CN109977999A - A method of non-rotating tool validity feature line is solved by discrete workpieces curved surface - Google Patents
A method of non-rotating tool validity feature line is solved by discrete workpieces curved surface Download PDFInfo
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Abstract
The invention discloses a kind of methods for solving non-rotating tool validity feature line by discrete workpieces curved surface, include the following steps: to solve the real work enveloping surface of non-rotating tool using warp/weft method and traditional Enveloping theory according to non-rotating tool geometries and tool relative motion relation；According to non-rotating tool feeding direction, by the workpiece design Surface tessellation of non-rotating tool bottom at a series of sections of molded line；Using shortest distance lines to principle sum number Iteration algorithm, it calculates separately out every and cuts the shortest distance and its intersection point point of the molded line to non-rotating tool real work enveloping surface, the validity feature line that the line of all intersection point points in the given margin of tolerance is constituted between non-rotating tool real work enveloping surface and workpiece machined surface；Intersection point point on validity feature line is sought into the shortest distance to workpiece design curved surface respectively, a series of intersection point points and shortest distance line segment are obtained on workpiece design curved surface, the set of all shortest distance line segments constitutes the error distribution function of non-rotating tool and workpiece design curved surface.This method can accurately solve non-rotating tool processes it is complex-curved when error distribution situation, provide important computations foundation for non-rotating tool pose refinement, have certain practical application value.
Description
Technical field
The present invention relates to a kind of multiaxis NC maching programmed method, more particularly to one kind are non-by the solution of discrete workpieces curved surface
The method of rotary tool validity feature line, belongs to numerical control processing field.
Background technique
The processing problems of semiclosed curved surface become one highly important bottleneck problem of current field of machining.Enclosed leaf
Wheel, leaf joint and turbine nozzle vane all in semiclosed and curved space among, when using staight shank jatharapanvartanasana tool processes
It is very easy to interfere.Allow to carry out milling, grinding and buffing to it from the two sides of runner respectively using rotary tool
Processing, it is also desirable to the tool processes of diameter very little are selected in order to avoid collision, to bring tool rigidity deficiency, processing efficiency
Low, the problems such as machining accuracy is poor.And flow channel space can be made full use of if using non-rotating tool (such as vibropolish tool), is increased
The rigidity of tool and the worksheet area of coated abrasive tool are processed, the service life of tool can be significantly extended.But it is non-due to lacking
Rotary tool cutter Location Calculation Method, therefore, up to the present, non-rotating tool in numerical control processing using very limited, also
Only it is applied to artificial engraving and bruting process.The tool design method and method for planning track of non-rotating tool are from principle
Design method and method for planning track comprising turning round rotary tool, therefore study and obtain the design and volume of non-rotating tool
Journey technology has great theory significance and application value.
Problem of Relative Movement between complex-curved is the important category of conjugation theory research, but current conjugation theory
Contact movement problem with clear contact point and contact line between two curved surfaces of main research.There are three kojis in numerical control processing
Face: tool work face, workpiece design curved surface and workpiece machined surface.So-called workpiece machined surface is actually by tool edge
Workpiece design curved surface on a plurality of driving line movement when envelope made of multirow enveloping surface set.Between these three types of surfaces
Relationship Comparison is complicated, but there is also certain to connect each other.Relative motion symbol between workpiece machined surface and tool surfaces
Traditional Enveloping theory or spatial conjugation motion theory are closed, there is line contact or face contact relationship therebetween: when using scanning fortune
Conjugate movement relationship is contacted for line when dynamic processing, when using manufacturing process to process for face contact relationship, the former contact line is just
It is the characteristic curve of envelope movement.It but is design curved surface and Machining of Curved Surface wheel for known condition in complex-curved numerical control processing
Wide degree tolerance, the shape of tool and the shape of workpiece machined surface are unknown.It is complex-curved being processed using rotary tool
When, technological design personnel need the structure snd size of property and possible processing method select tools according to design curved surface, so
The motion profile of tool is determined according to the property of curved surface afterwards.In the case of complex-curved for nonvolatile organic acid tool processes, at present
The tool mainly used include non-rotating engraving cutter, the non-rotating file with complex space shape and sand paper flexible,
Abrasive band, sand paper, sand lump etc..The geometry of these tools is gradually developed in human production activity over the past thousands of years
, be suitble to solve to rise and fall violent, semi-enclosed, with the lower processing object of rotary tool hardness ag(e)ing rate processing problems,
Such as concave-convex embossment, circular engravure production, carve characters etc..But inherently see, they are belonged to using non-orbiting and flexible
Tool processes are complex-curved or form complex-curved technical process.Professor Chen Zhixin of Shanghai Polytechnic Univ is total to hyperspace
Yoke Surface Theory has carried out deep research, but also fails to propose effectively to locate when research is related to numerical control processing conjugate problem
Reason method, this is because the high complexity of the problem itself.Conventional method when processing Problems of numerical control machining is to set at present
Meter curved surface is foundation, it is ensured that a point on tool being capable of work by the given driving line on curved surface, other than contact point
Have being relatively close to relationship all additional notes carried out with the width that remains triangle and height between workpiece, the former is based on
Line width, the latter are calculated for controlling mismachining tolerance.
But for compliant tool and non-rotating tool, the above method is also required further improvement, this is because non-rotating work
Tool is adding man-hour requirement to do elliptical vibration movement or straight-line oscillation campaign, and compliant tool then needs constantly to deform to adapt to curved surface
Feature.Therefore, aiming at the problem that error distribution between non-rotating tool and workpiece design curved surface is difficult to accurately solve, the present invention
It proposes a kind of method that non-rotating tool validity feature line is solved by discrete workpieces curved surface, finds out non-rotating work on this basis
Error distribution function between tool and workpiece design curved surface.
Summary of the invention
The purpose of the present invention is to propose to a kind of method for solving non-rotating tool validity feature line by discrete workpieces curved surface,
Error distribution is difficult to accurately to solve between tool and workpiece design curved surface when solving non-rotating tool Complex Surface in NC Machining
Problem provides important calculation basis for such non-rotating tool pose refinement.
The purpose of the present invention is what is be achieved through the following technical solutions:
A kind of method that non-rotating tool validity feature line is solved by discrete workpieces curved surface of the invention, comprising steps of
A, it according to non-rotating tool geometries and tool relative motion relation, is managed using warp/weft method and traditional envelope
By the real work enveloping surface for solving non-rotating tool；
B, according to non-rotating tool feeding direction, by the workpiece design Surface tessellation of non-rotating tool bottom at a series of sections
Molded line；
C, it using shortest distance lines to principle sum number Iteration algorithm, calculates separately out in step B every and cuts molded line to non-
The shortest distance and its intersection point point of rotary tool real work enveloping surface, the line of all intersection point points in the given margin of tolerance
Constitute the validity feature line between non-rotating tool real work enveloping surface and workpiece machined surface；
D, the intersection point point on the validity feature line in step C is sought into the shortest distance to workpiece design curved surface respectively, in workpiece
A series of intersection point points and shortest distance line segment are obtained on design curved surface, the set of all shortest distance line segments constitutes non-rotating tool
With the error distribution function of workpiece design curved surface.
The invention has the advantages that this method can be convenient the essence for realizing non-rotating tool numerical control processing validity feature line
It really solves, and further accurately obtains the error distribution situation between non-rotating tool and workpiece design curved surface, be such non-time
It changes a job and has pose refinement important calculation basis is provided, to be established for the complex-curved digital control programming method of non-rotating tool processes
Fixed certain theoretical basis, has certain practical application value.
Detailed description of the invention
Fig. 1 is the basic flow chart for solving the method for non-rotating tool numerical control processing validity feature line；
Fig. 2 is the non-rotating tool that working face is cylindrical surface；
Fig. 3 is the non-rotating tool that working face is drum type face；
Fig. 4 is the non-rotating tool real work enveloping surface on cylindrical surface of doing reciprocating linear motion；
Fig. 5 is the non-rotating tool real work enveloping surface for making elliptic motion cylindrical surface；
Fig. 6 is the non-rotating tool real work enveloping surface in drum type face of doing reciprocating linear motion；
Fig. 7 is the non-rotating tool real work enveloping surface for making elliptic motion drum type face；
Fig. 8 is to make validity feature line segment on non-rotating tool real work enveloping surface；
Fig. 9 is that non-rotating tool real work enveloping surface and workpiece design error between curved surface and be distributed.
Specific embodiment
A kind of method solving non-rotating tool validity feature line by discrete workpieces curved surface of the invention, basic procedure is such as
Shown in Fig. 1, preferable specific embodiment is, comprising:
Step A, it according to non-rotating tool geometries and tool relative motion relation, is wrapped using warp/weft method and tradition
Network theory solves the real work enveloping surface of non-rotating tool.The step A specifically:
(1) non-rotating tool design is carried out according to the geometry (such as ruled surface, free form surface) that workpiece designs curved surface
Analysis can choose the non-rotating tool on cylindrical surface, as shown in Figure 2 if workpiece design curved surface is ruled surface；If workpiece
Design curved surface is free form surface, then can choose the non-rotating cutter in drum type face, as shown in Figure 3.
It is contacted in biggish region to enable non-rotating tool to design curved surface with workpiece, increases real contact area,
Usually make the principal radius of curvature of non-rotating tool no more than the principal radius of curvature of design curved surface as far as possible, it may be assumed that
In formula,The non-rotating tool minimum principal radius of curvature is represented,The non-rotating tool maximum principal radius of curvature is represented,The workpiece design curved surface minimum principal radius of curvature is represented,Represent the non-rotating tool maximum principal radius of curvature.Therefore, if
It is cylindrical surface that workpiece, which designs curved surface, then the radius of curvature of the non-rotating tool on cylindrical surface should be no more than the curvature half of curve surface of workpiece
Diameter.If it is free form surface that workpiece, which designs curved surface, the minimum and maximum principal radius of curvature of the non-rotating tool in drum type face is answered
It is respectively smaller than the minimum and maximum principal radius of curvature of workpiece design curved surface.In addition, non-rotating tool maximum gauge t is generally depended on
Adjacent workpieces design the rigidity of space size and tool between curved surface, and general purpose tool maximum gauge is no more than two adjacent workpieces and sets
The half of minimum range between curved surface is counted, i.e.,Wherein dmin(SWi,SWi+1) indicate adjacent two workpiece
The S of curved surfaceWiAnd SWi+1Between minimum range.
(2) basic principle of the non-rotating tool polishing of division of non-rotating tool is that non-rotary tool and workpiece design
Curved surface makees relative high frequency ultrasonic motion at the two point of contact, removes workpiece material using the abrasive material on tool work surface.One
As non-rotating tool need to make reciprocal ultrasound linear motion, ultrasonic elliptic motion etc., therefore non-rotating tool work surface is drawn
Certain division principle need to be followed by dividing: if non-rotating tool makees reciprocal ultrasound linear motion, back and forth be transported along non-rotating tool
Dynamic direction, that is, tool work face warp direction carries out discrete division to tool work surface；If non-rotating tool makees ultrasound
Elliptic motion then carries out discrete stroke along the approximate direction, that is, tool work face weft/warp direction parallel with movement of tool
Point.
(3) the real work enveloping surface of non-rotating tool is solved since non-rotating tool will make ultrasound linear motion or ultrasound
Elliptic motion, and the linear motion of non-rotating tool, elliptic motion etc. usually all design at curved surface point of contact in tool and workpiece
Tangent plane on, so the non-rotating tool work face of reality at point of contact is not non-rotating tool design finished surface,
But the enveloping surface that non-rotating tool work face is moved along straight line, elliptic curve etc..Since non-rotating tool only makees plane motion,
Therefore non-rotating tool real work enveloping surface can use traditional envelope requirement completely and carry out direct solution.
Traditional Single parametric surface family { SaEnvelope requirement be
Φ (u, v, a)=(ru,rv,ra)=0 (2)
In formula, (u, v a) are family of surfaces { S to raVector equation, ruFor SaU to cut arrow, rvFor SaV to cut arrow, ra
For SaArrow is led to parameter a.That is, it is desirable that the real work enveloping surface for solving non-rotating tool must first calculate movement of tool
Any time a tool on characteristic curve La, the identified family of curves { L when a variationaIt is characteristic line cluster, i.e., non-rotating tool
Enveloping surface.And enveloping surface is then the real work enveloping surface of non-rotary tool in the given margin of tolerance.For any time a,
Discrete division is carried out to non-rotating tool according to the actual tool direction of motion and obtains a series of sections of molded line { Ci, i=1,2,3 ...,
N }, it cuts molded line number N and depends on discrete precision ε；Then it calculates separately every and cuts molded line CiOn meet the spy of above-mentioned envelope requirement
Levy point Pi；Set { the P of all features described above pointsiConstitute any time a tool on characteristic curve La, wherein in given tolerance model
Characteristic curve in enclosing is referred to as validity feature line segment L 'a；All features described above line LaSet { LaConstitute non-rotating kit
Network face Σ, wherein the enveloping surface in the given margin of tolerance is the real work enveloping surface Σ ' of non-rotating tool.
If the non-rotating tool on cylindrical surface does reciprocating linear motion along face of cylinder axis direction, non-rotating tool is obtained
Real work enveloping surface be extension tool cylindrical surface, as shown in Figure 4.If the non-rotating tool edge on cylindrical surface and cylindrical surface
The parallel plane of axis makees elliptic motion, then obtain non-rotating tool real work enveloping surface be tool semi-cylindrical+plane+
Tool semi-cylindrical, as shown in figure 5, wherein the width of plane is equal to elliptical long axis or short axle.If drum type face is non-rotating
Tool does reciprocating linear motion along axis of rotation direction, then the real work enveloping surface for obtaining non-rotating tool is half drum type of tool
Half drum type face of face+cylindrical surface+tool, as shown in Fig. 6, wherein the radius on cylindrical surface is drum type face maximum weft radius of circle, cylinder
Face axial length is equal to transverse or short axle.If the non-rotating tool in drum type face is made along the plane parallel with face of cylinder axis
Elliptic motion, then obtain non-rotating tool real work enveloping surface be half drum type face of tool+drum type face along oval sweeping surface+
Half drum type face of composite surface+tool is scanned along ellipse in drum type face in ellipse, as shown in fig. 7, due to the reality of the non-rotating tool
Working envelope face is more complicated, can further carry out simplifying processing for the complex combination sweeping surface in ellipse, be considered as
Approximate plane.
Step B, according to non-rotating tool feeding direction, by the workpiece design Surface tessellation under non-rotating tool at a system
Column cut molded line.The step B specifically:
Non-rotating tool be usually with workpiece design curved face contact point where tangent plane in be translatable, such as along non-rotating
The reciprocating motion of the axis direction of tool real work curved surface, along the translation in elliptical orbit direction etc..It has been solved in step A
The real work enveloping surface Σ ' of non-rotating tool out, be calculating instrument real work enveloping surface and finished work surface it
Between characteristic curve, solved using discrete workpieces design Surface Method, need given tool actual motion direction to tool thus
The workpiece design curved surface of beneath view field carries out discrete division, to obtain a series of sections of molded line Ci, i=1,2,3 ..., N,
The number for cutting molded line is determined by the computational accuracy ε of characteristic curve.
Step C, using shortest distance lines to principle sum number Iteration algorithm, every section of molded line in step B is calculated separately out
It is all to give the intersection point points in the margin of tolerance to the shortest distance and its intersection point point of non-rotating tool real work enveloping surface
Line constitutes the validity feature line between non-rotating tool real work enveloping surface and workpiece machined surface.The step C tool
Body are as follows:
(1) shortest distance to non-rotating tool is put since non-rotating tool is typically chosen cylindrical surface or drum type face as work
Make face, and cylindrical surface or drum type face belong to a part of the surface of revolution, therefore space any point is to the most short of tool work face
Distance can directly be calculated with the method for parsing.Steps are as follows for its calculating: crossing space any point and non-rotating work first
The axis of tool working face does a plane, and the plane and tool work face intersect at straight line or curve；Then in above-mentioned plane
For interior calculating spatial point to the minimum range of plane and straight line or curve, which is space any point to tool work face
The shortest distance.
(2) the validity feature line between non-rotating tool real work enveloping surface and workpiece machined surface is firstly for step
Any one provided in rapid B cuts molded line Ci, M data point is separated into using lattice Method, wherein M is by cutting the discrete of molded line
Precision ε is determined.Then, to wherein j-th of data point Pi,j, j=1,2 ..., M utilize the method provided in (1) to solve the point
The shortest distance onto non-rotating tool T working face Π crosses point Pi,jAnd ZTAxis (non-rotating tool work face axis vector)
Plane, which is handed over, has working face Π in curve Ki,j, then obtain point Pi,jTo the shortest distance d of tool work face Πi,j=dist
(Pi,j,Ki,j) and tool work face Π on intersection point point Qi,j.It is finally respectively compared and cuts molded line CiUpper M data point is to tool
The shortest distance d of working face Πi,j, to obtain cutting molded line CiTo tool work face Π shortest distance di,min=min { di,jAnd
Cut molded line CiUpper Pi,minTo the intersection point point Q of tool work face Πi,min.In order to improve computational accuracy and efficiency, can also use first
Biggish step-length finds out P 'i,min, then with point P 'i,minIt is asked for initial point using one dimensional optimization methods such as advance and retreat method, Fibonacci methods
Solve section molded line C for meeting given computational accuracy εiThe upper point P to the tool work face Π shortest distancei,minIt works with corresponding tool
Intersection point point Q on the Π of facei,min.Intersection point point Q on all of above tool work face Πi,minSet { Qi,min, i=1,2 ...,
N } just constitute non-rotating tool real work enveloping surface characteristic curve, and the tool characteristics line within the scope of given tolerance h is then
Constitute the validity feature line segment L between non-rotating tool real work enveloping surface and workpiece machined surfacec, as shown in Fig. 8.
Step D, the intersection point point in step C on validity feature line segment is sought into the shortest distance to workpiece design curved surface respectively,
A series of intersection point points and shortest distance line segment are obtained on workpiece design curved surface, the set of all shortest distance line segments constitutes non-rotating
The error distribution function of tool and workpiece design curved surface.The step D specifically:
It designs the error between curved surface accurately to solve non-rotating tool work face and workpiece and is distributed, and according to mismachining tolerance
Definition, from the intersection point point Q on tool work acquired in step C face Πi,min(characteristic point i.e. on tool work face) is to work
Part designs curved surface and calculates the shortest distance, and then obtains a series of intersection point pointWith practical shortest distance line segmentIt is above-mentioned
All practical shortest distance sectionsSetJust non-rotating tool work face and work are constituted
Part designs the error distribution function between curved surface, and wherein N is the number of the validity feature point on tool real work face, such as Fig. 9
It is shown.Error distribution achieved above can be used as the main calculation basis of non-rotating tool pose refinement.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art,
The characteristic curve method for solving for such as making ultrasonic circus movement, the non-rotating tool of ultrasonic cycloid motion, should all cover of the invention
Within protection scope.
Claims (5)
1. a kind of method for solving non-rotating tool validity feature line by discrete workpieces curved surface, which is characterized in that comprising steps of
A, it according to non-rotating tool geometries and tool relative motion relation, is asked using warp/weft method and traditional Enveloping theory
Solve the real work enveloping surface of non-rotating tool；
B, according to non-rotating tool feeding direction, by the workpiece design Surface tessellation of non-rotating tool bottom at a series of sections of types
Line；
C, it using shortest distance lines to principle sum number Iteration algorithm, calculates separately out in step B every and cuts molded line to non-rotating
The line of the shortest distance and its intersection point point of tool real work enveloping surface, all intersection point points in the given margin of tolerance is constituted
Validity feature line between non-rotating tool real work enveloping surface and workpiece machined surface；
D, the intersection point point on the validity feature line in step C is sought into the shortest distance to workpiece design curved surface respectively, is designed in workpiece
A series of intersection point points and shortest distance line segment are obtained on curved surface, the set of all shortest distance line segments constitutes non-rotating tool and work
The error distribution function of part design curved surface.
2. a kind of method that non-rotating tool validity feature line is solved by discrete workpieces curved surface according to claim 1,
It is characterized in that, the step A specifically:
(1) non-rotating tool design
It is analyzed according to the geometry (such as ruled surface, free form surface) that workpiece designs curved surface, if workpiece designs curved surface
For ruled surface, then it can choose the non-rotating tool on cylindrical surface；If it is free form surface that workpiece, which designs curved surface, drum can choose
The non-rotating cutter in type face；
It is contacted in biggish region to enable non-rotating tool to design curved surface with workpiece, increases real contact area, usually
Make the principal radius of curvature of non-rotating tool no more than the principal radius of curvature of design curved surface as far as possible, it may be assumed that
In formula,The non-rotating tool minimum principal radius of curvature is represented,The non-rotating tool maximum principal radius of curvature is represented,
The workpiece design curved surface minimum principal radius of curvature is represented,Represent the non-rotating tool maximum principal radius of curvature；Therefore, if workpiece
Design curved surface is cylindrical surface, then the radius of curvature of the non-rotating tool on cylindrical surface should be not more than the radius of curvature of curve surface of workpiece；
If it is free form surface that workpiece, which designs curved surface, the minimum and maximum principal radius of curvature of the non-rotating tool in drum type face should be distinguished
Less than the minimum and maximum principal radius of curvature of workpiece design curved surface；It is bent that non-rotating tool maximum gauge depends on adjacent workpieces design
The rigidity in space and tool between face, usual tool maximum gauge are no more than minimum range between two adjacent workpieces design curved surface
Half, i.e.,In formula, d (SWi,SWi+1) indicate the S of adjacent two curve surface of workpieceWiAnd SWi+1Between most narrow spacing
From；
(2) division of non-rotating tool
The basic principle of non-rotating tool polishing is non-rotary tool and workpiece design curved surface makees phase at the two point of contact
High frequency ultrasound is moved, removes workpiece material using the abrasive material on tool work surface；It wants to make by non-rotating tool reciprocal
Ultrasound linear motion, ultrasonic elliptic motion etc.；If non-rotating tool will make reciprocal ultrasound linear motion, along non-rotating tool
Direction, that is, warp direction of reciprocating motion carries out discrete division to tool work surface；If non-rotating tool makees the oval fortune of ultrasound
It is dynamic, then discrete division is carried out along the approximate direction, that is, weft parallel with movement of tool/warp direction；
(3) the real work enveloping surface of non-rotating tool solves
Since non-rotating tool will make ultrasound linear motion or ultrasonic elliptic motion, and the linear motion of tool or elliptic motion are all
In the tangent plane at tool and workpiece design curved surface point of contact, so the non-rotating tool work face of reality at point of contact is simultaneously
Not non-rotary tool designs finished surface, the enveloping surface that non-rotating tool work face is moved along straight line or elliptic curve；
Since non-rotating tool makees plane motion, practical non-rotating tool work face can be solved by traditional envelope requirement Lai；
Traditional Single parametric surface family { SaEnvelope requirement be
Φ (u, v, a)=(ru,rv,ra)=0 (2)
In formula, (u, v a) are family of surfaces { S to raVector equation, ruFor SaU to cut arrow, rvFor SaV to cut arrow, raFor SaIt is right
Parameter a leads arrow；That is, it is desirable that the real work enveloping surface for solving non-rotating tool must first calculate any of movement of tool
Characteristic curve L on moment a toola, the identified family of curves { L when a variationaIt is characteristic line cluster, i.e., non-rotating tool envelope
Face；And enveloping surface is then the real work enveloping surface of non-rotary tool in the given margin of tolerance；For any time a, according to
The actual tool direction of motion carries out discrete division to non-rotating tool and obtains a series of sections of molded line Ci, i=1,2,3 ..., N, curve
Number N depends on discrete precision ε；Then it calculates separately every and cuts molded line CiOn meet the characteristic point P of above-mentioned envelope requirementi；It is all
Set { the P of features described above pointiConstitute any time a tool on characteristic curve La, wherein the characteristic curve in the given margin of tolerance
Referred to as validity feature line segment L 'a；All features described above line LaSet { LaNon-rotating tool enveloping surface Σ is constituted, wherein
Enveloping surface in the given margin of tolerance is the real work enveloping surface Σ ' of non-rotating tool；If cylindrical surface is non-rotating
Tool does reciprocating linear motion along face of cylinder axis direction, then the real work enveloping surface for obtaining non-rotating tool is the work of extension
Has cylindrical surface；If the non-rotating tool on cylindrical surface makees elliptic motion along the plane parallel with face of cylinder axis, obtain non-time
Change a job tool real work enveloping surface be tool semi-cylindrical+plane+tool semi-cylindrical, wherein the width of plane be equal to ellipse
Long axis or short axle；If the non-rotating tool in drum type face does reciprocating linear motion along axis of rotation direction, obtain non-rotating
The real work enveloping surface of tool is half drum type face of tool+half drum type face of cylindrical surface+tool, and wherein the radius on cylindrical surface is drum type
Face maximum weft radius of circle, face of cylinder axis length are equal to transverse or short axle；If the non-rotating tool in drum type face along with
The parallel plane of face of cylinder axis makees elliptic motion, then the real work enveloping surface for obtaining non-rotating tool is half drum type face of tool
Drum type face is along oval half drum type face of sweeping curved surface+tool along oval sweeping surface+ellipse in+drum type face, due to the non-rotating work
The real work enveloping surface of tool is more complicated, can further carry out the combination sweeping surface in ellipse simplifying processing, by it
It is regarded as approximate plane.
3. a kind of method that non-rotating tool validity feature line is solved by discrete workpieces curved surface according to claim 1,
It is characterized in that, in the step B,
Non-rotating tool be usually with workpiece design curved face contact point where tangent plane in be translatable, such as along non-rotating tool
The linear reciprocating motion of the axis direction of real work curved surface, along the translation in elliptical orbit direction etc.；It has been solved in step 2
The real work enveloping surface Σ ' of non-rotating tool, to calculate the tool at the contact point that non-rotating tool and workpiece design curved surface
Real work enveloping surface and machined surface between characteristic curve, can by using discrete workpieces design Surface Method be asked
Solution；It needs to be carried out according to workpiece design curved surface of the non-rotating tool actual motion direction to tool bottom view field thus discrete
It divides, to obtain a series of sections of molded line Ci, i=1,2,3 ..., N, wherein the number N for cutting molded line can be by the calculating of characteristic curve
Precision ε is determined.
4. a kind of method that non-rotating tool validity feature line is solved by discrete workpieces curved surface according to claim 1,
It is characterized in that, the step C specifically:
(1) point arrives the shortest distance of non-rotating tool
Since non-rotating tool is typically chosen cylindrical surface or drum type face as working face, and cylindrical surface or drum type face belong to revolution
The a part in face, therefore the shortest distance in space any point to tool work face can directly be counted with the method for parsing
It calculates；It calculates that steps are as follows: the axis for crossing space any point and non-rotating tool work face first does a plane, the plane with
Tool work face intersects at straight line or curve；Then the spatial point is calculated in above-mentioned plane to plane and straight line or curve
Minimum range, the distance are the shortest distance of the space any point to tool work face；
(2) the validity feature line between non-rotating tool real work enveloping surface and workpiece machined surface
Molded line C is cut firstly for any one provided in step Bi, M data point is separated into using lattice Method, wherein M
It is determined by the discrete precision ε of curve；Then, to wherein j-th of data point Pi,j, j=1,2 ..., M utilize the side provided in (1)
Method solves the shortest distance on this to non-rotating tool T working face Π, that is, crosses point Pi,jAnd ZTAxis (non-rotating tool work face
Axis vector) plane hand over and have working face Π in curve Ki,j, then obtain point Pi,jTo the shortest distance of tool work face Π
di,j=dist (Pi,j,Ki,j) and tool work face Π on intersection point point Qi,j；It is finally respectively compared and cuts molded line CiUpper M type
Value point arrives the shortest distance d of tool work face Πi,j, to obtain cutting molded line CiTo tool work face Π shortest distance di,min=
min{di,jAnd section molded line CiUpper Pi,minTo the intersection point point Q of tool work face Πi,min；In order to improve computational accuracy and efficiency,
Can also P ' be found out with biggish step-length firsti,min, then with point P 'i,minIt is initial point using advance and retreat method, Fibonacci method etc. one
It ties up Optimization Method and goes out section molded line C for meeting given computational accuracy εiThe upper point P to the tool work face Π shortest distancei,minWith
Intersection point point Q on corresponding tool working face Πi,min；Intersection point point Q on all of above tool work face Πi,minSet
{Qi,min, i=1,2 ..., N } just constitute non-rotating tool real work enveloping surface characteristic curve, and in given tolerance h range
Interior tool characteristics line then constitutes the validity feature line between non-rotating tool real work enveloping surface and workpiece machined surface
Section Lc。
5. a kind of method that non-rotating tool validity feature line is solved by discrete workpieces curved surface according to claim 1,
It is characterized in that, the step D specifically:
It designs the error between curved surface accurately to solve non-rotating tool work face and workpiece and is distributed, and determined according to mismachining tolerance
Justice, from the intersection point point Q on tool work acquired in step C face Πi,min(characteristic point i.e. on tool work face) is set to workpiece
It counts curved surface and calculates the shortest distance, and then obtain a series of intersection point pointWith practical shortest distance line segmentIt is above-mentioned all
Practical shortest distance sectionSet Just non-rotating tool work face and workpiece are constituted
The error distribution function between curved surface is designed, wherein N is the number of the validity feature point on tool real work face；It is achieved above
Tool and workpiece design curved surface between error distribution can be used as the main calculating of non-rotating tool pose refinement according to.
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