CN108803487A - A kind of point profile errors prediction technique on part side milling surface - Google Patents

A kind of point profile errors prediction technique on part side milling surface Download PDF

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CN108803487A
CN108803487A CN201810940066.7A CN201810940066A CN108803487A CN 108803487 A CN108803487 A CN 108803487A CN 201810940066 A CN201810940066 A CN 201810940066A CN 108803487 A CN108803487 A CN 108803487A
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cutter
point
coordinate
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contact point
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CN108803487B (en
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丁国富
江磊
余杭卓
罗豪
张剑
马术文
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Southwest Jiaotong University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35408—Calculate new position data from actual data to compensate for contour error

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Abstract

The invention discloses a kind of point profile errors prediction technique on part side milling surface, steps 1：The ideal cutter location for obtaining estimation range obtains corresponding practical cutter location according to many-body theory and homogeneous coordinate transformation；Step 2：It is done on cutter side edge as cutter-contact point if choosing, according to the geometrical relationship of cutter location and cutter-contact point, calculates the corresponding ideal cutter-contact point of ideal cutter location practical cutter-contact point corresponding with practical cutter location；Step 3：The ideal cutter-contact point and practical cutter-contact point obtained according to step 2 builds ideal finished surfaceS i With actual processing surfaceS a ；Step 4：Calculate future position on the ideal finished surface obtained by step 3PNormal and actual processing surface intersection pointP a ；Calculate future positionPAnd intersection pointP a Distance, you can obtain future positionPThe point profile errors at place；The test and appraisal valence principle of the present invention is consistent with contour measuring method, and prediction is more accurate.

Description

A kind of point profile errors prediction technique on part side milling surface
Technical field
The present invention relates to Computerized Numerical Control processing technology fields, and in particular to a kind of point contour prediction on part side milling surface calculates Method.
Background technology
Flank machining refers to the processing method for carrying out milling to workpiece using milling cutter side edge, is usually used in adding for straight grain surface parts Work is a kind of important digital control processing mode；The profile errors of curved surface are widely used in part Flank machining geometric tolerance One of evaluation index；Currently, the measurement of profile error and computational methods are more mature, common computational methods have iteration calculation Method, genetic algorithm etc.；Such as Sun et al. (SUN Y, WANG X, GUO D.Machining localization and quality evaluation of parts with sculptured surfaces using SQP method[J] .International Journal of Advanced Manufacturing Technology,2009,42(11-12): A kind of sequential quadratic programming algorithm (SQP) solution orientation problem 1131-1139.) is proposed, is arrived with iterative search method solution point Curved surface minimum distance；(Liao Ping are based on genetic algorithm to Liao Ping and segmentation approximatioss accurately calculates complex-curved profile error [J] Mechanical engineering journal, 2010,46 (10):1-7.) et al. propose the side being combined using segmentation approximate algorithm and genetic algorithm Method has accurately calculated complex-curved profile error；Curved surface to be measured is carried out using three coordinate measuring machine (CMM) to get sampling ready, Curved surface to be measured is reconstructed by curved surface fitting methods such as NURBS, B-splines again, and then the method for carrying out profile tolerance assessment is also in daily use； What changes cloud et al. (the true free form surfaces wheel library degree error evaluation of He Gaiyun, Huang Xin, Guo Long and analysis on Uncertainty [J] electronic, horologicals Amount and instrument journal, 2017,31 (3):CMM sampling sites 395-401.) are utilized, then by B-spline interpolation reconstruction curved surface, profile is missed The uncertainty of measurement of difference is analyzed.
However, in certain precision machining processes, necessary not only for the profile error measured after processing, with greater need for adding The point profile errors that curved surface is predicted before work, to carry out craft precision analysis and compensation；It is directed to part side milling surface point at present The research of position profile errors prediction is less, as (Zhu Shao ties up complex parts five-axis milling machining precision predictions and compensation skill to Zhu Shaowei The Chengdu art research [D]：Southwest Jiaotong University, 2013.) each future position is calculated using five-axis machine tool composition error model to throw Shadow is to parts profile normal direction；Point profile errors are obtained, and analyze each error component proportion；(Peng refines, fourth for Peng's refining et al. National wealth, Zhu Shaowei etc. the developmental research of five-axis milling Machining Accuracy Prediction [J] China Mechanical Engineerings, 2014,25 (5): The profile errors at point of contact 647-650.) are calculated using the five-axis milling machining precision prediction software systems of research and development；With Projection of the upper research using ideal point and the volumetric position error of corresponding practical point in normal direction is as point profile errors； However in practical measurement process, the gauge head of three coordinate measuring machine along ideal measuring point normal direction close to actual surface, last gauge head A practical measuring point is contacted in actual surface, this practical measuring point is then calculated and thinks at a distance from measuring point with principle, as the ideal The point profile errors value of measuring point.Therefore, there are deviations for the predicted value of actual measured value and aforementioned prediction technique, so as to cause pre- It is inaccurate to survey result.
Invention content
The present invention provides a kind of part side milling surface consistent with measurement method suitable for Flank machining, prediction and evaluation principle Point profile errors prediction technique.
The technical solution adopted by the present invention is：A kind of point profile errors prediction technique on part side milling surface, including with Lower step：
Step 1：According to processing NC Code obtainings estimation range ideal cutter location PWCoordinate PWWith ideal generating tool axis vector VW, Under conditions of considering mismachining tolerance, corresponding practical cutter location P ' is obtained according to many-body theory and homogeneous coordinate transformationWCoordinate P′WWith practical generating tool axis vector V 'W(note：Tilted letter symbology scalar-title, bold italicized letters symbology vector-seat Mark, rear same)；
Step 2：It is done on cutter side edge as cutter-contact point if choosing, according to the geometrical relationship of cutter location and cutter-contact point, meter Calculate ideal cutter location PWThe corresponding ideal cutter-contact point coordinate P of seriesCWith practical cutter location P 'WThe corresponding practical cutter-contact point of series is sat Mark P 'C；
Step 3：The ideal cutter-contact point and practical cutter-contact point obtained according to step 2 builds ideal finished surface Si(u, v) and Actual processing surface Sa(u, v), u are curved surface lateral parameter (taking 0~1), and v is curved surface longitudinal direction parameter (taking 0~1)；
Step 4：Calculate the normal of future position P and actual processing surface on the ideal finished surface obtained by step 3 Intersection point Pa；Calculate future position P and intersection point PaDistance, you can obtain the point profile errors at future position P.
Further, P ' in the step 1WWith V 'WComputational methods be：Consider lathe geometric error, Spindle thermal error and The influence of clamping error introduces these error parameters and establishes error character transformation matrix, and these matrixes are multiplied in order, meter Calculate practical cutter spacing point coordinates P 'WWith practical generating tool axis vector V 'W：
P′w=(p 'x,p′y, p 'z)T=(ΠiTj′)-1(ΠiTj′)Pt (1)
V′w=(V 'x,V′y,V′z)T=(ΠiTj′(r))-1(ΠiTj′(r))Vt (2)
In formula：p′x, p 'y, p 'zIndicate coordinate of the practical cutter location in workpiece coordinate system,iTj' indicate from body " i " to body The error character transformation matrix of " j ", PtIndicate coordinate of the cutter location in tool coordinate system；V′x, V 'y, V 'zIndicate practical cutter shaft Coordinate of the vector in workpiece coordinate system,iTj' (r) indicates the rotation error eigentransformation matrix from body " i " to body " j ", VtTable Show coordinate of the generating tool axis vector in tool coordinate.
Further, ideal cutter location P in the step 2WThe corresponding ideal cutter-contact point P of seriesCComputational methods it is as follows：
If two adjacent cutter location PW_iAnd PW_i+1, calculate to obtain ideal cutter location PW_iTangent vector ti：
ti=[xi+1-xi yi+1-yi zi+1-zi]T (3)
In formula：xi,yi,ziFor cutter location PW_iCoordinate, i be cutter location serial number, xi+1,yi+1,zi+1For its adjacent cutter location PW_i+1Coordinate；
Calculate PW_iLocate knife rail method and swears ni：
In formula：nxi,nyi,nziCoordinate, V are sweared for methodiFor PW_iThe generating tool axis vector at place；
PW_iThe corresponding ideal cutter-contact point P of seriesC_i_k(k=1,2 ..., m) coordinate PC_i_kFor：
In formula：Pxi_k, Pyi_k, Pzi_kFor cutter-contact point coordinate, R is tool radius, and r is cutter radius of corner, and k is cutter-contact point Serial number, d are adjacent cutter-contact point axial spacing.
Using identical method, according to practical cutter location P 'W_iCoordinate P 'W_iAnd practical generating tool axis vector Vi', you can it calculates Obtain the corresponding practical cutter-contact point P ' of seriesC_i_k。
Further, by nurbs surface approximating method in the step 3, based on ideal cutter-contact point and practical cutter-contact point Ideal finished surface S is built respectivelyi(u, v) and actual processing surface Sa(u, v).Processing table can be obtained by the calculating of step 2 The serial variance cutter-contact point in face, these cutter-contact points are similar to sampled points of the online CMM on curved surface；Therefore it is quasi- that curved surface may be used Conjunction method builds finished surface；NURBS fitting precisions are high, are widely used in industry manufactures, therefore use nurbs surface here Approximating method.
Further, the method on component ideal finished surface and actual processing surface is as follows in the step 3：
The discrete cutter-contact point that step 2 is obtained is as data point Pij(i=1,2 ..., m；J=0,1,2 ..., n, wherein m are The line number of cutter-contact point arrangement, n are the columns of cutter-contact point arrangement), then 3 × 3 nurbs surface mathematical definitions are：
In formula：VI, jFor the control vertex of curved surface, wI, jFor the weight factor being associated with control vertex, Bi,3(u) and Bj,3(v) Respectively along u to 3 times and along v to 3 B-spline basic functions；
According to data point data computational node vector sum basic function, reverse Control point mesh and weight factor, you can obtain song Face equation.
Further, in the step 4 normal and actual processing surface intersection point PaIt is missed with the point profile at future position P The computational methods of difference are as follows：
S1：Calculate future position P (x on ideal finished surfacep, yp, zp) at method swear np：
In formula：WithS is indicated respectivelyi(u, v) u to v to local derviation arrow；
S2：Built the normal L of P points：
Normal L crosses future position P, and rectilinear direction is that method swears npDirection, normal equation are：
L (t)=P+tnp (8)
In formula：T is linear interpolation parameter, t >=0；
S3：Calculate the actual processing surface S ' after transformed coordinate systema(u,v)：
Control point weight factor takes 1, then can obtain S according to formula (6)aThe expression formula of (u, v) is：
By curved surface SaCoordinate system transformation where (u, v) and straight line L is the coordinate system that straight line L is Z axis, if transformation matrix is T,
The control vertex V of surface parameter equation after then convertingij'=TVij, the surface equation after transformation is：
S4：Calculate the intersection point P of normal and actual processing surfaceaWith the normal direction profile errors of point P
Under transformed coordinate, Z axis and curved surface S 'aThe x values and y values of (u, v) intersecting point coordinate are zero, i.e. S 'ax(u, v)=0, S′ay(u, v)=0：
In formula：V′xijWith V 'yijRespectively control vertex V 'ijX coordinate value and y-coordinate value；
Solution formula (11) can obtain the intersection point P under transformed coordinate systema′(x′pa,y′pa,z′pa), then before converting Intersecting point coordinate Pa(xpa, ypa, zpa) be：
(xpa, ypa, zpa)T=T-1(x′pa,y′pa,z′pa)T (12)
Further, in the step 4 future position P normal direction profile errors εpFor：
The beneficial effects of the invention are as follows：
(1) present invention predicts more accurate compared with the point profile errors prediction technique on existing part side milling surface；
(2) present invention is suitable for Flank machining, has important reference price to Flank machining quality evaluation and process planning Value；
(3) by establishing cutter-contact point normal direction profile errors computation model, the point profile for carrying out side milling surface misses the present invention Difference prediction, it is easy to use, it calculates simple.
Description of the drawings
Fig. 1 is flow diagram of the present invention.
Fig. 2 is present invention process system topology schematic diagram.
Fig. 3 is Flank machining schematic diagram of the present invention.
Fig. 4 is the point profile errors prediction principle figure on Flank machining surface of the present invention.
Fig. 5 is that the point profile errors on Flank machining surface of the present invention predict schematic diagram.
Fig. 6 is the point normal direction profile errors calculating value distribution Butut on part side milling surface in the embodiment of the present invention.
Fig. 7 is the prediction of point normal direction profile errors and the actual measurement comparison signal on part side milling surface in the embodiment of the present invention Figure.
Specific implementation mode
The present invention will be further described in the following with reference to the drawings and specific embodiments.
As shown in Figure 1, a kind of point profile errors prediction technique on part side milling surface, includes the following steps：
Step 1：Obtain the ideal cutter location P of estimation rangeWCoordinate PWWith ideal generating tool axis vector VW, considering processing mistake Under conditions of difference, corresponding practical cutter location P ' is obtained according to many-body theory and homogeneous coordinate transformationWCoordinate P 'WWith practical cutter shaft Vector V 'W；
Wherein ideal cutter location PWIt is obtained by cutter location file；According to many-body theory, entire process system can be regarded as one Multi-body system, by taking the lathe of XFYZBA structures as an example, the topological structure of entire process system is as shown in Figure 2；Influence machining accuracy Process system error there are many, what is played a major role has lathe geometric error, workpiece position and attitude error and Spindle thermal error.
If the coordinate of practical cutter location is P ' in workpiece coordinate systemW, practical generating tool axis vector is V 'W, P 'WWith V 'WCalculating Method is as follows：
V′W=(CΤ′X(r)FT′W(r))-1CT′Y(r)YT′Z(r)ZT′B(r)ZTB BT′A(r)BTA ATS′(r)Vt (2)
In formula：C is lathe bed, and X is X-axis, and F is fixture, and W is workpiece, and Y is Y-axis, and Z is Z axis, and B is B axle, and A is A axis, based on S Axis, T are cutter, PtThe position coordinates for being cutter location in tool coordinate system,jTiTo become from body " i " to the ideal movements of body " j " Matrix is changed,jTi' for error matrix from body " i " to body " j ",jTi' (r) is from body " i " to the rotation error matrix of body " j ", Vt For the generating tool axis vector in tool coordinate system,FT′WFor workpiece position and attitude error,AT′SFor Spindle thermal error；Lathe geometric error includesCT′X、CT′Y、YT′Z、ZT′BWithBT′A。
Step 2：It is done on cutter side edge as cutter-contact point if choosing, according to the geometrical relationship of cutter location and cutter-contact point, meter Calculate ideal cutter location PWThe corresponding ideal cutter-contact point P of seriesCWith practical cutter location P 'WThe corresponding practical cutter-contact point P ' of seriesC.It is logical It crosses and calculates the corresponding serial cutter-contact point of each position cutter location, can get the serial cutter-contact point on processing swept surface.
It is as follows that cutter location corresponds to cutter-contact point calculating process：
If ideal cutter location PW_iTangent vector be ti, according to adjacent cutter location PW_iAnd PW_i+1, t can be calculatedi：
ti=[xi+1-xi yi+1-yi zi+1-zi]T (3)
In formula：xi,yi,ziFor cutter location PW_iCoordinate, i be cutter location serial number, xi+1,yi+1,zi+1For its adjacent cutter location PW_i+1Coordinate；
Calculate PW_iLocate knife rail method and swears ni：
In formula：nxi,nyi,nziCoordinate, V are sweared for methodiFor PW_iThe generating tool axis vector at place.
PW_iThe corresponding ideal cutter-contact point P of seriesC_i_k(k=1,2 ..., m) coordinate PC_i_kFor：
In formula：Pxi_k, Pyi_k, Pzi_kFor cutter-contact point coordinate, R is tool radius, and r is cutter radius of corner, and k is cutter-contact point Serial number, d are adjacent cutter-contact point axial spacing.
Using identical method, according to practical cutter location P 'W_iCoordinate P 'W_iAnd practical generating tool axis vector V 'i, you can it calculates Obtain the corresponding practical cutter-contact point P ' of seriesC_i_k。
Step 3：By nurbs surface approximating method, the ideal cutter-contact point obtained based on step 2 and practical cutter-contact point difference The ideal finished surface S of structurei(u, v) and actual processing surface Sa(u, v), u are curved surface lateral parameter (taking 0~1), and v is vertical for curved surface To parameter (taking 0~1)；
The discrete cutter-contact point that step 2 is obtained is as data point Pij(i=1,2 ..., m；J=0,1,2 ..., n, wherein m are The line number of cutter-contact point arrangement, n are the columns of cutter-contact point arrangement), then 3 × 3 nurbs surface mathematical definitions are：
In formula：Vi,jFor the control vertex of curved surface, wi,jFor the weight factor being associated with control vertex, Bi,3(u) and Bj,3 (v) be respectively along u to 3 times and along v to 3 B-spline basic functions；
According to data point data computational node vector sum basic function, reverse Control point mesh and weight factor；It can divide in this way Ideal finished surface S is not obtainedi(u, v) and actual processing surface Sa(u, v).
Point profile errors measurement has contact and two kinds contactless, and wherein contact application is more extensive.Here The measuring principle of point profile errors is illustrated by taking contact type measurement as an example.As shown in figure 4, first passing through three-dimensional part model Obtain on ideal finished surface normal vector n at measurement point P and the pointp, measuring machine gauge head touches reality further along direction of normal The point Pa on border surface, then the profile errors of point P are εp=| PaP|；Due to actual spot of measurement Pa and practical cutter-contact point P ' line simultaneously Not necessarily perpendicular to normal vector；Therefore projection ε ' of the space error of ideal measurement point in normal directionpNeed not be equal to point wheel Wide error εp.As shown in fig. 5, it is assumed that ideal finished surface is Si, actual processing surface is Sa；Point P is ideal finished surface SiOn A future position, the point method arrow be np；Cross the normal L and actual processing surface S of point PaIntersect at point Pa；Then future position P and The distance ε of intersection point PapThe as profile errors of point P.
Step 4：Calculate the normal of future position P and actual processing surface on the ideal finished surface obtained by step 3 Intersection point Pa；Calculate future position P and intersection point PaDistance, you can obtain the point profile errors at future position P.
Intersecting point coordinate calculating is as follows：
S1：Calculate future position P (x on ideal finished surfacep, yp, zp) at method swear np：
In formula：WithS is indicated respectivelyi(u, v) u and v to local derviation arrow；
S2：Built the normal L of P points
Normal L crosses future position P, and rectilinear direction is that method swears npDirection, normal equation are：
L (t)=P+tnp (8)
In formula：T is linear interpolation parameter, t >=0；
S3：Calculate the actual processing surface S ' after transformed coordinate systema(u,v)：
When processing curve NURBS is fitted under normal circumstances, control point weight factor result of calculation is wij=1, then according to formula (6) S can be obtainedaThe expression formula of (u, v)：
By curved surface SaCoordinate system transformation where (u, v) and straight line L is the coordinate system that straight line L is Z axis, if transformation matrix is T；
Under coordinate after the conversion, the control vertex V of nurbs surface parametric equationij(i=0,1 ..., m；J=0,1 ..., N) V is converted toij'=TVij(i=0,1 ..., m；J=0,1 ..., n), then nurbs surface equation is converted to：
S4：Calculate the intersection point P of normal and actual surfaceaWith the normal direction profile errors of point P
Normal L and curved surface S is solved under old coordinate systemaThe intersection point of (u, v) is converted to and calculates curved surface S ' under new coordinate systema The intersection point of (u, v) and Z axis.Under transformed coordinate, the x values and y values of Z axis and the intersecting point coordinate of curved surface S (u, v) are zero, i.e. S 'ax (u, v)=0, S 'ay(u, v)=0：
In formula：Vxij' and Vyij' is respectively control vertex VijThe x coordinate value and y-coordinate value of '；
By the method for quasi-Newton iteration method optimizing, the intersection point P under transformed coordinate system can be obtaineda′(x′pa,y′pa,z′pa), Intersecting point coordinate P before then convertinga(xpa, ypa, zpa) be：
(xpa, ypa, zpa)T=T-1(x′pa,y′pa,z′pa)T (12)
According to intersection point Pa, then the normal direction profile errors ε of future position PpFor：
The normal direction profile errors of future position P are the point profile errors of Flank machining Surface prediction point.
Embodiment
By taking the serpentine part of one wall thickness 3mm of machine tooling of XFYZBA structures as an example, the effective of accuracy prediction algorithm is verified Property；The cutter-contact point distribution of local tool swept surface is calculated, selected section cutter-contact point 15 (chooses 15 along tool axis direction of feed Layer) × 20 (along milling direction of feed choose 20 row)=300, prediction result is as shown in Figure 6.
The results are shown in Figure 7 for it, and as can be seen from the figure predicted value is identical as measured value variation tendency, demonstrates this prediction The validity of algorithm.
The present invention calculates the ideal and practical cutter-contact point of Flank machining under the conditions of multiple error first；Then quasi- using curved surface The mode of conjunction obtains the ideal of part and the parametrization computation model on actual processing surface；According to profile errors measuring principle, build The normal direction profile errors computation model for having found each cutter-contact point, to realize the point profile errors on prediction side milling surface；It can For suface processing quality evaluation, the error compensation in process, accuracy prediction software programming etc.；With existing part The point profile errors prediction technique on side milling surface is evaluated the processing quality of five axis side millings and technique compared to more accurate Plan optimization has important reference value.

Claims (7)

1. a kind of point profile errors prediction technique on part side milling surface, which is characterized in that include the following steps：
Step 1：Obtain estimation range ideal cutter location PWCoordinate PWWith ideal generating tool axis vector VW, in the item for considering mismachining tolerance Under part, corresponding practical cutter location P ' is obtained according to many-body theory and homogeneous coordinate transformationWCoordinate P 'WWith practical generating tool axis vector V ′W；
Step 2：It is done on cutter side edge as cutter-contact point if choosing, according to the geometrical relationship of cutter location and cutter-contact point, calculates reason Think cutter location PWThe corresponding ideal cutter-contact point coordinate P of seriesCWith practical cutter location P 'WThe corresponding practical cutter-contact point coordinate of series PC′；
Step 3：The ideal cutter-contact point and practical cutter-contact point obtained according to step 2 builds ideal finished surface SiIt is (u, v) and practical Finished surface Sa(u, v), u are curved surface lateral parameter, and v is curved surface longitudinal direction parameter；
Step 4：Calculate the normal L and actual processing surface S of future position P on the ideal finished surface obtained by step 3a(u, v) Intersection point Pa；Calculate future position P and intersection point PaDistance, you can obtain the point profile errors at future position P.
2. a kind of point profile errors prediction technique on part side milling surface according to claim 1, which is characterized in that institute State P ' in step 1WWith V 'WComputational methods be：
P′w=(p 'x,p′y,p′z)T=(ΠiTj′)-1(ΠiTj′)Pt (1)
V′w=(Vx′,Vy′,Vz′)T=(ΠiTj′(r))-1(ΠiTj′(r))Vt (2)
In formula：p′x, p 'y, p 'zIndicate coordinate of the practical cutter location in workpiece coordinate system,iTj' indicate from body " i " to body " j " Error character transformation matrix, PtIndicate coordinate of the cutter location in tool coordinate system；Vx', Vy', Vz' indicate practical generating tool axis vector Coordinate in workpiece coordinate system,iTj' (r) indicates the rotation error eigentransformation matrix from body " i " to body " j ", VtIndicate knife Coordinate of the axial vector in tool coordinate system.
3. a kind of point profile errors prediction technique on part side milling surface according to claim 1, which is characterized in that institute State ideal cutter location P in step 2WThe corresponding ideal cutter-contact point P of seriesCComputational methods it is as follows：
If two adjacent cutter location PW_iAnd PW_i+1, calculate to obtain ideal cutter location PW_iTangent vector be ti：
ti=[xi+1-xi yi+1-yi zi+1-zi]T (3)
In formula：xi,yi,ziFor cutter location PW_iCoordinate, i be cutter location serial number, xi+1,yi+1,zi+1For its adjacent cutter location PW_i+1 Coordinate；
Calculate PW_iLocate knife rail method and swears ni：
In formula：nxi,nyi,nziCoordinate, V are sweared for methodiFor PW_iGenerating tool axis vector；
PW_iThe corresponding ideal cutter-contact point P of seriesC_i_k(k=1,2 ..., m) coordinate PC_i_kFor：
In formula：Pxi_k, Pyi_k, Pzi_kFor cutter-contact point coordinate, R is tool radius, and r is cutter radius of corner, and k is cutter-contact point serial number, D is adjacent cutter-contact point axial spacing；
Using identical method, according to practical cutter location P 'W_iCoordinate P 'W_iAnd practical generating tool axis vector Vi', you can it is calculated The corresponding practical cutter-contact point P ' of seriesC_i_k。
4. a kind of point profile errors prediction technique on part side milling surface according to claim 1, which is characterized in that institute It states by nurbs surface approximating method in step 3, ideal finished surface is built based on ideal cutter-contact point and practical cutter-contact point respectively Si(u, v) and actual processing surface Sa(u, v).
5. a kind of point profile errors prediction technique on part side milling surface according to claim 1, which is characterized in that institute The method for stating the ideal finished surface of structure in step 3 and actual processing surface is as follows：
The discrete cutter-contact point that step 2 is obtained is as data point Pij(i=0,1,2 ..., m；J=0,1,2 ..., n, wherein m are knife The line number of contact arrangement, n are the columns of cutter-contact point arrangement), then 3 × 3 nurbs surface mathematical definitions are：
In formula：VI, jFor the control vertex of curved surface, wI, jFor the weight factor being associated with control vertex, Bi,3(u) and Bj,3(v) respectively For along u to 3 times and along v to 3 B-spline basic functions；
According to data point data computational node vector sum basic function, reverse Control point mesh and weight factor, you can obtain curved surface side Journey.
6. a kind of point profile errors prediction technique on part side milling surface according to claim 5, which is characterized in that institute State the intersection point P of normal and actual processing surface in step 4aComputational methods are as follows：
S1：Calculate future position P (x on ideal finished surfacep, yp, zp) at method swear np：
In formula：WithS is indicated respectivelyi(u, v) u and v to local derviation arrow；
S2：Built the normal L of P points
Normal L crosses future position P, and rectilinear direction is that method swears npDirection, normal equation are：
L (t)=P+tnp (8)
In formula：T is linear interpolation parameter, t >=0；
S3：Calculate the actual processing surface S ' after transformed coordinate systema(u,v)：
Control point weight factor takes 1, then can obtain S according to formula (6)aThe expression formula of (u, v)：
By curved surface SaCoordinate system transformation where (u, v) and straight line L is the coordinate system that straight line L is Z axis, if transformation matrix is T；
The control vertex V of surface parameter equation after then convertingij'=TVij, the surface equation after transformation is：
S4：Calculate the intersection point P of normal and actual processing surfacea：
Under transformed coordinate, Z axis and curved surface S 'aThe x values and y values of the intersecting point coordinate of (u, v) are zero, i.e. S 'ax(u, v)=0, S′ay(u, v)=0：
In formula：V′xijWith V 'yijRespectively control vertex V 'ijX coordinate value and y-coordinate value；
Solution formula (11) can obtain the intersection point P under transformed coordinate systema′(x′pa,y′pa,z′pa), then the intersection point before converting is sat Mark Pa(xpa,ypa,zpa) be：
(xpa,ypa,zpa)T=T-1(x′pa,y′pa,z′pa)T (12)
7. a kind of point profile errors prediction technique on part side milling surface according to claim 1, which is characterized in that institute State the normal direction profile errors ε of future position P in step 4pFor：
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