The CNC Machining of cone-shaped helix milling cutter reachs figuration principle
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source:KAPLOWITZ CNC Machining
Summary: Introduced to use simple and easy mill to age device machines the method of cone-shaped helix milling cutter and figuration principle on common CNC Milling. Keyword: NC Machining And Forming Principle Of Bevel Helical Milling CuttersLiu Huran Et AlAbstract of principle of figuration of CNC Machining of cone-shaped helix milling cutter: The NC Machining Method By Using A Simple Milling Tooth Device And The Forming Principle Of Bevel Helical Milling Cutters Are Introduced. Keywords: Bevel Helical Milling Cutter NC Machining Forming Principle one, milling cutter of introductive and cone-shaped helix is to be used at processing work of complex curved surface (wait like antrum of blade, model) abnormity cutting tool, complication with each passing day as machining object, the application of this kind of cutting tool is increasingly wide also. The conventional treatment method that produces cone-shaped helix milling cutter changes like cam compensation method, leather belt way way, change the horn before be apart from law of guide screw law, the positive drive that be not a circle to wait to cannot realize cutting tool completely to wait and bandwidth waiting for blade. For this, the article puts forward to machine the method of cone-shaped helix milling cutter and its figuration principle on common CNC Milling. 2, the CNC Machining of cone-shaped helix milling cutter and figuration principle 1. Simple and easy mill ages device machines a method originally age through a simple and easy mill increasing on common CNC Milling device will come true. If the graph is shown 1 times, milling cutter of will only part (2 cutting tool) through 7 ∶ 24 awl handle and machine tool main shaft are linked together, electric machinery of numerical control of servo of FB15 of of a FANUC-BESK dc is added on workbench, through the input of sleeve and dividing head end is linked together. Graph 1 2. If the sets coordinate department setting that coordinate fastens pursues 2 are shown. Graph 2 pursue medium, (O (0) - X (0) Y (0) Z (0) ) fasten to secure coordinate, x (0) direction is a machine tool fore-and-aft, y (0) directional lead hangs down up, z (0) direction is a machine tool transverse; (O (1) - X (1) Y (1) Z (1) ) fasten to assist fixed coordinate, x (1) for workpiece axes direction, z (1) with Z (0) coincide, x (1) with X (0) included angle (angle of elevation) for τ ; (O (S) - X (S) Y (S) ) fasten to move coordinate with what cutting tool solid connects, y (S) with Y (0) parallel, x (S) with X (0) parallel, o (S) be in milling cutter center, o (S) coordinate is (Xc, yc, zc) . Coordinate commutation matrix is (1) 3. Edge curve equation is shown 3 times like the graph, on taper seat one waits a bit more aleatoric coordinate on curve of helix angle edge can express to be (2) the R in type -- the circumgyrate radius that P nods, ξ of R ＝ Xtg (ξ carries half horn on the head for awl) Ψ of -- P dot radius is opposite at Xoy planar deflexion horn pursues 3 basis is differential geometrical principle, the academic deflexion horn of conic corkscrewed yarn is (3) workpiece runner shaft coming back calls B axis, rotate when B axis after horn, have (4) has respectively to the two edge curve of photograph adjacent (5) (6) the Z in type -- δ of of tooth number -- if the graph is shown 4 times,first flank width prints the edge curve that go out with the computer. Graph TA of 4 tangent vector, TB is respectively (7) (8) ＝ of the Dr/dx in type - Ψ of Tg ξ D / Dx ＝ - Tg β / of of Sin ξ X 4. Equation of emery wheel surface and law vector to establish the osculatory condition of emery wheel and edge, need equation of surface of listed emery wheel and law vector above all. If the graph is shown 5 times, equation of emery wheel cone and law vector are respectively (9) (10) the R in type -- RA of radius of cone big circle -- A of θ of radius of circumgyrate of cone either dot -- α of positional parameter horn -- the horn end awl pursues equation of underside of 5 emery wheel and law vector are respectively (11, θ B -- of underside position parameter 5. When the osculatory condition of cutting tool and workpiece is machined, milling cutter cone and edge curve A are contacted, milling cutter underside and first flank B are tangent, reason has in osculatory dot (13) is in type (13) ～ (20) in 8 equation, have XA, XB, RA, RB, θ A, θ B, xc, yc, in all 9 unknown quantity, among them one is ginseng variable, the delegate machines a series of treatment positions in the process, reason equation group can seek solution. 6. Analytic law begs group of solution motion equation to see afore-mentioned equation groups to beg, take XB to be ginseng variable, ordinal a series of treatment positions in taking a series of XB to represent treatment course, type (17) can write into (21) by on type begs solution to give , take the place of again type (19) beg a Yc, it is independent variable with XA again, allow to take cost of a XA, by type (13) beg A giving θ , by type (16) beg a RA, take the place of again type (15) beg Yc, this Yc should with type (19) beg the Yc that go out equal, this need adjusts XA to be worth ability to come true repeatedly, reason former the translate into seeking solution of group of 8 dimension equation one dimension is nonlinear of equation seek solution. Finally by type (14) beg a Xc. Add man-hour to need X, y, linkage of B3 reference axis. 7. Another kind of means that half analytic law seeks group of solution motion equation to seek form of solution motion equation is half analytic law (half figuration law) . Specific means is as follows: It is facilitating treatment, when stipulating when edge curve A assumes office to was machined, all should turn at this o'clock to Z (1) inside 0 plane of ＝ , be in apogee position namely, at this moment the as it happens of A of deflexion horn Ψ of edge curve by workpiece form positional place to make up for, because this has 0 of ＝ of Ψ A ＋ (22) reason has in addition, set τ ＝ ξ , namely angle of elevation is equal to cone angle, have reason by ＝ of A of θ of Sin of β of Sin of ＋ of A of θ of Cos of β of the Cos that get 0 - 0 of ＝ of β of θ A ＋ (27) ＝ of A of θ - (β - 90 ° ) go up type relation also can pursue show 6 times. Graph 6 because this, type (14) ～ (16) changeover of denotive contact condition is of of of of of ξ of Cos of ／ of XA of ＝ of Xc of ＋ of Racos θ A (28) (R - RA) ＝ of Yc of Tg α ＋ of of 0 (29) ＋ of RAsin θ A, by type (22) beg a , by type (27) beg A giving θ , by type (31) beg a XB, by type (32) beg a Yc, again by type (29) beg a RA to be of of of of of of α of Yctg of ＋ of RA ＝ R (33) on type relation also can show geometrical figure 7 times by the graph intuitionistic beg piece. Finally by type (28) with type (30) beg a Xc, zc is ξ of Cos of ／ of Xc ＝ XA respectively - of of of of of RAcos θ A (34) Zc ＝ - of of of of of of RAsin θ A (35) treatment process needs X, y, z and linkage of B4 reference axis. With this kind of method treatment can get waiting for a law forward horn (namely the complement of α of horn of bottom of milling cutter awl) . Graph 7 3, when epilogue machines cone-shaped helix milling cutter by analytic law, on-line of music of the position of workpiece, edge be waited to all was not given beforehand by the position of treatment dot and 2 cutting tool, pass series of athletic function equation however beg solution to get. Press half analytic standard (half figuration law) when machining cone-shaped helix milling cutter, the position of workpiece and edge music on-line are nodded by treatment by give artificially (but still can satisfy all equation group finally) , 2 times the position of cutting tool passes series of athletic function equation beg solution to get (reason calls half analytic way) . Use method of this kind of treatment, edge curve is machined to rotate the position (be similar to figuration law) , dan Ren takes corresponding contact to nod is the blade such as the basis bandwidth and tangent condition are affirmatory, reason can call half figuration way again. Idea of this kind of method is clear, mathematical form is simple, computational method is simple, popularize application easily. CNC MillingCNC Machining