CN1413790A - Drum taper tool and method for side milling complex cambered centrifugal impeller using drum taper tool - Google Patents

Abstract

A conic drum-shaped cutting tool and its feed pitch, feed step length and method for calculating the position of cutting tool are disclosed. Its cutting part is a rotary surface. Its generating line is an arc with radius R. Its advantages are high productivity, high rigidity and high rotation flexibility. A method for laternally milling a centrifugal blade wheel with complex curved surface with the said cutting tool is also disclosed, which features less number of tracings, short tracing and high productivity.

Description

Drum-taper type cutter tool and utilize the method for the complex-curved centrifugal impeller of drum-taper type cutter tool side milling

One, affiliated technical field

The present invention relates to the complex-curved Computerized Numerical Control processing technology such as arbitrary surface impeller in machining and Computerized Numerical Control processing technology field, particularly a kind of drum-taper type cutter tool and utilize the complex-curved method of drum-taper type cutter tool side milling.

Two, background technology

At present, the cutter that adopts usually in centrifugal impeller fine finishining is spherical cutter, and the effective radius of clean-up of spherical cutter is little, and working (machining) efficiency is low.

C.Y.Wu. (Arbitrary surface flank milling of fan, compressor, andimpeller blades.Transactions of the ASME, Journal of Engineering forGas Turbines and Power, Vol.117,1995, p534～p539), proposed to utilize the method for tapered knife side milling arbitrary surface impeller blade, its cutting edge is a taper seat, referring to Fig. 1.He has broken through the processing arbitrary surface and must adopt spherical cutter or slotting cutter to carry out this mode of thinking of contact processing, and the processing mode of line contact efficiently is applied in the processing of arbitrary surface, and this method working (machining) efficiency is far longer than spherical cutter.

Find in the practice that adopt tapered knife processing arbitrary surface to have following defective: 1) this method requires relatively harshness to the direction of cutter in processing blade shape and the processing, and leaf curling can not be too big, otherwise can not find suitable cutter Working position.For given position on the processing curve, the feasible direction territory of cutter is very little, and rotation leeway is little; 2) if cutter and blade bump, because the feasible direction territory of cutter is little, the cutter slewing area is little, interferes cutter spacing to be difficult to revise.Therefore, mill in the system process in arbitrary surface ternary centrifugal impeller integral body, this method may be failed.

Liu Xiongwei, Zhang Dinghua etc. (" digital control processing theory and programming technique " Beijing: China Machine Press, 1994); Introduced the thinking of utilizing drum knife side milling curved surface, referring to Fig. 2, adopted this sharp method, the contact length of cutter and finished surface is bigger.Just utilize drum knife to introduce the basic principle of side milling in the document, do not relate to the calculating of drum knife curved sides milling cutter position.

Because impeller channel is a slype, adopt the drum type cutter, the ratio of rigidity of cutter is less, influences machining accuracy.

Three, summary of the invention

Defective or deficiency at above-mentioned prior art existence, an object of the present invention is to provide a kind of drum-taper type cutter tool, the characteristics of this drum-taper type cutter tool are, Tool in Cutting partly is the surface of revolution, bus is one section circular arc that radius is R, and the surface of revolution and handle of a knife are tangent, the no cutting edge in cutter bottom, principle not take place to be cut to curved surface in the value of R in this cutter, and promptly the radius of curvature of curved surface contact point should be greater than the R value; Drum-taper type cutter tool of the present invention is a kind of cutting tool efficiently, kept drum knife and tapered knife working (machining) efficiency with respect to spherical knife up, overcome the little weakness of drum knife rigidity simultaneously, than tapered knife greater flexibility is arranged again, can avoid easily cutting and colliding, be the whole process tool of a kind of desirable arbitrary surface 3 d impeller.

Another object of the present invention provides a kind of method of utilizing the complex-curved centrifugal impeller of drum-taper type cutter tool side milling, may further comprise the steps:

1) calculating of cutter path spacing and cutting step length

(1) calculating of cutter path spacing

Comprise that 1. curved surface is along the method transversal radius of curvature R of vector b _bCalculating; 2. the Tool in Cutting face is along effective radius of clean-up r of vector b _cCalculating.

(2) calculating of cutting step length

2) cutter spacing data computing

Comprise the calculating of the calculating of generating tool axis vector l and cutter computer center.

The present invention adopts drum-taper type cutter processing impeller, and under same processing conditions, cutter path length is short, and required process time is few, promptly adopts this cutter fine finishining arbitrary surface impeller, and working (machining) efficiency will be 3 times of conventional method.Simultaneously, it has greater flexibility than tapered knife, is easy to revise the interference of cutter and blade in the processing; And rigidity is higher than drum knife.

Four, description of drawings

Fig. 1 is conical knife structure figure;

Fig. 2 is the drum knife structure chart;

Fig. 3 is a drum-taper type cutter structure chart of the present invention;

Fig. 4 utilizes drum-taper type cutter side milling curved surface schematic diagram;

Fig. 5 is the calculating schematic diagram of search spacing d;

The schematic cross-section of Fig. 6 drum-taper type cutter cutting tip;

Fig. 7 is definite schematic diagram of cutter computer center;

Fig. 8 is the cutter path that adopts drum-taper type cutter to form;

Fig. 9 is the cutter path that adopts spherical cutter to form.

Five, the specific embodiment

The present invention is described in further detail below in conjunction with specific embodiment that accompanying drawing and inventor provide.5.1 the proposition of drum taper

The present invention proposes a kind of utilize the complex-curved centrifugal impeller of highly-efficient processing cutting tool, claim that this cutter is a drum-taper type cutter, referring to Fig. 3.Tool in Cutting partly is the surface of revolution, and bus is one section circular arc that radius is R, and the surface of revolution and handle of a knife are tangent, the no cutting edge in cutter bottom.Drum-taper type cutter has kept drum knife and the tapered knife working (machining) efficiency with respect to spherical knife up, overcome the little weakness of drum knife rigidity simultaneously, than tapered knife greater flexibility being arranged again, can avoid easily cutting and colliding, is the whole process tool of the centrifugal 3 d impeller of a kind of desirable arbitrary surface.The choosing with curved surface principle not to take place to be cut to of R in this cutter, promptly the radius of curvature of curved surface contact point should be greater than the R value.5.2 the calculating of cutter path spacing and cutting step length

The situation of utilizing drum-taper type cutter side milling curved surface as shown in Figure 4, r (u, w) expression curved surface, cutter contact point is some C, some O is the computer center of cutter, l is the cutter axis orientation vector, unit vector f is a cutting direction, and n is that the per unit system that C is ordered is vowed vector b=n * f, these three vectors have been formed a rectangular coordinate system, and initial point is at a C.In the processing of five coordinates, cutter also has two rotary freedoms.The inceptive direction of getting cutter shaft is consistent with vector b, and at first initial generating tool axis vector is rotated an angle [alpha] around vector f; Then, cutter rotates one angle-β around vector n again, and positive direction determines that with right-handed system this is because during Tool in Cutting, cutter shaft must be inclined to one side to cutting direction f, drags the cutter cutting with formation.As can be seen from Figure, cutter shaft when initial position, α=0, β=0.

In the Surface NC Machining, must calculate cutter path spacing and cutting step length.

(1) calculating of cutter path spacing

Vow that perpendicular to method f does a cross section at the C point, then vector b and CC ' must be in this planes, and as shown in Figure 5, the curved surface section line that obtains can be approx with one section arc representation, and radius is that the C point is designated as R along the method transversal radius of curvature of direction b on the curved surface _bEqually, the Tool in Cutting face is along the also available one section circular arc approximate representation of the section line of direction b, and its radius is designated as r for the method transversal radius of curvature of cutter C point along direction b _c

For given R _b, r _cAnd residual height h, cutter path spacing d can calculate with following formula $d=\sqrt{\frac{{8R}_b\·r_c\·h}{R_b\±r_c}}----\left(1\right)$ 1) curved surface is along the method transversal radius of curvature R of vector b _bCalculating

According to Differential Geometry knowledge, the tangent line b that curved surface C is ordered can be expressed as

b＝r _ud _u+r _wd _w

Wherein, d _u, d _wBe respectively vector b at tangent vector r _u, r _wOn component.

Then the method transversal radius of curvature along direction b is $R_b=\frac{I}{\mathrm{II}}=\frac{{\mathrm{Edu}}^2+2\mathrm{Fdudw}+{\mathrm{Gdw}}^2}{{\mathrm{Ldu}}^2+2\mathrm{Mdudw}+{\mathrm{Ndw}}^2}----\left(2\right)$

Wherein, I is a first fundamental form of surface, and E, F, G are respectively the first kind fundamental quantity of curved surface, and II is a second fundamental form of a surface, and L, M, N are respectively the second class fundamental quantity of curved surface.

If d _w=0, then $R_b=\frac{I}{\mathrm{II}}=\frac{E}{L}$

If d _w≠ 0, then formula (2) is done a conversion, have $R_b=\frac{I}{\mathrm{II}}=\frac{{E\left(\frac{\mathrm{du}}{\mathrm{dw}}\right)}^2+2F\frac{\mathrm{du}}{\mathrm{dw}}+G}{L{\left(\frac{\mathrm{du}}{\mathrm{dw}}\right)}^2+2M\frac{\mathrm{du}}{\mathrm{dw}}+N}----\left(3\right)$

As shown in Figure 4

b·f＝0

I.e. (r _uDu+r _wDw) f=0 $\frac{\mathrm{du}}{\mathrm{dw}}=-\frac{r_w\·f}{r_u\·f}----\left(4\right)$

Thus

Formula (4) substitution formula (3) can be obtained the radius of curvature R of Surface Method transversal _bValue.2) the Tool in Cutting face is along effective radius of clean-up r of vector b _cCalculating

The Tool in Cutting face is dissectd along the plane of crossing cutter shaft, shown partial cross section as Fig. 6, wherein heavy line is a cutting edge, and some O is the computer center of cutter, and some O ' is the center of cutter revolution bus, and R is the bus radius, and C is a cutter contact point.With an O is the origin of coordinates, cutter shaft to radially respectively as reference axis z and r.α is the angle of O ' C and r axle.From figure as can be known, have point of contact, promptly put C and be in the cutting tip that heavy line is represented among Fig. 6, the maximum deflection value α of angle [alpha] in order to make cutter and curved surface _MaxShould satisfy: ${\mathrm{\&alpha;}}_{\max }<\arcsin \frac{h}{R}$ By the geometrical relationship shown in Fig. 6, can obtain the coordinate that C orders and be:

By Fig. 4 and Fig. 6, can get according to Euler's formula, behind cutter tilt angle alpha and the β, at Tool in Cutting face contact point place, along the normal curvature of vector b direction be

k _c＝k ₁cos ²β+k ₂sin ²β

Wherein, k ₁And k ₂Be respectively the principal curvatures of this contact point, k ₁=1/R, k ₂=1/r=1/ (Rcos α-(R-d _c/ 2))

So effective radius of clean-up r of cutter _cFor

r _c＝1/k _c (5)

With formula (5) and formula (3) substitution formula (1),, can try to achieve cutter path spacing d because h is given.(2) calculating of cutting step length

In the multi-coordinate digital control processing of curved surface, the linear interpolation mode is generally adopted in the motion of cutter, and establishing the straight line approximate error that exists between the movement locus of cutter reality and the theoretical CC track is δ, and then cutting step length AB can be calculated as follows: $\mathrm{AB}\&ap;\sqrt{\frac{8\mathrm{\&delta;}}{k_f}}$

Wherein, K _fCurvature for tool track contact point place.5.3 cutter spacing data computing

The cutter spacing data comprise the calculating central position O and cutter axis orientation (unit vector) l of cutter, and the calculating of cutter spacing is relevant with the geomery of cutter.For the drum-taper type cutter tool, cutter spacing is calculated as follows.

(1) calculating of generating tool axis vector l

As shown in Figure 4, the initial position of generating tool axis vector is a vector b, at this moment, and α=β=0.At first making cutter is the center with an O ', around vector f anglec of rotation α, referring to Fig. 6.Making cutter again is the center with a C, around the vector n anglec of rotation-β.If generating tool axis vector is from the vector l of inceptive direction b behind vector f anglec of rotation α ₁, then

l ₁＝b·cosα+n·sinα

Generating tool axis vector l ₁Around vector n rotation-β angle, can obtain the final direction vector l of cutter shaft, have

l＝l ₁·cosβ-n×l ₁·sinβ+n·(l ₁·n)·(1-cosβ) (6)

(2) calculating of cutter computer center

Fig. 7 has shown cutter before and after vector f anglec of rotation α, the change situation of computer center.Wherein, some O ' is the center of circle of Tool in Cutting surface of revolution bus, some O ₁Be the computer center of cutter initial position, some O ₂Computer center for cutter behind the anglec of rotation α.

If vector O ' O ₁Behind vector f anglec of rotation α is O ' O ₂, vector O ' O ₂After vector n rotation-β angle for vector O ' O (not expressing among the figure), then pass through rotation transformation after, the final computer center's point O of cutter is

O=O '+O ' O (7) by Fig. 6 and Fig. 7 as can be known

O′＝C+n·R，O ₁＝C+n·(d _c/2)

Then

O′O ₁＝n·(d _c/2-R) (8)

Vector O ' O ₂O ' O is respectively with vector

O′O ₂＝O′O ₁·cosα+f×O′O ₁·sin (9)

O′O＝O′O ₂·cosβ-n×O′O ₂·sin?ββ+n·(O′O ₂·n)·(1-cosβ) (10)

With formula (8) substitution formula (9), formula (9) substitution formula (10) can be tried to achieve O ' O,, can try to achieve final computer center's point O of cutter again with formula (10) substitution formula (7).

Formula (6) and formula (7) have been determined the O of computer center of cutter axis orientation l and cutter respectively, and (O l) determines the cutter spacing data thus.

Adopt drum-taper type cutter processing blade of the present invention, the result shows, its cutter path number is far smaller than the track number when adopting spherical cutter, the ratio of the two is generally about 1: 3, under same processing conditions, cutter path length is short, and required process time is few, promptly adopt the smart arbitrary surface processing of this cutter impeller, working (machining) efficiency will be 3 times of conventional method.Simultaneously, it has greater flexibility than tapered knife, is easy to revise in the processing interference of cutter and blade; And rigidity is higher than drum knife.

Embodiment:

Utilize spherical cutter and drum-taper type cutter respectively, the cutter path in the processing of centrifugal impeller blade five coordinates is generated discuss.Blade is an arbitrary surface, represents with the cubic B batten.Used spherical cutter diameter is d _c=32mm, drum-taper type cutter knife bar diameter d _c=32mm, R=70mm, h=25mm is referring to Fig. 1.Allowing residual height is 0.1mm, respectively to the cutter path in above-mentioned two kinds of cutters calculating blade processing.

Result of calculation such as Fig. 8 and shown in Figure 9 adopt drum-taper type cutter, and the track number of processing this blade is 16, and the track total length is 6631mm; And adopt spherical cutter track number to reach 39 more than, and the track total length is 16453mm, the ratio of the two is 1: 2.5.Under same cutting speed, the working (machining) efficiency that adopts drum-taper type cutter is 2.5 times of spherical cutter.

Claims (3)

1. a drum-taper type cutter tool comprises handle of a knife and cutting tip, it is characterized in that, Tool in Cutting partly is the surface of revolution, and bus is one section circular arc that radius is R, and the surface of revolution and handle of a knife are tangent, the no cutting edge in cutter bottom.

2. drum-taper type cutter tool as claimed in claim 1 is characterized in that, the R span in the described cutter is that the radius of curvature of curved surface contact point should be greater than the R value.

3. a method of utilizing the complex-curved centrifugal impeller of drum-taper type cutter side milling is characterized in that, may further comprise the steps:

1) calculating of cutter path spacing and cutting step length

A. set up coordinate system

If curved surface be r (u, w), cutter and curved surface r (u, w) contact point for the some C, computer center's point of cutter is O, and the cutter axis orientation vector is l, and unit vector f is a cutting direction, and n is that the per unit system that C is ordered is vowed, vector b=n * f, these three vectors have been formed a rectangular coordinate system, and initial point is at a C; In the processing of five coordinates, cutter also has two rotary freedoms; The inceptive direction of getting cutter shaft is consistent with vector b, and at first initial generating tool axis vector is rotated an angle [alpha] around vector f; Then, cutter rotates one angle-β around vector n again, and positive direction determines that with right-handed system this is because during Tool in Cutting, cutter shaft must drag the cutter cutting with formation to cutting direction f skew; Cutter shaft when initial position, α=0, β=0;

B. the calculating of cutter path spacing

Vow that perpendicular to method f does a cross section at the C point, then vector b and CC ' must be in this planes, and the curved surface section line that obtains can be approx with one section arc representation, and radius is that the C point is designated as R along the method transversal radius of curvature of direction b on the curved surface _b, same, the Tool in Cutting face is along the also available one section circular arc approximate representation of the section line of direction b, and its radius is designated as r for the method transversal radius of curvature of cutter C point along direction b _c

For given R _b, r _cAnd residual height b, cutter path spacing d can calculate with following formula $d=\sqrt{\frac{{8R}_b\&CenterDot;r_c\&CenterDot;h}{R_b\&PlusMinus;r_c}}----\left(1\right)$

1. curved surface is along the method transversal radius of curvature R of vector b _bCalculating

According to Differential Geometry knowledge, the tangent line b that curved surface C is ordered can be expressed as

b＝r _ud _u+r _wd _w

Wherein, d _u, d _wBe respectively vector b at tangent vector r _u, r _wOn component.

Then the method transversal radius of curvature along direction b is $R_b=\frac{I}{\mathrm{II}}=\frac{{\mathrm{Edu}}^2+2\mathrm{Fdudw}+{\mathrm{Gdw}}^2}{{\mathrm{Ldu}}^2+2\mathrm{Mdudw}+{\mathrm{Ndw}}^2}----\left(2\right)$

Wherein, I is a first fundamental form of surface, and E, F, G are respectively the first kind fundamental quantity of curved surface, and II is a second fundamental form of a surface, and L, M, N are respectively the second class fundamental quantity of curved surface.

If d _w=0, then $R_b=\frac{1}{\mathrm{II}}=\frac{E}{L}$

If d _w≠ 0, then formula (2) is done a conversion, have $R_b=\frac{I}{\mathrm{II}}=\frac{E{\left(\frac{\mathrm{du}}{\mathrm{dw}}\right)}^2+2F\frac{\mathrm{du}}{\mathrm{dw}}+G}{L{\left(\frac{\mathrm{du}}{\mathrm{dw}}\right)}^2+2M\frac{\mathrm{du}}{\mathrm{dw}}+N}----\left(3\right)$

Because bf=0

I.e. (r _wDu+r _wDw) f=0 $\frac{\mathrm{du}}{\mathrm{dw}}=-\frac{r_w\&CenterDot;f}{r_u\&CenterDot;f}----\left(4\right)$

Thus

Formula (4) substitution formula (3) can be obtained the radius of curvature R of Surface Method transversal _bValue;

2. the Tool in Cutting face is along effective radius of clean-up r of vector b _cCalculating

The Tool in Cutting face is dissectd along the plane of crossing cutter shaft, and some O is the computer center of cutter, and some O ' is the center of cutter revolution bus, and R is the bus radius, and C is a cutter contact point;

With an O is the origin of coordinates, cutter shaft to radially respectively as reference axis z and r; α is the angle of O ' C and r axle; For cutter and curved surface are had point of contact, promptly put C and be in cutting tip, the maximum deflection value α of angle [alpha] _MaxShould satisfy: ${\mathrm{\&alpha;}}_{\max }<\arcsin \frac{h}{R}$ Can obtain the coordinate that C orders is:

Can get according to Euler's formula, behind cutter tilt angle alpha and the β,, be along the normal curvature of vector b direction at Tool in Cutting face contact point place

k _c＝k ₁cos ²β+k ₂sin ²β

Wherein, k ₁And k ₂Be respectively the principal curvatures of this contact point, k ₁=1/R, k ₂=1/r=1/ (Rcos α-(R-d _c/ 2))

So effective radius of clean-up r of cutter _cFor

r _c＝1/k _c (5)

With formula (5) and formula (3) substitution formula (1),, can try to achieve cutter path spacing d because h is given

C. the calculating of cutting step length

In the multi-coordinate digital control processing of curved surface, the linear interpolation mode is generally adopted in the motion of cutter, and establishing the straight line approximate error that exists between the movement locus of cutter reality and the theoretical CC track is δ, and then cutting step length AB can be calculated as follows: $\mathrm{AB}\&ap;\sqrt{\frac{8\mathrm{\&delta;}}{k_f}}$

Wherein, k _fCurvature for tool track contact point place;

2) cutter spacing data computing

The cutter spacing data comprise the calculating central position O and cutter axis orientation (unit vector) l of cutter, and the calculating of cutter spacing is relevant with the geomery of cutter, and for the drum-taper type cutter tool, cutter spacing is calculated as follows:

1. the calculating of generating tool axis vector l

The initial position of generating tool axis vector is a vector b, and at this moment, it is the center with an O ' that α=β=0 at first makes cutter, and around vector f anglec of rotation α, making cutter again is the center with a C, around the vector n anglec of rotation-β; If generating tool axis vector is from the vector l of inceptive direction b behind vector f anglec of rotation α ₁Then

l ₁＝b·cosα+n·sinα

Generating tool axis vector l ₁Around vector n rotation-β angle, can obtain the final direction vector l of cutter shaft, have

l＝l ₁·cosβ-n×l ₁·sinβ+n·(l ₁·n)·(1-cosβ) (6)

2. the calculating of cutter computer center

Cutter calculates the change situation of center cutter before and after vector f anglec of rotation α; Wherein, some O ' is the center of circle of Tool in Cutting surface of revolution bus, some O ₁Be the computer center of cutter initial position, some O ₂Computer center for cutter behind the anglec of rotation α;

If vector O ' O ₁Behind vector f anglec of rotation α is O ' O ₂, vector O ' O ₂After vector n rotation-β angle is vector O ' O, then pass through rotation transformation after, the final computer center's point O of cutter is

O=O '+O ' O (7) is promptly:

O′＝C+n·R，O ₁＝C+n·(d _c/2)

Then

O′O ₁＝n·(d _c/2-R) (8)

Vector O ' O ₂O ' O is respectively with vector

O′O ₂＝O′O ₁·cosα+f×O′O ₁·sinα (9)

O′O＝O′O ₂·cosβ-n×O′O ₂·sinβ+n·(O′O ₂·n)·(1-cosβ) (10)

With formula (8) substitution formula (9), formula (9) substitution formula (10) can be tried to achieve O ' O,, can try to achieve final computer center's point O of cutter again with formula (10) substitution formula (7).

Formula (6) and formula (7) have been determined the O of computer center of cutter axis orientation l and cutter respectively, and (O l) determines the cutter spacing data thus.

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