CN114995281A - Non-developable straight line curved surface optimal tool position planning method and device - Google Patents

Non-developable straight line curved surface optimal tool position planning method and device Download PDF

Info

Publication number
CN114995281A
CN114995281A CN202210502537.2A CN202210502537A CN114995281A CN 114995281 A CN114995281 A CN 114995281A CN 202210502537 A CN202210502537 A CN 202210502537A CN 114995281 A CN114995281 A CN 114995281A
Authority
CN
China
Prior art keywords
parameter
step length
processing step
tool
current
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210502537.2A
Other languages
Chinese (zh)
Inventor
王立平
段飞宇
李伟涛
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tsinghua University
Original Assignee
Tsinghua University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tsinghua University filed Critical Tsinghua University
Priority to CN202210502537.2A priority Critical patent/CN114995281A/en
Publication of CN114995281A publication Critical patent/CN114995281A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • G05B19/19—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 positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35349—Display part, programmed locus and tool path, traject, dynamic locus
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Landscapes

  • Engineering & Computer Science (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Numerical Control (AREA)

Abstract

A non-developable ruled surface optimal cutter position planning method and a device based on an equal-bow-height error method are suitable for side milling of non-developable ruled surfaces. The invention takes the upper and lower alignment lines of the non-developable straight-line curved surface as constraints to obtain the optimal tool position planning within the tolerance of the height of the bow, the error of the height of the bow is uniform and consistent, the number of tool positions is small, and the integral processing quality and the processing efficiency are improved.

Description

Non-developable straight line curved surface optimal tool position planning method and device
Technical Field
The invention belongs to the technical field of machining, relates to a method and a device for planning an optimal tool position of a non-developable ruled surface, and has important significance for realizing high-quality and high-efficiency machining of a complex non-developable ruled surface.
Background
Nowadays, with the development of various fields such as aerospace, delivery and the like, the demand for excellent high-end equipment is more and more urgent, and precision complex curved surface parts widely applied to the fields are required to be higher in indexes such as machining efficiency, forming precision and yield. The non-developable straight-line curved surface is a typical characteristic of the complex parts, generally processed by a multi-axis linkage numerical control machine tool, the multi-axis linkage numerical control processing needs the support of an automatic programming technology, a tool path planning method is used as a core technology of the automatic programming, and the quality of the tool path planning method determines the processing quality and the processing efficiency of the curved surface.
The existing various tool path planning algorithms are mainly different in that the determination methods of the machining step length are different, and the machining step length mainly influences the height error of the bow. Due to the variable curvatures of the non-developable straight-line curved surface at different positions, when the curved surface approximation is carried out by taking a fixed processing step length as a path track of a cutter, in order to ensure the processing precision requirement, the same feed step length leads the number of cutter points to be excessive; if the number of tool points is reduced, the actual maximum bow height error range within one machining step at locations where the curvature is too large may be greater than the bow height tolerance. Therefore, the existing tool path planning algorithm cannot well balance the whole processing quality and the processing efficiency of the part.
Disclosure of Invention
The invention provides a ruled surface optimal tool position planning method based on an equal bow height error method based on analysis of the change curvature of a non-developable ruled surface and the optimal step length in the tolerance of bow height, and by taking upper and lower alignment lines of the non-developable ruled surface as constraint conditions, thereby realizing the homogenization of the bow height error of the discrete step length along the path track of a ruled surface tool, minimizing the number of tool sites in the range required by the tolerance of bow height, and improving the overall processing quality and the processing efficiency.
The invention is realized by the following technical scheme.
A non-developable straight line curved surface optimal tool position planning method comprises the following steps:
step S1, obtaining corresponding cubic B-spline curve parameter equations according to respective control points of upper and lower directrices of the non-developable straight-line curved surface, and determining a parameter expression of the non-developable straight-line curved surface expressed by the upper and lower directrices;
step S2, respectively calculating the curvatures of the upper and lower alignment lines at the current tool position;
step S3, respectively calculating corresponding initial processing step length according to the curvature and the bow height tolerance of the upper and lower alignment lines at the current cutter position, wherein the curvature at the current cutter position is taken as the curvature between the next cutter position and the current cutter position according to the initial processing step length;
step S4, calculating the actual maximum bow height error of the upper and lower alignment lines under the initial processing step length;
step S5, checking the actual maximum bow height error of the upper and lower alignment lines respectively, and iteratively adjusting the initial processing step length to maximize the actual maximum bow height error within the bow height tolerance, thereby obtaining the maximum processing step length of the upper and lower alignment lines;
step S6, comparing the positions of the upper and lower alignment lines at the maximum processing step length, wherein the position closer to the current position of the tool is the position of the tool at the current optimal processing step length based on the equal bow height error;
and step S7, traversing the whole cutter path track to obtain the cutter positions under all the optimal processing step lengths, thereby obtaining the optimal cutter position planning position of the non-developable ruled surface based on the equal-arch height error method.
Optionally, in step S1, the obtaining corresponding cubic B-spline parameter equations according to the respective control points of the upper and lower directrices of the non-developable ruled surface, so as to determine the parameter expression of the non-developable ruled surface expressed by the upper and lower directrices respectively includes:
1) determining a plurality of cubic B-spline curves through a plurality of control points of the upper and lower directrix lines, wherein each cubic B-spline curve is determined by a plurality of continuous control points, and any one cubic B-spline curve is represented as:
P j (t)＝[x j (t)y j (t)]＝UM j Q j
wherein, P j (t) is cubic B-spline curve equation, t is curve parameter, j represents number of sections of spline curve, and U represents parameterMatrix, M j Representing a matrix of coefficients and associated with weights defined by curve control points, Q j Representing a matrix of control points, x j (t) is the component of the spline curve in the x-axis, y j (t) is the component of the spline curve in the y-axis;
2) solving the multi-segment cubic B spline curves corresponding to the upper and lower directrices respectively, and forming an upper directrices C according to the cubic B spline curves respectively 1 (u) and lower guideline C 2 (u)；
3) Parameter expression formula for establishing non-developable straight-line curved surface and adopting upper and lower alignment lines to express
P(u,v)＝(1-v)C 1 (u)+vC 2 (u)(0≤v≤1)
And u and v are curved surface parameters, u controls the corresponding positions of the upper and lower directrices, and v controls the position of a point on the straight bus.
Optionally, in step S2, the respectively calculating curvatures of the upper and lower directrices at the current tool position includes:
step S21, constructing the parameter equation of the upper and lower directrices as:
Figure BDA0003635968040000021
Figure BDA0003635968040000022
wherein, a 1x ，b 1x ，c 1x ，d 1x ，a 1y ，b 1y ，c 1y ，d 1y ，a 2x ，b 2x ，c 2x ，d 2x ，a 2y ，b 2y ，c 2y ，d 2y Is a polynomial coefficient of a parameter equation and is a known quantity;
in step S22, the curvature formulas of the upper and lower directrices are
Figure BDA0003635968040000023
Figure BDA0003635968040000024
Step S23, the parameters u corresponding to the upper and lower alignment contact position at the current cutter position are respectively substituted to obtain the curvature rho at the current cutter position 1 (u 1i ) Curvature ρ of lower guideline at current tool position 2 (u 2i ) Wherein u is 1i Representing the upper guideline surface parameter, u, at the current tool position 2i The lower guideline surface parameters at the current tool position are indicated.
Optionally, in step S3, the calculating the corresponding initial machining step according to the curvature of the upper and lower alignment lines at the current tool position and the tolerance of the bow height respectively includes:
Figure BDA0003635968040000031
wherein, Δ L 1 The initial processing step length of the upper alignment line at the current cutter position is obtained;
ΔL 2 the initial processing step length of the lower alignment line at the current cutter position is obtained;
ρ 1 is the curvature of the upper guideline at the current tool position;
ρ 2 is the curvature of the lower guideline at the current tool position;
e is the bow height tolerance.
Optionally, in step S4, the calculating an actual maximum bow height error of the upper and lower alignment lines at the initial machining step includes:
in step S41, the initial parameter interval of the upper alignment line is
Figure BDA0003635968040000032
Let u a ＝u 1i ，
Figure BDA0003635968040000033
Step S42, let u I ＝u a +(1-λ)(u b -u a )，u II ＝u a +λ(u b -u a ) λ is interval compression coefficient, and point C is calculated 1 (u I ) Bow height error of (c):
Figure BDA0003635968040000034
and point C 1 (u II ) Bow height error of (c):
Figure BDA0003635968040000035
wherein, V I ，V II ，V L Are respectively a vector, V I ＝C 1 (u 1i )C 1 (u I )，V II ＝C 1 (u 1i )C 1 (u II )，
Figure BDA0003635968040000036
Step S43, if ε I ＞ε II Then let u b ＝u II (ii) a Otherwise, let u a ＝u I ；
Step S44, determine | ∈ I -ε II If the value of | < delta epsilon is true, wherein delta epsilon is iteration precision, and if true, the actual maximum bow height error epsilon of the upper alignment line under the initial processing step length is output 1 ＝(ε I +ε II ) /2, and corresponding maximum bow height error point parameter u 1 ＝(u I +u II ) 2; otherwise, go back to step S42;
step S45, obtaining the actual maximum bow height error epsilon of the lower alignment line under the initial processing step length by adopting the method from the steps S41 to S44 2 And corresponding parameter u 2 ；
In step S46, a function ∈ ═ f (u) is defined a ,u b ) Is a maximum bow height error function, then
Figure BDA0003635968040000041
Optionally, in step S5, the respectively checking the actual maximum arch height errors of the upper and lower alignment lines, and iteratively adjusting the respective initial processing step lengths so that the actual maximum arch height error is maximized within the arch height tolerance includes:
in step S51, the initial parameter interval of the upper alignment line is
Figure BDA0003635968040000042
Judging the actual maximum bow height error epsilon of the upper alignment line under the initial processing step length 1 Whether or not:
e-Δe≤ε 1 ≤e
wherein e is the bow height tolerance, and delta e is the error precision;
wherein, the upper and lower alignment cutting contact points at the current cutter position are respectively C 1 (u 1i )，C 2 (u 2i ) The corresponding points of the upper and lower alignment lines under the respective initial processing step length are respectively
Figure BDA0003635968040000043
ΔL 1 、ΔL 2 Are respectively the initial processing step length of the upper and lower alignment lines,
if yes, outputting the curved surface parameters of the corresponding points
Figure BDA0003635968040000044
If not, processing according to the following two conditions:
(1) if epsilon 1 If > e, then execute in sequence
a1) Let u a ＝u 1i ，
Figure BDA0003635968040000045
b1) Find the parameter interval [ u ] a ,u b ]Is at the midpoint of
Figure BDA0003635968040000046
Calculating f (u) 1i ,u m )；
c1) If it isf(u 1i ,u m ) If > e, then let u b ＝u m (ii) a Otherwise, let u a ＝u m ；
d1) Judgment of f (u) 1i ,u m ) Whether e-delta e ≦ f (u) is satisfied 1i ,u m ) E is less than or equal to e, if yes, the parameter u is output 1i+1 ＝u m (ii) a If not, go to step b 1);
(2) if epsilon 1 < e- Δ e, then execute in sequence
a2) Order to
Figure BDA0003635968040000047
Wherein eta is an upper limit interval coefficient;
b2) find the parameter interval [ u ] a ,u b ]Is at the midpoint of
Figure BDA0003635968040000048
Calculating f (u) 1i ,u m )；
c2) If f (u) 1i ,u m ) If > e, let u b ＝u m (ii) a Otherwise, let u a ＝u m ；
d2) Judgment of f (u) 1i ,u m ) Whether e-delta e is less than or equal to f (u) 1i ,u m ) E is less than or equal to e, if yes, the parameter u is output 1i+1 ＝u m (ii) a If not, go to step b 2);
namely, the corresponding point parameter u of the upper alignment line under the maximum processing step length in the tolerance of the bow height is obtained 1i+1 ；
The corresponding point parameter u of the lower alignment line under the maximum processing step length in the arch high tolerance is obtained by solving the method which is the same as the step S51 2i+1 。
Optionally, in step S6, the comparing the tool positions of the upper and lower alignment lines in the respective maximum machining step, where a position closer to the current tool position is the tool position in the optimal machining step based on the iso-bow height error, includes:
current tool position is u i The contact point cutting parameter corresponding to the upper alignment line is u 1i Current tool position is u i The contact point cutting parameter corresponding to the lower alignment line is u 2i The upper alignment line is at maximum plusTool position at step length
Figure BDA0003635968040000051
Corresponding to the upper alignment cut contact parameter of u 1i+1 Tool position of upper alignment line at maximum machining step length
Figure BDA0003635968040000052
Corresponding to the lower quasi-line cutting contact parameter of u' 2i+1 Of u's' 2i+1 Is the above directrix tangent contact parameter u 1i+1 The corresponding lower alignment line contact point parameters under the accurate cutter position are obtained;
tool position of lower alignment line under maximum processing step length
Figure BDA0003635968040000053
The corresponding upper quasi-line tangent contact parameter is u' 1i+1 Tool position of lower guideline at maximum machining step length
Figure BDA0003635968040000054
The parameter of the contact point corresponding to the lower alignment line is u 2i+1 Of u's' 1i+1 Is the following alignment line contact point parameters u 2i+1 The parameters of the upper alignment line contact point corresponding to the accurate cutter position are obtained;
judging whether the following conditions are met:
u′ 2i+1 ＜u 2i+1
if so, the position of the cutter under the optimal machining step length
Figure BDA0003635968040000055
If not, then
Figure BDA0003635968040000056
Optionally, in step S1, 13 cubic B-splines are determined by the 16 control points of the upper guideline, and 13 cubic B-splines are determined by the 16 control points of the lower guideline, wherein each cubic B-spline is determined by four consecutive control points, wherein 16 control points and M j The matrix is given by International Standard "machining center test ConditionAnd (6) discharging.
U＝[1 t t 2 t 3 ]，
Figure BDA0003635968040000057
Figure BDA0003635968040000058
Figure BDA0003635968040000059
Wherein q is j,x 、q j+1,x 、q j+2,x 、q j+3,x Representing four successive control points, q, on the x-axis j,y 、q j+1,y 、q j+2,y 、q j+3,y Representing four consecutive control points on the y-axis.
Optionally, in step S41, the initial parameter interval of the upper guideline is
Figure BDA0003635968040000061
Let u a ＝u 1i ，
Figure BDA0003635968040000062
Before, still include:
the upper and lower alignment cutting contacts at the current tool position are respectively C 1 (u 1i )，C 2 (u 2i ) The following equations are solved separately:
Figure BDA0003635968040000063
obtaining the corresponding point of the upper alignment line under the initial processing step length
Figure BDA0003635968040000064
And the corresponding point of the lower alignment line under the initial processing step length
Figure BDA0003635968040000065
The invention also provides an electronic device, which comprises a processor and a memory, wherein the memory is stored with a non-developable straight-line curved surface optimal tool position planning program, and when the processor executes the non-developable straight-line curved surface optimal tool position planning program, the non-developable straight-line curved surface optimal tool position planning method is completed.
Compared with the prior art, the invention has the following advantages and prominent technical effects: the invention takes the upper and lower alignment lines of the non-developable ruled surface as constraint conditions, adopts a method of accurately searching the maximum processing step length in a range and selecting the best to determine the next cutter position, the bow height error is checked more accurately, the obtained cutter position planning is uniform and consistent in the bow height error of each discrete straight line section and is closer to the bow height tolerance, the number of cutter positions is less, the overall processing quality and the processing efficiency are improved, the optimal cutter position planning of the non-developable ruled surface based on the equal bow height error is realized, and the invention has good application prospect.
Drawings
Fig. 1 is a flow chart showing the non-developable ruled surface optimal tool space planning based on the iso-bow height error method according to the embodiment of the present invention.
FIG. 2 is a schematic diagram of a non-developable ruled surface part according to an embodiment of the present invention.
FIG. 3 is a schematic view of alignment lines on a ruled surface according to an embodiment of the present invention.
FIG. 4 is a schematic diagram illustrating the solution of upper and lower fiducial line contact points at tool positions according to an embodiment of the present invention.
FIG. 5 is a schematic diagram illustrating the step method of the iso-bow height error according to the embodiment of the present invention.
Fig. 6 is a schematic diagram showing tool position selection in an optimum machining step size according to the embodiment of the present invention.
FIG. 7 is a diagram showing a comparison between the optimal tool position planning method and the discrete tool contact points automatically generated by the software according to the embodiment of the present invention.
Fig. 8 is a view showing a bow height error distribution diagram in the optimal tool position planning method according to the embodiment of the present invention.
Reference numerals: 1-non-developable ruled surface; 2, aligning; 3, lower alignment; 4, cutting tools.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a flow chart of optimal tool location planning of a non-developable straight-line curved surface based on an equal bow height error method. The method comprises the steps of firstly determining a parameter equation of a ruled surface to be processed, deriving to obtain curvatures of upper and lower alignment lines of the ruled surface at a cutter position, secondly calculating initial processing step lengths corresponding to the upper and lower alignment lines respectively according to the curvatures and arch height tolerance, checking arch height errors, further iteratively adjusting the processing step lengths to maximize the processing step lengths within the arch height tolerance, finally comparing the cutter positions of the upper and lower alignment lines under the respective processing step lengths to obtain the cutter position under the optimal processing step length within the arch height tolerance, traversing the path track of the whole cutter, and finishing the optimal cutter position planning of the non-developable ruled surface based on an equal arch height error method. The invention takes the upper and lower alignment lines of the non-developable straight-line curved surface as constraint conditions, adopts a method of accurately searching the maximum processing step length in a range and selecting the best to determine the next cutter position, the bow height error is checked more accurately, the obtained cutter position planning is uniform and consistent in the bow height error of each discrete straight line section and is closer to the bow height tolerance, the number of cutter positions is less, the overall processing quality and the processing efficiency are improved, the optimal cutter position planning of the non-developable straight-line curved surface based on the equal bow height error is realized, and the invention has good application prospect. The specific implementation steps are as follows:
step 1, obtaining a corresponding cubic B-spline curve parameter equation according to respective control points (16 control points which are known to be set by a user) of upper and lower directrices of a non-developable ruled surface shown in FIG. 2, and determining a parameter expression of the non-developable ruled surface expressed by the upper and lower directrices;
1) the 13 cubic B-spline curves are determined by the 16 control points of the upper and lower directrix lines, where each cubic B-spline curve is determined by four consecutive control points, as shown in FIG. 3. Any cubic B-spline curve can be represented as:
P j (t)＝[x j (t)y j (t)]＝UM j Q j
wherein t is a curve parameter, j represents the number j of sections of the spline curve as 1-13, U represents a parameter matrix, and M is j Representing a matrix of coefficients and associated with weights defined by curve control points, Q j Representing a matrix of control points, x j (t) is the component of the curve on the x-axis, y j (t) is the component of the curve in the y-axis; respectively, as follows:
U＝[1 t t 2 t 3 ]，
Figure BDA0003635968040000071
Figure BDA0003635968040000072
Figure BDA0003635968040000073
wherein q is j,x 、q j+1,x 、q j+2,x 、q j+3,x Representing four successive control points, q, on the x-axis j,y 、q j+1,y 、q j+2,y 、q j+3,y Representing four control points on the y-axis. The 16 control points are defined by international standard ISO 10791-7:2020 machining center test conditions part seven: test on finished test piece, M j The matrix is also given by the international standard.
2) Solving 13 sections of cubic B-spline curves corresponding to the upper and lower directrices respectively as follows, and respectively forming an upper and lower directrices C according to the respective cubic B-spline curves 1 (u) andC 2 (u)：
Figure BDA0003635968040000081
wherein, z is 0 and 20 is the horizontal plane of the lower alignment line and the horizontal plane of the upper alignment line.
3) Determining a parameter expression of the non-developable ruled surface represented by an upper alignment line and a lower alignment line:
P(u,v)＝(1-v)C 1 (u)+vC 2 (u)(0≤v≤1)
wherein, C 1 (u) and C 2 (u) are the upper and lower directrices of the ruled surface, i.e. the two directrices determined in step 1, u and v are surface parameters, u controls the corresponding positions of the upper and lower directrices, and v controls the position of the point on the straight generatrix.
Step 2, calculating the curvatures of the upper and lower alignment lines at the position of the cutter;
1) the parameter equations of the upper and lower directrices are respectively:
Figure BDA0003635968040000082
Figure BDA0003635968040000083
wherein, a 1x ，b 1x ，c 1x ，d 1x ，a 1y ，b 1y ，c 1y ，d 1y ，a 2x ，b 2x ，c 2x ，d 2x ，a 2y ，b 2y ，c 2y ，d 2y Is a polynomial coefficient of a parameter equation and is a known quantity;
the derivation of each parameter equation can be obtained:
x′ 1 (u)＝3a 1x u 2 +2b 1x u+c 1x ，x 1 ″(u)＝6a 1x u+2b 1x
y′ 1 (u)＝3a 1y u 2 +2b 1y u+c 1y ，y 1 ″(u)＝6a 1y u+2b 1y
x′ 2 (u)＝3a 2x u 2 +2b 2x u+c 2x ，x 2 ″(u)＝6a 2x u+2b 2x
y′ 2 (u)＝3a 2y u 2 +2b 2y u+c 2y ，y 2 ″(u)＝6a 2y u+2b 2y
the curvatures of the upper and lower alignment lines at different positions are respectively
Figure BDA0003635968040000091
Figure BDA0003635968040000092
2) The contact points of the cutter and the upper and lower alignment lines at the current position are solved through the coordinates of the cutter point and the cutter axis vector, as shown in FIG. 4, the coordinate of the cutter point is T 0 ＝(x 0 ,y 0 ,z 0 ) The axis vector of the knife is
Figure BDA0003635968040000093
The radius of the cutter is R, and the following equation system is solved:
Figure BDA0003635968040000094
namely, the coordinates C of the cutting tool and the contact point of the lower alignment line at the current position are obtained 2 ＝(x 2i ,y 2i ) z＝0 If (x, y), the coordinate of the contact point between the corresponding tool and the upper alignment line is C 1 ＝(x 1i ,y 1i ) z＝20 Wherein x is 1i ，y 1i Respectively expressed as:
Figure BDA0003635968040000095
will cut contact point coordinate C 1 ，C 2 Substituting into the parameter equation of the upper and lower alignment lines to obtain the current contact point coordinate C 1 ，C 2 The corresponding parameters on the upper and lower alignment lines are u 1i ，u 2i Substituting the corresponding curvature expression to obtain the curvature rho of the upper and lower alignment lines at the current tool position 1 (u 1i )，ρ 2 (u 2i )。
Step 3, respectively calculating corresponding initial processing step lengths according to the curvatures and the bow height tolerances of the upper and lower alignment lines at the position of the cutter;
the initial machining step size is based on the curvature of the directrix at the current tool position (i.e., the solid-line arc in fig. 5), and is solved assuming that the curvature around the tool position is constant (i.e., the dashed-line arc in fig. 5) (i.e., the chord length Δ L calculated from the curvature around the tool position is constant) i As the initial machining step at curvature at the current tool position), as shown in fig. 5, from the geometric relationship:
Figure BDA0003635968040000101
wherein, Δ L 1 ，ΔL 2 Respectively the initial machining step length, rho, of the upper and lower directrix at the position of the tool 1 ，ρ 2 The curvatures of the upper and lower alignment lines at the position of the cutter are respectively, and e is the tolerance of the height of the bow, and is 0.01 mm.
Step 4, calculating the actual maximum bow height error of the upper and lower alignment lines under the initial processing step length;
1) the upper and lower alignment cutting contacts at the position of the cutter are respectively C 1 (u 1i )，C 2 (u 2i ) The following equations are solved separately:
Figure BDA0003635968040000102
that is, the corresponding points of the upper and lower alignment lines under the respective initial processing step length
Figure BDA0003635968040000103
2) Calculating the actual maximum bow height error epsilon of the upper and lower alignment lines under the initial processing step length as shown in fig. 5, and specifically comprising the following steps:
(1) the initial parameter interval of the upper alignment line is
Figure BDA0003635968040000104
Let u be a ＝u 1i ，
Figure BDA0003635968040000105
(2) Let u I ＝u a +(1-λ)(u b -u a )，u II ＝u a +λ(u b -u a ) Lambda is interval compression coefficient, and 0.6 is taken; calculate point C separately 1 (u I )，C 1 (u II ) Bow height error of (c):
Figure BDA0003635968040000106
Figure BDA0003635968040000107
wherein epsilon I ，ε II Respectively, is a point C on the upper alignment line 1 (u I ) And C 1 (u II ) Height error of bow of point, V I ，V II ，V L Are respectively a vector V I ＝C 1 (u 1i )C 1 (u I )，V II ＝C 1 (u 1i )C 1 (u II )，
Figure BDA0003635968040000108
(3) If epsilon I ＞ε II Then let u b ＝u II (ii) a Otherwise, let u a ＝u I ；
(4) Judgment of|ε I -ε II If the iteration precision is less than the preset value, the actual maximum bow height error epsilon of the upper alignment line under the initial processing step length is output 1 ＝(ε I +ε II ) 2 and maximum bow height error point parameter u 1 ＝(u I +u II ) 2; otherwise, turning to the step (2);
(5) calculating the actual maximum bow height error epsilon of the lower alignment line under the initial processing step length by adopting the same method of the above (1) - (4) 2 And corresponding parameter u 2 ；
(6) Define function ε ═ f (u) a ,u b ) Is a maximum bow height error function, then
Figure BDA0003635968040000111
Step 5, checking the height error of the upper alignment line and the lower alignment line, and iteratively adjusting the respective processing step length to maximize the height error within the height tolerance of the upper alignment line and the lower alignment line;
the initial parameter interval of the upper alignment line is
Figure BDA0003635968040000112
Judging the actual maximum bow height error epsilon of the upper alignment line under the initial processing step length 1 Whether or not:
e-Δe≤ε 1 ≤e
wherein e is the bow height tolerance and is 0.01mm, and delta e is the error precision and is 0.0005 mm;
if yes, outputting the corresponding point parameter
Figure BDA0003635968040000113
If not, the method is divided into two cases:
(1) if epsilon 1 ＞e
a) Let u be a ＝u 1i ，
Figure BDA0003635968040000114
b) Find the parameter interval [ u ] a ,u b ]Is at the midpoint of
Figure BDA0003635968040000115
Calculating f (u) 1i ,u m )；
c) If f (u) 1i ,u m ) If > e, let u b ＝u m (ii) a Otherwise, let u a ＝u m ；
d) Judgment of f (u) 1i ,u m ) Whether e-delta e is less than or equal to f (u) 1i ,u m ) E is less than or equal to e, if yes, the parameter u is output 1i+1 ＝u m (ii) a If not, turning to the step b);
(2) if epsilon 1 ＜e-Δe
a) Order to
Figure BDA0003635968040000116
Wherein eta is an upper limit interval coefficient and is taken as 3;
b) find the parameter interval [ u ] a ,u b ]Is at the midpoint of
Figure BDA0003635968040000117
Calculating f (u) 1i ,u m )；
c) If f (u) 1i ,u m ) If > e, let u b ＝u m (ii) a Otherwise, let u a ＝u m ；
d) Judgment of f (u) 1i ,u m ) Whether e-delta e is less than or equal to f (u) 1i ,u m ) E is less than or equal to e, if yes, the parameter u is output 1i+1 ＝u m (ii) a If not, turning to the step b);
namely, the corresponding point parameter u of the upper alignment line under the maximum processing step length in the tolerance of the bow height is obtained 1i+1 The same method is adopted to solve the corresponding point parameter u of the lower alignment line under the maximum processing step length in the bow height tolerance 2i+1 ；
Step 6, comparing the positions of the upper and lower alignment lines at the maximum processing step length, wherein the position closer to the previous cutter position is the cutter position at the optimal processing step length based on the equal bow height error;
as shown in fig. 6, the last tool position is u i The parameters of the contact point corresponding to the upper and lower alignment lines are u 1i ，u 2i Tool position of upper alignment line at maximum machining step length
Figure BDA0003635968040000121
The parameters of the contact points corresponding to the upper and lower directrices are respectively u 1i+1 ，u′ 2i+1 Of u's' 2i+1 Is the above directrix tangent contact parameter u 1i+1 The corresponding lower alignment line contact point parameters under the accurate cutter position are obtained; tool position of lower alignment line under maximum processing step length
Figure BDA0003635968040000122
U 'is corresponding to the upper and lower quasi-line tangent contact point parameters respectively' 1i+1 ，u 2i+1 Of u's' 1i+1 Is the following quasi-linear contact parameter, u 2i+1 The parameters of the upper alignment line contact point corresponding to the accurate cutter position are obtained; judging whether the following conditions are met:
u′ 2i+1 ＜u 2i+1
if so, the position of the cutter under the optimal machining step length
Figure BDA0003635968040000124
If not, then
Figure BDA0003635968040000123
And 7, traversing the path track of the whole cutter to obtain the positions of the cutter under all the optimal processing step lengths, namely finishing the optimal cutter position planning of the non-developable straight-line curved surface based on the equal-bow-height error method.
The optimal tool position planning method and the discrete contact point pair automatically generated by software are shown in fig. 7, the number of tool positions in the tool position planning method is 121, the number of tool positions automatically generated by software is 153, and the number is reduced by 20%; the height error distribution based on the optimal tool location planning method is shown in fig. 8, and the height errors in all discrete straight line segments are within a set range (0.0095,0.01), so that the high efficiency and the effectiveness of the method are verified.
The present invention also provides an electronic device, which is an apparatus capable of automatically performing numerical calculation and/or information processing according to a preset or stored instruction. For example, it may be a smartphone, tablet, laptop, desktop computer, server, etc. The electronic device includes at least, but is not limited to, a memory, a processor, which are communicatively coupled to each other. Wherein: the memory includes at least one type of computer-readable storage medium including flash memory, a hard disk, a multimedia card, a card-type memory (e.g., SD or DX memory, etc.), a Random Access Memory (RAM), Static Random Access Memory (SRAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), Programmable Read Only Memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the storage may be an internal storage unit of the electronic device, such as a hard disk or a memory of the electronic device. In other embodiments, the memory may also be an external storage device of the electronic apparatus, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like provided on the electronic apparatus. Of course, the memory may also include both an internal storage unit of the electronic apparatus and an external storage device thereof. In this embodiment, the memory is generally used for storing an operating system and various types of application software installed in the electronic device, such as the non-developable ruled surface optimal tool space planning program code. In addition, the memory may also be used to temporarily store various types of data that have been output or are to be output.
The processor may be a Central Processing Unit (CPU), controller, microcontroller, microprocessor, or other data Processing chip in some embodiments. The processor is generally configured to control the overall operation of the electronic device, such as performing control and processing related to data interaction or communication with the electronic device. In this embodiment, the processor is configured to run a program code stored in the memory or process data, for example, run the non-developable ruled surface optimal tool space planning program.
The memory containing the readable storage medium may include an operating system, a non-developable ruled surface optimal tool space planning program, and the like. The processor implements the above steps when executing the non-developable ruled surface optimal tool position planning program in the memory, and details are not repeated herein. In this embodiment, the non-developable ruled surface optimal tool space planning program stored in the memory may be divided into one or more program modules, and the one or more program modules are stored in the memory and may be executed by one or more processors to complete the present application.
The present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof, and it is therefore intended that all such changes and modifications as fall within the true spirit and scope of the invention be indicated by the appended claims.

Claims (10)

1. The optimal tool position planning method for the non-developable ruled surface is characterized by comprising the following steps of:
step S1, obtaining corresponding cubic B-spline curve parameter equations according to respective control points of upper and lower directrix of the non-developable ruled surface, thereby determining a parameter expression represented by the upper and lower directrix of the non-developable ruled surface;
step S2, respectively calculating the curvatures of the upper and lower alignment lines at the current tool position;
step S3, respectively calculating corresponding initial processing step length according to the curvature and the bow height tolerance of the upper and lower alignment lines at the current cutter position, wherein the curvature at the current cutter position is taken as the curvature between the next cutter position and the current cutter position according to the initial processing step length;
step S4, calculating the actual maximum bow height error of the upper and lower alignment lines under the initial processing step length;
step S5, checking the actual maximum bow height error of the upper and lower alignment lines respectively, and iteratively adjusting the initial processing step length to maximize the actual maximum bow height error within the bow height tolerance, thereby obtaining the maximum processing step length of the upper and lower alignment lines;
step S6, comparing the positions of the upper and lower alignment lines at the maximum processing step length, wherein the position closer to the current position of the tool is the position of the tool at the current optimal processing step length based on the equal bow height error;
and step S7, traversing the whole cutter path track to obtain cutter positions under all the optimal processing steps, thereby obtaining the optimal cutter position planning position of the non-developable ruled surface based on the equal-arch height error method.
2. The method of claim 1, wherein in step S1, the step of obtaining the cubic B-spline parametric equation according to the respective control points of the upper and lower directrices of the non-developable ruled surface respectively to determine the parametric expression of the non-developable ruled surface expressed by the upper and lower directrices comprises:
1) determining a plurality of cubic B-spline curves through a plurality of control points of the upper and lower directrix lines, wherein each cubic B-spline curve is determined by a plurality of continuous control points, and any one cubic B-spline curve is represented as:
P j (t)＝[x j (t) y j (t)]＝UM j Q j
wherein, P j (t) is cubic B-spline equation, t is curve parameter, j represents number of sections of spline curve, U represents parameter matrix, M j Representing a matrix of coefficients and associated with weights defined by curve control points, Q j Representing a matrix of control points, x j (t) is the component of the spline curve in the x-axis, y j (t) is the component of the spline curve in the y-axis;
2) solving the multi-segment cubic B spline curves corresponding to the upper and lower directrices respectively, and forming an upper directrices C according to the respective cubic B spline curves 1 (u) and lower guideline C 2 (u)；
3) Parameter expression formula for establishing non-developable straight-line curved surface and adopting upper and lower alignment lines to express
P(u,v)＝(1-v)C 1 (u)+vC 2 (u) (0≤v≤1)
And u and v are curved surface parameters, u controls the corresponding positions of the upper and lower directrices, and v controls the position of a point on the straight bus.
3. The method for planning the optimal tool position for the non-developable ruled surface according to claim 2, wherein in step S2, the calculating the curvatures of the upper and lower directrix lines at the current tool position respectively comprises:
step S21, constructing the parameter equation of the upper and lower directrices as:
C 1 (u):
Figure FDA0003635968030000011
C 2 (u):
Figure FDA0003635968030000012
wherein, a 1x ，b 1x ，c 1x ，d 1x ，a 1y ，b 1y ，c 1y ，d 1y ，a 2x ，b 2x ，c 2x ，d 2x ，a 2y ，b 2y ，c 2y ，d 2y Is a polynomial coefficient of a parameter equation and is a known quantity;
in step S22, the curvature formulas of the upper and lower directrices are
Figure FDA0003635968030000021
Figure FDA0003635968030000022
Step S23, substituting the upper and lower alignment contact points at the current tool positionThe parameter u corresponding to the point position obtains the curvature rho of the current cutter position 1 (u 1i ) Curvature ρ of lower guideline at current tool position 2 (u 2i ) Wherein u is 1i Representing the upper guideline surface parameter, u, at the current tool position 2i Representing the lower guideline surface parameters at the current tool position.
4. The method for optimal tool position planning for non-developable ruled surfaces according to claim 3, wherein in step S3, the calculating the corresponding initial machining step length according to the curvature and the tolerance of the upper and lower alignment lines to the height of the bow at the current tool position comprises:
Figure FDA0003635968030000023
wherein, Δ L 1 The initial processing step length of the upper alignment line at the current cutter position is obtained;
ΔL 2 the initial processing step length of the lower alignment line at the current cutter position is obtained;
ρ 1 is the curvature of the upper guideline at the current tool position;
ρ 2 is the curvature of the lower guideline at the current tool position;
e is the bow height tolerance.
5. The method for optimally planning the tool position of the non-developable ruled surface according to claim 4, wherein in step S4, the calculating the actual maximum bow height error of the upper and lower alignment lines at the initial machining step length comprises:
in step S41, the initial parameter interval of the upper alignment line is
Figure FDA0003635968030000024
Let u a ＝u 1i ，
Figure FDA0003635968030000025
Step S42, let u I ＝u a +(1-λ)(u b -u a )，u II ＝u a +λ(u b -u a ) λ is interval compression coefficient, and point C is calculated 1 (u I ) Bow height error of (c):
Figure FDA0003635968030000026
and point C 1 (u II ) Bow height error of (c):
Figure FDA0003635968030000031
wherein, V I ，V II ，V L Are respectively vector, V I ＝C 1 (u 1i )C 1 (u I )，V II ＝C 1 (u 1i )C 1 (u II )，
Figure FDA0003635968030000032
Step S43, if ε I ＞ε II Then let u b ＝u II (ii) a Otherwise, let u a ＝u I ；
Step S44, determine | ∈ I -ε II If the value of | < delta epsilon is true, wherein delta epsilon is iteration precision, and if true, the actual maximum bow height error epsilon of the upper alignment line under the initial processing step length is output 1 ＝(ε I +ε II ) /2, and corresponding maximum bow height error point parameter u 1 ＝(u I +u II ) 2; otherwise, go back to step S42;
step S45, obtaining the actual maximum bow height error epsilon of the lower alignment line under the initial processing step length by adopting the method from the steps S41 to S44 2 And corresponding parameter u 2 ；
In step S46, the function ∈ ═ f (u) is defined a ,u b ) Is a maximum height error function, then
Figure FDA0003635968030000033
6. The method for optimal tool location planning for a non-developable ruled surface according to claim 5, wherein in step S5, the checking the actual maximum bow height error of the upper and lower alignment lines respectively, and iteratively adjusting the respective initial processing step length to maximize the actual maximum bow height error within the tolerance of the bow height comprise:
step S51, the initial parameter interval of the upper alignment line is
Figure FDA0003635968030000034
Judging the actual maximum bow height error epsilon of the upper alignment line under the initial processing step length 1 Whether or not:
e-Δe≤ε 1 ≤e
wherein e is the bow height tolerance, and delta e is the error precision;
wherein, the upper and lower alignment cutting contact points at the current cutter position are respectively C 1 (u 1i )，C 2 (u 2i ) The corresponding points of the upper and lower alignment lines under the respective initial processing step length are respectively
Figure FDA0003635968030000035
ΔL 1 、ΔL 2 Are respectively the initial processing step length of the upper and lower alignment lines,
if yes, outputting the curved surface parameters of the corresponding points
Figure FDA0003635968030000036
If not, processing according to the following two conditions:
(1) if epsilon 1 If > e, then execute in sequence
a1) Let u a ＝u 1i ，
Figure FDA0003635968030000037
b1) Obtaining ginsengNumber interval u a ,u b ]Is at the midpoint of
Figure FDA0003635968030000038
Calculating f (u) 1i ,u m )；
c1) If f (u) 1i ,u m ) If > e, let u b ＝u m (ii) a Otherwise, let u a ＝u m ；
d1) Judgment of f (u) 1i ,u m ) Whether e-delta e is less than or equal to f (u) 1i ,u m ) E is less than or equal to e, if yes, the parameter u is output 1i+1 ＝u m (ii) a If not, go to step b 1);
(2) if epsilon 1 < e- Δ e, then execute in sequence
a2) Order to
Figure FDA0003635968030000041
Wherein eta is an upper limit interval coefficient;
b2) find the parameter interval [ u ] a ,u b ]Is at the midpoint of
Figure FDA0003635968030000042
Calculating f (u) 1i ,u m )；
c2) If f (u) 1i ,u m ) If > e, let u b ＝u m (ii) a Otherwise, let u a ＝u m ；
d2) Judgment of f (u) 1i ,u m ) Whether e-delta e is less than or equal to f (u) 1i ,u m ) E is less than or equal to e, if yes, the parameter u is output 1i+1 ＝u m (ii) a If not, go to step b 2);
namely, the corresponding point parameter u of the upper alignment line under the maximum processing step length in the tolerance of the bow height is obtained 1i+1 ；
The same method as the step S51 is adopted to solve and obtain the corresponding point parameter u of the lower alignment line under the maximum processing step length within the arch height tolerance 2i+1 。
7. The method for planning the optimal tool position on the non-developable ruled surface according to claim 6, wherein in step S6, the comparing the tool positions of the upper and lower directrix lines under the respective maximum processing step length, wherein the position closer to the current tool position is the tool position under the optimal processing step length based on the equal bow height error, comprises:
current tool position is u i The contact point cutting parameter corresponding to the upper alignment line is u 1i Current tool position is u i The contact point cutting parameter corresponding to the lower alignment line is u 2i Tool position of upper alignment line at maximum machining step length
Figure FDA0003635968030000043
Corresponding to the upper alignment cut contact parameter of u 1i+1 Tool position of upper alignment line at maximum machining step length
Figure FDA0003635968030000044
Corresponding to the lower quasi-line cutting contact parameter of u' 2i+1 Of u's' 2i+1 Is the above directrix tangent contact parameter u 1i+1 The corresponding lower alignment line contact point parameters under the accurate cutter position are obtained;
tool position of lower alignment line under maximum processing step length
Figure FDA0003635968030000045
Corresponding to the upper quasi-line cutting contact parameter of u' 1i+1 Tool position of lower guideline at maximum machining step length
Figure FDA0003635968030000046
The parameter of the contact point corresponding to the lower alignment line is u 2i+1 Of u's' 1i+1 Is the following directrix tangent contact parameter u 2i+1 The parameters of the upper alignment line contact point corresponding to the accurate cutter position are obtained;
judging whether the following conditions are met:
u′ 2i+1 ＜u 2i+1
if so, the position of the cutter under the optimal machining step length
Figure FDA0003635968030000047
If not, then
Figure FDA0003635968030000048
8. The method for optimal tool location planning for a non-developable ruled surface according to claim 2, wherein in step S1, 13 cubic B-spline curves are determined by the 16 control points of the upper guideline, and 13 cubic B-spline curves are determined by the 16 control points of the lower guideline, wherein each cubic B-spline curve is determined by four consecutive control points, wherein 16 control points and M are determined together j The matrix is given by the international standard machining center inspection conditions,
U＝[1t t 2 t 3 ]，
Figure FDA0003635968030000051
wherein q is j,x 、q j+1,x 、q j+2,x 、q j+3,x Representing four successive control points, q, on the x-axis j,y 、q j+1，y 、q j+2,y 、q j+3,y Representing four consecutive control points on the y-axis.
9. The method for planning the optimal tool position of a non-developable ruled surface according to claim 5, wherein in step S41, the initial parameter interval of the upper guideline is
Figure FDA0003635968030000052
Let u a ＝u 1i ，
Figure FDA0003635968030000053
Before, still include:
the upper and lower alignment line cutting contacts at the current cutter position are respectively C 1 (u 1i )，C 2 (u 2i ) The following equations are solved separately:
Figure FDA0003635968030000054
obtaining the corresponding point of the upper alignment line under the initial processing step length
Figure FDA0003635968030000055
And the corresponding point of the lower alignment line under the initial processing step length
Figure FDA0003635968030000056
10. An electronic device, comprising a processor and a memory, wherein a non-developable ruled surface optimal tool space planning program is stored in the memory, and when the processor executes the non-developable ruled surface optimal tool space planning program, the non-developable ruled surface optimal tool space planning method according to any one of claims 1 to 9 is completed.
CN202210502537.2A 2022-05-10 2022-05-10 Non-developable straight line curved surface optimal tool position planning method and device Pending CN114995281A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210502537.2A CN114995281A (en) 2022-05-10 2022-05-10 Non-developable straight line curved surface optimal tool position planning method and device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210502537.2A CN114995281A (en) 2022-05-10 2022-05-10 Non-developable straight line curved surface optimal tool position planning method and device

Publications (1)

Publication Number Publication Date
CN114995281A true CN114995281A (en) 2022-09-02

Family

ID=83025808

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210502537.2A Pending CN114995281A (en) 2022-05-10 2022-05-10 Non-developable straight line curved surface optimal tool position planning method and device

Country Status (1)

Country Link
CN (1) CN114995281A (en)

Similar Documents

Publication Publication Date Title
EP0841606B1 (en) Three-dimensional machining method and recording medium stored with a three-dimensional machining control program
US20120265331A1 (en) Five-axis flank milling system for machining curved surface and the tool-path planning method thereof
CN110688709B (en) Workpiece point cloud model-based skin process model correction method
Lasemi et al. A freeform surface manufacturing approach by integration of inspection and tool path generation
CN106774154B (en) A kind of space curve interpolating method based on osculating plane theory
CN106774153A (en) A kind of profile tolerance compensation method of S-shaped rose cutter
Xu et al. Contour parallel tool path planning based on conformal parameterisation utilising mapping stretch factors
CN108594764B (en) Equal-residual-height tool contact point track generation method for triangular mesh model
Petersen et al. Finite element remeshing: a metal forming approach for quadrilateral mesh generation and refinement
CN111723441B (en) Plastic part pre-deformation part modeling method, system, device and storage medium
CN113435086A (en) Automatic planning method and system for increase and decrease alternation process facing material increase and decrease composite manufacturing
CN117250909A (en) Free-form surface numerical control machining path planning method based on geodesic
Liu et al. An efficient iso-scallop tool path generation method for three-axis scattered point cloud machining
CN114995281A (en) Non-developable straight line curved surface optimal tool position planning method and device
Min et al. An improved b-spline fitting method with arc-length parameterization, g 2-continuous blending, and quality refinement
Van Dang et al. Enhanced vector flow of significant directions for five-axis machining of STL surfaces
CN116954150B (en) Third-order geometrically continuous numerical control tool path smoothing method based on instruction point correction
Liang et al. Tool path planning on triangular mesh surfaces based on the shortest boundary path graph
CN113504764A (en) Continuous line segment numerical control machining path smoothing method based on position vector weighted integral
CN116339243A (en) Involute-based numerical control system interpolation curve fitting system and equipment
CN112305994B (en) Straight line segment smoothing method, device and equipment based on average filtering and storage medium
TWI667559B (en) Automatic surface error compensation method and computer program product therefor
Park et al. Near net-shape five-axis face milling of marine propellers
CN113204213A (en) Tool path generation method based on STL model, intelligent terminal and storage device
CN101408906A (en) Automatic generation system and method of cut edge parts

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination