CN110426992A - A kind of curved surface subregion contour parallel milling cutter path planing method - Google Patents

A kind of curved surface subregion contour parallel milling cutter path planing method Download PDF

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CN110426992A
CN110426992A CN201910728791.2A CN201910728791A CN110426992A CN 110426992 A CN110426992 A CN 110426992A CN 201910728791 A CN201910728791 A CN 201910728791A CN 110426992 A CN110426992 A CN 110426992A
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cutter
contact point
follows
arc length
inner ring
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CN110426992B (en
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马建伟
鲁晓
秦逢泽
李冠霖
曲梓文
贾振元
刘巍
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Dalian University of Technology
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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
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    • G05B2219/45136—Turning, lathe
    • 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
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    • G05B2219/49001—Machine tool problems

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Abstract

A kind of curved surface subregion contour parallel milling cutter path planing method of the present invention belongs to complex curved surface parts high-precision high-efficiency Milling Process technical field, is related to a kind of curved surface subregion contour parallel milling cutter path planing method based on Deng Can supreme people's court.This method limits scallop-height at processing subzone boundaries, according to its geometrical characteristic and the critical cutter-contact point curve of cutter intersection point type structure, based on Deng Can supreme people's court along line-spacing direction generative theory/practical cutter-contact point.It establishes inner ring arc length error calculating and classifies, determine positive region to be repaired, calculate theoretical cutter-contact point corrected range through sensitivity analysis, along theoretical/practical cutter-contact point of line-spacing adjustment in direction.The total arc length error of machining direction is calculated, cutter-contact point arc length variation/adjustment amount is calculated through sensitivity analysis, is determined along machining direction and correct practical cutter-contact point, cutter path is completed and plans again.This method is suitable for complex-curved subregion contour parallel milling, can reduce and connect tool marks, improves processing quality.

Description

A kind of curved surface subregion contour parallel milling cutter path planing method
Technical field
The invention belongs to complex curved surface parts high-precision high-efficiency Milling Process technical field, it is related to a kind of based on Deng Can supreme people's court Curved surface subregion contour parallel milling cutter path planing method.
Background technique
With the rapid development in the Important Projects fields such as aerospace, energy source and power, automobile ship, local geometric sudden turn of events class Complex-curved important Parts are widely applied in various high-end equipments.Since such part surface type is complicated and has local geometric anxious Become feature, the unified technological parameter integral processing method of tradition is difficult to meet the manufacture demand of the high-quality and high-efficiency of such part.It is full The double requirements of foot such part processing quality and processing efficiency carry out part zone point often according to the difference of geometrical characteristic It cuts and is planned with subregion cutter path.The planning of subregion cutter path includes that row cuts two kinds of tool path patterns of feed and ring cutting feed. However, existing method is mostly used by periphery when applying to the planning of contour parallel milling cutter path in subregion process in The cutter path Planning Model of the heart easily leads to boundary cutter path Duplication using subzone boundaries as cutter path outer ring It is excessively high, cause surface residual stress suddenly to increase, aggravates tool wear；And the cutter path inner ring through outer ring recursion is difficult to ensure at this Residual high error meets processing request, and it is overproof to easily lead to mismachining tolerance at all subregion inner ring, or even occurs obviously connecing tool marks, seriously Restrict comprehensive raising of complex curved surface parts processing quality.There is an urgent need to study a kind of curved surface based on Deng Can supreme people's court as a result, Region contour parallel milling cutter path planing method, to guarantee at complex-curved subregion contour parallel milling subzone boundaries and at inner ring Processing quality.
" integrated ring cutting track and the type chamber for becoming radius cycloidal path of Li Jing Rong et al. patent publication No. CN106647634A Teeth processing route generating method ", the patent take the mode that outer profile inwardly biases, Internal periphery is outwardly biased to construct ring cutting feed rail Mark carries out region segmentation based on contour parallel milling material removing rate, and is constraint Regional planning ring cutting track with material removing rate With cycloid tool track, help to promote processing efficiency, and tool life.However, this method does not consider that ring cutting adds Work area domain boundary process quality issue, and easily there is cutter path splicing not inside machining area in bidirectional offset cutter path The problem of working as, causes mismachining tolerance overproof or even generates to connect tool marks, therefore have office to complex-curved high-quality and high-efficiency processing is promoted It is sex-limited.Document " Parameter-based spiral tool path generation for free-form surface Machining ", Takasugi, Precision Engineering, 2018,52,370-379, it proposes a kind of based on parameter Change the helical tooth blade orbit generation method on machining area boundary.This method design takes into account the parametric surface processing of cutter-contact point spacing Region inner cutter PATH GENERATION, from machining area inside helical tooth blade track is quickly calculated to boundary, can be with Effectively guarantee the processing quality of complex-curved interior zone.However, this method easily causes machining area boundary to connect knife not When, and then induction boundary mismachining tolerance is overproof and obviously connects tool marks, therefore it is processed not to be suitable for subregion change technological parameter Journey has certain limitation.
Summary of the invention
The present invention is directed to prior art defect, has invented a kind of curved surface subregion contour parallel milling cutter path planing method. According to surface geometry feature, critical cutter-contact point curve is constructed based on Deng Can supreme people's court and completes contour parallel milling cutter path and is just planned, It establishes inner ring arc length error calculating and determines positive region to be repaired, complete cutter path along line-spacing adjustment in direction theory cutter-contact point Amendment solves practical cutter-contact point along line-spacing direction/machining direction corrected range, is homogenized inner ring arc length error, finally realizes knife It plans again tool track.Thus under the premise of ensuring boundary processing quality, the tool marks that connect at subregion inner ring are effectively reduced, are realized Complex-curved high-precision high-efficiency processing.
The technical scheme is that a kind of curved surface subregion contour parallel milling cutter path planing method, which is characterized in that This method limits scallop-height at processing subzone boundaries, according to its geometrical characteristic and the critical cutter-contact point of cutter intersection point type structure Curve, based on Deng Can supreme people's court along line-spacing direction generative theory/practical cutter-contact point.It establishes inner ring arc length error calculating and divides Class determines positive region to be repaired, calculates theoretical cutter-contact point corrected range through sensitivity analysis, theoretical/practical along line-spacing adjustment in direction Cutter-contact point.The total arc length error of machining direction is calculated, cutter-contact point arc length variation and adjustment amount are calculated through sensitivity analysis, along feed Direction, which determines, corrects practical cutter-contact point, completes cutter path and plans again.Specific step is as follows for method:
Step 1, residual high normal surface subregion contour parallel milling cutter path is waited just to plan
Complex curved surface parts contour parallel milling subregion is expressed as S (u, v), boundary curve is C (u (t), v (t)), P0 For any point on boundary, P is remembered0Locating boundary is tangentially (du0,dv0), curved surface normal direction is n, perpendicular to boundary is tangential and curved surface The direction of normal direction is the line-spacing direction at the boundary point, is expressed as (du0',dv0').Scallop-height is h at limited boundary, by micro- Point geometric theory is it is found that the maximum value of scallop-height appears in the geodesic curve in line-spacing direction, therefore in P0Two lateral edge line-spacing sides To geodesic curve on there are two critical cutter-contact point P1And P2To guarantee P0Place's scallop-height meets processing request.In P0Place, along row Curved surface first fundamental form I and curved surface second fundamental form II away from direction are respectively as follows:
Wherein, E, F, G are curved surface first kind fundamental quantity, and L, M, N are the second class of curved surface fundamental quantity, and expression formula is as follows:
Wherein, Su、SvFor the first-order partial derivative of curved surface S (u, v), Suu、Suv、SvvFor the second-order partial differential coefficient of curved surface S (u, v), n For the normal vector of curved surface S (u, v).
P can be calculated according to first fundamental form of surface and second fundamental form0Principal curvatures k along line-spacing directionnAre as follows:
Because boundary is tangential and line-spacing direction is mutually perpendicular to, can be expressed as:
(Sudu0+Svdv0)(Sudu0'+Svdv0')=0 (4)
So line-spacing direction may be calculated:
Formula (5) are substituted into formula (3), obtain P0Principal curvatures k along line-spacing directionnAre as follows:
Work as knWhen=0, P0Place is plane；Work as knWhen < 0, P0Place is convex surface；Work as knWhen > 0, P0Place is concave surface.P0Place is along row Geodesic curve radius of curvature away from direction is Rc, calculate are as follows:
In process, effective cutting shape and tool category and processing method are closely related for different cutters.In error In allowed band, the effective cutting shape that osculating circle of the profile at cutter-contact point is the point is scanned with cutter, and partly by osculating circle Diameter is as the effective radius of clean-up r of cuttere, calculation method is as follows:
When cutter is rose cutter, the effective radius of clean-up r of cuttereAre as follows:
re=R (8)
When cutter is flat-end cutter, the effective radius of clean-up r of cuttereAre as follows:
When cutter is ring type milling cutter, the effective radius of clean-up r of cuttereAre as follows:
Wherein, R is cutter real radius, and r is milling cutter annulus radius surface, and λ is top rake during five-axis robot, ω five Side drift angle in axis process.
According to the effective radius of clean-up r of cuttereWith the size relationship between cutter real radius R, by all kinds of milling cutters it is equivalent at The cylindrical surface and radius that radius is R are reThe milling cutter model that is combined into of spherical surface；It, can be by cutter enveloping surface according to the milling cutter model Between intersection point be divided into two classes: 1. spherical surface intersects with spherical surface；2. cylindrical surface is intersected with spherical surface.This intersection point type is between cutter Distance changes, if the cutter of adjacent two subregion is milling cutter 1 and milling cutter 2, effective radius of clean-up is respectively r1eAnd r2e(r1e≥ r2e), the real radius of milling cutter 2 is given, if R1For the real radius of milling cutter 1, R1=j is intersection point type change critical condition.It is comprehensive The concavo-convex characteristic and intersection point type for considering curved surface are closed, line-spacing computation model is as follows between establishing subregion:
1) plane machining
Milling cutter 1 is with milling cutter 2 when plane intersects, and by geometrical relationship between cutter, intersection point type change critical condition is calculated are as follows:
When intersection point type is that spherical surface intersects with spherical surface between cutter, R1>=j, when intersection point type is cylindrical surface between cutter When intersecting with spherical surface, R1< j.
For two kinds of intersection point types, line-spacing d between subregiontIt calculates are as follows:
2) convex surface processes
Milling cutter 1 with milling cutter 2 when convex surface is intersected, it is small in view of the evaluation for connecing knife line-spacing, convex surface is equivalent to spherical outside surface, RcAs convex surface local radius of curvature.By geometrical relationship between cutter, intersection point type change critical condition is calculated are as follows:
When intersection point type is that spherical surface intersects with spherical surface between cutter, R1>=j, when intersection point type is cylindrical surface between cutter When intersecting with spherical surface, R1< j.
For two kinds of intersection point types, line-spacing d between subregiontIt calculates are as follows:
3) concave surface processes
Milling cutter 1 with milling cutter 2 when concave surface is intersected, it is small in view of the evaluation for connecing knife line-spacing, concave surface is equivalent to Internal Spherical Surface, RcAs concave surface local radius of curvature.By geometrical relationship between cutter, intersection point type change critical condition is calculated are as follows:
When intersection point type is that spherical surface intersects with spherical surface between cutter, R1>=j, when intersection point type is cylindrical surface between cutter When intersecting with spherical surface, R1< j.
For two kinds of intersection point types, line-spacing d between subregiontIt calculates are as follows:
Critical cutter-contact point P for ease of calculation1、P2With P0Between spatial relation (distance relation and direction relations), Take P0For P1With P2Between geodesic midpoint, l0For P0P1With P0P2Length.According to geometrical relationship, different curve concavo-convex characteristic Under l0It calculates are as follows:
Comprehensively consider spatial relation (distance relation and the direction pass of the critical cutter-contact point of adjacent subarea domain boundaries on either side System), establish critical cutter-contact point Pi(i=1,2) computation model are as follows:
Wherein, P0uWith P0vRespectively P0First-order partial derivative.P can be solved to obtain according to formula (18)iWith P0Between parameter become Change amountWithAre as follows:
In the computation model, critical cutter-contact point P1With P2Always exist in pairs, and is located at P0Opposite orientation, P0、P1With P2In processing subregion S (u, v), P0For known boundaries point, according to calculated result, P0、P1With P2It indicates are as follows:
The critical cutter-contact point of the corresponding whole in boundary can be calculated using the above method, these critical cutter-contact points are subjected to curve Fitting, can be obtained the critical cutter-contact point curve based on Deng Can supreme people's court.When all subregion cutter-contact point is respectively positioned on critical cutter-contact point song When on line, it is ensured that boundary residual high error in adjacent subarea domain meets processing request.
Definition is theoretical cutter-contact point by other cutter-contact points that outer ring cutter-contact point recursion generates, according to action in cutter path The cutter-contact point that error requirements generate is practical cutter-contact point.Contour parallel milling cutter path is planned according to Deng Can supreme people's court, each layer The theoretical cutter-contact point and practical cutter-contact point of ring calculate as follows:
IfFor n-th of cutter-contact point on outer ring,For on pth layer ringWhat recursion generated Theoretical cutter-contact point, thenLocating machining direction is For m-th of practical knife touching on pth layer ring Point, thenLocating machining direction is For the line-spacing between cutter-contact point theoretical in adjacent ring, i.e.,WithThe distance between,For the step-length between adjacent practical cutter-contact point on pth layer ring, i.e.,WithBetween away from From e is the action error of setting, with the symbiosis of Deng Can supreme people's court at q layers of ring.To construct the critical cutter-contact point based on Deng Can supreme people's court Curve is first cutter path (outer ring) of contour parallel milling, appoints and takes on outer ring a little as the starting point along machining direction recursionEstablish the functional relation between the adjacent cutter-contact point step-length of outer ring and action error are as follows:
Wherein,ForLocal radius of curvature of the place along machining direction.To accurately generate the cutter-contact point on outer ring, root The functional relation between arc length and step-length is established according to the concavo-convex characteristic of curved surface are as follows:
Wherein,WithRespectivelyCurved surface normal curvature and arc length of the place along machining direction.
Arc length is calculated according to first form curve integralAre as follows:
Wherein,For starting pointThe parameter value at place, convolution (22)-(23) can solveLocate corresponding parameter valueThus cutter-contact point of the outer ring along machining direction recursionAre as follows:
All cutter-contact points of outer ring can be solved by formula (24), are known by definition, theoretical cutter-contact point and practical knife touch on outer ring Point is identical, expression are as follows:
With each cutter-contact point of outer ringAs the starting point along line-spacing direction recursion, successively recursion remaining cutter rail can be obtained Theoretical cutter-contact point on mark, theory of correspondences cutter-contact point between adjacent ringWithRecurrence relation expression are as follows:
Wherein,WithBetween Parameters variation amountWithIt calculates are as follows:
Wherein,WithForLocate corresponding curved surface first kind fundamental quantity,WithForPlace Corresponding the second class of curved surface fundamental quantity.ForLength, calculation method is as follows:
Wherein,ForCurved surface normal curvature along line-spacing direction.
Successively recursion all theoretical cutter-contact points of contour parallel milling can be obtained by formula (26)-(28), until inner ring edge itself The residual high error constraints such as be unsatisfactory between the adjacent theoretical cutter-contact point in line-spacing direction, at this point, using the corresponding upper one layer of ring of the point as Inner ring.However, theoretical cutter-contact point is obtained according only to the residual high error in line-spacing direction, it is difficult to which the action error for meeting machining direction is wanted It asks, thus cannot function as the use of the practical cutter-contact point in numerical control processing.It carries out curve fitting to the theoretical cutter-contact point of each layer ring To a plurality of cutter path, it is expressed as hi(u (t), v (t)) appoints and takes on each layer ring a little as starting pointAccording to formula (21)-(23) the practical cutter-contact point along machining direction recursion is calculatedCorresponding parameter valueAnd then it can incite somebody to actionIt indicates Are as follows:
So far, all theoretical cutter-contact point and practical cutter-contact point of contour parallel milling, cutter path be can get by Deng Can supreme people's court Just planning is accomplished.
Step 2, inner ring arc length error calculating is established
Based on step 1 realize etc. residual high normal surface subregion contour parallel milling cutter path just plan easily cause inner ring arc Long error, and then cause to occur obviously connecing tool marks at inner ring.In order to inhibit inner ring arc length error, inner ring arc length error calculation is established Model is simultaneously classified.
IfForLocal radius of curvature of the place along line-spacing direction, hq(u (t), v (t)) indicates inner ring,It indicatesPlace along line-spacing direction geodesic curve,For the geodesic curve and inner ring intersection point,WithRespectively ForLocate corresponding inner ring spacing and inner ring arc length.
ConstructionGeodesic curve of the place along line-spacing directionDue toForWith hq(u (t), v (t)) intersection point, it calculates are as follows:
Pass throughWithCoordinate value can determineLocate corresponding inner ring spacing are as follows:
It is established according to the concavo-convex characteristic of curved surfaceLocate the functional relation between inner ring arc length and inner ring spacing are as follows:
Wherein,ForCurved surface normal curvature of the place along line-spacing direction.
With reference to the calculation method of formula (28), can derive in the case where waiting residual high error constraintsInner ring arc length is discussed in processing Are as follows:
It willLocate inner ring arc length errorExpression are as follows:
Convolution (31)-(34) are establishedLocate inner ring arc length error calculating are as follows:
Two classes are classified as according to inner ring arc length error size:
1)
In the type, the corresponding next layer of recursion ring of inner ring will appear the problem of cutter path is intersected, for this feelings Condition does not need to add new cutter-contact point, only can realize the two-way equal of inner ring arc length error by correcting existing practical cutter-contact point Change.
2)
In the type, it is excessively high that the corresponding next layer of recursion ring of inner ring will appear cutter path Duplication, is unsatisfactory for etc. residual The problem of high error requirements, to avoid introducing excessive error to other cutter-contact points, needs to add new knife touching in response to this Then point is just able to achieve the two-way homogenizing of inner ring arc length error according to newly-increased cutter-contact point to existing practical cutter-contact point amendment.
Step 3, along the practical cutter-contact point amendment in line-spacing direction part
The inner ring arc length error calculating that the theory/practical cutter-contact point and step 2 obtained in conjunction with step 1 is established, for Different inner ring arc length error patterns determine the positive region to be repaired of cutter path, carry out the practical cutter-contact point in part along line-spacing direction It corrects as follows:
1)
In this seed type, do not need to add new cutter-contact point.IfForTheory after line-spacing adjustment in direction Cutter-contact point,ForAlong the practical cutter-contact point of line-spacing adjustment in direction,WithIt respectively indicatesLocate machining direction and line-spacing direction,WithThe region endpoint that arc length error is not zero respectively in inner ring,WithRespectivelyWithBetween amendment arc length and corrected range.
WithBetween region be inner ring on need modified cutter path region, if only correct this region of inner ring Cutter-contact point, easily cause inner ring arc length error transfer and accumulate in one layer of intermediate ring, equally will appear mismachining tolerance it is overproof and Tool marks obviously are connect, thus are needed inner ring arc length error-correction model to each layer ring.Due in inner ringWithBetween theoretical knife Contact is respectively by outer ringWithBetween theoretical cutter-contact point along line-spacing direction successively recursion generate, to avoid cutter path Mutation, withWithIn the theoretical cutter-contact point that pth layer ring recursion generatesWithArea to be modified as the floor ring Domain boundary.By adjusting the region cutter path along the recursion criterion in line-spacing direction, local theory's knife touching of each layer ring can be corrected Point.
2)
In this seed type, need to add new cutter-contact point.It is with Deng Can supreme people's court that the theoretical cutter-contact point in inner ring is inside One layer of recursion generates new inner ring, and calculates corresponding practical cutter-contact point according to action error requirements.ForWhat recursion generated Theoretical cutter-contact point in new inner ring,WithThe region endpoint that arc length error is not zero in respectively new inner ring.
By etc. residual high law theory cutter-contact point recursion criterion know that new inner ring arc length error is due to cutter path weight at new inner ring Folded rate is excessively high, is unsatisfactory for etc. caused by residual high error requirements, according toLocate the associated arguments of inner ring arc length error, it willPlace is new Inner ring arc length errorExpression are as follows:
Convolution (32)-(33) and formula (36) are establishedLocate new inner ring arc length error calculating are as follows:
WithBetween region be new inner ring on need modified cutter path region, due in new inner ring WithBetween theoretical cutter-contact point respectively by outer ringWithBetween theoretical cutter-contact point along line-spacing direction successively recursion It generates, withWithIn the theoretical cutter-contact point that pth layer ring recursion generatesWithAs the to be modified of this layer of ring Zone boundary.By adjusting the region cutter path along the recursion criterion in line-spacing direction, local theory's knife of each layer ring can be corrected Contact.
For different inner ring arc length error patterns, after the positive region to be repaired for determining cutter path, correcting region is treated respectively Theory/practical cutter-contact point carry out along line-spacing direction amendment.Known by theory of geodesics,It is located atAlong line-spacing direction In geodesic curve.To occur that scallop-height is too small between the adjacent cutter-contact point in part after avoiding adjustment, to along the adjacent theory in line-spacing direction Cutter-contact pointWithBetween residual high errorArc length s total to geodesic curvetInfluence relationship carry out sensitivity analysis, take To stImpact factor beIt calculates as follows:
Wherein, stForWithBetween arc length,WithRespectivelySurface Method of the place along line-spacing direction is bent Rate and local radius of curvature.
To avoid positive region inner cutter to be repaired track excessively intensive, it is arrangedEach adjacent theoretical cutter-contact point of recursion it Between residual high calibration corrections be definite value Δ hn.WhenWhen, inner ring arc length error is expressed according to formula (38) Are as follows:
WhenWhen, new inner ring arc length error is expressed according to formula (38) are as follows:
Adjacent theoretical cutter-contact point can be calculated by formula (39)-(40)WithBetween arc length correction amountAre as follows:
Each theoretical cutter-contact point can be further solved along line-spacing direction according to the arc length correction amount between adjacent theoretical cutter-contact point Amendment arc length are as follows:
It is established according to the concavo-convex characteristic of curved surfaceLocate corrected range and correct the functional relation between arc length are as follows:
Comprehensively considerWithBetween spatial relation (distance relation and direction relations), establish along line-spacing side To modified theoretical cutter-contact point computation model are as follows:
Wherein,WithRespectivelyFirst-order partial derivative.It can be solved according to formula (44)WithBetween Parameters variation amountWithAre as follows:
Due to theoretical cutter-contact pointIt can be by carrying out the successively recursion acquisition of Deng Can supreme people's court to outer ring, therefore, along line-spacing direction Modified theory cutter-contact pointIt indicates are as follows:
Since the amendment of theoretical cutter-contact point can cause the amendment of cutter path, and then practical cutter-contact point is caused to be corrected. Modified cutter path is obtained by carrying out curve fitting to the theoretical cutter-contact point along line-spacing adjustment in direction, uses hαp(u(t),v (t)) the pth layer ring after line-spacing adjustment in direction, construction are indicatedGeodesic curve of the place along line-spacing direction Due to the practical cutter-contact point along line-spacing adjustment in directionForWith hαp(u (t), v (t)) intersection point calculates Are as follows:
It can be solved by formula (47) and obtain all practical cutter-contact points along line-spacing adjustment in direction, pass through the part along line-spacing direction The amendment of practical cutter-contact point, can be preferably by among the line-spacing of inner ring arc length error-correction model to each practical cutter-contact point of positive region to be repaired Guarantee to meet residual high error requirements inside processing subregion.
Step 4, along the practical cutter-contact point amendment in machining direction part
The residual high error requirements for only meeting line-spacing direction by the practical cutter-contact point of amendment obtained in step 3, since knife touches The adjustment of point easily causes the distance of adjacent cutter-contact point on machining direction to change, and then it is overproof to induce action error.It need to be towards not The corresponding positive region to be repaired with inner ring arc length error pattern is carried out along the practical cutter-contact point amendment in the part of machining direction.
IfForAlong the modified practical cutter-contact point of machining direction,With It respectively indicatesLocate machining direction and line-spacing direction,WithRespectively along the adjacent theoretical cutter-contact point of machining direction WithBetween step-length and arc length,WithRespectively along the adjacent revised theory cutter-contact point in line-spacing directionWithBetween step-length and arc length,WithRespectively along the adjacent practical cutter-contact point of machining directionWithBetween Step-length and arc length,WithRespectively along the adjacent practical cutter-contact point of amendment in line-spacing directionWithBetween step Long and arc length,WithRespectivelyWithBetween amendment arc length and corrected range.
Since inner ring arc length error value is different, lead to the positive region to be repaired of cutter path difference.WhenWhen, the local cutter-contact point of shared q layers of ring needs to correct,WithRespectively pth layer ring is to be repaired Positive region boundary；WhenWhen, the local cutter-contact point needs that q+1 layers of ring are shared including new inner ring are repaired Just,WithThe respectively zone boundary to be modified of pth layer ring.Although positive region to be repaired is different, each layer ring is real Border cutter-contact point is identical along the amendment principle of machining direction, thus the practical cutter-contact point quantity of pth layer ring in positive region to be repaired is arranged For φ, for two kinds of different inner ring arc length error patterns, practical cutter-contact point correction result is calculated as follows on pth layer ring:
By cutter path just planning with along the practical cutter-contact point correction result in part in line-spacing direction, can calculateWithAndWithBetween step-length be respectively as follows:
It is solved according to the concavo-convex characteristic of curved surfaceWithBetween arc length are as follows:
WithBetween arc length are as follows:
Wherein,WithForWithPlace along machining direction curved surface normal curvature,WithForWithLocate the local radius of curvature of machining direction.
Comparison each adjacent theoretical cutter-contact point along the zone boundary to be modified of line-spacing direction part practical cutter-contact point amendment front and back Arc length summation, total arc length error delta s along machining direction can be calculatedα pAre as follows:
Identical as adjacent theoretical cutter-contact point arc length calculating process, matching test (49) and formula (50) can be calculated along line-spacing direction office The adjacent practical cutter-contact point arc length of machining direction of the practical cutter-contact point amendment correspondence in portionWithTherefore, on each layer ring Arc length variation between the adjacent practical cutter-contact point of machining directionIt calculates are as follows:
Δsα pAlso it is simultaneously the arc length summation of each adjacent practical cutter-contact point in zone boundary to be modified, establishes along machining direction Adjacent practical cutter-contact pointWithBetween action errorTo the impact factor of the total arc length of cutter pathAre as follows:
Wherein,WithRespectivelyCurved surface normal curvature and radius of curvature of the place along machining direction.
To avoid practical cutter-contact point on positive region inner layers ring to be repaired excessively intensive, each adjacent reality on pth layer ring is set Action calibration corrections are definite value Δ e between the cutter-contact point of borderp.Use the arc length correction amount of practical cutter-contact point by edge according to formula (53) Total arc length error of machining direction is expressed are as follows:
Action calibration corrections Δ e can be solved by formula (51) and formula (54)pAre as follows:
And then practical cutter-contact point adjacent along machining direction can be calculatedWithBetween arc length correction amountAre as follows:
Convolution (52) is with formula (56) it is found that practical cutter-contact point should be along the amendment arc length of machining direction repairs along line-spacing direction Difference between arc length variation caused by after just and the arc length correction amount for keeping action error constant calculates are as follows:
Its corrected range can be further solved according to the amendment arc length between adjacent practical cutter-contact point are as follows:
Wherein,ForCurved surface normal curvature of the place along machining direction.
Comprehensively considerWithBetween spatial relation (distance relation and direction relations), establish along feed side To modified practical cutter-contact point computation model are as follows:
Wherein,WithRespectivelyFirst-order partial derivative.It can be solved according to formula (59)With Between Parameters variation amountWithAre as follows:
Wherein,WithForLocate corresponding curved surface first kind fundamental quantity.
Due to the practical cutter-contact point along line-spacing adjustment in directionIt can be obtained by formula (47), therefore, be repaired along machining direction Positive practical cutter-contact pointIt indicates are as follows:
By formula (61) can solve obtain it is all along the modified practical cutter-contact point of machining direction, by along the part of machining direction The amendment of practical cutter-contact point, can be preferably by among the step-length of inner ring arc length error-correction model to each practical cutter-contact point of positive region to be repaired Guarantee to meet action error requirements inside processing subregion.So far, the curved surface subregion ring cutting of inner ring arc length error-correction model is taken into account Process tool track is planned again is able to whole realizations.
After the completion of cutter path is planned again, by post-processing, the processed file that can identify of output lathe, realize based on etc. The curved surface subregion contour parallel milling cutter path planing method of residual supreme people's court.
Remarkable result and benefit of the invention is that this method is directed in subregion process, at subregion cutter path inner ring There is the problem of obviously connecing tool marks, by limiting subzone boundaries scallop-height, processing subregion is generated based on Deng Can supreme people's court Theoretical/practical cutter-contact point, establishes inner ring arc length error calculating, successively theoretical/real along line-spacing direction and step-length adjustment in direction Border cutter-contact point realizes inner ring arc length error-correction model, and then completes curved surface subregion circular cutter trajectory planning, effectively ensures sub-district It while the boundary processing quality of domain, reduces and connects tool marks at subregion cutter path inner ring, it is whole to improve curved surface subregion ring cutting Body processing quality provides technical support for complex-curved high-precision high-efficiency processing.
Detailed description of the invention
Fig. 1-method overall flow figure.
Fig. 2-curved surface subregion processes each processing subregion cutter-contact point boundary formation.A-subregion 1, B-subregion 2, C- Subregion 3, D-subregion 4.
Fig. 3-takes into account the cutter path of inner ring arc length error-correction model planning flow chart again.
The cutter path that the single processing subregion of Fig. 4-is planned again.
Surface roughness at Fig. 5-tradition Deng Can supreme people's court's cutter path planning post-processing subregion inner ring；Abscissa is to take Sample length (mm), ordinate are profile offset distance (μm), and Ra indicates machined surface roughness (μm).
Surface roughness at Fig. 6-the method for the invention cutter path planning post-processing subregion inner ring；Abscissa is Sample length (mm), ordinate are profile offset distance (μm), and Ra indicates machined surface roughness (μm).
Specific embodiment
Combination technology scheme and the attached drawing specific embodiment that the present invention will be described in detail.
When curved surface subregion becomes tool sharpening, mould is planned by the cutter path on periphery to center since existing method mostly uses It is overproof to easily lead to mismachining tolerance at all subregion inner ring for formula, or even occurs obviously connecing tool marks, and the serious complex curved surface parts that restrict add Comprehensive raising of working medium amount.For this case, tool marks are connect at subregion cutter path inner ring in order to reduce, have invented a kind of base In the curved surface subregion contour parallel milling cutter path planing method of Deng Can supreme people's court, overall flow is as shown in Fig. 1.
By taking various sizes of milling cutter is along different cutter path Milling Process saddle cambers as an example, by UG software and MATLAB Software, implementation process that the present invention will be described in detail.Firstly, establishing a saddle camber using UG NX software, it is divided into 4 Subregion is numbered from A to D.For the processing differences for embodying different subregions, with radius be respectively 4mm and 2mm ball head knife into Row alternating contour parallel milling.Secondly, residual high error is 0.02mm at setting subzone boundaries, action error is 0.02mm, is utilized MATLAB software constructs critical cutter-contact point curve and iterates to calculate to take up an official post to boundary through formula (1)-(7) according to surface geometry feature Geodesic curve radius of curvature of the meaning point along line-spacing direction.According to the effective radius of cutter and intersection point type, in conjunction with geodesic curve curvature half Diameter obtains on boundary line-spacing between the subregion of arbitrary point through formula (8)-(16) iterative calculation.Then, according between the subregion acquired Line-spacing establishes the equation group of arbitrary point on boundary by formula (17)-(20), solves the critical knife touching in the corresponding two sides of each boundary point Discrete cutter-contact point is fitted to curve by MATLAB software by point, completes critical cutter-contact point curve construction referring to attached drawing 2.
Then, using critical cutter-contact point curve as the outermost layer ring of curved surface subregion contour parallel milling cutter path, critical It is intensively taken on cutter-contact point curve as the starting point along line-spacing direction recursion.It is obtained by formula (21)-(28) along line-spacing direction Recurrence relation calculates all theoretical cutter-contact points that recursion generates contour parallel milling through MATLAB software, until inner ring itself is along line-spacing Spacing such as is unsatisfactory at the residual high error constraints between the adjacent theoretical cutter-contact point in direction.It is corresponding upper a little as inner ring to choose the point. The theoretical cutter-contact point of each layer scattering is fitted to curve by MATLAB software and obtains a plurality of initial contour parallel milling cutter path, then The practical cutter-contact point in each layer cutter path is generated by formula (29) recursion, cutter path is completed and just plans.
The theoretical cutter-contact point and practical cutter-contact point just planned cutter path are modified, and are calculated inner ring arc length error and are divided Class successively carries out correcting along the cutter-contact point of line-spacing direction and machining direction, by inner ring arc length error-correction model to positive region to be repaired Each cutter-contact point, planning flow chart is as shown in Fig. 3 again for cutter path.It is programmed using MATLAB, is counted by formula (30)-(37) Inner ring arc length error is calculated, determines zone boundary to be modified, while to each positive region to be repaired along the adjacent theoretical knife touching in line-spacing direction Scallop-height carries out sensitivity analysis between point, convolution (38), obtains between each theoretical cutter-contact point scallop-height to geodesic curve The impact factor of total arc length can get each theory through formula (39)-(43) according to the inner ring arc length error of calculating and each impact factor Cutter-contact point determines revised theoretical cutter-contact point by formula (44)-(46) along the arc length correction amount and corrected range in line-spacing direction, The practical cutter-contact point after all adjustment in direction along line-spacing is obtained using formula (47).
Towards positive region to be repaired, carry out along the practical cutter-contact point amendment in the part of machining direction.Along the amendment cutter rail obtained Mark calculates the arc length variation along the adjacent practical cutter-contact point of machining direction through formula (48)-(52).Simultaneously again to each positive region to be repaired The action error between the adjacent practical cutter-contact point of machining direction carry out sensitivity analysis, calculated through formula (53) and obtain corresponding shadow Ring the factor.By MATLAB software, the corrected range between adjacent practical cutter-contact point is calculated according to formula (54)-(58), counts It is 0.0544mm, minimum value 0.0207mm that each layer ring, which is calculated, along the practical cutter-contact point corrected range maximum value of machining direction.Pass through Formula (59)-(61) determine revised practical cutter-contact point, complete the curved surface subregion circular cutter for taking into account inner ring arc length error-correction model Plan that the cutter path that wherein region C is planned again is referring to attached drawing 4 again in tool track.
For the validity for verifying the method, the residual high normal surface subregion circular cutter trajectory plannings such as tradition and this hair are carried out The comparative experiments of bright the method cutter path planning.Difference processing subregion gives identical working process parameter and processing is wanted It asks, respectively speed of mainshaft 4000r/min, cutting-in 0.3mm, feed speed 250mm/min can be complete according to the machined parameters of setting It is processed at the actual cut of the part.
The experimental results showed that process surface roughness at (1.848 μm) acquisition workpiece subregion inner ring relatively etc. residual for this method Supreme people's court, which processes (2.719 μm), reduces by 32.03%, and subzone boundaries (1.766 μm) surface roughness is processed compared with Deng Can supreme people's court (1.834 μm) reduce by 3.71%.Deng Can supreme people's court machining profile deviation smooth fluctuations at subzone boundaries, at subregion inner ring It steeply rises, appearance obviously connects tool marks, as shown in Fig. 5.This method machining profile deviation is at subzone boundaries and at inner ring Equal smooth fluctuations, without obviously tool marks are connect, as shown in Fig. 6.This method is processed maximum at (6.9 μm) acquisition workpiece subregion inner ring Profile variation, which processes (14.8 μm) compared with Deng Can supreme people's court, reduces by 53.38%, and subzone boundaries (6.5 μm) largest contours deviation is relatively etc. residual Supreme people's court, which processes (6.7 μm), reduces by 2.99%.
This further demonstrates methods proposed by the invention to show under the premise of ensuring processing quality at subzone boundaries It writes and inhibits to connect tool marks at processing subregion inner ring, improve the processing quality of complex curved surface parts comprehensively.

Claims (1)

1. a kind of curved surface subregion contour parallel milling cutter path planing method, which is characterized in that this method limits processing subregion Boundary scallop-height is based on Deng Can supreme people's court edge according to its geometrical characteristic and the critical cutter-contact point curve of cutter intersection point type structure Line-spacing direction generative theory/practical cutter-contact point；It establishes inner ring arc length error calculating and classifies, determine positive region to be repaired, pass through Sensitivity analysis calculates theoretical cutter-contact point corrected range, along theoretical/practical cutter-contact point of line-spacing adjustment in direction；It is total to calculate machining direction Arc length error calculates cutter-contact point arc length variation/adjustment amount through sensitivity analysis, determines along machining direction and corrects practical knife touching Point is completed cutter path and is planned again；Specific step is as follows for method:
Step 1, residual high normal surface subregion contour parallel milling cutter path is waited just to plan
Complex curved surface parts contour parallel milling subregion is expressed as S (u, v), boundary curve is C (u (t), v (t)), P0For boundary P is remembered at upper any point0Locating boundary is tangentially (du0,dv0), curved surface normal direction is n, perpendicular to boundary is tangential and curved surface normal direction Direction is the line-spacing direction at the boundary point, is expressed as (du0',dv0')；Scallop-height is h at limited boundary, by Differential Geometry It is theoretical it is found that the maximum value of scallop-height appears in the geodesic curve in line-spacing direction, therefore in P0The survey in two lateral edge line-spacing directions There are two critical cutter-contact point P on ground wire1And P2To guarantee P0Place's scallop-height meets processing request；In P0Place, along line-spacing direction Curved surface first fundamental form I and curved surface second fundamental form II be respectively as follows:
Wherein, E, F, G are curved surface first kind fundamental quantity, and L, M, N are the second class of curved surface fundamental quantity, and expression formula is as follows:
Wherein, Su、SvFor the first-order partial derivative of curved surface S (u, v), Suu、Suv、SvvFor the second-order partial differential coefficient of curved surface S (u, v), n is song The normal vector of face S (u, v)；
P can be calculated according to first fundamental form of surface and second fundamental form0Principal curvatures k along line-spacing directionnAre as follows:
Because boundary is tangential and line-spacing direction is mutually perpendicular to, express are as follows:
(Sudu0+Svdv0)(Sudu0'+Svdv0')=0 (4)
So line-spacing direction calculating are as follows:
Formula (5) are substituted into formula (3), obtain P0Principal curvatures k along line-spacing directionnAre as follows:
Work as knWhen=0, P0Place is plane；Work as knWhen < 0, P0Place is convex surface；Work as knWhen > 0, P0Place is concave surface；P0Place is along line-spacing side To geodesic curve radius of curvature be Rc, calculate are as follows:
In process, effective cutting shape and tool category and processing method are closely related for different cutters；Allow in error In range, osculating circle of the profile at cutter-contact point is scanned with cutter and is the effective cutting shape of the point, and close radius of circle is made For the effective radius of clean-up r of cuttere, calculation method is as follows:
When cutter is rose cutter, the effective radius of clean-up r of cuttereAre as follows:
re=R (8)
When cutter is flat-end cutter, the effective radius of clean-up r of cuttereAre as follows:
When cutter is ring type milling cutter, the effective radius of clean-up r of cuttereAre as follows:
Wherein, R is cutter real radius, and r is milling cutter annulus radius surface, and λ is top rake during five-axis robot, and ω is that five axis add Side drift angle during work；
According to the effective radius of clean-up r of cuttereWith the size relationship between cutter real radius R, it is at radius by all kinds of milling cutters are equivalent The cylindrical surface of R and radius are reThe milling cutter model that is combined into of spherical surface；It, can will be between cutter enveloping surface according to the milling cutter model Intersection point is divided into two classes: 1. spherical surface intersects with spherical surface；2. cylindrical surface is intersected with spherical surface；This intersection point type changes with distance between cutter Become, if the cutter of adjacent two subregion is milling cutter 1 and milling cutter 2, effective radius of clean-up is respectively r1eAnd r2e(r1e≥r2e), it gives The real radius of milling cutter 2, if R1For the real radius of milling cutter 1, R1=j is intersection point type change critical condition；Comprehensively consider curved surface Concavo-convex characteristic and intersection point type, line-spacing computation model is as follows between establishing subregion:
1) plane machining
Milling cutter 1 is with milling cutter 2 when plane intersects, and by geometrical relationship between cutter, intersection point type change critical condition is calculated are as follows:
When intersection point type is that spherical surface intersects with spherical surface between cutter, R1>=j, when intersection point type is cylindrical surface and ball between cutter When face is intersected, R1< j；
For two kinds of intersection point types, line-spacing d between subregiontIt calculates are as follows:
2) convex surface processes
Milling cutter 1 with milling cutter 2 when convex surface is intersected, it is small in view of the evaluation for connecing knife line-spacing, convex surface is equivalent to spherical outside surface, RcI.e. For convex surface local radius of curvature；By geometrical relationship between cutter, intersection point type change critical condition is calculated are as follows:
When intersection point type is that spherical surface intersects with spherical surface between cutter, R1>=j, when intersection point type is cylindrical surface and ball between cutter When face is intersected, R1< j；
For two kinds of intersection point types, line-spacing d between subregiontIt calculates are as follows:
3) concave surface processes
Milling cutter 1 with milling cutter 2 when concave surface is intersected, it is small in view of the evaluation for connecing knife line-spacing, concave surface is equivalent to Internal Spherical Surface, RcI.e. For concave surface local radius of curvature；By geometrical relationship between cutter, intersection point type change critical condition is calculated are as follows:
When intersection point type is that spherical surface intersects with spherical surface between cutter, R1>=j, when intersection point type is cylindrical surface and ball between cutter When face is intersected, R1< j；
For two kinds of intersection point types, line-spacing d between subregiontIt calculates are as follows:
Critical cutter-contact point P for ease of calculation1、P2With P0Between spatial relation (distance relation and direction relations), take P0 For P1With P2Between geodesic midpoint, l0For P0P1With P0P2Length；According to geometrical relationship, under different curve concavo-convex characteristic l0It calculates are as follows:
Comprehensively consider the spatial relation of the critical cutter-contact point of adjacent subarea domain boundaries on either side, i.e. distance relation and direction relations, Establish critical cutter-contact point Pi(i=1,2) computation model are as follows:
Wherein, P0uWith P0vRespectively P0First-order partial derivative；P can be solved to obtain according to formula (18)iWith P0Between Parameters variation amountWithAre as follows:
In the computation model, critical cutter-contact point P1With P2Always exist in pairs, and is located at P0Opposite orientation, P0、P1With P2 In processing subregion S (u, v), P0For known boundaries point, according to calculated result, P0、P1With P2It indicates are as follows:
The critical cutter-contact point of the corresponding whole in boundary is calculated using the above method, these critical cutter-contact points are carried out curve fitting, Obtain the critical cutter-contact point curve based on Deng Can supreme people's court；When all subregion cutter-contact point is respectively positioned on critical cutter-contact point curve, protect The card residual high error of adjacent subarea domain boundary meets processing request；
Definition is theoretical cutter-contact point by other cutter-contact points that outer ring cutter-contact point recursion generates, according to action error in cutter path It is required that the cutter-contact point generated is practical cutter-contact point；Contour parallel milling cutter path is planned according to Deng Can supreme people's court, each layer ring Theoretical cutter-contact point and practical cutter-contact point calculate as follows:
IfFor n-th of cutter-contact point on outer ring,For on pth layer ringThe theory that recursion generates Cutter-contact point, thenLocating machining direction is For m-th of practical cutter-contact point on pth layer ring, thenLocating machining direction is For the line-spacing between cutter-contact point theoretical in adjacent ring, i.e.,WithBetween Distance,For the step-length between adjacent practical cutter-contact point on pth layer ring, i.e.,WithThe distance between, e is setting Action error, with the symbiosis of Deng Can supreme people's court at q layers of ring；To construct the critical cutter-contact point curve based on Deng Can supreme people's court as ring cutting First outer ring cutter path of processing is appointed and is taken on outer ring a little as the starting point along machining direction recursionEstablish outer ring phase Functional relation between adjacent cutter-contact point step-length and action error are as follows:
Wherein,ForLocal radius of curvature of the place along machining direction；To accurately generate the cutter-contact point on outer ring, according to song The concavo-convex characteristic in face establishes the functional relation between arc length and step-length are as follows:
Wherein,WithRespectivelyCurved surface normal curvature and arc length of the place along machining direction；
Arc length is calculated according to first form curve integralAre as follows:
Wherein,For starting pointThe parameter value at place, convolution (22)-(23) can solveLocate corresponding parameter valueCause And outer ring is along the cutter-contact point of machining direction recursionAre as follows:
All cutter-contact points of outer ring are solved by formula (24), are known by definition, theoretical cutter-contact point is identical as practical cutter-contact point on outer ring, Expression are as follows:
With each cutter-contact point of outer ringAs the starting point along line-spacing direction recursion, successively recursion is obtained in remaining cutter path Theoretical cutter-contact point, theory of correspondences cutter-contact point between adjacent ringWithRecurrence relation expression are as follows:
Wherein,WithBetween Parameters variation amountWithIt calculates are as follows:
Wherein,WithForLocate corresponding curved surface first kind fundamental quantity,WithForPlace corresponds to Curved surface the second class fundamental quantity；ForLength, calculation method is as follows:
Wherein,ForCurved surface normal curvature along line-spacing direction；
By formula (26)-(28), successively recursion obtains all theoretical cutter-contact points of contour parallel milling, until inner ring itself is along line-spacing side To the residual high error constraints such as being unsatisfactory between adjacent theoretical cutter-contact point；At this point, using the corresponding upper one layer of ring of the point as inner ring；So And theoretical cutter-contact point is obtained according only to the residual high error in line-spacing direction, it is difficult to meet the action error requirements of machining direction, thus The practical cutter-contact point that cannot function as in numerical control processing uses；The theoretical cutter-contact point of each layer ring is carried out curve fitting to obtain a plurality of knife Have track, is expressed as hi(u (t), v (t)) appoints and takes on each layer ring a little as starting pointAccording to formula (21)-(23) Calculate the practical cutter-contact point along machining direction recursionCorresponding parameter valueAnd then it can incite somebody to actionIt indicates are as follows:
So far, all theoretical cutter-contact point of contour parallel milling can get by Deng Can supreme people's court and practical cutter-contact point, cutter path is just advised It draws and is accomplished；
Step 2, inner ring arc length error calculating is established
Based on step 1 realize etc. residual high normal surface subregion contour parallel milling cutter path just plan easily cause inner ring arc length miss Difference, and then cause to occur obviously connecing tool marks at inner ring；In order to inhibit inner ring arc length error, inner ring arc length error calculating is established And classify；
IfForLocal radius of curvature of the place along line-spacing direction, hq(u (t), v (t)) indicates inner ring,Table ShowPlace along line-spacing direction geodesic curve,For the geodesic curve and inner ring intersection point,WithRespectivelyLocate corresponding inner ring Spacing and inner ring arc length；
ConstructionGeodesic curve of the place along line-spacing directionDue toForWith hq(u(t),v (t)) intersection point calculates are as follows:
Pass throughWithCoordinate value can determineLocate corresponding inner ring spacing are as follows:
It is established according to the concavo-convex characteristic of curved surfaceLocate the functional relation between inner ring arc length and inner ring spacing are as follows:
Wherein,ForCurved surface normal curvature of the place along line-spacing direction；
With reference to the calculation method of formula (28), can derive in the case where waiting residual high error constraintsInner ring arc length is discussed in processingAre as follows:
It willLocate inner ring arc length errorExpression are as follows:
Convolution (31)-(34) are establishedLocate inner ring arc length error calculating are as follows:
Two classes are classified as according to inner ring arc length error size:
1)
In the type, the corresponding next layer of recursion ring of inner ring will appear the problem of cutter path is intersected, in response to this, no It needs to add new cutter-contact point, only can realize the two-way homogenizing of inner ring arc length error by correcting existing practical cutter-contact point；
2)
In the type, it is excessively high that the corresponding next layer of recursion ring of inner ring will appear cutter path Duplication, be unsatisfactory for etc. it is residual it is high accidentally The problem of difference requires to avoid introducing excessive error to other cutter-contact points, needs to add new cutter-contact point in response to this, Then the two-way homogenizing of inner ring arc length error is just able to achieve to existing practical cutter-contact point amendment according to newly-increased cutter-contact point；
Step 3, along the practical cutter-contact point amendment in line-spacing direction part
The inner ring arc length error calculating that the theory/practical cutter-contact point and step 2 obtained in conjunction with step 1 is established, for difference Inner ring arc length error pattern determines the positive region to be repaired of cutter path, carries out along the practical cutter-contact point amendment in the part in line-spacing direction It is as follows:
1)
In this seed type, do not need to add new cutter-contact point；IfForTheoretical knife touching after line-spacing adjustment in direction Point,ForAlong the practical cutter-contact point of line-spacing adjustment in direction,WithIt respectively indicatesPlace Machining direction and line-spacing direction,WithThe region endpoint that arc length error is not zero respectively in inner ring,WithPoint It is notWithBetween amendment arc length and corrected range；
WithBetween region be inner ring on need modified cutter path region, if only correct this region of inner ring knife touching Point easily causes inner ring arc length error transfer and accumulates in one layer of intermediate ring, and it is overproof and obviously connect equally to will appear mismachining tolerance Tool marks, thus need inner ring arc length error-correction model to each layer ring；Due in inner ringWithBetween theoretical cutter-contact point point Not by outer ringWithBetween theoretical cutter-contact point along line-spacing direction successively recursion generate, to avoid cutter path from being mutated, WithWithIn the theoretical cutter-contact point that pth layer ring recursion generatesWithRegional edge to be modified as this layer of ring Boundary；By adjusting the region cutter path along the recursion criterion in line-spacing direction, local theory's cutter-contact point of each layer ring can be corrected；
2)
In this seed type, need to add new cutter-contact point；With Deng Can supreme people's court by the inside recursion of theoretical cutter-contact point in inner ring One layer generates new inner ring, and calculates corresponding practical cutter-contact point according to action error requirements；ForRecursion generates new interior Theoretical cutter-contact point on ring,WithThe region endpoint that arc length error is not zero in respectively new inner ring；
By etc. residual high law theory cutter-contact point recursion criterion know that new inner ring arc length error is due to cutter path Duplication at new inner ring It is excessively high, it is unsatisfactory for etc. caused by residual high error requirements, according toLocate the associated arguments of inner ring arc length error, it willLocate new inner ring Arc length errorExpression are as follows:
Convolution (32)-(33) and formula (36) are establishedLocate new inner ring arc length error calculating are as follows:
WithBetween region be new inner ring on need modified cutter path region, due in new inner ringWithBetween theoretical cutter-contact point respectively by outer ringWithBetween theoretical cutter-contact point along line-spacing direction, successively recursion is raw At, withWithIn the theoretical cutter-contact point that pth layer ring recursion generatesWithArea to be modified as the floor ring Domain boundary；By adjusting the region cutter path along the recursion criterion in line-spacing direction, local theory's knife touching of each layer ring can be corrected Point；
For different inner ring arc length error patterns, after the positive region to be repaired for determining cutter path, the reason of correcting region is treated respectively The amendment along line-spacing direction is carried out by/practical cutter-contact point；Known by theory of geodesics,It is located atGeodetic along line-spacing direction On line；To occur that scallop-height is too small between the adjacent cutter-contact point in part after avoiding adjustment, to along the adjacent theoretical knife touching in line-spacing direction PointWithBetween residual high errorArc length s total to geodesic curvetInfluence relationship carry out sensitivity analysis, takeTo st's Impact factor isIt calculates as follows:
Wherein, stForWithBetween arc length,WithRespectivelyCurved surface normal curvature of the place along line-spacing direction With local radius of curvature；
To avoid positive region inner cutter to be repaired track excessively intensive, it is arrangedIt is residual between each adjacent theoretical cutter-contact point of recursion High calibration corrections are definite value Δ hn；WhenWhen, inner ring arc length error is expressed according to formula (38) are as follows:
WhenWhen, new inner ring arc length error is expressed according to formula (38) are as follows:
Adjacent theoretical cutter-contact point can be calculated by formula (39)-(40)WithBetween arc length correction amountAre as follows:
Each theoretical cutter-contact point is further solved along the amendment in line-spacing direction according to the arc length correction amount between adjacent theoretical cutter-contact point Arc length are as follows:
It is established according to the concavo-convex characteristic of curved surfaceLocate corrected range and correct the functional relation between arc length are as follows:
Comprehensively considerWithBetween spatial relation (distance relation and direction relations), foundation repaired along line-spacing direction Positive theoretical cutter-contact point computation model are as follows:
Wherein,WithRespectivelyFirst-order partial derivative；It can be solved according to formula (44)WithBetween ginseng Number variable quantityWithAre as follows:
Due to theoretical cutter-contact pointIt can be by carrying out the successively recursion acquisition of Deng Can supreme people's court to outer ring, therefore, along line-spacing adjustment in direction Theoretical cutter-contact pointIt indicates are as follows:
Since the amendment of theoretical cutter-contact point can cause the amendment of cutter path, and then practical cutter-contact point is caused to be corrected；Pass through It carries out curve fitting to the theoretical cutter-contact point along line-spacing adjustment in direction and obtains modified cutter path, use hαp(u (t), v (t)) table Show the pth layer ring after line-spacing adjustment in direction, constructsGeodesic curve of the place along line-spacing directionDue to edge The practical cutter-contact point of line-spacing adjustment in directionForWith hαp(u (t), v (t)) intersection point calculates are as follows:
It can be solved by formula (47) and obtain all practical cutter-contact points along line-spacing adjustment in direction, it is practical by the part along line-spacing direction Cutter-contact point is corrected among the line-spacing of inner ring arc length error-correction model to each practical cutter-contact point of positive region to be repaired, can preferably be guaranteed Meet residual high error requirements inside processing subregion；
Step 4, along the practical cutter-contact point amendment in machining direction part
The residual high error requirements for only meeting line-spacing direction by the practical cutter-contact point of amendment obtained in step 3, due to cutter-contact point Adjustment easily causes the distance of adjacent cutter-contact point on machining direction to change, and then it is overproof to induce action error；It need to be towards in difference The corresponding positive region to be repaired of ring arc length error pattern is carried out along the practical cutter-contact point amendment in the part of machining direction；
IfForAlong the modified practical cutter-contact point of machining direction,WithRespectively It indicatesLocate machining direction and line-spacing direction,WithRespectively along the adjacent theoretical cutter-contact point of machining directionWithBetween step-length and arc length,WithRespectively along the adjacent revised theory cutter-contact point in line-spacing directionWith Between step-length and arc length,WithRespectively along the adjacent practical cutter-contact point of machining directionWithBetween step-length With arc length,WithRespectively along the adjacent practical cutter-contact point of amendment in line-spacing directionWithBetween step-length and arc It is long,WithRespectivelyWithBetween amendment arc length and corrected range；
Since inner ring arc length error value is different, lead to the positive region to be repaired of cutter path difference；When When, the local cutter-contact point of shared q layers of ring needs to correct,WithThe respectively zone boundary to be modified of pth layer ring；WhenWhen, the local cutter-contact point that q+1 layers of ring are shared including new inner ring needs to correct,With The respectively zone boundary to be modified of pth layer ring；Although positive region to be repaired is different, each practical cutter-contact point of layer ring is along feed The amendment principle in direction is identical, thus the practical cutter-contact point quantity that pth layer ring in positive region to be repaired is arranged is φ, not for two kinds With inner ring arc length error pattern, practical cutter-contact point correction result is calculated as follows on pth layer ring:
By cutter path just planning with along the practical cutter-contact point correction result in part in line-spacing direction, can calculateWithAndWithBetween step-length be respectively as follows:
It is solved according to the concavo-convex characteristic of curved surfaceWithBetween arc length are as follows:
WithBetween arc length are as follows:
Wherein,WithForWithPlace along machining direction curved surface normal curvature,WithForWith Locate the local radius of curvature of machining direction；
Compare the arc of each adjacent theoretical cutter-contact point along the zone boundary to be modified of line-spacing direction part practical cutter-contact point amendment front and back Long summation can calculate total arc length error delta s along machining directionα pAre as follows:
Identical as adjacent theoretical cutter-contact point arc length calculating process, matching test (49) and formula (50) can be calculated along line-spacing direction part in fact The adjacent practical cutter-contact point arc length of machining direction of border cutter-contact point amendment correspondenceWithTherefore, the feed on each layer ring Arc length variation between the adjacent practical cutter-contact point in directionIt calculates are as follows:
Δsα pAlso it is simultaneously the arc length summation of each adjacent practical cutter-contact point in zone boundary to be modified, establishes adjacent along machining direction Practical cutter-contact pointWithBetween action errorTo the impact factor of the total arc length of cutter pathAre as follows:
Wherein,WithRespectivelyCurved surface normal curvature and radius of curvature of the place along machining direction；
To avoid practical cutter-contact point on positive region inner layers ring to be repaired excessively intensive, each adjacent practical knife on pth layer ring is set Action calibration corrections are definite value Δ e between contactp；It will be along feed with the arc length correction amount of practical cutter-contact point according to formula (53) Total arc length error in direction is expressed are as follows:
Action calibration corrections Δ e can be solved by formula (51) and formula (54)pAre as follows:
And then practical cutter-contact point adjacent along machining direction can be calculatedWithBetween arc length correction amountAre as follows:
Convolution (52) and formula (56) are it is found that practical cutter-contact point should be after line-spacing adjustment in direction along the amendment arc length of machining direction Difference between caused arc length variation and the arc length correction amount for keeping action error constant calculates are as follows:
Its corrected range can be further solved according to the amendment arc length between adjacent practical cutter-contact point are as follows:
Wherein,ForCurved surface normal curvature of the place along machining direction；
Comprehensively considerWithBetween spatial relation (distance relation and direction relations), foundation repaired along machining direction Positive practical cutter-contact point computation model are as follows:
Wherein,WithRespectivelyFirst-order partial derivative；It can be solved according to formula (59)WithBetween Parameters variation amountWithAre as follows:
Wherein,WithForLocate corresponding curved surface first kind fundamental quantity；
Due to the practical cutter-contact point along line-spacing adjustment in directionIt can be obtained by formula (47), it is therefore, modified along machining direction Practical cutter-contact pointIt indicates are as follows:
It can be solved by formula (61) and obtain all along the modified practical cutter-contact point of machining direction, passed through along the part of machining direction actually Cutter-contact point is corrected among the step-length of inner ring arc length error-correction model to each practical cutter-contact point of positive region to be repaired, can preferably be guaranteed Meet action error requirements inside processing subregion；So far, the curved surface subregion contour parallel milling of inner ring arc length error-correction model is taken into account Cutter path is planned again is able to whole realizations；
After the completion of cutter path is planned again, by post-processing, the processed file that can identify of output lathe, realize based on etc. residual height The curved surface subregion contour parallel milling cutter path planing method of method.
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