CN103631197B - Skew ruled surface blade-side cutter spindle vector program method - Google Patents

Abstract

The invention discloses a kind of skew ruled surface blade-side cutter spindle vector program method belonging to NC machining technical field.Steps of the method are: 1) ask for the equidistant surface of skew ruled surface；2) asymptotic direction on equidistant surface is asked for；3) along the point that asymptotic direction step-size in search is δ；4) repeat step 2), 3) search equidistant surface on an asymptotic curve；5) asymptotic curve processed and determine generating tool axis vector；6) repeat step 2), 3), 4), 5), it is thus achieved that the generating tool axis vector of whole skew ruled surface.The method that the present invention proposes, when planning generating tool axis vector, breaches the constraint of existing methods thinking, first does the equidistant surface of ruled surface, then plans generating tool axis vector on equidistant surface.The theoretical error that the method produces controls at micron order, and the theoretical error produced than existing method reduces an order of magnitude, has reached the high-precision requirement of blade processing, is a kind of preferably generating tool axis vector planing method.

Description

Skew ruled surface blade-side cutter spindle vector program method

Technical field

The invention belongs to NC machining technical field, straight burr can not be opened up particularly to one Face blade-side cutter spindle vector program method.

Background technology

Skew ruled surface uses Flank machining efficiency high, but linear contact lay itself exists theoretical error, Therefore, domestic manufacturing enterprise, in order to reach high-precision processing request, often abandons efficient side Milling method, uses ball head knife point milling, changes precision with efficiency.Skew ruled surface side milling theory is poor Control be a difficult point, wherein the planning of generating tool axis vector is the most key, directly affects ruled surface Mismachining tolerance, in existing Flank machining generating tool axis vector planing method, mainly method along bus The distance of vector one tool radius of biasing obtains generating tool axis vector.Existing ruled surface side milling cutter shaft Have following several:

(1) single-point law of planning.As Fig. 1 (a) show the planning of generating tool axis vector single-point law of planning Principle, r₁、r₂It is respectively the directrix of skew ruled surface blade, by straight edge line along on it one The law vector translation tool radius distance of some p forms generating tool axis vector T, and this method can be at Ye Ding Produced with blade root and cut, as Fig. 1 (b) show single-point law of planning produce mistake cut situation.

(2) two laws of planning.As Fig. 2 (a) show the planning of 2 laws of planning of generating tool axis vector Principle, chooses 2 p on straight edge line₁、p₂, bias cutter along this law vector of 2 respectively The distance of radius forms generating tool axis vector T.A kind of method also having improvement is that these 2 is not choosing At the end points of bus, but it is selected on the position in bus parameter V direction 0.25 and 0.75, with This forms generating tool axis vector.This method is better than single-point method, but it is relatively big to cross the amount of cutting in the middle part of straight edge line, If Fig. 2 (b) is that the mistake that 2 laws of planning produce cuts situation.

(3) least square multi-agent plan method.It is illustrated in figure 3 generating tool axis vector least square many The planning principle of some law of planning, uniformly chooses several points on straight edge line, and along law vector direction The distance of biasing radius R, uses these bias points of least square line matching, obtains cutter Axial vector T.The method essence is the popularization of 2 laws of planning, simply processed error of cutting is divided Cloth is on each point of bus.

Existing single-point law of planning, 2 laws of planning and least square multi-agent plan method, be all By biasing tool radius along law vector direction on ruled surface, form generating tool axis vector.Due to can not There is distortion in exhibition ruled surface blade, on skew ruled surface same bus, law vector direction is different, The generating tool axis vector being consequently formed, will be inevitably generated and cut error.

The present invention breaches the constraint of existing methods thinking, it is proposed that a kind of new generating tool axis vector rule The method of drawing.In the method, the planning of generating tool axis vector no longer directly utilizes ruled surface itself and plans, But plan on the equidistant surface of ruled surface.The equidistant surface of skew ruled surface is no longer ruled surface, But general free form surface, but owing to obtaining on the basis of ruled surface, its shape is still So it is similar to ruled surface, therefore yet suffers from a line on this equidistant surface and be similar to straight line, find This line is as generating tool axis vector.The generating tool axis vector that thus method obtains can make mismachining tolerance at cutter With tend to optimum under processed ruled surface contact state, it is thus achieved that high machining accuracy.

Summary of the invention

For the defect of above-mentioned prior art, the present invention proposes a kind of skew ruled surface blade-side Cutter spindle vector program method, it is characterised in that comprise the following steps:

1) equidistant surface of skew ruled surface is asked for；

2) asymptotic direction of a search starting point on equidistant surface is asked for；

3) this search starting point point along asymptotic direction step-size in search δ is asked for；

4) repeat step 2), 3) search equidistant surface on an asymptotic curve；

5) this asymptotic curve processed and determine generating tool axis vector；

6) determine next search starting point with certain cutting step length, repeat step 2), 3), 4), 5), it is thus achieved that the generating tool axis vector of whole skew ruled surface.

Described step 1) in equidistant surface be cutter half relative to the offset or dish of skew ruled surface Footpath r.

Described step 2) in progressive direction be that on equidistant surface, some curvature is the direction of zero.

Described step 3) in step-size in search δ people be given, it is ensured that the asymptotic curve searched On counted 10～20, in order to can be by the follow-up least square fitting section of being in line.

Described step 5) in employing method of least square asymptotic curve is processed.

Described step 6) in certain cutting step length determined by mismachining tolerance.

The beneficial effect of the invention: use the present invention to plan the generating tool axis vector of skew ruled surface, its Theoretical error can be controlled in micron order, and the error produced than existing method reduces an order of magnitude, Its machining accuracy can reach the high-precision requirement of ruled surface blade processing.The method being used for can not In the high accuracy Flank machining of exhibition ruled surface, substitute existing time-consuming some milling, relative to a milling Method, can improve working (machining) efficiency more than ten times, be greatly shortened the blade processing cycle.

Accompanying drawing explanation

Fig. 1 (a) is the planning principle of generating tool axis vector single-point law of planning；

Fig. 1 (b) is that the mistake that single-point law of planning produces cuts situation；

Fig. 2 (a) is the planning principle of 2 laws of planning of generating tool axis vector；

Fig. 2 (b) is that the mistake that 2 laws of planning produce cuts situation；

Fig. 3 is the planning principle of generating tool axis vector least square multi-agent plan method；

Fig. 4 is skew ruled surface generating tool axis vector planing method principle proposed by the invention；

Fig. 5 is the search along progressive direction；

Fig. 6 is certain Centrufugal compressor impeller geometric modeling；

Fig. 7 is certain Centrifugal Compressor Blades moulding and generating tool axis vector；

Fig. 8 is that the generating tool axis vector local that the method in two-point method, method of least square and the present invention generates is put Big figure；

Fig. 9 is that the produced amount of cutting of crossing of the method in two-point method, method of least square and the present invention compares.

Detailed description of the invention

Below in conjunction with the accompanying drawings the inventive method is described further.

It is illustrated in figure 4 skew ruled surface generating tool axis vector planing method proposed by the invention Principle.

(1) equidistant surface of skew ruled surface is asked for；

Due to S on skew ruled surface₁Generally represented by two groups of equal numbers of directrix data, S on skew ruled surface₁Equidistant surface S₂For free form surface, be generally given by space lattice, Therefore, first have to skew ruled surface S₁It is separated into space lattice along generatrix direction, then does Equidistant surface S₂。

If (u v) is S on skew ruled surface to q₁A bit, n is the unit normal vector of q point, cutter Tool radius r is offset or dish, then equidistant surface S₂On corresponding to a q some p (u, v) be:

P=q+n × r (1)

According to said method, equidistant surface S can be obtained₂Dot array data.

(2) asymptotic direction of a search starting point on equidistant surface is asked for；

Owing to straight curvature of a curve is zero, according to curved surface Differential Properties, some curvature on curved surface Be zero direction be progressive direction, therefore with set point as starting point, go out along progressive direction search one by one Article one, line, then this line segment is closest to straight line.

If (u v) is equidistant surface S to p₂A upper known point, the single order local derviation vector of this point is respectively p_u、 p_v, second order local derviation vector is respectively p_uu、p_uv、p_vv, law vector is n.Know according to Differential Geometry Know, then curved surface first fundamental quantity of this point is:

E=p_u·p_u, F=p_u·p_v, G=p_v·p_v

Second fundamental quantity is:

L=p_uuN, M=p_uvN, N=p_vv·n

Along normal curvature k in du/dv direction at some p_nFor curved surface second fundamental form II and the first base The ratio of this form I:

$k_n=\frac{II}{I}=\frac{{\mathrm{Ldu}}^2+2Mdudv+{\mathrm{Ndv}}^2}{{\mathrm{Edu}}^2+2Fdudv+{\mathrm{Gdv}}^2}---\left(2\right)$

Owing to direction progressive at a p is normal curvature k_nIt is the direction of zero, accordingly, it would be desirable to try to achieve One direction du/dv or dv/du so that some p is in curvature k that this side up_nIt is zero.By Fig. 4 Understanding, unit progressive direction f and the v of equidistant surface of equidistant surface is to close, therefore along progressive direction During search, in expression formula du/dv or dv/du of progressive direction f, dv is not zero.

Therefore to formula (2) molecule denominator with divided by (dv)², then formula (2) becomes:

$k_n=\frac{L{\left(\frac{du}{dv}\right)}^2+2M\frac{du}{dv}+N}{E{\left(\frac{du}{dv}\right)}^2+2F\frac{du}{dv}+G}---\left(3\right)$

K to be made_nIt is zero, it is necessary to making the molecule in formula (3) is zero, it may be assumed that

$L{\left(\frac{du}{dv}\right)}^2+2M\frac{du}{dv}+N=0---\left(4\right)$

Formula (4) is a quadratic equation with one unknown about du/dv, second fundamental quantity L, M, N is it is known that therefore can obtain the solution of du/dv.

Solution in formula (5) has two values, correspond to the progressive direction of contrary two respectively, knot Close specifically along the direction of search of equidistant surface, choose one of them solution and scan for as progressive direction.

(3) this search starting point point along asymptotic direction step-size in search δ is asked for；

As it is shown in figure 5, set p, (u v) is equidistant surface S₂A upper known point, p_u、p_vIt is respectively it Local derviation vector, the progressive direction of unit of this point is f, and step-size in search is δ.According to formula (5), If expressing solution du/dv=c in progressive direction, then have:

$\left\{\begin{array}{c}{p}_u\·du+p_v\·dv=f\·\mathrm{\δ}\\ du/dv=c\end{array}\right.---\left(6\right)$

The value of du, dv can be obtained by above formula.

Point p₁(u+du, v+dv) is the point that p point obtains along progressive direction step-size in search δ.

(4) asymptotic curve on step (2), (3) search equidistant surface is repeated；

Repeat step (2) and (3), according to the method first asking progressive direction to search again for, until Equidistant surface S₂Border, whole piece asymptotic curve pp can be searched₁。

(5) this asymptotic curve processed and determine generating tool axis vector；

Said method is used to search for according to progressive direction, although curvature is the direction of zero along curved surface Obtain asymptotic curve, but this curve be not straight line, although actually this curve approximation in Straight line.Accordingly, it would be desirable to progressive curve is processed.

To this end, with the asymptotic curve pp searched₁On point based on, use method of least square Finding straight line, this straight line is the distance nearest straight line of asymptotic curve, using it as Current generating tool axis vector.

(6) determine next search starting point with certain cutting step length, repeat step (2), (3), (4), (5), it is thus achieved that the generating tool axis vector of whole skew ruled surface.

Parameter u direction along Fig. 4, determines cutting step length according to mismachining tolerance, the most again Fix a search starting point, and obtain next asymptotic curve along progressive direction.Repetition step (2), (3), (4), (5), until obtain whole skew ruled surface generating tool axis vector.

Embodiment

If Fig. 6 is certain Centrufugal compressor impeller geometric modeling, wherein, impeller blade is length leaf Sheet, deviated splitter vane is skew ruled surface, now with the pressure face side milling of one of them linear leaf As a example by processing, if Fig. 7 is certain Centrifugal Compressor Blades moulding and generating tool axis vector.Wherein, curved surface S₁For original skew ruled surface, curved surface S₂For the equidistant surface of skew ruled surface, can not open up The length of curve of two directrixes of ruled surface is respectively 96.439mm, 96.372mm, and bus is the longest The a length of 24.919mm in one end, a length of 5.894mm in the shortest one end, use a diameter of 8mm Slotting cutter side milling, the method being utilized respectively in two-point method, method of least square and the present invention plan Side mill axial vector, takes a representational straight edge line in the middle of blade, i.e. during u=0.4945, The generating tool axis vector generated is as drawn a circle shown in position in figure, partial enlargement is as shown in Figure 8.In planning Generating tool axis vector place line segment on take 11 points, and obtain these points respectively and arrive ruled surface Minimum range, deducts tool radius as mismachining tolerance, the error condition of each point using minimum range As shown in Figure 9.

As can be seen from Figure 8, the cutter that existing two-point method and method of least square are formed is utilized Axial vector is substantially consistent with the parameter line such as grade during u=0.4945, and can not distinguish two from figure The difference of bar cutter shaft.But the generating tool axis vector that the method utilizing the present invention to propose generates, its deviation U=0.4945 waits parameter line, and the generating tool axis vector generated with existing method has significantly difference.

It can be seen in figure 9 that 2 law of planning maximum erroies 0.0664mm, least square Multipoint method error 0.0418mm, error 0.0034mm that the planing method of the present invention produces.Table Bright method proposed by the invention, theoretical error is less than the theoretical error that existing method is formed by one The individual order of magnitude.Therefore, when processing skew ruled surface, use this method planning generating tool axis vector, Time-consuming some Milling Machining can be substituted by efficient side milling method.

The above, the only present invention preferably detailed description of the invention, but the protection model of the present invention Enclosing and be not limited thereto, any those familiar with the art is in the skill that the invention discloses In the range of art, the change that can readily occur in or replacement, all should contain in protection scope of the present invention Within.Therefore, protection scope of the present invention should be as the criterion with scope of the claims.

Claims (6)

1. a skew ruled surface blade-side cutter spindle vector program method, it is characterised in that Comprise the following steps:

1) equidistant surface of skew ruled surface is asked for；

2) asymptotic direction of a search starting point on equidistant surface is asked for；

3) this search starting point point along asymptotic direction step-size in search δ is asked for；

4) repeat step 2), 3) search equidistant surface on an asymptotic curve；

5) this asymptotic curve processed and determine generating tool axis vector；

6) determine next search starting point with certain cutting step length, repeat step 2), 3), 4), 5), it is thus achieved that the generating tool axis vector of whole skew ruled surface.

A kind of skew ruled surface blade-side cutter spindle vector the most according to claim 1 Planing method, it is characterised in that the equidistant surface in described step 1) is relative to skew ruled surface Offset or dish be tool radius r.

A kind of skew ruled surface blade-side cutter spindle vector rule the most according to claim 1 The method of drawing, it is characterised in that described step 2) in progressive direction be a little bent on equidistant surface Rate is the direction of zero.

A kind of skew ruled surface blade-side cutter spindle vector rule the most according to claim 1 The method of drawing, it is characterised in that the step-size in search δ people in described step 3) is given, it is ensured that 10～20 have been counted, in order to can be by follow-up method of least square on the asymptotic curve searched Fit to straightway.

A kind of skew ruled surface blade-side cutter spindle vector rule the most according to claim 1 The method of drawing, it is characterised in that the employing method of least square in described step 5) is to asymptotic curve Process.

A kind of skew ruled surface blade-side cutter spindle vector the most according to claim 1 Planing method, it is characterised in that cutting step length certain in described step 6) is by mismachining tolerance Determine.