Milling cutter week ages the blade of face of the knife before helix is ground

Truncate of end panel of chamfer of helix of 1 milling cutter turns week of horny η milling cutter ages helix chamfer is a when after making helix move at the same time by a few line segment, form compound helicoid that connects. Form of its typical cut of helix chamfer end panel is shown 1 times like the graph. From the graph the body of end panel cut of chamfer of 1 knowable helix forms by 4 line segment: BC of next linear AB, sunken circular arc, go up convex arc DC and linear DE. Face of the knife before blade grinds week of tine helix is blade grinds linear AB paragraph make it wins a provision before horny γ A.

Before AB of face of the knife before blade grinds week of tine helix, answer above all will before knife face AB turns to what open wide locally in order to facilitate grinding. Rotational horn η can press type calculates: α of A+ of γ of B=tg(of γ of Tg η =tg) (in 1) type: TG α =yoB/xoB (2)x0B, Y0B is the coordinate that B nods. Graph the coordinate on 3 emery wheel and milling cutter is a graph if the form of end panel cut after horn of η of roll of 4 helix motion pursues show 2 times. After η of foregone and rotational horn emery wheel of not difficult cipher out is opposite at milling cutter axes slant buy quantity E, Ey and Ez(see graph 3) .

1.

The coordinate department on 2 emery wheel and milling cutter is become after Rs of diameter of emery wheel of form of dish of preliminary make choice of, when face of the knife before grinding helix, the emery wheel installation on milling cutter is shown 3 times like the graph. Coordinate is taken to fasten O-xyz on milling cutter, coordinate is taken to fasten O-XYZ on emery wheel.

The coordinate in department of milling cutter coordinate is the origin O that emery wheel coordinate fastens (A, ey, ez) , among them A is apart from for the center of emery wheel and milling cutter. In A=Rs+R-h (3) type: H -- the chamfer of chamfer of week tine helix is deep; φ is ω of = of installation horn φ + (2 ° of 1 ° ～ ) (the helicoid that after AB makes helix move, 4)2 forms point-blank is equational 2.

In the equational type of 1 linear AB: B=cos η + η of Sin of · of Tg γ A (η of Sin of 5-a) C=b · (η of Sin of 5-b) C=b · (5-b) D=sin η - η of Cos of · of Tg γ A (η of Cos of 5-c) E=b · (5-d) B -- linear AB is in the intercept on Y0 axis (before form of milling cutter cut is rotational) 2.

The coordinate that the helicoid equation after 2 linear AB make helix move makes be connected with milling cutter solid fastens O-XYZ, relative to Yu Xi cutter shaft line makes helix move, linear AB will form a helicoid in the space, its equation is as follows: In type: θ -- helix motion parameter (detailed sees graph 4) ; P -- helix motion parameter, p=H2 π , h is the lead of chamfer of milling cutter helix. Face of the knife before the law vector helix of face of the knife before 3 helix is equational (6) can be written into vector type namely the law vector of face of the knife before reason sets helix is 1, the reason in having type has the heft on axis of X1, Y1, Z1 to be: Type of 4 contacts condition adds up to theory according to to bite, without the contact of law of twinkling pericardium sth resembling a net conditional type is (φ of A-x1+p · Tg) · Nx1=0 of Ny1+z1 of · of φ of Nz1+A · Tg X1(t, θ ) , Y(t, θ ) , Z1(t, θ ) , Nx1(t, θ ) , Ny1(t, θ ) reach Nz1(t, θ ) take the place of to go up type is changed brief hind: (θ of · of Q+p2 · B) Sin θ + (θ of · of D · P2 - S)cos θ + φ of Tg of · of P of · of · D of T+E)+A of · of the Q=(D in W=0 (10) type; (φ of Tg of · of P of · of · B of T-C)+A of 10-a) S=F(B · ; (φ of Tg of 10-b) W=F(A+p · ) (〕 of T+E) of T-C)+D(D · of · of B(B of 10-c) F= 〔 (type of 10-d) contact condition is with T, θ surmounts equation for a variable, because this is OK will (10) pattern simplified a book is F(t, θ ) the equation that type of condition of =0 (11) contact is the face of straight grain of a normal on face of the knife before helix essentially. Couplet of face of the knife before 5 spaces contact equation of face of straight grain of line general normal and helix establishs solution, line space is contacted to contact the line is two afore-mentioned curved surface to cross a line between be free, of face of the knife before it is located in helix apparently. Because the length of AB of generatrix of face of the knife before helix is average not long, not long also and its contact line is accordingly similar at linear. Graph the Rsmin of the smallest radius of emery wheel of 6 dish form will press the 5 osculatory lines in department of emery wheel coordinate (the contacts a line each a little bit coordinate that 12) calculates, era enters next type, can change osculatory line in department of emery wheel coordinate. In type, reach -- in department of milling cutter coordinate, contact the coordinate that nods each on the line. Graph the 5 dimensional positions that contact a line to be in department of emery wheel coordinate. From inside the graph knowable, osculatory line is similar at a space linear, accordingly we can use osculatory line two end points (P1, what replace even the azimuthal λ of the line of Pn) osculatory line to be nodded in Pn approximately is azimuthal. Set osculatory line the coordinate of two end points is P1(X1 respectively, y1, z1) reachs Pn(Xn, yn, zn) , what the azimuthal λ that contacts a line is osculatory line to go up in YZ plane is umbriferous the included angle ε between the umbriferous line that is Tg μ =(Yn-Y1)/(Z­n-Z1) (15) to contact a line to go up in XZ plane with the included angle μ of Z axis and Z axis is Tg ε = | Xn-X1 | / (because Zn-Z1) (16) contacts a line it is curve of a space, because face of the knife before helix of this milling cutter should be on grinding machine of numerical control tool,grinding just can be obtained accurate before horny cost. If be in on common tool grinding machine before helix of grinding milling cutter when knife face, should contact the space the line umbriferous go up to XZ plane, a paragraph of circular arc that goes up with the circle next replaces the umbriferous line that contacts a line approximately. To make sure this is round must the lowest with osculatory line a bit can clench the teeth, the smallest radius of emery wheel of this round i.e. of the smallest radius should satisfy next type: Rsmin= | Xn | (The Rsmin in 17) type -- the smallest radius of dish form emery wheel; Xn -- the nadir on osculatory line the Xn coordinate of Pn. The cut form of face of the knife before the 7 milling cutter helix that beg grinding treatment to come out with law of the sth resembling a net that oppose a package 7.

The equation of line of 1 approximate in department of milling cutter coordinate contact is pressed (the dish form emery wheel that 17) type decides is circumferential the arc of some Duan Yuan that go up is approximate contact line, change this approximate contact line in department of milling cutter coordinate now, referenced graph 3 can get: The Rs in type -- press (the emery wheel radius that 17) type decides or its correction, rs ≥ Rsmin; V -- the rotational horn of emery wheel; Ye -- the emery wheel actual installation on Y axis the position. 7.

The cut form of face of the 2 knives before begging milling cutter helix makes contact line equation approximately (axes of 18) edge milling cutter makes helix move, the approximate surface equation that can get area of the knife before helix makes Zb=0, namely the Z1 value that θ =-z1/p (20) nods each on line of will approximate contact takes the place of (20) type, get a series of value of {θ } , again {θ } , {x1} , {y1} value takes the place of (19) type, can get the similar cut look of face of the knife before helix. When the installation parameter of 8 emery wheel can seek range of the knife before going out to grind helix of tine of milling cutter week in blade through afore-mentioned computation, the diameter of emery wheel reachs his to install parameter to be: Rs ≥ | Xn | In type: E -- the emery wheel that decides first slants buy quantity; E is solid -- the real value of emery wheel slants buy quantity. 9 example (form of cut of milling cutter end sees graph 1)9.

The parameter of face of the knife before the parameter of chamfer of helix of 1 milling cutter and helix of tine of week of auxiliary computation milling cutter (the other parameter that has nothing to do with computation did not include) R=22.

5 Mm; Rs=50 Mm; 30 ′ of ° of A=11 of H=8mm;AB=3 Mm; γ ; ω =30 ° .

Assist computation: The A=22 of γ of Tg of intercept B=x · of linear AB.

30 ′ of ° of 5 · Tg11 =4.

5788 Mm; P: of helix motion parameter? =244 of ° of Tg60 of · of π of · of =45 of ° of Tg60 of · of D of · of Zuo = π .

=38 of π of 8555 ∴ P=H2.

9700; center is apart from A: A=R+Rs-h=22.

5+50-8=64.

5mm.

9.

A=19 of γ of XoB=R-3cos of ∵ of η of horn of roll of truncate of end panel of chamfer of helix of 2 milling cutter.

5603yoB=3sin γ A=0.

5982tg α =yoB/xoB=0.

45 ′ of ° of =1 of 0306 ∴ α and α of B=tg(of γ of Tg η =tg + γ A)=(tg α + A)=0 of γ of Tg of Tg γ A)/(1-tg α .

2356, 16 ′ of ° of ∴ η =13 take ° of ∴ η =13 approximately 9.

φ of 3 installation horn and slant ° of =30 of φ of horn of installation of buy quantity E + ° of 2 ° =32 slants =4 of φ of η Cos of buy quantity E=Rsin.

2930 Mm; =3 of φ of Ey=e · Cos.

=2 of φ of Sin of 6401 Mmez=e · .

2749 Mm.

9.

The equational X=1 of 4 linear AB.

0093 T-1.

5658 T=(22.

5 ∶ - 0.

15 ∶ 19.

5)y=0.

1509 T+4.

3017z=09.

Type of 5 contacts condition [3000 · of Q+1549 · (θ ) ] Sin θ + [40.

5482 · (θ ) - S]cos θ + W=09.

6 contacts line fastens medium coordinate X=[-43 in emery wheel coordinate.

8190 -44.

0312 -44.

2431 -44.

4537 -44.

6628 -44.

8713 -45.

0794.

.

.

- 45.

2867 -45.

4933 -45.

6993 -45.

9054 -46.

1087 -46.

3132 -46.

5177.

.

.

- 46.

7194 -46.

9232 -47.

1249 -47.

3267 -47.

5265 -47.

7252 -47.

9270] ; Y=[0.

2063 0.

1572 0.

1065 0.

0549 0.

0009 -0.

0541 -0.

1107.

.

.

- 0.

1687 -0.

2280 -0.

2379 -0.

3514 -0.

4143 -0.

4795 -0.

5463.

.

.

- 0.

6132 -0.

6829 -0.

7531 -0.

8248 -0.

8970 -0.

9701 -1.

0467] ; Z=[12.

8504 13.

1410 13.

4261 13.

7003 13.

9662 14.

2259 14.

4797.

.

.

14.

7282 14.

9712 15.

2404 15.

4450 15.

6675 15.

8931 16.

1177.

.

.

16.

3285 16.

5466 16.

7553 16.

9630 17.

1613 17.

3544 17.

5592] ; If the dimensional contact clue that according to afore-mentioned data the picture gives pursues 6 are shown. Graph line of 6 spaces contact pursues the cut form of face of the knife before helix of tine of week of 7 milling cutter 9.

Week of 7 milling cutter ages the week of coordinate milling cutter of face of the knife before helix ages the coordinate data of face of the knife before helix is as follows: (This station slightly) graph the 7 milling cutter that go out to press coordinate to draw the cut form of face of the knife before week tine helix. A of γ of the horn before the coordinate that nods from A can calculate those who give point of the A after blade is ground.

The A of γ of included angle Δ of face of the knife before ∵ and Xb axis is A=(8 of Tg Δ γ .

6588-8.

6506)/(21.

3894-20.

6935)=0.

η of A= of γ of ∴ of ′ of A=42 of 0118 Δ γ + 42 ′ of ° of Δ γ A=13.

Although this value compares the 30 ′ of γ A=11 ° of a requirement to slant a few bigger, but still be relatively reasonable before horny cost. 10 conclusion because the osculatory line of face of the knife before helix is curve of a space, because this uses figuration grinding and talent of grinding of numerical control machine tool only,obtain accurate before horny cost. With face of the knife before helix of tine of week of milling cutter of grinding of dish form emery wheel, it is to use planar circular arc to replace a space to contact a line character actually. The horn before the result milling cutter of such grinding all slants big, outside because contact line error,be being divided, the interference of emery wheel also is a reason. Because dish form emery wheel becomes the installation that decide part, and the helix angle that nods each on face of the knife before helix however each are not identical. When face of the knife before helix of tine of week of milling cutter of grinding of emery wheel of the form that use dish although grind,go out before horn slants big, but controallable inside relatively reasonable range, require equipment because of this method place simple, the operation is convenient, accordingly aborning applies extensively. CNC Milling CNC Machining