CN105425727A - Five-axis side milling machining cutter path smoothing method - Google Patents

Abstract

The invention provides a five-axis side milling machining cutter path smoothing method. The method comprises calculating the initial cutter location, and calculating the machine tool turning axle angle corresponding to the direction of a cutter axis through a dynamitic model of a specific machine tool; performing interpolation for the machine tool turning axle angle of the initial cutter location and the cutter nose point location, and obtaining a cutter nose point location trajectory and a machine tool rotation angle change curve; according to the cutter nose point location trajectory and the cutter axis vector, showing a side milling machining cutter path; calculating the rigidity matrix, corresponding to the cutter path, of the machine tool rotation angle curve; according to a differential evolution algorithm, calculating the point that the distance between the point to the cutter enveloping surface is shortest among the points on the design surface; and according to a weighted least square method, establishing a five-axis side milling machining cutter path smoothing model, and obtaining an optimized the initial cutter location and the cutter nose point location curve and a smooth machine tool rotation angle curve after solution. The five-axis side milling machining cutter path smoothing method solves the problem about smoothing and geometric deviation control of the five-axis side milling machining cutter path, and is suitable for five-axis side milling machining on a free form surface, a ruled surface or a curved surface similar to the ruled surface.

Description

Five axle Flank machining cutter path method for fairing

Technical field

The present invention relates to computer graphics and five-shaft numerical control Flank machining technical field, particularly, relate to a kind of five axle Flank machining cutter path method for fairing.

Background technology

The processing of complex curved surface parts is carried out on lathe.Therefore, when planning tool sharpening path, need the dynamic property considering lathe, avoid the rotation shaft angle of lathe to change a lot.Flank machining tool-path planning in the past carries out under workpiece coordinate system, by making cutter axis orientation fairing thus wish the motion also fairing of each axle of lathe under workpiece coordinate system.But the postpositive disposal due to five-axis machine tool is nonlinear model, each axle that five axle tool sharpening tracks of fairing do not represent lathe under workpiece coordinate system moves also fairing, especially when cutter is through the singular regions of lathe, even if very little change occurs the axis of cutter, the turning axle of lathe can produce very large pendulum angle.Therefore the characteristic considering lathe is needed when planning tool sharpening path.For Flank machining, the subtle change of cutter axis orientation may cause larger geometric error, so also need when planning five axle Flank machining cutter path to consider geometric error.

Do not find explanation or the report of technology similar to the present invention at present, not yet collect similar data both at home and abroad yet.

Summary of the invention

For defect of the prior art, the object of the invention is to utilize two-parameter ball race Enveloping theory, a kind of five axle Flank machining cutter path method for fairing are provided.

The present invention is achieved by the following technical solutions.

A kind of five axle Flank machining cutter path method for fairing, comprise the steps:

Step S1: calculate initial cutter spacing, according to the lathe selected, calculates rotary axis of machine tool angle corresponding to initial cutter spacing cutter axis orientation by Post-processing Algorithm;

Step S2: interpolation tool nose point position and rotary axis of machine tool angle, obtains point of a knife point location track line and the generating tool axis vector curve in tool sharpening path;

Step S3: the stiffness matrix calculating rotary axis of machine tool anglec of rotation curve corresponding to cutter path;

Step S4: to calculate in design surface any point to the minimum distance of cutter enveloping surface according to the distance function of differential evolution and point to curved surface;

Step S5: set up five axle Flank machining cutter path fairing models according to weighted least-squares method;

Step S6: according to Gauss-Newton method iterative fairing model;

Step S7: the point of a knife point location track line of the cutter path after being optimized and the rotary axis of machine tool anglec of rotation curve of fairing, and then export NC (numerical control) file.

Preferably, described step S2 comprises the steps:

Step S2.1: the cutter axis orientation of cutter adopts two anglecs of rotation of lathe to represent.

Preferably, for five axle Double swing head lathes, cutter axis orientation O (t) is expressed as:

$O\left(t\right)=\left[\begin{array}{c}{O}_i\left(t\right)\\ O_j\left(t\right)\\ O_k\left(t\right)\end{array}\right]=\left[\begin{array}{c}sin\left(C_C\left(t\right)\right)sin\left(C_A\left(t\right)\right)\\ -cos\left(C_C\left(t\right)\right)sin\left(C_A\left(t\right)\right)\\ cos\left(C_A\left(t\right)\right)\end{array}\right]---\left(2\right)$

Wherein C _a(t), C _ct () represents the lathe anglec of rotation curve that cutter track is corresponding, O respectively _it () represents the x coordinate of generating tool axis vector O (t), O _jt () represents the y coordinate of O (t), O _kt () represents the z coordinate of O (t); Flank machining cutter path adopts point of a knife locus of points P (t) under workpiece coordinate system and generating tool axis vector curve O (t) to represent; Therefore cutter path S (w; A, t) be expressed as:

S(w；a，t)＝P(t)+a·H·O(t)(2)

Wherein represent the reference mark set of cutter path, comprise the reference mark of tool nose locus of points line traffic control point and lathe anglec of rotation curve, a, t represent the parameter of cutter path respectively, and H represents that tool blade is long; If the reference mark number of point of a knife point position curve is l, then m=3l+l+l; Utilize formula (2) to represent Flank machining cutter path, directly optimize two anglecs of rotation of lathe.

Preferably, described step S3 comprises the steps:

Step S3.1: make the reference mark of lathe anglec of rotation curve be respectively wherein l is the reference mark number of point of a knife point position curve, represent that l ties up real number space, utilize formula (3) to measure the fairness F of cutter path _smooth:

$F_{smooth}=\[{\∫}_0^1({\left(\frac{d^2{C}_A\left(t\right)}{{\mathrm{dt}}^2}\right)}^2+{\left(\frac{d^2{C}_C\left(t\right)}{{\mathrm{dt}}^2}\right)}^2+{\left(\frac{{\mathrm{dC}}_A\left(t\right)}{dt}\right)}^2+{\left(\frac{{\mathrm{dC}}_C\left(t\right)}{dt}\right)}^2)dt\]---\left(3\right)$

Its matrix form is:

$F_{smooth}=D_A^T{\mathrm{KD}}_A+D_C^T{\mathrm{KD}}_C$

Wherein K represents stiffness matrix, the element K in stiffness matrix K _ijcomputing formula is:

$K_{ij}={\∫}_0^1\left(B_i^{\′}\right(t\left)B_j^{\′}\right(t)+B_i^{\′\′}(t\left)B_j^{\′\′}\right(t\left)\right)dt,1\≤i\≤l,1\≤j\≤l.$

Preferably, described step S4 comprises the steps:

Step S4.1: according to two-parameter ball race envelope method, can to calculate in design surface any point p to the distance of cutter enveloping surface X (a, t) without the need to constructing enveloping surface; In design surface, any point is to the distance d of cutter enveloping surface X (a, t) _{p, X}w () computing formula is:

$d_{p,X}\left(w\right)=\underset{(a,t)}{min}\left(\right||p-S(w;a,t\left)\right||-r(w;a,t\left)\right)---\left(4\right)$

Wherein r (w; A, t) represent the radius of cutter envelope ball race;

Step S4.2: utilize differential evolution, according to any point p in formula (4) calculating design surface to the minimum distance of cutter enveloping surface, and obtains the parameter (a, t) of closest approach on cutter path S (a, t).

Preferably, described step S5 comprises the steps:

Step S5.1: carry out fairing-optimized to cutter path, need the reference mark adjusting cutter path, the geometrical deviation between cutter enveloping surface and design surface can be increased like this, therefore, need during fairing cutter path to consider geometrical deviation simultaneously, the Flank machining tool-path planning model of the fairing lathe anglec of rotation can be set up by weighted least-squares method:

Wherein λ is fairing weight.

Preferably, described step S6 comprises the steps:

Step 6.1: the model in formula (5) is non-Linear least squares minimization problem, adopt Gauss-Newton method iterative, solution procedure is as follows:

Order $Y=\left[\begin{array}{ccc}{\[0\]}_{3l\×3l}& {\[0\]}_{3l\×3l}& {\[0\]}_{3l\×3l}\\ {\[0\]}_{l\×l}& K& {\[0\]}_{l\×l}\\ {\[0\]}_{l\×l}& {\[0\]}_{l\×l}& K\end{array}\right],$ Then formula (5) is expressed as:

Wherein Y represents the matrix be made up of stiffness matrix K; represent the reference mark set of cutter path.

If w ^kfor current solution, by objective function at w ^kplace makes first-order linear Taylor expansion, obtains corresponding Linear least squares minimization problem:

$F=\underset{i=1}{\overset{n}{\Σ}}{\[d_{p_i,X}\left(w^k\right)+{\left({\mathrm{\Δw}}^k\right)}^T{\mathrm{\Δd}}_{p_i,X}\left(w^k\right)\]}^2+\mathrm{\λ}\[{\left(w^k\right)}^{T}Y\left(w^k\right)+2{\left(w^k\right)}^T{\mathrm{Y\Δw}}^k+{\left({\mathrm{\Δw}}^k\right)}^{T}Y\left({\mathrm{\Δw}}^k\right)\]$

Wherein Δ w ^krepresent optimum solution, then optimum solution Δ w ^kfor:

Δw ^k＝[(A ^k) ^T(A ^k)+λY] ^-1((A ^k) ^Tb ^k+(w ^k) ^TY)

Try to achieve Δ w ^kafter, make w ^k+1=w ^k+ Δ w ^k, and carry out iteration next time, when iterations exceedes maximum iteration time or Δ w ^kchange be less than setting value, then algorithm terminates.

Preferably, according to output cutter spacing number or the requirement of cutter position of cusp bow high level error, point of a knife point location track line after optimization and lathe anglec of rotation curve up-sampling, then export NC file.

Compared with prior art, the present invention has following beneficial effect:

The problem of the rotary axis of machine tool acute variation occurred when 1, the invention solves five-axis machine tool Flank machining curved surface, makes the turning axle motion smoothing of lathe by optimized algorithm, consider the geometric accuracy requirement of the rear part of processing simultaneously.

2, the present invention is applicable to free form surface, ruled surface or class ruled surface curved surface five axle Flank machining.

Accompanying drawing explanation

By reading the detailed description done non-limiting example with reference to the following drawings, other features, objects and advantages of the present invention will become more obvious:

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is tool sharpening path point of a knife point location track line schematic diagram in the present invention;

Fig. 3 is tool sharpening path cutter axis orientation schematic diagram in the present invention;

Fig. 4 is five axle Double swing head lathe schematic diagram in the present invention;

Fig. 5 is S shape design curved surface schematic diagram in the present invention;

Fig. 6 is the lathe C axle change curve that before and after optimizing in the present invention, cutter path is corresponding;

Fig. 7 is the lathe A axle change curve that before and after optimizing in the present invention, cutter path is corresponding.

Embodiment

Below embodiments of the invention are elaborated: the present embodiment is implemented under premised on technical solution of the present invention, give detailed embodiment and concrete operating process.It should be pointed out that to those skilled in the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.

Embodiment

Present embodiments provide a kind of five axle Flank machining cutter path method for fairing, below in conjunction with accompanying drawing, the present embodiment is described in detail.

In the present embodiment, as shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5, the present embodiment, according to two-parameter ball race Enveloping theory computational geometry deviation, utilizes weighted least-squares method to set up five axle Flank machining cutter path fairing models.

Five axle side milling cutter paths can adopt point of a knife locus of points P (t) under workpiece coordinate system and generating tool axis vector curve O (t) to represent

S(w；a，t)＝P(t)+a·H·O(t)

Wherein represent the reference mark set of cutter path, comprise the reference mark of tool nose locus of points line traffic control point and lathe anglec of rotation curve, H represents that tool blade is long.Design surface to the computing formula of the distance of cutter enveloping surface X (a, t) is a bit

$d_{p,X}\left(w\right)=\underset{(a,t)}{min}\left(\right||p-S(w;a,t\left)\right||-r(w;a,t\left)\right)$

Wherein p represents a bit in design surface, S (w; A, t) represent cutter axis face, r (w; A, t) be the radius of a ball.

The reference mark of lathe anglec of rotation curve is made to be respectively following formula is utilized to measure the fairness of cutter path

$F_{smooth}=\[{\∫}_0^1({\left(\frac{d^2{C}_A\left(t\right)}{{\mathrm{dt}}^2}\right)}^2+{\left(\frac{d^2{C}_C\left(t\right)}{{\mathrm{dt}}^2}\right)}^2+{\left(\frac{{\mathrm{dC}}_A\left(t\right)}{dt}\right)}^2+{\left(\frac{{\mathrm{dC}}_C\left(t\right)}{dt}\right)}^2)dt\]$

Its matrix form is:

$F_{smooth}=D_A^T{\mathrm{KD}}_A+D_C^T{\mathrm{KD}}_C$

Wherein K represents stiffness matrix.The Flank machining tool-path planning model of the fairing lathe anglec of rotation can be set up by weighted least-squares method

Wherein λ is fairing weight.

The five axle Flank machining cutter path method for fairing that the present embodiment provides, as shown in Figure 1.First, generating initial cutter spacing, calculating rotary axis of machine tool angle corresponding to initial cutter spacing cutter axis orientation according to specifying the kinematics model of lathe; Utilize 3 B-spline curves interpolation tool nose point positions and rotary axis of machine tool angle, obtain point of a knife point position curve and lathe anglec of rotation curve; Point of a knife locus of points line and lathe anglec of rotation curve is utilized to represent Flank machining cutter track; Calculate the stiffness matrix of lathe anglec of rotation curve corresponding to cutter track; Differential evolution is utilized to calculate the geometrical deviation in tool sharpening path; Set up five axle Flank machining cutter path fairing models according to weighted least-squares method, and utilize this Optimized model of Gauss-Newton method iterative; Export cutter location number according to the high level error constraint of tool nose point bow or appointment, in point of a knife locus of points line and lathe anglec of rotation curve up-sampling data point, export NC file.

In the present embodiment, circular cutter Flank machining free form surface as shown in Figure 5 as shown in Figure 2, similar method can be applied to other revolving cutter Flank machining, specifically comprises the steps:

Step 1: generate initial cutter spacing, calculates rotary axis of machine tool angle corresponding to initial cutter spacing cutter axis orientation according to specifying the kinematics model of lathe;

Step 2: utilize 3 B-spline curves interpolation tool nose point positions and rotary axis of machine tool angle, obtains point of a knife point position curve and lathe anglec of rotation curve;

Step 3: the stiffness matrix calculating lathe anglec of rotation curve corresponding to cutter path;

Step 4: utilize differential evolution to calculate the geometrical deviation in tool sharpening path;

Step 5: set up five axle Flank machining cutter path fairing models according to weighted least-squares method;

Step 6: utilize this Optimized model of Gauss-Newton method iterative; When the knots modification that iterations equals setting value or reference mark is less than the threshold value of setting, complete model optimization, obtain the point of a knife locus of points line after optimizing and lathe anglec of rotation curve;

Step 7: require according to discretization error or export cutter spacing number, at point of a knife locus of points line and lathe anglec of rotation curve up-sampling, obtaining NC file.

The five axle Flank machining cutter path method for fairing that the present embodiment provides, comprising: calculate initial cutter spacing, and by specifying the kinematics model of lathe to calculate rotary axis of machine tool angle corresponding to cutter axis orientation; The rotary axis of machine tool angle of the initial cutter spacing of interpolation and tool nose point position, obtain point of a knife point location track line and lathe anglec of rotation change curve; Flank machining cutter path is represented according to point of a knife point location track line and generating tool axis vector; Calculate the stiffness matrix of lathe anglec of rotation curve corresponding to cutter path; The closest approach of the point in design surface to cutter enveloping surface is calculated according to differential evolution; Five axle Flank machining cutter path fairing models are set up, the lathe anglec of rotation change curve of the tool nose be optimized after solving some position curve and fairing according to weighted least-squares method.The present embodiment solves the problem of five axle Flank machining cutter path fairing and geometrical deviation control, is applicable to free form surface, ruled surface or class ruled surface curved surface five axle Flank machining.

Above specific embodiments of the invention are described.It is to be appreciated that the present invention is not limited to above-mentioned particular implementation, those skilled in the art can make various distortion or amendment within the scope of the claims, and this does not affect flesh and blood of the present invention.

Claims (8)

1. five axle Flank machining cutter path method for fairing, is characterized in that, comprise the steps:

Step S1: calculate initial cutter spacing, according to the lathe selected, calculates rotary axis of machine tool angle corresponding to initial cutter spacing cutter axis orientation by Post-processing Algorithm;

Step S2: interpolation tool nose point position and rotary axis of machine tool angle, obtains point of a knife point location track line and the generating tool axis vector curve in tool sharpening path;

Step S3: the stiffness matrix calculating rotary axis of machine tool anglec of rotation curve corresponding to cutter path;

Step S4: to calculate in design surface any point to the minimum distance of cutter enveloping surface according to the distance function of differential evolution and point to curved surface;

Step S5: set up five axle Flank machining cutter path fairing models according to weighted least-squares method;

Step S6: according to Gauss-Newton method iterative fairing model;

Step S7: the point of a knife point location track line of the cutter path after being optimized and the rotary axis of machine tool anglec of rotation curve of fairing, and then export NC file.

2. five axle Flank machining cutter path method for fairing according to claim 1, it is characterized in that, described step S2 comprises the steps:

Step S2.1: the cutter axis orientation of cutter adopts two anglecs of rotation of lathe to represent.

3. five axle Flank machining cutter path method for fairing according to claim 2, it is characterized in that, for five axle Double swing head lathes, cutter axis orientation O (t) is expressed as:

$O\left(t\right)=\left[\begin{array}{c}{O}_i\left(t\right)\\ O_j\left(t\right)\\ O_k\left(t\right)\end{array}\right]=\left[\begin{array}{c}sin\left(C_C\right(t\left)\right)sin\left(C_A\right(t\left)\right)\\ -cos\left(C_C\right(t\left)\right)sin\left(C_A\right(t\left)\right)\\ cos\left(C_A\right(t\left)\right)\end{array}\right]---\left(1\right)$

Wherein C _a(t), C _ct () represents the lathe anglec of rotation curve that cutter track is corresponding, O respectively _it () represents the x coordinate of generating tool axis vector O (t), O _jt () represents the y coordinate of O (t), O _kt () represents the z coordinate of O (t); Flank machining cutter path adopts point of a knife locus of points P (t) under workpiece coordinate system and generating tool axis vector curve O (t) to represent; Therefore cutter path S (w; A, t) be expressed as:

S(w；a，t)＝P(t)+a·H·O(t)(2)

Wherein represent the reference mark set of cutter path, comprise the reference mark of tool nose locus of points line traffic control point and lathe anglec of rotation curve, a, t represent the parameter of cutter path respectively, and H represents that tool blade is long; If the reference mark number of point of a knife point position curve is l, then m=3l+l+l; Utilize formula (2) to represent Flank machining cutter path, directly optimize two anglecs of rotation of lathe.

4. five axle Flank machining cutter path method for fairing according to claim 1, it is characterized in that, described step S3 comprises the steps:

Step S3.1: make the reference mark of lathe anglec of rotation curve be respectively wherein l is the reference mark number of point of a knife point position curve, represent that l ties up real number space, utilize formula (3) to measure the fairness F of cutter path _smooth:

$F_{smooth}=\[{\∫}_0^1({\left(\frac{d^2{C}_A\left(t\right)}{{\mathrm{dt}}^2}\right)}^2+{\left(\frac{d^2{C}_C\left(t\right)}{{\mathrm{dt}}^2}\right)}^2+{\left(\frac{{\mathrm{dC}}_A\left(t\right)}{dt}\right)}^2+{\left(\frac{{\mathrm{dC}}_C\left(t\right)}{dt}\right)}^2)dt\]---\left(3\right)$

Its matrix form is:

$F_{smooth}=D_A^T{\mathrm{KD}}_A+D_C^T{\mathrm{KD}}_C$

Wherein K represents stiffness matrix, the element K in stiffness matrix K _ijcomputing formula is:

$K_{ij}={\∫}_0^1\left(B_i^{\′}\right(t\left)B_j^{\′}\right(t)+B_i^{\′\′}(t\left)B_j^{\′\′}\right(t\left)\right)dt,1\≤i\≤l,1\≤j\≤l.$

5. five axle Flank machining cutter path method for fairing according to claim 1, it is characterized in that, described step S4 comprises the steps:

Step S4.1: according to two-parameter ball race envelope method, can to calculate in design surface any point p to the distance of cutter enveloping surface X (a, t) without the need to constructing enveloping surface; In design surface, any point is to the distance d of cutter enveloping surface X (a, t) _{p, X}w () computing formula is:

$d_{p,X}\left(w\right)=\underset{(a,t)}{min}\left(\right||p-S(w;a,t\left)\right||-r(w;a,t\left)\right)---\left(4\right)$

Wherein r (w; A, t) represent the radius of cutter envelope ball race;

Step S4.2: utilize differential evolution, according to any point p in formula (4) calculating design surface to the minimum distance of cutter enveloping surface, and obtains the parameter (a, t) of closest approach on cutter path S (a, t).

6. five axle Flank machining cutter path method for fairing according to claim 1, it is characterized in that, described step S5 comprises the steps:

Step S5.1: carry out fairing-optimized to cutter path, need the reference mark adjusting cutter path, the geometrical deviation between cutter enveloping surface and design surface can be increased like this, therefore, need during fairing cutter path to consider geometrical deviation simultaneously, the Flank machining tool-path planning model of the fairing lathe anglec of rotation can be set up by weighted least-squares method:

Wherein λ is fairing weight.

7. five axle Flank machining cutter path method for fairing according to claim 1, it is characterized in that, described step S6 comprises the steps:

Step 6.1: the model in formula (5) is non-Linear least squares minimization problem, adopt Gauss-Newton method iterative, solution procedure is as follows:

Order $Y=\left[\begin{array}{ccc}{\[0\]}_{3l\×3l}& {\[0\]}_{3l\×3l}& {\[0\]}_{3l\×3l}\\ {\[0\]}_{l\×l}& K& {\[0\]}_{l\×l}\\ {\[0\]}_{l\×l}& {\[0\]}_{l\×l}& K\end{array}\right],$ Then formula (5) is expressed as:

Wherein Y represents the matrix be made up of stiffness matrix K;

If w ^kfor current solution, by objective function at w ^kplace makes first-order linear Taylor expansion, obtains corresponding Linear least squares minimization problem:

$F=\underset{i=1}{\overset{n}{\Σ}}{\[d_{p_i,X}\left(w^k\right)+{\left({\mathrm{\Δw}}^k\right)}^T{\mathrm{\Δd}}_{p_i,X}\left(w^k\right)\]}^2+\mathrm{\λ}\[{\left(w^k\right)}^{T}Y\left(w^k\right)+2{\left(w^k\right)}^T{\mathrm{Y\Δw}}^k+{\left({\mathrm{\Δw}}^k\right)}^{T}Y\left({\mathrm{\Δw}}^k\right)\]$

Wherein Δ w ^krepresent optimum solution, then optimum solution Δ w ^kfor:

Δw ^k＝[(A ^k) ^T(A ^k)+λY] ^-1((A ^k) ^Tb ^k+(w ^k) ^TY)

Try to achieve Δ w ^kafter, make w ^k+1=w ^k+ Δ w ^k, and carry out iteration next time, when iterations exceedes maximum iteration time or Δ w ^kchange be less than setting value, then algorithm terminates.

8. five axle Flank machining cutter path method for fairing according to claim 1, it is characterized in that, according to output cutter spacing number or the requirement of cutter position of cusp bow high level error, point of a knife point location track line after optimization and lathe anglec of rotation curve up-sampling, then export NC file.