CN113608496B - Spatial path G 2 Transfer fairing method, apparatus and computer readable storage medium - Google Patents
Spatial path G 2 Transfer fairing method, apparatus and computer readable storage medium Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/19—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
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- 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
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Abstract
The invention discloses a space path G 2 The switching smoothing method adopts a cutter point position track line and a cutter axis vector to represent a processing cutter path, and respectively establishes a cutter point path G 2 The transfer fairing model and the arbor direction path transfer fairing model; the method comprises the steps of setting a knife point path to be formed by connecting a plurality of sections of line segments, expressing the spatial position relation between two adjacent line segments in the knife point path by adopting a rotation matrix, and establishing a knife point spatial position path switching fairing model; the spatial position path of the knife point after the fairing is formed by an inserted fairing curve and a residual position path, so that the displacement direction of the knife shaft moves along with the position of the knife point through curve parameters in the parameter interpolation process, and the residual position curve is subjected to the re-parameterization of a residual straight line segment or a residual circular arc segment by utilizing a cubic B spline curve. The invention also discloses equipment for realizing the steps of the method and a computer readable storage medium. The invention comprehensively considers the space position connection form of three line segments and can realize error analysis control.
Description
Technical Field
The present invention relates to a method for switching a processing path, and more particularly to a spatial path G 2 Switching smooth squareMethods, apparatus, and computer readable storage media.
Background
At present, generation of a machining path is an indispensable pre-preparation work in the field of robot machining, most of existing robot machining paths are used for planning a tool path required by machining through CAD/CAM software, corresponding NC codes are generated through post-processing corresponding to a robot, and in a current industrial robot control system, most commonly used movement form instructions are in the form of straight lines (G01) and circular arcs (G02/G03). For NC codes corresponding to the machining paths, as the point position curve and the cutter axis direction curve of the cutter point can only reach G0 or G1 continuously at the spans connected by the movement instructions, in order to improve the machining efficiency of the robot, the fairing treatment is required to be carried out on the linear and circular arc machining paths, and the spline curves are used for replacing the original numerical control machining sections, so that the machining paths of the robot reach curvature continuity (G2 continuity).
The patent CN108132645a discloses a curve fitting method for ensuring the continuity of the whole tool path G2, which provides a curve fitting method for ensuring the continuity of the whole tool path G2, wherein a curve which is formed by sectionally fitting discrete tool paths and bridging between splines and is continuous in the whole tool path G2 and meets the requirements of processing errors and smoothness is obtained. The method only focuses on the transfer fairing between the straight line segments and lacks the fairing treatment on the linear and circular arc processing paths.
The "inter-track G2 continuous fairing switching method, apparatus, and computer-readable storage medium" disclosed in patent CN108803480a provides a method for inter-track G2 continuous fairing switching that focuses on straight-line and circular-arc switching, but does not take into account the specific relationship between the spatial positions of straight-line segments and circular-arc segments, and does not relate to switching of the path in the direction of the cutter axis.
The existing methods for processing path fairing are mainly divided into global fairing and local switching fairing, and for local switching fairing, the existing researches are mainly aimed at switching fairing between motion form instructions of straight line segments (G01), but for a motion form instruction containing an arc (G02)G03 The research of the numerical control processing section of the motion form instruction is less, and the numerical control processing section has the problem of low continuity (G0 or G1 is continuous), so that the processing speed of the robot is limited to a certain extent, and the processing efficiency is reduced. Meanwhile, the existing method does not specifically consider the spatial position relation between the straight line segment and the circular arc segment and between the circular arc segments. In the research of the conventional straight line-straight line switching fairing method, the path of the cutter shaft direction is defined in the unit sphereIn the conventional methods, the problem that the direction error cannot be analyzed and expressed mostly exists, and the difficulty is brought to a certain extent for the error control in the cutter shaft direction.
Disclosure of Invention
The present invention provides a spatial path G for solving the technical problems existing in the prior art 2 A transfer fairing method, apparatus, and computer readable storage medium.
The invention adopts the technical proposal for solving the technical problems in the prior art that: space path G 2 The switching smoothing method adopts a cutter point position track line and a cutter axis vector to represent a processing cutter path, and respectively establishes a cutter point path G 2 The transfer fairing model and the arbor direction path transfer fairing model; the method comprises the steps of setting a knife point path to be formed by connecting a plurality of sections of line segments, expressing the spatial position relation between two adjacent line segments in the knife point path by adopting a rotation matrix, and establishing a knife point spatial position path switching fairing model; the spatial position path of the knife point after the fairing is formed by an inserted fairing curve and a residual position path, so that the displacement direction of the knife shaft moves along with the position of the knife point through curve parameters in the parameter interpolation process, and the residual position curve is subjected to the re-parameterization of a residual straight line segment or a residual circular arc segment by utilizing a cubic B spline curve.
Further, the method comprises the following steps:
step 1, establishing a tool nose point path G 2 A transfer fairing model; solving the straight line segment switching fairing control point and the arc segment switching fairing control point and errorAnalyzing and controlling;
step 2, setting a tool tip point space position path switching fairing error, and respectively carrying out space straight line section switching fairing, and space arc section switching fairing;
step 3, defining a path in the cutter shaft direction on the surface of the unit sphere, defining the central angle of the switching section as a characteristic parameter, and solving the switching error and the characteristic parameter of the path in the cutter shaft direction according to a space arc section and arc section switching fairing method;
step 4, a series of discrete cutter points are given, so that the displacement direction of the cutter shaft moves along with the position of the cutter point through curve parameters, the residual straight line section or the residual circular arc section is re-parameterized on the residual position curve by utilizing a cubic B spline curve, and the continuous angular speed and angular acceleration of the cutter shaft at the span section is realized; and after the tool nose point path and the tool shaft direction path are switched to smooth and the parameters are synchronous, carrying out speed planning in combination with the set constraint conditions to generate interpolation points required by actual machining.
Further, the method also comprises the following steps:
step 5, for the space straight line segment and the arc segment G in the knife point space position path 2 And (5) carrying out simulation analysis on the switching fairing.
Further, the method also comprises the following steps:
step 6, verifying a processing tool path G by using a five-degree-of-freedom hybrid robot processing platform 2 The processing precision and the processing efficiency of the switching fairing method.
Further, in step 1, using a cubic B-spline curve, G of the nose point path at the span is realized 2 Continuous.
Further, step 1 includes the following sub-steps:
step 1.1, under the given transfer length, transferring two straight line segments in the corresponding knife point path, and establishing a following knife point path G 2 The transfer fairing model is used for resolving and solving transfer fairing control points of the two straight line segments;
step 1.2, under the given transfer length, transferring two circular arc sections in the corresponding knife point path to establish a following knife point path G 2 The transfer fairing model is used for resolving and solving transfer fairing control points of the two arc sections;
in the method, in the process of the invention,
p (u) is a cubic B spline curve equation;
d i each control point is a cubic B spline curve;
N i,3 (U) is a cubic B-spline basis function defined on a node vector u= (0,0,0,0,0.5,1,1,1,1);
P i (u) is a spline curve;
P l,i+1 (u) is a remaining straight line segment;
P c,i+1 (u) is a residual arc curve;
m e,i for remaining arc curve P c,i+1 (u) at point d 4,i (u=0) a unit direction vector of the tangent line;
C i+1 is the center coordinates of the arc section;
d 4,i for spline curve P i (u) and residual arc curve P c,i+1 The point of attachment of (u);
r i+1 is the radius length of the arc segment.
Further, in step 2, the spatial position error at the transition point is defined as the hausdorff distance from the origin path segment to the fairing path segment.
Further, step 2 comprises the following sub-steps:
step 2.1, defining a space switching fairing error as:
ε p,i ＝||P i -P i (u)||
in the method, in the process of the invention,
ε p,i a spatially transit fairing error equal to the hausdorff distance from the original position path segment to the fairing path segment;
P i is the corner point of the original position path;
P i (u) is a cubic B-spline curve waypoint;
step 2.2, carrying out switching fairing on the space straight line segment and the straight line segment;
step 2.3, carrying out switching fairing on the space straight line segment and the arc segment;
when the space straight line segment and the circular arc segment are subjected to switching fairing, the length and the central angle of the switching segment are defined as characteristic parameters; by means of a posture matrix R i Describing the relative positional relationship of the straight line segment and the circular arc segment, and expressing as follows:
m s,i ＝R i m e,i
wherein m is e,i For control point d 4,i Unit tangent vector at m s,i For point P i To point P i+1 Is a unit direction vector of (a); d, d 4,i For spline curve P i (u) a junction with the arc segment curve;
and establishing a relational expression between the following characteristic parameters according to the definition expression of the switching fairing error:
in the method, in the process of the invention,
r i+1 the path radius length of the arc section;
l s,i the straight line section is in transfer length;
c s,i the linear section is switched with a proportional coefficient;
θ e,i the central angle corresponding to the arc segment switching path is the size;
solving the characteristic parameters based on error change rule analysis;
step 2.4: carrying out switching fairing on the space arc section and the arc section; when the space arc section and the arc section are switched and smooth, the length of the switching section and the central angle are defined as characteristic parameters, and three attitude angles are adopted to define an attitude matrix T i ，
[t s,i ,b s,i ,n s,i ]＝T i [t e,i ,b e,i ,n e,i ]；
b s,i ＝n s,i ×t s,i ；
b e,i ＝n e,i ×t e,i ；
In the method, in the process of the invention,
t s,i is a circular arc sectionAt point P i A tangent vector at the position;
n s,i is a circular arc sectionPoint P i A unit direction vector to the central angle;
t e,i is a circular arc sectionAt point P i A tangent vector at the position;
n e,i is a circular arc sectionPoint P i A unit direction vector to the central angle;
establishing characteristic parameters { theta }. Alpha.according to the definition expression of the switching fairing error s,i ,θ e,i ∈(0,π/2]Error epsilon of } and fairing p,i And meanwhile, analyzing and solving the characteristic parameters based on error change rule analysis.
The invention also provides a space path G 2 A transit fairing device comprising a memory and a processor, the memory for storing a computer program; the processor is used for executing the computer program and realizing the space path G when executing the computer program 2 The switching fairing method step.
The present invention also provides a computer-readable storage medium storing a computer program characterized in that: the computer program, when executed by the processor, implements the above-mentioned spatial path G 2 The switching fairing method comprises the steps.
The invention has the advantages and positive effects that:
the method provided by the invention comprehensively considers the connection form of three types of spatial positions, such as straight line, circular arc and the like, and can realize error analysis control.
The invention respectively establishes G of path basic units such as straight line segments, circular arc segments and the like by inserting a cubic B spline as a fairing curve 2 A continuous transfer fairing model provides an analytical control point construction method.
The invention provides a parameter synchronization strategy based on the re-parameterization of a residual position path, which can ensure a synchronized tool path G 2 Continuously, the related algorithm can be used as a pre-processing module independent of the numerical control system of the robot.
Drawings
FIG. 1 shows a spatial linear arc processing path G 2 And (5) switching a fairing flow chart.
Fig. 2 is a schematic diagram of straight line segment path switching fairing.
Fig. 3 is a schematic diagram of a circular arc segment path switching fairing.
Fig. 4 is a schematic diagram of a space straight line and arc segment path switching fairing.
Fig. 5 is a schematic diagram of a space arc and arc segment path switching fairing.
Fig. 6 is a schematic view of path switching fairing in the arbor direction.
FIG. 7 is a spatial linear arc processing path G 2 And (5) a transfer fairing simulation schematic diagram.
Detailed Description
For a further understanding of the invention, its features and advantages, reference is now made to the following examples, which are illustrated in the accompanying drawings in which:
referring to fig. 1 to 7, a spatial path G 2 The switching smoothing method adopts a cutter point position track line and a cutter axis vector to represent a processing cutter path, and respectively establishes a cutter point path G 2 The transfer fairing model and the arbor direction path transfer fairing model; the method comprises the steps of setting a knife point path to be formed by connecting a plurality of sections of line segments, expressing the spatial position relation between two adjacent line segments in the knife point path by adopting a rotation matrix, and establishing a knife point spatial position path switching fairing model; the space position path of the knife point after the fairing is formed by an inserted fairing curve and a residual position path, so that the displacement direction of the knife shaft moves along with the position of the knife point through curve parameters in the parameter interpolation process, and the residual position curve is subjected to the re-parameterization of a residual straight line segment or a residual circular arc segment by utilizing a quintic B spline curve. And re-parameterizing, namely, fitting the remaining straight line segments or the remaining circular arc segments by using a quintic B spline curve again to obtain new fairing curve parameters.
G 2 Transfer fairing, also known as G2 transfer fairing, G 2 Indicating that there is a common tangent plane at the connecting line, and a common principal curvature.
Further, a kind of emptyInter-path G 2 The transfer fairing method can comprise the following steps:
step 1, a nose point path G can be established 2 A transfer fairing model; solving and analyzing errors of the straight line segment switching fairing control point and the arc segment switching fairing control point respectively;
step 2, setting a knife point spatial position path switching fairing error, and respectively carrying out spatial straight line segment and straight line segment switching fairing, spatial straight line segment and circular arc segment switching fairing, and spatial circular arc segment and circular arc segment switching fairing;
step 3, defining a cutter shaft direction path on the surface of the unit sphere, defining the central angle of the switching section as a characteristic parameter, and solving a cutter shaft direction path switching error and the characteristic parameter according to a space arc section and arc section switching fairing method;
step 4, a series of discrete cutter points can be given, so that the displacement direction of the cutter shaft moves along with the position of the cutter point through curve parameters, the residual straight line segment or the residual circular arc segment is re-parameterized on the residual position curve by utilizing a cubic B spline curve, and the continuity of the angular speed and the angular acceleration of the cutter shaft at the span is realized; and after the transfer smoothing and parameter synchronization of the cutter point path and the cutter shaft direction path, carrying out speed planning in combination with the set constraint conditions to generate interpolation points required by actual machining.
Further, the method can further comprise the following steps:
step 5, the space straight line segment and the arc segment G of the knife point space position path can be processed 2 And (5) carrying out simulation analysis on the switching fairing.
Further, the method can further comprise the following steps:
step 6, a five-degree-of-freedom series-parallel robot processing platform of the model of TriMule800 and the like can be utilized to verify a processing tool path G 2 The processing precision, the processing efficiency and the like of the switching fairing method are effective.
Further, in step 1, a cubic B-spline curve may be used to realize G of the nose point path at the span 2 Continuous.
Further, step 1 may comprise the following sub-steps:
step 1.1, under a given transfer length, the following knife point path G can be established corresponding to two straight line segments in the knife point path 2 The transfer fairing model is used for resolving and solving transfer fairing control points of the two straight line segments;
step 1.2, under the given transfer length, the following knife tip point path G can be established corresponding to the transfer of two circular arc sections in the knife tip point path 2 The transfer fairing model is used for resolving and solving transfer fairing control points of the two arc sections;
in the method, in the process of the invention,
p (u) is a cubic B spline curve equation;
d i each control point is a cubic B spline curve;
N i,3 (U) is a cubic B-spline basis function defined on a node vector u= (0,0,0,0,0.5,1,1,1,1);
P i (u) is a spline curve;
P l,i+1 (u) is a remaining straight line segment;
P c,i+1 (u) is a residual arc curve;
m e,i for remaining arc curve P c,i+1 (u) at point d 4,i (u=0) a unit direction vector of the tangent line;
C i+1 is the center coordinates of the arc section;
d 4,i for spline curve P i (u) and residual arc curve P c,i+1 The point of attachment of (u);
r i+1 is the radius length of the arc segment.
Further, in step 2, the spatial position error at the transition point may be defined as the hausdorff distance from the home position path segment to the smooth path segment.
Further, step 2 may include the following sub-steps:
step 2.1, the definable spatial transfer fairing error is:
ε p,i ＝||P i -P i (u)||
in the method, in the process of the invention,
ε p,i a spatially transit fairing error equal to the hausdorff distance from the original position path segment to the fairing path segment;
P i is the corner point of the original position path;
P i (u) is a cubic B-spline curve waypoint;
step 2.2, carrying out switching fairing on the space straight line segment and the straight line segment;
step 2.3, carrying out switching fairing on the space straight line segment and the arc segment;
when the space straight line segment and the circular arc segment are subjected to switching fairing, the length and the central angle of the switching segment can be defined as characteristic parameters; by means of a posture matrix R i Describing the relative positional relationship of the straight line segment and the circular arc segment can be expressed as:
m s,i ＝R i m e,i
wherein m is e,i For control point d 4,i Unit tangent vector at m s,i For point P i To point P i+1 Is a unit direction vector of (a); d, d 4,i For spline curve P i (u) a junction point with the arc segment curve.
The relational expression between the following characteristic parameters can be established according to the definition expression of the transfer fairing error:
in the method, in the process of the invention,
r i+1 the path radius length of the arc section;
l s,i the straight line section is in transfer length;
c s,i the linear section is switched with a proportional coefficient;
θ e,i the central angle corresponding to the arc segment switching path is the size;
solving the characteristic parameters based on error change rule analysis;
step 2.4: carrying out switching fairing on the space arc section and the arc section; when the space arc section and the arc section are switched and smooth, the length of the switching section and the central angle can be defined as characteristic parameters, and three attitude angles can be adopted to define an attitude matrix T i ，
[t s,i ,b s,i ,n s,i ]＝T i [t e,i ,b e,i ,n e,i ]；
b s,i ＝n s,i ×t s,i ；
b e,i ＝n e,i ×t e,i ；
In the method, in the process of the invention,
t s，i is a circular arc sectionAt point P i A tangent vector at the position;
n s,i is a circular arc sectionPoint P i A unit direction vector to the central angle;
t e,i is a circular arc sectionAt point P i A tangent vector at the position;
n e,i is a circular arc sectionPoint P i A unit direction vector to the central angle;
the characteristic parameter { theta } can be established according to the definition expression of the switching fairing error s,i ,θ e,i ∈(0,π/2]Error epsilon of } and fairing p,i The relation expression can be simultaneously based on error change rule analysis, and the characteristic parameters can be analyzed and solved.
The invention also provides a space path G 2 A transit fairing apparatus embodiment, the apparatus comprising a memory for storing a computer program and a processor; the processor is used for executing the computer program and realizing the space path G when executing the computer program 2 The switching fairing method step.
The present invention also provides a computer-readable storage medium embodiment, the computer-readable storage medium storing a computer program characterized in that: the computer program, when executed by the processor, implements the above-mentioned spatial path G 2 The switching fairing method step.
The workflow and working principle of the invention are further described in the following with a preferred embodiment of the invention:
step 1: establishing a knife point path G 2 Transfer fairing model:
step 1.1: straight line segment switching fairing control point solution
Realizing the cross-section cutter point by using a cubic B spline curveG of Point Path 2 Continuous.
In the figure, L as shown in FIG. 1 i+1 And l r,i+1 Representing the lengths of the original and remaining path segments, respectively, l e,i And l s,i+1 Indicating the length of the transition segment. Point P i To point P i+1 The unit direction vector of (2) is denoted as m e,i Point P i+1 To point P i The unit direction vector of (2) is denoted as m s,i+1 . To ensure spline curve P i (u) and straight line segment P l,i+1 (u) at the connection point d 4,i G at position 2 Continuously, the relationship should be satisfied:
by solving the above equation, at a given transition length l e,i And l s,i+1 In this case, the transfer curve P can be determined i Control point { d of (u) 2,i ,d 3,i ,d 4,i ' and transfer curve P i+1 Control point { d of (u) 0,i+1 ,d 1,i+1 ,d 2,i+1 Analytical expressions of }.
Step 1.2: arc segment switching fairing control point solution
Step 1.1, realizing G of a path of a spanned point out of the tool tip point by utilizing a cubic B spline curve 2 Continuous. As shown in FIG. 2, the central angle, arc length, center and radius of the arc segment are respectively denoted as gamma i+1 、L i+1 、C i+1 And r i+1 。θ e,i And theta s,i+1 And respectively represent the corresponding central angles of the switching sections. Making spline curve P i (u) and straight line segment P l,i+1 (u) at the connection point d 4,i G at position 2 Continuous, should be full ofFoot is in the same relationship as step 1.1, while for the arc segment:
m is recorded e,i For remaining arc curve P c,i+1 (u) at point d 4,i (u=0) unit direction vector of tangent line.
By solving the equation, at a given arc radius r i+1 And central angle theta s,i+1 In this case, the transfer curve P can be determined i Control point { d of (u) 2,i ,d 3,i ,d 4,i ' and transfer curve P i+1 Control point { d of (u) 0,i+1 ,d 1,i+1 ,d 2,i+1 Analytical expressions of }.
Step 2: spatial position path switching fairing:
step 2.1: definition of spatially switched fairing errors
The spatial position error at the transfer point is defined as the hausdorff distance of the original position path segment to the fairing path segment, then the fairing error can be expressed as:
ε p,i ＝||P i -P i (u)||
step 2.2: space straight line and straight line section switching fairing
And carrying out a relational expression between the straight line and the straight line switching fairing error and the characteristic parameters according to the prior literature method, and solving the related characteristic parameters.
Step 2.3: space straight line and circular arc section switching fairing
The straight line segment and the circular arc segment are transferred and smooth, and the length/central angle { l ] of the transferred segment is calculated s,i ,θ e,i Defined as characteristic parameters. Wherein the straight line segment and the circular arc segment in the space have a certain relative position relationship, as shown in figure 3, so that the attitude matrix R is utilized i Describing straight line segments and circular arc segmentsThe relative positional relationship can be expressed as:
m s,i ＝R i m e,i
wherein m is e,i For control point d 4,i Unit tangent vector at m s,i For point P i To point P i+1 Is a unit direction vector of (a);
establishing characteristic parameters { l } according to the definition expression of the switching fairing error s,i ,θ e,i A relational expression between the two,
meanwhile, based on error change rule analysis, the characteristic parameters are solved.
Step 2.4: space arc and arc section switching fairing
As shown in FIG. 4, the arc segment and the arc segment are transferred and smooth, and the transfer segment length/central angle { θ } s,i ,θ e,i ∈(0,π/2]The characteristic parameters are defined, and three attitude angles are needed to define an attitude matrix R because of complex and various connection forms of space arcs and arc segments i
[t s,i ,b s,i ,n s,i ]＝R i [t e,i ,b e,i ,n e,i ]
Establishing characteristic parameters { theta }. Alpha.according to the definition expression of the switching fairing error s,i ,θ e,i ∈(0,π/2]Error epsilon of } and fairing p,i And meanwhile, solving the characteristic parameters based on error change rule analysis.
Step 3: the path switching fairing in the cutter shaft direction:
step 3.1: defining the cutter shaft direction path on the surface of the unit sphereAs shown in FIG. 5, it is also known that the switching fairing on the single sphere is similar to the switching fairing of the circular arc segment and the circular arc segment in the space in step 2.4, and will switchSegment circle corner->Defining characteristic parameters, and according to the characteristic, solving the path switching error and the characteristic parameters in the cutter shaft direction according to the step 2.4.
Step 4: parameter synchronization and track generation:
step 4.1: given a series of discrete cutter points, the position path after fairing is composed of an inserted fairing curve and a residual position path through the steps 2 and 3, in the parameter interpolation process, the cutter point position is regarded as main movement, the cutter shaft direction follows the cutter point position movement through curve parameters, if interpolation points are calculated by adopting the same curve parameters of the position curve and the direction curve, jump is generated at the span of the cutter shaft angular speed and the angular acceleration. In order to overcome the problems, a residual position curve re-parameterization algorithm is provided, and on the basis, a residual straight line segment or a residual circular arc segment is re-parameterized by utilizing a cubic B spline curve, so that the first-order derivative and the second-order derivative of a direction curve relative to a position curve arc length parameter s can be ensured to be continuous at a span, and further the continuous angular speed and angular acceleration of a cutter shaft at the span can be realized.
Step 4.2: and after the position curve and the direction curve are switched to smooth and parameter synchronization, carrying out corresponding speed planning by combining corresponding constraint conditions.
Step 4.3: generating interpolation points required for actual processing.
Step 5: space straight arc processing path G 2 And (3) switching fairing simulation analysis:
step 5.1: and (3) establishing a processing path comprising a space straight line and an arc section, and obtaining a tool path after fairing by utilizing the steps 2, 3 and 4 on the basis of the original path.
Step 5.2: and carrying out corresponding analysis by using the data obtained by simulation analysis.
Step 6: space straight arc processing path G 2 The transfer fairing flow is shown in fig. 7, and the validity of the method is verified by using a TriMule800 five-degree-of-freedom hybrid robot processing platform.
The above-described embodiments are only for illustrating the technical spirit and features of the present invention, and it is intended that those skilled in the art can understand the content of the present invention and implement it accordingly, and it is not intended that the present invention be limited only by the present embodiments, i.e., that equivalent changes or modifications to the spirit of the present invention be disclosed, but also fall within the scope of the present invention.
Claims (7)
1. Space path G 2 The transfer smoothing method is characterized in that a machining tool path is represented by a tool point position track line and a tool axis vector, and tool point position paths G are respectively established 2 The transfer fairing model and the arbor direction path transfer fairing model; the method comprises the steps of setting a knife point path to be formed by connecting a plurality of sections of line segments, expressing the spatial position relation between two adjacent line segments in the knife point path by adopting a rotation matrix, and establishing a knife point spatial position path switching fairing model; the spatial position path of the knife point after the fairing is formed by an inserted fairing curve and a residual position path, so that the displacement direction of the knife shaft moves along with the position of the knife point through curve parameters in the parameter interpolation process, and the residual position curve is subjected to the re-parameterization of a residual straight line segment or a residual circular arc segment by utilizing a cubic B spline curve;
the method comprises the following steps:
step 1, establishing a tool nose point path G 2 A transfer fairing model; solving and analyzing errors of the straight line segment switching fairing control point and the arc segment switching fairing control point respectively;
step 2, setting a tool tip point space position path switching fairing error, and respectively carrying out space straight line section switching fairing, and space arc section switching fairing;
step 3, defining a cutter shaft direction path on the surface of the unit sphere, defining the central angle of the switching section as a characteristic parameter, and solving a cutter shaft direction path switching error and the characteristic parameter according to a space arc section and arc section switching fairing method;
step 4, a series of discrete cutter points are given, so that the displacement direction of the cutter shaft moves along with the position of the cutter point through curve parameters, the residual straight line section or the residual circular arc section is re-parameterized on the residual position curve by utilizing a cubic B spline curve, and the continuous angular speed and angular acceleration of the cutter shaft at the span section is realized; after the transfer smoothing and parameter synchronization of the cutter point path and the cutter shaft direction path, carrying out speed planning in combination with the set constraint conditions to generate interpolation points required by actual machining;
in the step 2, the spatial position error at the switching point is defined as the hausdorff distance from the original position path section to the fairing path section;
step 2 comprises the following sub-steps:
step 2.1, defining a space switching fairing error as:
ε p,i ＝||P i -P i (u)||
in the method, in the process of the invention,
ε p,i a spatially transit fairing error equal to the hausdorff distance from the original position path segment to the fairing path segment;
P i is the corner point of the original position path;
P i (u) is a cubic B-spline curve waypoint;
step 2.2, carrying out switching fairing on the space straight line segment and the straight line segment;
step 2.3, carrying out switching fairing on the space straight line segment and the arc segment;
when the space straight line segment and the circular arc segment are subjected to switching fairing, the length and the central angle of the switching segment are defined as characteristic parameters; by means of a posture matrix R i Describing the relative positional relationship of the straight line segment and the circular arc segment, and expressing as follows:
m s,i ＝R i m e,i
wherein m is e,i For control point d 4,i Unit tangent vector at m s,i For point P i To point P i+1 Is a unit direction vector of (a); d, d 4,i For spline curve P i (u) a junction with the arc segment curve;
and establishing a relational expression between the following characteristic parameters according to the definition expression of the switching fairing error:
in the method, in the process of the invention,
r i+1 the path radius length of the arc section;
l s,i the straight line section is in transfer length;
c s,i the linear section is switched with a proportional coefficient;
θ e,i the central angle corresponding to the arc segment switching path is the size;
solving the characteristic parameters based on error change rule analysis;
step 2.4: carrying out switching fairing on the space arc section and the arc section; when the space arc section and the arc section are switched and smooth, the length of the switching section and the central angle are defined as characteristic parameters, and three attitude angles are adopted to define an attitude matrix T i ，
[t s,i ,b s,i ,n s,i ]＝T i [t e,i ,b e,i ,n e,i ]；
b s,i ＝n s,i ×t s,i ；
b e,i ＝n e,i ×t e,i ；
In the method, in the process of the invention,
t s,i is a circular arc section P i-1 P i At point P i A tangent vector at the position;
n s,i is a circular arc section P i-1 P i Point P i A unit direction vector to the central angle;
t e,i is a circular arc section P i P i+1 At point P i A tangent vector at the position;
n e,i is a circular arc section P i P i+1 Point P i A unit direction vector to the central angle;
establishing characteristic parameters { theta }. Alpha.according to the definition expression of the switching fairing error s,i ,θ e,i ∈(0,π/2]Error epsilon of } and fairing p,i Relational expression between them with variation in errorAnd analyzing and solving the characteristic parameters based on the rule analysis.
2. The spatial path G of claim 1 2 The switching fairing method is characterized by further comprising the following steps:
step 5, for the space straight line segment and the arc segment G in the knife point space position path 2 And (5) carrying out simulation analysis on the switching fairing.
3. The spatial path G of claim 2 2 The switching fairing method is characterized by further comprising the following steps:
step 6, verifying a processing tool path G by using a five-degree-of-freedom hybrid robot processing platform 2 The processing precision and the processing efficiency of the switching fairing method.
4. The spatial path G of claim 1 2 The transfer fairing method is characterized in that in the step 1, G of a tool nose point path at a span is realized by utilizing a cubic B spline curve 2 Continuous.
5. The spatial path G of claim 4 2 The switching fairing method is characterized in that the step 1 comprises the following sub-steps:
step 1.1, under the given transfer length, transferring two straight line segments in the corresponding knife point path, and establishing a following knife point path G 2 The transfer fairing model is used for resolving and solving transfer fairing control points of the two straight line segments;
step 1.2, under the given transfer length, transferring two circular arc sections in the corresponding knife point path to establish a following knife point path G 2 The transfer fairing model is used for resolving and solving transfer fairing control points of the two arc sections;
in the method, in the process of the invention,
p (u) is a cubic B spline curve equation;
d i each control point is a cubic B spline curve;
N i,3 (U) is a cubic B-spline basis function defined on a node vector u= (0,0,0,0,0.5,1,1,1,1);
P i (u) is a spline curve;
P l,i+1 (u) is a remaining straight line segment;
P c,i+1 (u) is a residual arc curve;
m e,i for remaining arc curve P c,i+1 (u) at point d 4,i (u=0) a unit direction vector of the tangent line;
C i+1 is the center coordinates of the arc section;
d 4,i for spline curve P i (u) and residual arc curveP c,i+1 The point of attachment of (u);
r i+1 is the radius length of the arc segment.
6. Space path G 2 A transit fairing device comprising a memory and a processor, wherein the memory is configured to store a computer program; the processor being adapted to execute the computer program and to implement the spatial path G as claimed in any one of claims 1 to 5 when the computer program is executed 2 The switching fairing method step.
7. A computer-readable storage medium storing a computer program, characterized in that: the computer program, when executed by a processor, implements the spatial path G as claimed in any one of claims 1 to 5 2 The switching fairing method step.
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