grinding along spherical curve. Had set P2 to nod and perpendicular at straight generatrix hand in P0P of emery wheel axes to be nodded at P point-blank, criterion demand exceeds directional vector P2P to be able to beg a P to nod coordinate, can beg an as planar as Y=y0 node on linear P0P then P(x, y0, the contrail of Z) (namely profiling curve) . If set the unit vector on vector P2P to be T={, , } , radius of cylinder emery wheel is R1, have (7) begs an unit vector T={, , } , criterion equation of P dot contrail is RP=r2+R1t(8) the equation of linear P0P is Rp=rp0+l(rp-rp0)/(rp-rp0)(9) this are linear the nodical contrail with planar Y=y0 is profiling curve namely. Because length place is restricted, the article no longer enumerate the embody type of afore-mentioned trunk maths models. Need to point out, the mathematical model that this section gives out is more more compact than the corresponding maths model in other document, and corresponding profiling curve more be made easily and facilitate replace (the need) that machines different specifications cutting tool in order to suit, have clear advantage consequently. When face of the knife after treatment, existence optimizes the issue that selects value of Y0, R1, choosing a principle is the horn after it is certain to should make cutting tool is had already, want to make sure point point has enough strength again. Specific processing technique the article is omitted. The fundamental of CNC Machining of blame of ball head milling cutter of article introduction and trunk maths model already passed 5 epilogue to produce the successful test and verify of practice, with hi-tech of Harbin Institute of Technology at present the product of series of ball head milling cutter of joint development already put garden area on the market. The production of low cost batch that the article removes pair of ball head milling cutter has direct sense outside, to " a few specification about milling cutter of head of ball of CNC Machining of 2 axes linkage " in the batch production of milling cutter of alluding circumgyrate of other special type also has referenced value. But should notice, article content mirrorred ball head milling cutter to be not the basic frame of CNC Machining principle only, if need to implement this treatment method on craft, need to fill to be not trunk model accordingly together according to other document and article frame, reoccupy is produced at guidance. CNC Milling