CN112859750B - Processing track local fairing method for geometric fairing and speed planning synchronous design - Google Patents

Processing track local fairing method for geometric fairing and speed planning synchronous design Download PDF

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CN112859750B
CN112859750B CN201911185509.7A CN201911185509A CN112859750B CN 112859750 B CN112859750 B CN 112859750B CN 201911185509 A CN201911185509 A CN 201911185509A CN 112859750 B CN112859750 B CN 112859750B
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梅雪松
赵飞
黄晓勇
陶涛
盛晓超
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Xian Jiaotong University
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Abstract

The invention discloses a local fairing method for a processing track synchronously designed by geometric fairing and speed planning, which comprises the following steps of: step 1: acquiring the fairing length upper limit value of a fairing curve; step 2: calculating an reachable speed value according to the fairing length upper limit value obtained in the step 1; and step 3: calculating the shortest fairing length when the normal constraint is met according to the reachable speed value obtained in the step 2; and 4, step 4: determining the optimal fairing length according to the fairing length upper limit value obtained in the step 1 and the shortest fairing length obtained by calculation in the step 3; and 5: and 4, performing smooth curve and speed planning synchronous design according to the optimal smooth length determined in the step 4. The method of the invention designs the fairing curve according to the actual reachable speed on the premise of geometric constraint, so that the synchronous design strategy reduces the profile error on the premise of ensuring the processing efficiency. The method has important significance in the occasions where the machining efficiency and the contour accuracy are important.

Description

Processing track local fairing method for geometric fairing and speed planning synchronous design
Technical Field
The invention belongs to the field of numerical control machine tool track interpolation, and particularly relates to a local machining track fairing method with synchronous geometric fairing and speed planning design.
Background
Computer aided design software usually adopts NURBS (non-uniform rational B-spline) and other parameter spline curves to design complex curved surface parts, but few numerical control systems can directly process the complex curved surface parts. Computer aided manufacturing software typically discretizes a parametric curve into a continuous small segment trajectory to meet the tooling format requirements of a numerical control system. However, the direction of the speed at the point of line segment joining is not continuous, requiring the numerically controlled machine tool to drop to zero at that point. Such frequent acceleration and deceleration frequently causes chattering in the amount of cut at the time of machining by a machine tool, and also causes impact due to friction or backlash.
The local fairing technology changes the parameter curve into a smooth track with continuous curvature after the parameter curve is inserted into the corner, so that the speed of a machine tool is effectively prevented from being reduced to zero, and the efficiency and the quality of part processing are improved. Document 1, "beer art X, laver S, Tournier c.5-axis local centering of linear tool path discontinuities [ J ]. International Journal of Machine Tools and human efficiency, 2013,73: 9-16" discloses a local smoothing method for a processing track, which introduces Bspline at corners of continuous small line segments to realize high-order continuity of the processing track and realize contour error control of the smoothing track. Document 2 "sequence B, Ishizaki K, Shamoto E.A Current optimal sharp corner mirror smoothing and generating for high-speed fed generation of NC systems along linear tools [ J ]. The International Journal of advanced Manufacturing Technology,2015,76(9-12): 1977-. In the traditional method, a fairing process is divided into two successive steps of geometric fairing and speed planning, and a curvature extreme value is reduced in a mode of sacrificing contour precision in a geometric fairing stage so as to improve a speed extreme value. However, the speed extreme is determined by the track length, curvature extreme, tangential/normal kinematic constraints, and so on, and therefore, a single lifting curvature extreme does not necessarily improve the processing efficiency. In the case where both the machining efficiency and the contour accuracy are important, the method is contradictory and prominent.
In summary, the existing local corner fairing method does not involve geometric fairing and speed planning synchronous design, and has important significance for ensuring the improvement of processing efficiency and contour precision.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a method for processing track local fairing by synchronous design of geometric fairing and speed planning, which can improve the processing efficiency and the contour processing precision.
In order to solve the technical problems, the invention solves the problems by the following technical scheme:
a local fairing method for a processing track synchronously designed by geometric fairing and speed planning comprises the following steps:
step 1: acquiring the fairing length upper limit value of a fairing curve;
step 2: calculating an reachable speed value according to the fairing length upper limit value obtained in the step 1;
and step 3: calculating the shortest fairing length when the normal constraint is met according to the reachable speed value obtained in the step 2;
and 4, step 4: determining the optimal fairing length according to the fairing length upper limit value obtained in the step 1 and the shortest fairing length obtained by calculation in the step 3;
and 5: and 4, performing smooth curve and speed planning synchronous design according to the optimal smooth length determined in the step 4.
Further, the step 1 specifically comprises:
formed by two adjacent straight line segments Pi-1PiAnd PiPi+1A pair of symmetrical clothoid curves is inserted into the formed corner, and the upper limit value l of the fairing length of the fairing curveiComprises the following steps:
Figure BDA0002292303390000021
wherein: i is the corner position of the smooth corner in the continuous track; | | represents the length of the straight line segment;
Figure BDA0002292303390000022
for a given approximation error epsilon corresponding to the fairing length of the fairing,
Figure BDA0002292303390000023
expressed as:
Figure BDA0002292303390000031
wherein: beta is aiIs a tangent line at the midpoint of the fairing curve and a straight line Pi-1PiThe midpoint of the fairing curve is defined as a critical point;
Figure BDA0002292303390000032
further, in the step 2, the velocity v can be reachedEtAnalytically calculated by the following formula:
maxvEt
st.vEt≤F
Figure BDA0002292303390000033
Figure BDA0002292303390000034
wherein: v. ofSThe critical speed of the fairing curve of the previous corner and the initial speed designed for the current corner are obtained; a. thetIs a tangential acceleration; j. the design is a squaretThe degree of tangential jump is adopted; f is the target speed; sSEIs the distance from the center point of the fairing line of the last corner to the center point of the fairing line of the current corner, SSEExpressed as:
SSE＝lBi-1+Li+lBi-li
wherein: lBiIs the arc length of the fairing line of the current corner, expressed as
Figure BDA0002292303390000035
lBi-1The arc length of the fairing curve determined for the last inflection point, if i is equal to 1, lBi-1＝0；LiIs a straight line segment Pi-1PiLength of (d).
Further, in the step 3, the velocity v can be reachedEtThe corresponding shortest fairing length when normal constraint is satisfied is:
Figure BDA0002292303390000036
wherein: normal constraint consisting of normal acceleration AnNormal jump JnAnd bow difference delta; ST (. beta.) ofi) Is composed of
Figure BDA0002292303390000037
Abbreviations of (a).
Further, the step 4 specifically includes:
optimal fairing length of fairing curve during synchronous design of geometric fairing and speed planning
Figure BDA0002292303390000038
Expressed as:
Figure BDA0002292303390000039
further, the step 5 specifically includes:
characteristic parameter a of optimal fairing curveiExpressed as:
Figure BDA0002292303390000041
any point on the optical compliance curve is represented as:
P(θ)＝P0+aiC(θ)t+aiS(θ)n
wherein: p0Is a smooth curve and a straight line segment Pi-1PiT is a straight line segment Pi-1PiCollinear unit vector of (1), n being the plane Pi-1Pi-PiPi+1A unit normal vector of inner t; theta is a tangent line of the point P and a straight line segment Pi-1PiThe included angle of (A);
critical velocity v at mid-point of current fairing curveEExpressed as:
Figure BDA0002292303390000042
based on the initial velocity vSCritical velocity vEDetermining an S-shaped speed curve according to the length of the smooth track, the tangential acceleration and the tangential jerk.
Compared with the prior art, the invention has at least the following beneficial effects: the invention provides a local fairing method for synchronous design of geometric fairing and speed planning. The method has important significance in the occasions where the machining efficiency and the contour accuracy are important. The algorithm of the invention has the advantages of curve parameter analysis and determination, arc length analysis and calculation, controllable profile error and high profile precision, and the algorithm has small calculation load and is beneficial to real-time online fairing.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic view of a corner partial fairing insert clothoid curve using the present invention;
FIG. 2 is a geometric comparison of a fairing curve and a comparison of a motion curve for fairing embodiments using the present invention and geometric constraint-only design;
FIG. 3 is a plot of track velocity, acceleration, and jerk versus fairing embodiments of the present invention and geometric constraint-only design.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent 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.
As a specific embodiment of the present invention, a method for local fairing of a processing trajectory by synchronous design of geometric fairing and speed planning includes the following steps:
step 1: acquiring the fairing length upper limit value of a fairing curve, specifically:
formed by two adjacent straight line segments Pi-1PiAnd PiPi+1A pair of symmetrical clothoid curves is inserted into the formed corner, and the upper limit value l of the fairing length of the fairing curveiComprises the following steps:
Figure BDA0002292303390000051
wherein: i is the corner position of the smooth corner in the continuous track; | | represents the length of the straight line segment;
Figure BDA0002292303390000052
for a given approximation error epsilon corresponding to the fairing length of the fairing,
Figure BDA0002292303390000053
expressed as:
Figure BDA0002292303390000054
wherein: beta is aiIs a tangent line at the midpoint of the fairing curve and a straight line Pi-1PiThe midpoint of the fairing curve is defined as a critical point; the calculation is carried out by adopting a Fresnel integral numerical method,
Figure BDA0002292303390000061
step 2: calculating an reachable speed value according to the fairing length upper limit value obtained in the step 1, which is as follows:
arc length l from the junction of straight line segment and smooth curve to the midpoint of the curveBiExpressed as:
Figure BDA0002292303390000062
wherein: SC (Single chip computer)(βi) Is composed of
Figure BDA0002292303390000063
Shorthand of formula (I);
distance S from the center point of the fairing curve of the last corner to the center point of the fairing curve of the current cornerSEComprises the following steps:
SSE＝lBi-1+Li+lBi-li
wherein: lBiIs the arc length of the fairing line of the current corner, expressed as
Figure BDA0002292303390000064
lBi-1The arc length of the fairing curve determined for the last inflection point, if i is equal to 1, no fairing curve exists at the starting point, so lBi-1＝0；LiIs a straight line segment Pi-1PiLength of (d);
achievable velocity vEtDefined as the maximum satisfying tangential acceleration, tangential jerk and target speed, so that the achievable velocity vEtAnalytically calculated from the following formula:
maxvEt
st.vEt≤F
Figure BDA0002292303390000065
Figure BDA0002292303390000066
wherein: v. ofSThe critical speed of the fairing curve of the previous corner and the initial speed designed for the current corner are obtained; a. thetIs a tangential acceleration; j. the design is a squaretThe degree of tangential jump is adopted; f is the target speed.
And step 3: calculating the shortest fairing length when the normal constraint is met according to the reachable speed value obtained in the step 2, which is specifically as follows:
allowable velocity vEnDefined as the extreme velocity value under normal constraint at the critical point, from the normalAcceleration, normal jerk, bow difference and curvature extreme value are determined together, and allowable speed vEnExpressed as:
Figure BDA0002292303390000067
wherein: a. thenNormal acceleration limit, JnIs the normal jerk limit value, delta is the bow difference value, TsTo interpolate the period,. kappaiIs the curvature extreme of the critical point;
the curvature extremum is a function of the fairing length, i.e.:
Figure BDA0002292303390000071
wherein: ST (. beta.) ofi) Is composed of
Figure BDA0002292303390000072
Abbreviations of (a);
allowable velocity vEnCan be expressed as a function of the fairing length, i.e.:
Figure BDA0002292303390000073
will reach velocity vEtViewed as allowable velocity vEnTo achieve the velocity vEtSatisfy the normal constraint, the fairing length should take the maximum value of all inequalities in the satisfied formula, namely, the velocity v can be reachedEtThe corresponding shortest fairing length when normal constraint is satisfied is:
Figure BDA0002292303390000074
and 4, step 4: determining the optimal fairing length according to the fairing length upper limit value obtained in the step 1 and the shortest fairing length obtained by calculation in the step 3, wherein the method specifically comprises the following steps:
optimal light of fairing curve when synchronous design of geometric fairing and speed planningAlong the length
Figure BDA0002292303390000075
Expressed as:
Figure BDA0002292303390000076
and 5: and 4, performing smooth curve and speed planning synchronous design according to the optimal smooth length determined in the step 4, specifically:
characteristic parameter a of optimal fairing curveiExpressed as:
Figure BDA0002292303390000077
any point on the optical compliance curve is represented as:
P(θ)＝P0+aiC(θ)t+aiS(θ)n
wherein: p0Is a smooth curve and a straight line segment Pi-1PiT is a straight line segment Pi-1PiCollinear unit vector of (1), n being the plane Pi-1Pi-PiPi+1A unit normal vector of inner t; theta is a tangent line of the point P and a straight line segment Pi-1PiThe included angle of (A);
critical velocity v at mid-point of current fairing curveEExpressed as:
Figure BDA0002292303390000081
based on the initial velocity vSCritical velocity vEDetermining an S-shaped speed curve according to the length of the smooth track, the tangential acceleration and the tangential jerk.
As shown in fig. 1, 2 and 3, in combination with the above embodiments, examples are provided as follows:
this example is for explainingiWhen n is less than the upper limit value of the fairing length only under the geometric constraint, the method can set the fairing length according to the actual speedAnd a smooth curve is measured, so that better contour accuracy is obtained on the premise of ensuring the processing efficiency.
(1) The tangential/normal acceleration limit An/At is 150mm/s2, the tangential/normal jerk limit Jn/Jt is 3000mm/s3, the maximum target speed F is 20mm/s, the bow difference δ is 2 μm, the tool location coordinates are P1(0,0), P2(2,0.1), and P3(4,0), and the approximation error ∈ is set to 25 μm.
(2) Calculating the fairing length corresponding to the fairing curve meeting the approximation error epsilon according to a preset approximation error epsilon:
Figure BDA0002292303390000082
considering the influence of the length of the straight line segment, the upper limit value of the fairing length of the fairing curve under the geometric constraint is as follows:
li＝min{lε,||P1P2||,||P2P3||}。
(3) calculating the arc length from the junction of the straight line segment and the fairing curve to the critical point of the fairing curve under the geometric constraint
Figure BDA0002292303390000083
Distance S from the center point of the fairing curve of the last corner to the center point of the fairing curve of the current cornerSEComprises the following steps:
SSE＝lBi-1+Li+lBi-li
wherein: l isiStraight line P1P2The length of the segment (c) is greater than the length of the segment (c), since the embodiment includes only one cornerBi-1＝0；
Predicted achievable velocity vEtThe values are as follows:
maxvEt
st.vEt≤F
Figure BDA0002292303390000091
Figure BDA0002292303390000092
wherein: v. ofSThe critical velocity of the fairing line of the previous corner, v in this exampleS＝0。
(4) Calculating the critical velocity as vEtThe shortest fairing length satisfying normal constraint is:
Figure BDA0002292303390000093
(5) obtaining optimal fairing length
Figure BDA0002292303390000094
(6) Calculating the characteristic parameters of the optimal fairing curve under the synchronous design of geometric fairing and speed planning
Figure BDA0002292303390000095
The speed limit at the critical point is
Figure BDA0002292303390000096
Based on the initial velocity vSCritical velocity vEThe length of a smooth track, the tangential acceleration and the tangential jerk are determined by adopting a Bang-Bang control principle to determine an S-shaped speed curve.
(7) The fairing curve related to the invention and the fairing curve under the geometric constraint are shown in figure 2, and the track speed, the tangential acceleration and the tangential jerk are shown in figure 3, so that the result shows that the algorithm of the invention can generate a fairing track with higher profile precision on the premise of meeting the processing efficiency.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (6)

1. A local fairing method for a processing track synchronously designed by geometric fairing and speed planning is characterized by comprising the following steps:
step 1: acquiring the fairing length upper limit value of a fairing curve;
step 2: calculating an reachable speed value according to the fairing length upper limit value obtained in the step 1;
and step 3: calculating the shortest fairing length when the normal constraint is met according to the reachable speed value obtained in the step 2;
and 4, step 4: determining the optimal fairing length according to the fairing length upper limit value obtained in the step 1 and the shortest fairing length obtained by calculation in the step 3;
and 5: and 4, performing smooth curve and speed planning synchronous design according to the optimal smooth length determined in the step 4.
2. The method for local fairing of the processing track synchronously designed according to the geometric fairing and the speed planning as claimed in claim 1, wherein the step 1 is specifically as follows:
formed by two adjacent straight line segments Pi-1PiAnd PiPi+1A pair of symmetrical clothoid curves is inserted into the formed corner, and the upper limit value l of the fairing length of the fairing curveiComprises the following steps:
Figure FDA0002292303380000011
wherein: i is the corner position of the smooth corner in the continuous track; | | represents the length of the straight line segment;
Figure FDA0002292303380000012
for a given approximation error epsilon corresponding to the fairing length of the fairing,
Figure FDA0002292303380000013
expressed as:
Figure FDA0002292303380000014
wherein: beta is aiIs a tangent line at the midpoint of the fairing curve and a straight line Pi-1PiThe midpoint of the fairing curve is defined as a critical point;
Figure FDA0002292303380000015
3. the method for local fairing of processing trajectory with synchronous geometric fairing and speed planning design as claimed in claim 2, wherein in step 2, the achievable speed v isEtAnalytically calculated by the following formula:
max vEt
st.vEt≤F
Figure FDA0002292303380000021
Figure FDA0002292303380000022
wherein: v. ofSThe critical speed of the fairing curve of the previous corner and the initial speed designed for the current corner are obtained; a. thetIs a tangential acceleration; j. the design is a squaretThe degree of tangential jump is adopted; f is the target speed; sSEIs the distance from the center point of the fairing line of the last corner to the center point of the fairing line of the current corner, SSEExpressed as:
SSE＝lBi-1+Li+lBi-li
wherein: lBiIs the arc length of the fairing line of the current corner, expressed as
Figure FDA0002292303380000023
lBi-1The arc length of the fairing curve determined for the last inflection point, if i is equal to 1, lBi-1＝0；LiIs a straight line segment Pi-1PiLength of (d).
4. A method as claimed in claim 3, wherein in step 3, the achievable speed v is a local speed vEtThe corresponding shortest fairing length when normal constraint is satisfied is:
Figure FDA0002292303380000024
wherein: normal constraint consisting of normal acceleration AnNormal jump JnAnd bow difference delta; ST (. beta.) ofi) Is composed of
Figure FDA0002292303380000025
Abbreviations of (a).
5. The method for local fairing of the processing track synchronously designed according to the geometric fairing and the speed planning as claimed in claim 4, wherein the step 4 is specifically:
geometric fairing and speed planning synchronous designOptimum fairing length of curve
Figure FDA0002292303380000026
Expressed as:
Figure FDA0002292303380000027
6. the method for local fairing of the processing track with synchronous geometric fairing and speed planning design according to claim 5, wherein the step 5 is specifically as follows:
characteristic parameter a of optimal fairing curveiExpressed as:
Figure FDA0002292303380000031
any point on the optical compliance curve is represented as:
P(θ)＝P0+aiC(θ)t+aiS(θ)n
wherein: p0Is a smooth curve and a straight line segment Pi-1PiT is a straight line segment Pi-1PiCollinear unit vector of (1), n being the plane Pi-1Pi-PiPi+1A unit normal vector of inner t; theta is a tangent line of the point P and a straight line segment Pi-1PiThe included angle of (A);
critical velocity v at mid-point of current fairing curveEExpressed as:
Figure FDA0002292303380000032
based on the initial velocity vSCritical velocity vEDetermining an S-shaped speed curve according to the length of the smooth track, the tangential acceleration and the tangential jerk.
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Publication number Priority date Publication date Assignee Title
CN103592891A (en) * 2013-09-28 2014-02-19 大连理工大学 Method for cutter-axis vector fairing of complex curved surface five-axis numerical control machining based on kinematical constraints
CN103676788A (en) * 2013-12-31 2014-03-26 苏州大学 Smooth processing-oriented numerical control processing track processing method
CN103809510A (en) * 2012-11-09 2014-05-21 沈阳高精数控技术有限公司 Free curved surface reciprocating type cutter path planning method for high-precision processing
CN104007705A (en) * 2014-05-05 2014-08-27 上海交通大学 Prospective interpolation system for compressing and smoothening small segment paths
JP2014161918A (en) * 2013-02-21 2014-09-08 Seiko Epson Corp Robot control system, robot, robot control method, and program
CN106826829A (en) * 2017-02-22 2017-06-13 武汉工程大学 A kind of industrial robot fairing trace generator method of Controllable Error
CN110163973A (en) * 2019-04-26 2019-08-23 宁波财经学院 A kind of zone boundary ring method for fairing

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103809510A (en) * 2012-11-09 2014-05-21 沈阳高精数控技术有限公司 Free curved surface reciprocating type cutter path planning method for high-precision processing
JP2014161918A (en) * 2013-02-21 2014-09-08 Seiko Epson Corp Robot control system, robot, robot control method, and program
CN103592891A (en) * 2013-09-28 2014-02-19 大连理工大学 Method for cutter-axis vector fairing of complex curved surface five-axis numerical control machining based on kinematical constraints
CN103676788A (en) * 2013-12-31 2014-03-26 苏州大学 Smooth processing-oriented numerical control processing track processing method
CN104007705A (en) * 2014-05-05 2014-08-27 上海交通大学 Prospective interpolation system for compressing and smoothening small segment paths
CN106826829A (en) * 2017-02-22 2017-06-13 武汉工程大学 A kind of industrial robot fairing trace generator method of Controllable Error
CN110163973A (en) * 2019-04-26 2019-08-23 宁波财经学院 A kind of zone boundary ring method for fairing

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