The computation of curvature of magic art of cover of the knife before columnar milling cutter

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Summary: In assure to devise a way below the premise of forward horn, the law curvature computation of face of the knife before derivation gave milling cutter of columnar helix blade is formulary, the production that is high-powered columnar milling cutter provided academic basis. Keyword: CuttersMao Shimin Et AlAbstract of 　 of Helicoid Face Of Cylindrical Milling of 　 of Of of 　 of 　 Curvature of Normal of curvature of magic art of cover of the knife before columnar milling cutter: Under The Condition That The Normal Rake Ground Is Precise Equal To That Designed, the Calculation Formulas Of The Normal Curvature Of The Helicoid Face Of Cylindrical Milling Cutters Are Derived. It Is The Theoretical Base For The Manufacturing Of High Performance Cylindrical Milling Cutters. Keywords: 　 of 　 of Cylindrical Milling Cutter Helicoid Face Normal Curvature 1. Introductive to before knife face is planar cutting tool, before the azimuth of face of the knife before horn and other geometry angle can decide completely together; And to before the cutting tool that knife face is curved surface, face of the knife before geometrical angle can decide only cuts plane in what edge is in, the appearance of face of the knife before cannot deciding. Before the appearance of knife face, especially of face of the knife before edge is in curve a circumstance to be opposite a bits, decide bits and platoon bits effect very big, it is the index of a main function of cutting tool. Document [1] considered how to be ground accurately piece cylindrical the law of helix blade milling cutter is forward horn. The article will be on this foundation, farther of forward to assuring a standard horn before knife face undertakes study, beg the law curvature that gives it to be in in edge, especially the law curvature of as perpendicular as edge direction, know extent of the knife before edge is in thereby curve a state, to make property admirable milling cutter provides academic basis. 2. Knife face describes a plan before the circumstance of face of the 1 knife before be milling cutter of cylinder of grinding of the circle outside using emery wheel, the meaning of grinding principle and each symbol already was in document [1] in made a specification. Knife face equation is before [1] among them θ and to join variable, of θ and parameter curve direction cut arrow and for the graph the relative position of 1 emery wheel and cutting tool this is run-of-mill the equation that cut arrow, to the graph 1 medium M nods the unit that M chooses way of two parameter curve to cut arrow to still use R θ and R φ to express, they are 　 (5) in type, the helix parameter of face of the knife before P is, the N of unit law arrow that the M of 　 of 　 of included angle 　 that is M dot and Xoz plane nods (to by before knife face points to the chamfer that hold bit) for 　 3. 　 of φ of law curvature K by the graph 1, emery wheel end panel and before knife face (1) crossing a line is the circle that radius is Rc, the curvature that it nods in M is. Because be flat curve, this bits of unit advocate C of law arrow β is (graph 1) with the included angle θ between θ of the 1 Cos that it is 　 1 ＝ .

W of β of Cos of ＝ Nxsin φ - φ of Nzcos of ＋ of W of β of Nysin φ Sin (10) by Moniai theorematic [2] but 　 of curvature of do sth in the proper way 4. θ of law curvature K and short distance flinch 　 of rate G θ because before knife face is columnar helicoid, θ parameter curve is ／ of D of radius R ＝ the corkscrewed yarn on the columnar face of 2. Columnar corkscrewed yarn assumes office the curvature K of a bit and flinch rate τ is constant, they are (refer to [2] the exemple of P41 2) 　 　 corkscrewed yarn assumes office of a bit advocate law arrow and corkscrewed yarn axis are vertical intersect (refer to [3] the exercises of P59 3) , the unit that so M orders advocate law arrow is ＝ O, - Sin, - Cos (14) with before the included angle θ between N of arrow of knife cover magic art 2 for Cos θ 2 ＝ .

＝ - Nysin - Nzcos (15) so, θ of law curvature K is the edge on columnar helicoid a corkscrewed yarn (θ parameter curve) assume office the helicoid law arrow of a bit and helicoid axes (X axis) included angle also is fixed, so of this corkscrewed yarn advocate the angle of cut of law arrow and bit more corresponding helicoid law arrow also is fixed. Can get from this (refer to [2] the theorem of P237 3) 　 　 5. Magic art of cover of the knife before the law curvature that M nods is reached pursues to 　 of M of ρ of radius of cut form curvature 2 for M the dot cuts the condition inside plane. Made perpendicular way, it also is the law transversal direction of the crucial point of M point point, the law curvature of this direction expresses with KN, criterion the short distance of this direction flinchs rate for - G θ . Graph 2 　 M nods cut plane and the included angle Δ between to be θ of R of Cos Δ ＝ .

R φ (18) law curvature of direction and short distance flinch lead ＋ of Δ of Cos of Δ of Sin of θ of 2G of ＋ of Δ of Cos2 of θ of K of ＝ of φ of contented 　 K KNsin2 Δ so 　 KN ＝ (K φ - Δ of K θ Cos2 - Δ of Cos of Δ of 2G θ Sin) ／ , can get α of either direction R (graph 2) α of law curvature K and short distance flinch frank G α is ＋ of α of Cos2 of θ of K of ＝ of 　 K θ KNsin2 of ＋ of α of Cos of α of 2G θ Sin α (21) ＝ of α of 　 　 G (, the law curvature issue that M selects is solved completely already. In actual cutting, direction drifting bits is absent commonly RN direction, press (21) the law curvature that type can seek a way drifting bits, can consider to shed bits section plane then (not be a law certainly sectional) inside before of knife face curve a state. 6. Calculate exemple and specification to be in order to establish milling cutter exemple, 50mm of ＝ of D of milling cutter diameter, 45 ° of ＝ of helix angle β , the law is forward 15 ° of ＝ of horny γ N, 10mm of ＝ of grinding deepness H, what use 35mm of ＝ of Rc of emery wheel radius, the ＋ of W of included angle β between emery wheel axes and cutting tool axes 90 ° ＝ 136. 5 ° , grinding center is apart from H ＝ 48. 874mm, grinding slants be apart from E ＝ - 8. 338. Get K θ ＝ 0. 005176379, g θ ＝ 0. 02, k φ ＝ 0. 00250113, Δ ＝ 120. 7778326 ° , ρ M ＝ 39. 4074mm. To certain cutting condition and a specific bits, break bits and platoon bits requirement, be put in an ideal before knife face curves a state, token can come with ρ M when designing cutting tool commonly. Should press given when the ρ M that computation of grinding craft parameter gives cannot satisfy a requirement, can change a few adjustable parameter, for example recount Rc and β W. CNC Milling CNC Machining