CN114535365A - Multipoint discrete precision straightening planning method for plane curved linear guide rail - Google Patents

Multipoint discrete precision straightening planning method for plane curved linear guide rail Download PDF

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CN114535365A
CN114535365A CN202210129921.2A CN202210129921A CN114535365A CN 114535365 A CN114535365 A CN 114535365A CN 202210129921 A CN202210129921 A CN 202210129921A CN 114535365 A CN114535365 A CN 114535365A
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straightening
guide rail
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张永权
李乐
吴子栋
黄河
刘猛
刘士杰
卢红
凌鹤
黎章杰
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Wuhan University of Technology WUT
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
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    • B21D3/00—Straightening or restoring form of metal rods, metal tubes, metal profiles, or specific articles made therefrom, whether or not in combination with sheet metal parts
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Abstract

The invention discloses a multipoint discrete precision straightening planning method for a plane curved linear guide rail, which comprises the following steps of: establishing a comprehensive coordinate system; converting the linear guide rail deflection line under the workpiece measurement coordinate system into a workpiece reference coordinate system to obtain a discrete expression of the guide rail deflection line; based on the boundary condition of single-step straightening, obtaining a matrix expression comprising the number of straightening steps, the straightening step sequence, the straightening span of each straightening step and the starting and ending point coordinates according to the linear guide rail bending line expression; converting the linear guide rail deflection line under the workpiece reference coordinate system into a workpiece straightening coordinate system, applying a straightening stroke on a local coordinate system of a straightening pressure head, and obtaining a linear guide rail deflection line expression after each straightening step under the workpiece straightening coordinate system; and after the straightening is finished, reversely converting the linear guide rail deflection line expression under the workpiece straightening coordinate system into a workpiece reference coordinate system, and calculating the linear precision of the linear guide rail. The invention can effectively improve the straightening efficiency and the straightening precision.

Description

Multipoint discrete precision straightening planning method for plane curved linear guide rail
Technical Field
The invention relates to the technical field of mechanical numerical control material forming, in particular to a multipoint discrete precision straightening planning method for a plane bending linear guide rail.
Background
The linear guide rail is used as a key functional component of a linear feeding system and is widely applied to numerical control machining equipment and automation equipment. The ever-increasing linear feeding motion with high speed, high acceleration, high stability and high precision of the numerical control equipment puts higher requirements on the linear precision of the linear guide rail. The straightening is used as a key process in the processing and manufacturing process of the linear guide rail, so that the linear precision of the guide rail is improved, and the wear resistance and the service life of the guide rail are ensured.
Aiming at the linear guide rail with large initial deflection, long length and complex bending shape, the single-step straightening has large limitation, can not finish the linearity correction through the single-step straightening, and can achieve the purpose of linearity correction only by adopting multi-step precision straightening. Therefore, in order to improve the efficiency of straightening processing and better improve the straightening precision, the invention provides a multipoint discrete precision straightening planning method for a plane bending linear guide rail.
Disclosure of Invention
The invention aims to solve the technical problem that the defects in the prior art are overcome, and the multipoint discrete precision straightening planning method for the plane curved linear guide rail is provided, so that the state of a deflection line of the linear guide rail in the straightening process can be ensured to be updated after each straightening step, the straightening efficiency can be improved, and the straightening efficiency and the straightening precision can be effectively improved.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a multipoint discrete precision straightening planning method for a plane curved linear guide rail comprises the following steps:
1) establishing a comprehensive coordinate system of the multi-point discrete precision straightening process of the plane bending linear guide rail, wherein the comprehensive coordinate system describing the multi-point discrete precision straightening process comprises a workpiece measurement coordinate system { S }MReference coordinate system of workpiece { S }WS, a workpiece straightening coordinate systemSS and local coordinate system of straightening pressure headT}；
2) Measuring the workpiece to a coordinate system SMConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece reference coordinate systemWGenerating a linear guide rail plane deflection line according to a linear guide rail plane deflection line expression below;
3) according to the reference coordinate system S of the workpieceWSolving the number of straightening steps, the straightening step sequence, the straightening span of each straightening step and the start and end point coordinates based on the boundary condition of single-step straightening by using a linear guide rail plane bending line expression under the condition of the single-step straightening;
4) according to the determined straightening step number, straightening step sequence, straightening span and starting and ending point coordinates of each straightening step, sequentially aiming at each straightening step sequence, and in a workpiece reference coordinate system { SWObtaining the initial deflection of each straightening step sequence through the straightening span and the start-end point coordinate corresponding to each straightening step sequence, and obtaining the straightening stroke and the section corner of each straightening step sequence;
5) establishing a straightening reference plane (P) of the multi-point discrete precision straightening process of the plane bending linear guide railreSequentially referencing the workpiece to a coordinate system { S } according to the straightening step sequenceWConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece straightening coordinate systemSThe expression of the plane bending line of the linear guide rail under (S) is shown in the local coordinate system of the straightening pressure head (S)TApply straightening stroke and apply the straightening stroke in the workpiece straightening coordinate system { S }SObtaining the expression of the plane deflection line of the linear guide rail after each straightening step;
6) straightening coordinate system { S) of the workpiece after multipoint discrete straighteningSLinear guide rail plane deflection curve meter underConverse conversion of expression into workpiece reference coordinate system { SWEstablishing a control point set of a guide rail deflection line according to a linear guide rail plane deflection line expression undernPijAnd (i is 1,2, K, n), calculating the linear precision of the plane bending linear guide rail.
According to the technical scheme, in the step 1),
the workpiece measurement coordinate system { SM:OM-XMYMThe measurement coordinate system is a measurement coordinate system of the linear guide rail type strip-shaped workpiece and is used for describing initial bending line information of the workpiece;
the workpiece reference coordinate system { SW:OW-XWYWThe system is a workpiece reference coordinate system of a linear guide rail type strip-shaped workpiece along different straightening directions (pressing and pulling), and is used for describing the actual position of the workpiece along the span direction in the multipoint discrete straightening process;
the workpiece straightening coordinate system { SS:OS-XSYSThe straightening coordinate system is fixed at the edge of the supporting point and is used for describing the process of finding a straightening reference and the straightening process of the workpiece;
the local coordinate system (S) of the straightening pressure headT:OT-XTYTThe local coordinate systems in different straightening directions are used for describing specific straightening strokes in different bending directions.
According to the technical scheme, in the step 2),
based on the off-line deflection measurement of the linear guide rail, measuring a coordinate system S on a workpieceMThe discrete expression of the plane deflection line of the lower linear guide rail is as follows:
Figure BDA0003502053520000021
wherein L isWLength of linear guide rail, LrFor discrete resolution of the rail deflection line along the length direction, element "1" is used to ensure consistency in the homogeneous coordinate transformation calculation process.
Making a great circle in a workpiece measuring coordinate system by a homogeneous coordinate transformation methodSMConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece reference coordinate systemWThe expression of the linear guide plane deflection line under. In the reference coordinate system of the workpiece { S }WThe discrete expression of the plane deflection line of the lower linear guide rail is as follows:
Figure BDA0003502053520000031
wherein, TMRepresenting the translation transformation matrix along the span direction, i representing the straightening step sequence, and j representing the sequence of coordinate points on the guide rail deflection line.
According to the technical scheme, in the step 3),
based on the workpiece reference coordinate system { S) in step 2)WAnd (4) a plane deflection line expression of the lower linear guide rail, wherein a matrix expression of the straightening step number, the straightening step sequence and the straightening span and starting and ending point coordinates of each straightening step is as follows according to the boundary condition of single-step straightening:
Figure BDA0003502053520000032
wherein, the first row element n represents the total straightening step number, the second row element represents the straightening step sequence, the third row element represents the straightening span of each straightening step, the fourth row element and the fifth row element represent the coordinate values of the starting point of the corresponding straightening step in the workpiece reference coordinate system, and the sixth row element and the seventh row element represent the coordinate values of the end point of the corresponding straightening step in the workpiece reference coordinate system.
The boundary conditions of the single-step straightening of the linear guide rail are as follows:
Figure BDA0003502053520000033
wherein L ismaxAnd LminThe maximum and minimum adjusting distances which can be reached in the span direction of the straightening equipment; mnThe maximum bending moment which can be achieved by the straightening equipment; mrFor straightening theoretical modelMaximum bending moment allowed by the die; delta. for the preparation of a coatingrangeApplying a range of motion allowed by the straightening load direction to the straightening equipment; the profile function represents the profile requirement to be met by the guide rail deflection line in the straightening part of the guide rail, i.e. the support span, where niRepresenting the number of inflection points, ncRepresenting the number of control points of the flexible line of the guide, deltamaxThe maximum value of the deflection of the straightening part of the guide rail.
According to the technical scheme, in the step 4),
based on the straightening step number, the straightening step sequence and the straightening span and starting and ending point coordinate matrixes of each straightening step determined in the step 3), aiming at each straightening step sequence, in a workpiece reference coordinate system { SWSequentially obtaining the initial deflection of each straightening step sequence, and obtaining the straightening stroke and the section corner of each straightening step sequence:
Figure BDA0003502053520000041
wherein, delta0Representing the initial deflection corresponding to the midpoint position of each straightening step, namely the position with the maximum initial deflection in the straightening step; deltasRepresenting the initial deflection delta from each straightening step0Corresponding straightening stroke, theta represents the rotation angle of the linear guide rail around the supporting point at the position of the supporting point after the straightening of each straightening step is finished, and deltasAnd the calculation process of theta and the factors of the section shape, the size, the material, the initial deflection and the like of the guide rail of the line to be straightened.
According to the technical scheme, in the step 5),
straightening reference plane PreRepresents a vertical plane connected by span support points; according to the straightening step sequence, sequentially referencing the workpiece with a coordinate system { S }WDiscrete expression of plane bending line of linear guide rail under the condition of (S) is converted into a workpiece straightening coordinate systemSBased on the straightening stroke and the section rotation angle of each straightening step determined in the step 4), in a local coordinate system of a straightening pressure head { S }TApplying a straightening stroke under the control of a straightening stroke control device, and aligning the workpiece in a workpiece straightening coordinate system (S)SGet each straightening step sequenceThe linear guide plane deflection line expression of (1).
The rail deflection line comprises three sections: the straightening part is distributed on the left side of the span supporting point, the non-straightening part is distributed on the right side of the span supporting point, and the part to be straightened is arranged between the span supporting points. Aiming at the ith straightening step, two conditions are required to be met when the straightening is finished: starting point of straightening step and workpiece straightening coordinate system { S }SThe original points are coincided, namely the guide rail is positioned in a workpiece straightening coordinate system (S) after the i-1 th straightening stepSThe deflection line under } translates in the span direction; the starting point and the ending point of the straightening step are connected along the span direction, and the guide rail bending line is positioned on a straightening reference plane { P }reWithin (S), i.e. the guide rail deflection line is wound around the workpiece straightening coordinate system (S)SRotation angle of origin alphai。
The translation transformation may be represented as:
Figure BDA0003502053520000042
wherein, Ti FRepresenting a translation transformation matrix.
Guide rail deflection wire-wound workpiece straightening coordinate system { SSThe rotational variation of the origin can be expressed as:
Figure BDA0003502053520000043
wherein the content of the first and second substances,
Figure BDA0003502053520000044
representing a rotation transformation matrix, alphaiCan be obtained by the following formula:
Figure BDA0003502053520000045
wherein the content of the first and second substances,
Figure BDA0003502053520000046
and
Figure BDA0003502053520000047
respectively representing the end point of the ith straightening step in the straightening coordinate system of the workpiece { SSThe horizontal and vertical coordinate values below.
After the straightening is finished in the ith straightening step, the straightening part is changed into a straight line, the straightened part distributed on the left side of the span supporting point and the non-straightened part distributed on the right side of the supporting point respectively rotate around the similar supporting point, and the rotation angle theta is changediThe rotation direction is opposite for the corresponding section corner of each straightening step.
To this end, the discrete expression of the guide rail deflection line after the completion of the ith straightening step can be expressed as:
Figure BDA0003502053520000051
wherein the content of the first and second substances,
Figure BDA0003502053520000052
and
Figure BDA0003502053520000053
representing the rotational transformation matrices of the straightened portion to the left of the span support point and the unbent portion to the right of the support point, respectively. In particular, the 1 st straightening step is not distributed on the straightened portion on the left side of the span support point, and the nth straightening step is not distributed on the unbent portion on the right side of the span support point.
According to the technical scheme, in the step 6),
straightening coordinate system { S) of workpiece after multipoint discrete straighteningSReversely converting the linear guide rail plane flexible line expression under the condition to a workpiece reference coordinate system (S)WEstablishing a control point set of a guide rail flexible linenPijAnd (i is 1,2, K, n), calculating the linear precision of the plane bending linear guide rail.
Workpiece straightening coordinate system SSThe control points formed on the deflection line of the middle guide rail are in the reference coordinate system of the workpiece { S }WA lower can be denoted as }nPij}：
Figure BDA0003502053520000054
Wherein N represents the number of straightening steps, i (i is more than or equal to 1 and less than or equal to N, i belongs to N*) Represents the straightening step sequence, j (j is 1,2) represents the starting point and the end point of the straightening step,
Figure BDA0003502053520000055
rotation transformation matrix, T, representing the origin of the guide rail deflection line around the workpiece straightening coordinate systemi FRepresenting a translation transformation matrix of the guide rail deflection line along the span direction,
Figure BDA0003502053520000056
representing a matrix of rotational transformations of the straightened portion distributed to the left of the span support point around the proximate support point.
The linear precision calculation of the plane bending linear guide rail adopts a minimum area method, and the straightness of the guide rail is collected into a control point after the multi-step straightening is finishednPijBased on 1,2, K, n, the minimum tolerance band is obtained by two straight lines parallel to each other. Two mutually parallel straight lines can be represented as:
Figure BDA0003502053520000061
wherein, a, b1And b2Is a parallel line related parameter obtained by the coordinates of a control point on a guide rail deflection line.
Thus, the objective function for rail straightness assessing the minimum tolerance band can be expressed as:
Figure BDA0003502053520000062
the invention has the following beneficial effects:
the invention establishes a set of comprehensive coordinate system aiming at multi-step straightening of the plane bending linear guide rail, is concise and clear, can realize the conversion of the discrete expression of the linear guide rail bending line in each coordinate system by a homogeneous coordinate transformation method, can obtain the latest discrete expression of the linear guide rail bending line after each straightening step as a new initial bending line, ensures the accuracy of the bending line of the parts before each straightening processing, and finally calculates the linear accuracy of the linear guide rail according to the selected control point set. The method effectively improves the straightening processing efficiency of the plane bending linear guide rail and the linear precision of the linear guide rail.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a multipoint discrete precision straightening planning method for a plane curved linear guide rail in an embodiment of the invention;
FIG. 2 is a schematic view of a pressure direction straightening processing of the numerical control straightening system for the plane bending linear guide rail in the embodiment of the invention;
FIG. 3 is a drawing direction straightening processing schematic diagram of a numerical control straightening system for a plane bending linear guide rail in the embodiment of the invention;
FIG. 4 is a schematic diagram of a comprehensive coordinate system of a multi-point discrete precision straightening process for a plane curved linear guide rail in the embodiment of the invention;
FIG. 5 is a schematic illustration of the initial deflection, straightening stroke and cross-sectional corner for a flat curved linear guide in an embodiment of the present invention;
FIG. 6 is a schematic view of a single step straightening process for a flat curved linear guide in an embodiment of the present invention;
FIG. 7 is a schematic view of a multi-step straightening process for a flat curved linear guide in an embodiment of the present invention;
FIG. 8 is a schematic diagram of the embodiment of the present invention for determining the linear precision of a linear guide rail by using the minimum area method;
in the figure, 1-left side supporting point, 2-right side supporting point, 3-straightening stroke applying mechanism and 4-linear guide rail.
Detailed Description
The present invention will be described in detail below with reference to the drawings and examples.
Referring to fig. 1, the multipoint discrete precision straightening planning method for the plane curved linear guide rail in one embodiment of the invention includes the following steps:
1) establishing a comprehensive coordinate system of the multi-point discrete precision straightening process of the plane bending linear guide rail, wherein the comprehensive coordinate system describing the multi-point discrete precision straightening process comprises a workpiece measurement coordinate system { S }MReference coordinate system of workpiece { S }WS, a workpiece straightening coordinate systemSAnd local coordinate system of straightening pressure head (S)T}；
2) Measuring the workpiece to a coordinate system SMConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece reference coordinate systemWGenerating a linear guide rail plane deflection line according to a linear guide rail plane deflection line expression below;
3) according to the reference coordinate system S of the workpieceWObtaining the number of straightening steps, the straightening step sequence, the straightening span of each straightening step and the start-end point coordinate based on the boundary condition of single-step straightening by using a linear guide rail plane bending line expression under the condition;
4) according to the determined straightening step number, straightening step sequence, straightening span and starting and ending point coordinates of each straightening step, sequentially aiming at each straightening step sequence, and in a workpiece reference coordinate system { SWObtaining the initial deflection of each straightening step sequence through the straightening span and the start-end point coordinate corresponding to each straightening step sequence, and obtaining the straightening stroke and the section corner of each straightening step sequence;
5) establishing a straightening reference plane (P) of the multi-point discrete precision straightening process of the plane bending linear guide railreSequentially referencing the workpiece to a coordinate system { S } according to the straightening step sequenceWConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece straightening coordinate systemSThe expression of the plane bending line of the linear guide rail under (S) is shown in the local coordinate system of the straightening pressure head (S)TApplying a straightening stroke under the control of a straightening stroke control device and setting a workpiece straightening coordinate system (S)SGet each straighteningThe linear guide rail plane deflection line expression after the step sequence;
6) straightening coordinate system { S) of workpiece after multipoint discrete straighteningSReversely converting the linear guide rail plane flexible line expression under the condition of (S) into a workpiece reference coordinate system (S)WEstablishing a control point set of a guide rail deflection line according to a linear guide rail plane deflection line expression undernPijAnd (i is 1,2, K, n), calculating the linear precision of the plane bending linear guide rail.
Further, in the step 1),
the workpiece measurement coordinate system { SM:OM-XMYMThe measurement coordinate system is a measurement coordinate system of the linear guide rail type strip-shaped workpiece and is used for describing initial bending line information of the workpiece;
the workpiece reference coordinate system { SW:OW-XWYWThe system is a workpiece reference coordinate system of a linear guide rail type strip-shaped workpiece along different straightening directions (pressing and pulling), and is used for describing the actual position of the workpiece along the span direction in the multipoint discrete straightening process;
the workpiece straightening coordinate system { SS:OS-XSYSThe straightening coordinate system is fixed at the edge of the supporting point and is used for describing the process of finding a straightening reference and the straightening process of the workpiece;
the local coordinate system (S) of the straightening pressure headT:OT-XTYTThe local coordinate systems in different straightening directions are used for describing specific straightening strokes in different bending directions.
Further, in the step 2), a coordinate system { S ] is measured on the workpiece based on the linear guide rail offline deflection measurementMThe discrete expression of the lower linear guide rail plane flexible line is as follows:
Figure BDA0003502053520000081
wherein L isWLength of linear guide rail, LrFor discrete resolution of the rail-deflection line along its length, element "1" is used to ensure homogeneityConsistency in the coordinate transformation calculation process.
Further, the workpiece is measured with a coordinate system S by a homogeneous coordinate transformation methodMConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece reference coordinate systemWThe expression of the linear guide plane deflection line under. In the reference coordinate system of the workpiece { SWThe discrete expression of the plane deflection line of the lower linear guide rail is as follows:
Figure BDA0003502053520000082
wherein, TMRepresenting the translation transformation matrix along the span direction, i representing the straightening step sequence, and j representing the sequence of coordinate points on the guide rail deflection line.
Further, in the step 3), the workpiece reference coordinate system { S) is based on the workpiece reference coordinate system { S) in the step 2)WAnd (4) a plane deflection line expression of the lower linear guide rail, wherein a matrix expression of the straightening step number, the straightening step sequence and the straightening span and starting and ending point coordinates of each straightening step is as follows according to the boundary condition of single-step straightening:
Figure BDA0003502053520000083
wherein, the first row element n represents the total straightening step number, the second row element represents the straightening step sequence, the third row element represents the straightening span of each straightening step, the fourth row element and the fifth row element represent the coordinate values of the starting point of the corresponding straightening step in the workpiece reference coordinate system, and the sixth row element and the seventh row element represent the coordinate values of the end point of the corresponding straightening step in the workpiece reference coordinate system.
Further, the boundary conditions of the single-step straightening of the linear guide rail are as follows:
Figure BDA0003502053520000091
wherein L ismaxAnd LminUp to the span direction of the straightening equipmentA maximum and minimum adjustment distance; mnThe maximum bending moment which can be achieved by the straightening equipment; mrThe maximum bending moment allowed by the straightening theoretical model; deltarangeApplying a range of motion allowed by the straightening load direction to the straightening equipment; the profile function represents the profile requirement to be met by the guide rail deflection line in the straightening part of the guide rail, i.e. the support span, where niRepresenting the number of inflection points, ncRepresenting the number of control points of the flexible line of the guide, deltamaxThe maximum value of the deflection of the straightening part of the guide rail.
Further, in the step 4), based on the straightening step number, the straightening step sequence and the straightening span and starting and ending point coordinate matrix of each straightening step determined in the step 3), aiming at each straightening step, in the workpiece reference coordinate system { S }WSequentially obtaining the initial deflection of each straightening step sequence, and obtaining the straightening stroke and the section corner of each straightening step sequence:
Figure BDA0003502053520000092
wherein, delta0Representing the initial deflection corresponding to the midpoint position of each straightening step, namely the position with the maximum initial deflection in the straightening step; deltasRepresenting the initial deflection delta from each straightening step0Corresponding straightening stroke, theta represents the rotation angle of the linear guide rail around the supporting point at the position of the supporting point after the straightening of each straightening step is finished, and deltasAnd the calculation process of theta and the factors of the section shape, the size, the material, the initial deflection and the like of the guide rail of the line to be straightened.
Further, in the step 5), the straightening reference plane { P }reRepresents a vertical plane connected by span support points; according to the straightening step sequence, sequentially referencing the workpiece to a coordinate system { S }WDiscrete expression of plane bending line of linear guide rail under the condition of (S) is converted into a workpiece straightening coordinate systemSBased on the straightening stroke and the section rotation angle of each straightening step determined in the step 4), in a local coordinate system of a straightening pressure head { S }TApplying a straightening stroke under the control of a straightening coordinate system of the workpiece { S }SGet every under }The expression of the plane bending line of the linear guide rail after the straightening step sequence.
Further, the rail deflection line comprises three sections: the straightening part is distributed on the left side of the span supporting point, the non-straightening part is distributed on the right side of the span supporting point, and the part to be straightened is arranged between the span supporting points. Aiming at the ith straightening step, two conditions are required to be met when the straightening is finished: starting point of straightening step and workpiece straightening coordinate system { S }SThe original points are coincided, namely the guide rail is positioned in a workpiece straightening coordinate system (S) after the i-1 th straightening stepSThe deflection line under } translates in the span direction; the starting point and the ending point of the straightening step are connected along the span direction, and the guide rail bending line is positioned on a straightening reference plane { P }reWithin (S), i.e. the guide rail deflection line is wound around the workpiece straightening coordinate system (S)SRotation angle of origin alphai。
Further, the translation transformation may be represented as:
Figure BDA0003502053520000101
wherein, Ti FRepresenting a translation transformation matrix.
Further, the guide rail deflection wire winds the workpiece straightening coordinate system { S }SThe rotational variation of the origin can be expressed as:
Figure BDA0003502053520000102
wherein the content of the first and second substances,
Figure BDA0003502053520000103
representing a rotation transformation matrix, alphaiCan be obtained by the following formula:
Figure BDA0003502053520000104
wherein the content of the first and second substances,
Figure BDA0003502053520000105
and
Figure BDA0003502053520000106
respectively representing the end point of the ith straightening step in the straightening coordinate system of the workpiece { SSThe horizontal and vertical coordinate values below.
Further, after the straightening is finished in the ith straightening step, the straightening part becomes a straight line, the straightened part distributed on the left side of the span supporting point and the non-straightened part distributed on the right side of the supporting point respectively rotate around the similar supporting point, and the rotation angle theta is changed byiThe rotation direction is opposite for the corresponding section corner of each straightening step.
Further, the discrete expression of the guide rail deflection line after the completion of the ith straightening step can be expressed as:
Figure BDA0003502053520000107
wherein the content of the first and second substances,
Figure BDA0003502053520000108
and
Figure BDA0003502053520000109
representing the rotational transformation matrices of the straightened portion to the left of the span support point and the unbent portion to the right of the support point, respectively. In particular, the 1 st straightening step is not distributed on the straightened portion on the left side of the span support point, and the nth straightening step is not distributed on the unbent portion on the right side of the span support point.
Further, in the step 6), the workpiece straightening coordinate system { S) after the multipoint discrete straightening is finished is adoptedSReversely converting the linear guide rail plane flexible line expression under the condition to a workpiece reference coordinate system (S)WEstablishing a control point set of guide rail flexible linenPijAnd (i is 1,2, K, n), calculating the linear precision of the plane bending linear guide rail.
Further, the workpiece straightening coordinate system { SSThe control points formed on the deflection line of the middle guide rail are in the reference coordinate system of the workpiece { S }WLower can be denoted as-nPij}：
Figure BDA0003502053520000111
Wherein N represents the number of straightening steps, i (i is more than or equal to 1 and less than or equal to N, and i belongs to N*) Represents the straightening step sequence, j (j is 1,2) represents the starting point and the end point of the straightening step,
Figure BDA0003502053520000112
rotation transformation matrix, T, representing the origin of the guide rail deflection line around the workpiece straightening coordinate systemi FRepresenting a translation transformation matrix of the guide rail deflection line along the span direction,
Figure BDA0003502053520000113
representing a matrix of rotational transformations of the straightened portion distributed to the left of the span support point around the proximate support point.
Further, the linear precision of the plane bending linear guide rail is calculated by a minimum area method, and the straightness of the guide rail is collected into a control point after the multi-step straightening is finishednPijOn the basis of 1,2, K, n, the minimum tolerance band is obtained by two mutually parallel straight lines. Two mutually parallel straight lines can be represented as:
Figure BDA0003502053520000114
wherein, a, b1And b2Is a parallel line related parameter obtained by the coordinates of a control point on a guide rail deflection line.
Further, the objective function of the rail straightness assessing minimum tolerance band may be expressed as:
Figure BDA0003502053520000115
in one embodiment of the invention, the working principle is as follows:
FIG. 2 and FIG. 3 show the straightening processing in the pressing direction and the straightening processing in the pulling direction of the numerical control straightening system respectivelyAnd the working diagrams are respectively used for straightening strokes in different directions. In the figure, 1 and 2 are four supporting points which provide support for the straightening processing of the linear guide rail; 3, a mechanism for applying a straightening stroke to realize straightening processing, wherein the straightening processing comprises an upper end straightening point and a lower end straightening point; l isiRepresenting the span, as the horizontal distance between two support points, with the mechanism 3 located at the center of the support points 1,2, i.e. LiAt/2; and 4 represents a plane curved linear guide rail. When the bending line of the linear guide rail protrudes upwards, the straightening processing in the pressing direction is performed, the lower ends of the 1 and the 2 are used as supporting points, and the straightening point at the upper end of the mechanism 3 applies a straightening stroke from top to bottom; when the bending line of the linear guide rail is sunken downwards, the straightening processing in the pulling direction is performed, the upper ends of the 1 and 2 are used as supporting points, and the straightening point at the lower end of the mechanism 3 applies a straightening stroke from bottom to top.
1. Establishing a comprehensive coordinate system in a multi-point discrete precision straightening process
Step 1 in fig. 1 illustrates the completion of establishing a comprehensive coordinate system of a multi-point discrete precision straightening process of a planar curved linear guide rail. In order to effectively link the measurement of the linear guide rail, the support of the linear guide rail and the processing of the linear guide rail, a set of complete comprehensive coordinate system needs to be established based on the processing characteristics of the numerical control straightening system, as shown in fig. 4, the method specifically comprises the following steps:
workpiece measurement coordinate system SM:OM-XMYM}: the measuring coordinate system is a linear guide rail type strip-shaped workpiece and is used for describing initial bending line information of the workpiece;
reference coordinate system of the workpiece { S }W:OW-XWYW}: the system comprises a reference coordinate system of a linear guide rail type strip-shaped workpiece along different straightening directions (pressing and pulling), and is used for describing the actual position of the workpiece along the span direction in the multipoint discrete straightening process;
workpiece straightening coordinate system SS:OS-XSYS}: the straightening coordinate system is fixed on the edge of the supporting point and is used for describing the process of finding a straightening reference and the straightening process of the workpiece;
local coordinate system { S ] of straightening pressure headT:OT-XTYT}: is along withLocal coordinate systems in the same straightening direction are used for describing specific straightening strokes in different bending directions.
2. Establishing linear guide rail flexible line expression
Step 2 of fig. 1 illustrates the completion of establishing the expression of the flat curved linear guide flexible line. Aiming at a plane bending linear guide rail, measuring a coordinate system { S ] on a workpiece in an off-line deflection measurement modeMObtaining a discrete expression of the linear guide rail flexible line:
Figure BDA0003502053520000121
wherein L isWLength of linear guide rail, LrFor discrete resolution of the rail deflection line along the length direction, element "1" is used to ensure consistency in the homogeneous coordinate transformation calculation process.
The linear guide rail is arranged in a workpiece measurement coordinate system { S ] by a homogeneous coordinate transformation methodMConverting the discrete expression of the flexible line under the condition of (S) into a workpiece reference coordinate systemWThe expression of the linear guide plane deflection line under:
Figure BDA0003502053520000122
wherein, TMRepresenting the translation transformation matrix along the span direction, i representing the straightening step sequence, and j representing the sequence of coordinate points on the guide rail deflection line.
3. Generating the number of straightening steps, the sequence of the straightening steps and the straightening span and the starting and ending point coordinates of each straightening step
Step 3 in figure 1 illustrates the completion of the straightening step number, the straightening step sequence and the determination of the straightening span and the start and end point coordinates of each straightening step. The boundary conditions of single-step straightening are as follows:
Figure BDA0003502053520000131
wherein L ismaxAnd LminThe maximum and minimum adjusting distances which can be reached in the span direction of the straightening equipment; m is a group ofnThe maximum bending moment which can be achieved by the straightening equipment; m is a group ofrThe maximum bending moment allowed by the straightening theoretical model; deltarangeApplying a range of motion allowed by the straightening load direction to the straightening equipment; the profile function represents the profile requirement to be met by the guide rail deflection line in the straightening part of the guide rail, i.e. the support span, where niRepresenting the number of inflection points, ncRepresenting the number of control points of the flexible line of the guide, deltamaxThe maximum value of the deflection of the straightening part of the guide rail.
Based on the boundary condition, from the workpiece reference coordinate system { S }WGenerating a matrix expression of the straightening step number, the straightening step sequence and the straightening span and starting and ending point coordinates of each straightening step by using a plane bending line expression of the lower linear guide rail:
Figure BDA0003502053520000132
wherein, the first row element n represents the total straightening step number, the second row element represents the straightening step sequence, the third row element represents the straightening span of each straightening step, the fourth row element and the fifth row element represent the coordinate values of the starting point of the corresponding straightening step in the workpiece reference coordinate system, and the sixth row element and the seventh row element represent the coordinate values of the end point of the corresponding straightening step in the workpiece reference coordinate system.
4. Obtaining straightening stroke and cross-section angle
Step 4 of FIG. 1 illustrates the completion of the determination of the parameters of initial deflection, straightening stroke and cross-sectional turning angle. Based on the number of straightening steps, the straightening step sequence and the straightening span and starting and ending point coordinates of each straightening step, in a workpiece reference coordinate system { SWObtaining the initial deflection of each straightening step, and obtaining the corresponding straightening stroke and section corner:
Figure BDA0003502053520000133
wherein, delta0Representing each straightening stepThe initial deflection corresponding to the midpoint position of (1), i.e., the position of the straightening step at which the initial deflection is the greatest, has a value of delta0＝δmax；δsRepresenting the initial deflection delta from each straightening step0Corresponding to the straightening stroke, theta represents the rotation angle of the linear guide rail around the supporting point at the position of the supporting point after the straightening of each straightening step is finished, as shown in figure 5, deltasAnd the calculation process of theta and the factors of the section shape, the size, the material, the initial deflection and the like of the guide rail of the line to be straightened.
5. And straightening the linear guide rail under the workpiece straightening coordinate system to obtain a linear guide rail deflection line expression after each straightening step.
The straightening of the linear guide and the acquisition of the expression of the linear guide deflection line after each straightening step are completed as described in step 5 of figure 1. According to the straightening step sequence, sequentially referencing the workpiece with a coordinate system { S }WDiscrete expression of plane bending line of linear guide rail under the condition of (S) is converted into a workpiece straightening coordinate systemSBased on the obtained straightening stroke and section corner of each straightening step, in a local coordinate system of a straightening pressure head { S }TApplying a straightening stroke under the control of a straightening stroke control device, and aligning the workpiece in a workpiece straightening coordinate system (S)SAnd solving the expression of the plane bending line of the linear guide rail after each straightening step.
As shown in FIG. 6, a straightening reference plane PreRepresents a vertical plane connected by a span support point. The rail deflection line comprises three sections: the straightening part is distributed on the left side of the span supporting point, the non-straightening part is distributed on the right side of the span supporting point, and the part to be straightened is arranged between the span supporting points. Aiming at the ith straightening step, two conditions are required to be met when the straightening is finished: starting point of straightening step and workpiece straightening coordinate system { S }SThe original points are coincided, namely the guide rail is positioned in a workpiece straightening coordinate system (S) after the i-1 th straightening stepSThe deflection line under } translates in the span direction; the starting point and the ending point of the straightening step are connected along the span direction, and the guide rail bending line is positioned on a straightening reference plane { P }reWithin (S), i.e. the guide rail deflection line is wound around the workpiece straightening coordinate system (S)SRotation angle of origin alphai。
The straightening process and coordinate transformation of the plane bending linear guide rail are shown in the attached figure 7.
The translation transformation may be represented as:
Figure BDA0003502053520000141
wherein, Ti FRepresenting a translation transformation matrix.
Guide rail deflection wire-wound workpiece straightening coordinate system { SSThe rotational transformation of the origin can be expressed as:
Figure BDA0003502053520000142
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003502053520000143
representing a rotation transformation matrix, alphaiCan be obtained by the following formula:
Figure BDA0003502053520000144
wherein the content of the first and second substances,
Figure BDA0003502053520000145
and
Figure BDA0003502053520000146
respectively representing the end point of the ith straightening step in the straightening coordinate system of the workpiece { SSThe horizontal and vertical coordinate values below.
After the straightening is finished in the ith straightening step, the straightening part is changed into a straight line, the straightened part distributed on the left side of the span supporting point and the non-straightened part distributed on the right side of the supporting point respectively rotate around the similar supporting point, and the rotation angle theta is changediThe rotation direction is opposite for the corresponding section corner of each straightening step.
To this end, the discrete expression of the guide rail deflection line after the completion of the ith straightening step can be expressed as:
Figure BDA0003502053520000151
wherein the content of the first and second substances,
Figure BDA0003502053520000152
and
Figure BDA0003502053520000153
representing the rotational transformation matrices of the straightened portion to the left of the span support point and the unbent portion to the right of the support point, respectively. In particular, the 1 st straightening step is not distributed on the straightened portion on the left side of the span support point, and the nth straightening step is not distributed on the unbent portion on the right side of the span support point.
6. Calculating linear precision of plane bending linear guide rail
The calculation of the linear accuracy of the planar curved linear guide is completed as described in step 6 of fig. 1. Straightening coordinate system { S) of workpiece after multipoint discrete straighteningSReversely converting the linear guide rail plane flexible line expression under the condition to a workpiece reference coordinate system (S)WEstablishing a control point set of guide rail flexible linenPijAnd (i is 1,2, K, n), and calculating the linear precision of the planar curved linear guide rail according to Step n shown in fig. 7.
Workpiece straightening coordinate system SSThe control points formed on the deflection line of the middle guide rail are in the reference coordinate system of the workpiece { S }WLower can be denoted as-nPij}：
Figure BDA0003502053520000154
Wherein N represents the number of straightening steps, i (i is more than or equal to 1 and less than or equal to N, and i belongs to N*) Represents the straightening step sequence, j (j is 1,2) represents the starting point and the end point of the straightening step,
Figure BDA0003502053520000155
rotation transformation matrix, T, representing the origin of the guide rail deflection line around the workpiece straightening coordinate systemi FRepresenting a translation transformation matrix of the guide rail deflection line along the span direction,
Figure BDA0003502053520000156
representing a matrix of rotational transformations of the straightened portion distributed to the left of the span support point around the proximate support point.
The linear precision calculation of the plane bending linear guide rail adopts a minimum area method, and the straightness of the guide rail is collected into a control point after the multi-step straightening is finishednPijBased on 1,2, K, n, the minimum tolerance band is obtained by two mutually parallel straight lines, as shown in fig. 8. Two mutually parallel straight lines can be represented as:
Figure BDA0003502053520000161
wherein, a, b1And b2Is a parallel line related parameter obtained by the coordinates of a control point on a guide rail deflection line.
Thus, the objective function for rail straightness assessing the minimum tolerance band can be expressed as:
Figure BDA0003502053520000162
in conclusion, the accurate expression of the bending line of the plane bending linear guide rail is obtained through offline deflection measurement, and a comprehensive coordinate system for straightening the linear guide rail is established, the invention provides a method for realizing the conversion of the bending line of the linear guide rail in a workpiece measuring coordinate system, a workpiece reference coordinate system and a workpiece straightening coordinate system by utilizing a homogeneous coordinate transformation method, and the initial deflection, the straightening stroke and the section corner of each straightening step are obtained through the number of the straightening steps, the straightening step sequence, the straightening span and the starting and ending data of the straightening steps; meanwhile, the discrete expression of the bending line of the linear guide rail is continuously updated through translation and rotation transformation before and after each straightening step, so that the precision of the bending line model of the linear guide rail is effectively improved, and the straightening processing precision is further improved; and finally, calculating the integral linear precision of the linear guide rail through the selected representative control point set. The invention effectively improves the straightening processing efficiency and precision of the plane bending linear guide rail.
The above is only a preferred embodiment of the present invention, and certainly, the scope of the present invention should not be limited thereby, and therefore, the present invention is not limited by the scope of the claims.

Claims (7)

1. A multipoint discrete precision straightening planning method for a plane bending linear guide rail is characterized by comprising the following steps:
1) establishing a comprehensive coordinate system of the multi-point discrete precision straightening process of the plane bending linear guide rail, wherein the comprehensive coordinate system describing the multi-point discrete precision straightening process comprises a workpiece measurement coordinate system { S }MReference coordinate system of workpiece { S }WS, a workpiece straightening coordinate systemSAnd local coordinate system of straightening pressure head (S)T}；
2) Measuring the workpiece in a coordinate system { S }MConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece reference coordinate systemWGenerating a linear guide rail plane deflection line according to a linear guide rail plane deflection line expression below;
3) according to the reference coordinate system S of the workpieceWObtaining the number of straightening steps, the straightening step sequence, the straightening span of each straightening step and the start-end point coordinate based on the boundary condition of single-step straightening by using a linear guide rail plane bending line expression under the condition;
4) according to the determined straightening step number, straightening step sequence, straightening span and starting and ending point coordinates of each straightening step, sequentially aiming at each straightening step sequence, and in a workpiece reference coordinate system { SWObtaining the initial deflection of each straightening step sequence through the straightening span and the start-end point coordinate corresponding to each straightening step sequence, and obtaining the straightening stroke and the section corner of each straightening step sequence;
5) establishing a straightening reference plane (P) of the multi-point discrete precision straightening process of the plane bending linear guide railreSequentially referencing the workpiece to a coordinate system { S } according to the straightening step sequenceWConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece straightening coordinate systemSExpression of linear guide rail plane bending line under straightening pressure head in local coordinate system{STApplying a straightening stroke under the control of a straightening stroke control device and setting a workpiece straightening coordinate system (S)SObtaining the expression of the plane deflection line of the linear guide rail after each straightening step;
6) straightening coordinate system { S) of workpiece after multipoint discrete straighteningSReversely converting the linear guide rail plane flexible line expression under the condition of (S) into a workpiece reference coordinate systemWEstablishing a control point set of a guide rail deflection line according to a linear guide rail plane deflection line expression undernPijAnd (i is 1,2, K, n), calculating the linear precision of the plane bending linear guide rail.
2. The method for multipoint discrete precision straightening planning of a curved linear guide according to claim 1, characterized in that in step 1),
the workpiece measurement coordinate system { SM:OM-XMYMThe measurement coordinate system is a measurement coordinate system of the linear guide rail type strip-shaped workpiece and is used for describing initial bending line information of the workpiece;
the workpiece reference coordinate system { SW:OW-XWYWThe system is a workpiece reference coordinate system of a linear guide rail type strip-shaped workpiece along different straightening directions (pressing and pulling), and is used for describing the actual position of the workpiece along the span direction in the multipoint discrete straightening process;
the workpiece straightening coordinate system { S }S:OS-XSYSThe straightening coordinate system is fixed at the edge of the supporting point and is used for describing the process of finding a straightening reference and the straightening process of the workpiece;
the local coordinate system (S) of the straightening pressure headT:OT-XTYTIs a local coordinate system in different straightening directions for describing the specific straightening strokes in different bending directions.
3. The method for multipoint discrete precision straightening planning of a curved linear guide rail according to claim 1, characterized in that in step 2), the coordinate system { S ] is measured in the workpiece based on the linear guide rail offline deflection measurementMDiscrete expression of lower linear guide rail plane flexible lineComprises the following steps:
Figure FDA0003502053510000025
wherein L isWLength of linear guide rail, LrThe element '1' is used for ensuring the consistency in the homogeneous coordinate transformation calculation process for the discrete resolution of the guide rail flexible line along the length direction;
measuring a coordinate system { S) of a workpiece by a homogeneous coordinate transformation methodMConverting the expression of the plane bending line of the linear guide rail under the condition of (S) into a workpiece reference coordinate systemWLinear guide plane deflection line expressions below. In the reference coordinate system of the workpiece { SWThe discrete expression of the plane deflection line of the lower linear guide rail is as follows:
Figure FDA0003502053510000026
wherein, TMRepresenting the translation transformation matrix along the span direction, i representing the straightening step sequence, and j representing the sequence of coordinate points on the guide rail deflection line.
4. Method for multipoint discrete precision straightening planning of a curved linear guide according to claim 1, characterized in that in step 3) the workpiece reference frame { S } is based on claim 3WAnd (4) a plane deflection line expression of the lower linear guide rail, wherein a matrix expression of the straightening step number, the straightening step sequence and the straightening span and starting and ending point coordinates of each straightening step is as follows according to the boundary condition of single-step straightening:
Figure FDA0003502053510000023
wherein, the first row element n represents the total straightening step number, the second row element represents the straightening step sequence, the third row element represents the straightening span of each straightening step, the fourth row element and the fifth row element represent the coordinate values of the starting point of the corresponding straightening step in the workpiece reference coordinate system, and the sixth row element and the seventh row element represent the coordinate values of the end point of the corresponding straightening step in the workpiece reference coordinate system;
the boundary conditions of the single-step straightening of the linear guide rail are as follows:
Figure FDA0003502053510000024
wherein L ismaxAnd LminThe maximum and minimum adjusting distances which can be reached in the span direction of the straightening equipment; mnThe maximum bending moment which can be achieved by the straightening equipment; mrThe maximum bending moment allowed by the straightening theoretical model; deltarangeApplying a range of motion allowed by the straightening load direction to the straightening equipment; the profile function represents the profile requirement to be met by the guide rail deflection line in the straightening part of the guide rail, i.e. the support span, where niRepresenting the number of inflection points, ncRepresenting the number of control points of the flexible line of the guide, deltamaxThe maximum value of the deflection of the straightening part of the guide rail.
5. The method for multipoint discrete precision straightening planning of a curved linear guide rail according to claim 1, characterized in that in step 4), based on the number of straightening steps, the straightening step sequence and the straightening span and start-stop point coordinate matrix of each straightening step determined in claim 4, for each straightening step sequence, in a workpiece reference coordinate system { S }WSequentially obtaining the initial deflection of each straightening step sequence, and obtaining the straightening stroke and the section corner of each straightening step sequence:
Figure FDA0003502053510000031
wherein, delta0Representing the initial deflection corresponding to the midpoint position of each straightening step, namely the position with the maximum initial deflection in the straightening step; deltasRepresenting the initial deflection delta from each straightening step0Corresponding straightening stroke, theta for each straightening stepThe rotating angle delta of the linear guide rail around the supporting point at the position of the supporting point after straighteningsAnd the calculation process of theta and the factors of the section shape, the size, the material, the initial deflection and the like of the guide rail of the wire to be straightened.
6. The method for multipoint discrete precision straightening planning of a curved linear guide rail according to claim 1, characterized in that in the step 5), the straightening reference plane { P } isreRepresents a vertical plane connected by span support points; according to the straightening step sequence, sequentially referencing the workpiece to a coordinate system { S }WDiscrete expression of plane flexible line of linear guide rail under (S) is converted into a workpiece straightening coordinate system (S)S-based on the straightening stroke and the cross-section turning angle of each straightening step as determined in claim 5, in a local coordinate system of the straightening ram { S }TApplying a straightening stroke under the control of a straightening stroke control device, and aligning the workpiece in a workpiece straightening coordinate system (S)SObtaining the expression of the plane deflection line of the linear guide rail after each straightening step;
the rail deflection line comprises three sections: the straightening part is distributed on the left side of the span supporting point, the non-straightening part is distributed on the right side of the span supporting point, and the part to be straightened is arranged between the span supporting points. Aiming at the ith straightening step, two conditions are required to be met when the straightening is finished: starting point of straightening step and workpiece straightening coordinate system { S }SThe original points are coincided, namely the guide rail is positioned in a workpiece straightening coordinate system (S) after the i-1 th straightening stepSThe deflection line under } translates in the span direction; the starting point and the ending point of the straightening step are connected along the span direction, and the guide rail bending line is positioned on a straightening reference plane { P }reWithin (S), i.e. the guide rail deflection line is wound around the workpiece straightening coordinate system (S)SRotation angle of origin alphai；
The translation transformation may be represented as:
Figure FDA0003502053510000032
wherein, Ti FRepresenting a translation transformation matrix;
guide rail deflection wire-wound workpiece straightening coordinate system { SSRotational variation of the originCan be expressed as:
Figure FDA0003502053510000041
wherein the content of the first and second substances,
Figure FDA0003502053510000042
representing a rotation transformation matrix, alphaiCan be obtained by the following formula:
Figure FDA0003502053510000043
wherein the content of the first and second substances,
Figure FDA0003502053510000044
and
Figure FDA0003502053510000045
respectively representing the end point of the ith straightening step in the straightening coordinate system of the workpiece { SSHorizontal and vertical coordinate values below;
after the straightening is finished in the ith straightening step, the straightening part is changed into a straight line, the straightened part distributed on the left side of the span supporting point and the unbent part on the right side of the supporting point respectively rotate around the similar supporting point, and the rotation angle theta is formediThe rotating direction is opposite for the corresponding section corner of each straightening step;
to this end, the discrete expression of the guide rail deflection line after the completion of the ith straightening step can be expressed as:
Figure FDA0003502053510000046
wherein the content of the first and second substances,
Figure FDA0003502053510000047
and
Figure FDA0003502053510000048
representing the rotational transformation matrices of the straightened portion to the left of the span support point and the unbent portion to the right of the support point, respectively. In particular, the 1 st straightening step is not distributed on the straightened portion on the left side of the span support point, and the nth straightening step is not distributed on the unbent portion on the right side of the span support point.
7. The method for planning multipoint discrete precision straightening of a curved linear guide rail according to claim 1, characterized in that in the step 5), the workpiece straightening coordinate system { S ] after the multipoint discrete straightening is finished is adoptedSReversely converting the linear guide rail plane flexible line expression under the condition to a workpiece reference coordinate system (S)WEstablishing a control point set of guide rail flexible linenPijCalculating the linear precision of the plane bending linear guide rail (i is 1,2, K, n);
workpiece straightening coordinate system SSThe control points formed on the deflection line of the middle guide rail are in the reference coordinate system of the workpiece { S }WLower can be denoted as-nPij}：
Figure FDA0003502053510000051
Wherein N represents the number of straightening steps, i (i is more than or equal to 1 and less than or equal to N, and i belongs to N*) Represents the straightening step sequence, j (j is 1,2) represents the starting point and the end point of the straightening step,
Figure FDA0003502053510000052
rotation transformation matrix, T, representing the origin of the guide rail deflection line around the workpiece straightening coordinate systemi FRepresenting a translation transformation matrix of the guide rail deflection line along the span direction,
Figure FDA0003502053510000053
representing a rotation transformation matrix of the straightened part distributed on the left side of the span supporting point around the similar supporting point;
the linear precision of the plane bending linear guide rail is calculated by adopting a minimum area method and the straightness of the guide railControl point collection for straightening linearity in multiple stepsnPijOn the basis of 1,2, K, n, the minimum tolerance band is obtained by two mutually parallel straight lines. Two mutually parallel straight lines can be represented as:
Figure FDA0003502053510000054
wherein, a, b1And b2Is a parallel line related parameter obtained by the coordinates of a control point on a guide rail deflection line.
Thus, the objective function for rail straightness assessing the minimum tolerance band can be expressed as:
Figure FDA0003502053510000055
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Application publication date: 20220527