CN112270079B - Three-dimensional free bending active bending die movement pose analysis method - Google Patents
Three-dimensional free bending active bending die movement pose analysis method Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D11/00—Bending not restricted to forms of material mentioned in only one of groups B21D5/00, B21D7/00, B21D9/00; Bending not provided for in groups B21D5/00 - B21D9/00; Twisting
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Abstract
The invention discloses a three-dimensional free bending active bending die movement pose analysis method, wherein in the bending forming process, the axis of a pipe of each forming section is rotated to be parallel to the z axis of a global coordinate system, the coordinates of characteristic points of the forming section under the global coordinate system are recalculated based on a rotation change matrix, the movement direction, the offset distance and the rotation angle of the bending die are judged according to the azimuth of the characteristic points in the x-y plane of the global coordinate system, and finally the bending die pose in the bending forming process is analyzed. The invention discloses a bending die movement pose analysis method matched with active three-dimensional free bending equipment, which fully plays the advantage that the active three-dimensional free bending equipment can realize one-time accurate forming of a bending piece with a complex space axis.
Description
Technical Field
The invention belongs to the technical field of advanced manufacturing of metal complex components, and particularly relates to a three-dimensional free bending active bending die movement pose analysis method.
Background
The bending piece with the space complex configuration is widely applied to the fields of aerospace, nuclear energy, new energy automobiles and the like, for example, a conduit part of a thermal pipeline system widely used by a spacecraft has complex two-dimensional plane and three-dimensional space axis and is used in a special environment for a long time. In the actual service process, the heat pipe with complex axial shape is required to be clung to the inner wall and the outer wall of the cabin, the working temperature is guaranteed through effective heat exchange, if the axial space shape of the component is inaccurate, the poor lamination of the heat control bending component and the cabin wall is easy to cause, and the heat exchange efficiency is reduced. The bending member manufactured by the prior art can not simultaneously meet the key technical indexes such as three-dimensional axis precision, section distortion rate, forming integrity and the like, and abrasion and axis dislocation can often occur due to factors such as strong vibration, corrosion or mechanical damage and the like in the actual service process, so that the pipeline medium conveying efficiency and the service life of a guide pipe are seriously influenced.
The three-dimensional free bending technology can realize high-precision flexible forming of pipes and profiles with complex space axes, and the three-dimensional free bending equipment with the active bending die has stronger forming capability and higher forming precision. The accuracy of the axis of the bending piece depends on whether the motion pose control and analysis of the active bending die are accurate or not to a great extent, however, a complete set of active bending die motion pose analysis method still lacks in the current three-dimensional free bending technology, traditional means such as continuous trial and error and correction and the like are still adopted in the process of forming the bending piece with a complex axis, the axis shape of the bending piece is difficult to be accurately formed at one time, and whether the formed piece can interfere with equipment or not is difficult to be judged in advance, so that the method is one of the problems to be solved in the three-dimensional free bending technology.
Disclosure of Invention
The invention provides a three-dimensional free bending active bending die movement pose analysis method aiming at the blank of the current three-dimensional free bending technology in the aspects of movement pose control and analysis of an active bending die.
The invention adopts the following technical scheme:
before bending, firstly extracting the axis of a pipe according to the configuration of a bending piece, and dividing and marking forming sections in sequence; establishing a global coordinate system of the pipe axis, and obtaining space coordinates of a straight line starting point, a straight line-arc tangent point and an arc ending point; constructing the space pose of the bending die based on a global coordinate system of the pipe axis; in the bending forming process, the axis of the pipe is rotated to be parallel to the z axis of the global coordinate system for each forming section, point coordinates are recalculated based on the transformation, the moving direction of the bending die is judged, the offset distance and the rotating angle are calculated, and the pose of the bending die in the bending forming process is analyzed.
The analysis method comprises the following steps:
extracting the pipe axis according to the spatial configuration of a target bending piece before bending and forming, dividing the pipe axis into forming sections according to geometric characteristics, marking each forming section as i, and marking according to the sequence: i= (1), (2), (3) … …; the dividing principle of the forming sections is to divide each straight-curved member comprising straight-line sections and arc sections into one forming section according to the configuration of the straight-curved member comprising the straight-line sections and the arc sections, and if all the straight-line sections and the arc sections are divided, a single straight-line section is left, and then the straight-line section is regarded as one forming section;
secondly, establishing a global coordinate system O of the pipe axis at the starting point position of the first section of the pipe axis 0 -xyz, sequentially extracting the spatial coordinates of a linear part starting point, a linear-arc tangent point and an arc part ending point of each forming section in sequence, wherein the arc ending point of each forming section coincides with the linear starting point of the next forming section;
thirdly, the axis of the current forming section i consists of a straight line part and an arc line part, and the current forming section i starts from the straight line part; calculating the position of the linear part at O according to the space coordinates of the starting point of the linear part and the point of tangency with the arc part 0 Direction vector in coordinate systemDirection vector +.>Respectively are provided withAround O 0 Rotation alpha of x-axis and y-axis of coordinate system i And beta i Obtaining a transformation matrix T i Through the transformation matrix T i Converting the space coordinates of the forming section i and the following forming sections so that the linear section direction of the converted forming section i is equal to O 0 The z-axis of the coordinate system is parallel;
fourthly, when analyzing the motion pose of the bending die, keeping the pose corresponding to the straight line part of the forming section i at the straight line starting point and the tangent point of the straight line and the arc line of the bending die unchanged; and for the arc part of the forming section i, the connecting line between the tangent point of the straight line and the arc part and the ending point of the arc part is at O 0 The projection direction of the x-y plane in the coordinate system is used for judging the offset direction and the rotation direction of the bending die;
fifthly, when calculating the offset distance of the bending die, the straight line part of the forming section i corresponds to the pose of the bending die and does not change, so the offset distance of the bending die is 0; for the arc part of the forming section i, the arc part is required to be changed according to the arc radius R i And U i -R i The relation obtains the offset distance U of the bending die corresponding to the arc line i Calculating the offset distance U of the bending die decomposition in the x and y directions by combining the offset direction of the bending die i-x And U i-y ；
Sixthly, when the rotation angle of the bending die is calculated, the linear part of the forming section i corresponds to the bending die and does not generate rotary motion, so the rotation angle is 0; for the arc part of the forming section i, the bending die offset distance U is determined according to the fifth step i And calculating the configuration size of the three-dimensional free bending equipment to obtain the bending die rotation angle.
In the second step of the analysis method, according to the established global coordinate system O of the pipe axis 0 -xyz, extracting the spatial coordinates of the line start point, the line-arc tangent point and the arc end point of each segment in turn according to the sequence of the shaped segment labels:
in the third step of the analysis method, the linear part of the current forming section i is positioned at O 0 Direction vector of coordinate systemBy giving the direction vector->Respectively around O 0 Rotation alpha of x-axis and y-axis of coordinate system i 、β i Obtaining a conversion matrix->By rotating the matrix T i Changing coordinates of the forming section i to enable the linear part of the forming section i after conversion to be in contact with O 0 The z-axes of the coordinate system being parallel and according to a rotation matrix T i Calculating to obtain the positions of the rest segments in O 0 And (5) down-converting the coordinate system.
In the fourth step of the analysis method, the bending die is analyzed in O 0 When the gesture moves in the x-y plane of the coordinate system, the bending die does not generate offset motion for the straight line part of the forming section i, and the advancing length of the pipe is as followsFor the arc part of the forming section i, the coordinate of the space position of the tangent point of the straight line and the arc part and the termination point of the arc part is shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: />Pipe advancing length during arc section forming>
In the fifth step of the analysis method, when the offset distance of the bending die is analyzed, the straight line part of the forming section i is not offset due to the bending die, and the offset distance is 0; for the arc part of the forming section i, U is established according to experiments i -R i Relationship U i ＝f(R i ) Determining a current arc radius R i Corresponding bending die offset distance U i And according to the bending die movement direction (m i-x ,m i-y ) The distance of the bending die respectively shifting in the x and y directions can be calculatedIn the sixth step, when the rotation angle of the bending die is analyzed, the linear part of the forming section i corresponds to the motion process that the bending die does not rotate, and the rotation angle is 0; for the arc portion of the forming section i, the bending die offset distance U determined according to the fifth step is required i Determining the rotation angle of a bending die according to the guiding distance A of the three-dimensional free bending forming equipment
According to the analysis method, the space position of the bending die is actively adjusted in real time according to the axial line configuration of the pipe, the bending die has four degrees of freedom in moving along the x/y axis and rotating around the y/x axis in the moving process, the movement in the x-y plane and the rotation around any axis in the x-y plane can be synthesized, and the requirements that the three-dimensional free bending active bending die can form a component with any bending direction and any bending angle in space and keep perpendicularity with the pipe axial line in real time in the forming process are met.
The analysis method is O when forming to the tangent point position of the straight line and the arc line of each section 0 The z-axis of the coordinate system is parallel to the tube feed direction, so that the subsequent arc portion of the forming section is at O 0 The projection directions in the x-y plane of the coordinate system are the offset direction and the rotation direction of the bending die.
According to the analysis method, the length of the arc line segment is calculated according to the space coordinates of the tangent point of the straight line and the arc line in the forming segment i and the space coordinates of the end point of the arc line and the tangential direction of the start point of the arc line, and the length of the straight line segment is combined, so that the pipe feeding length of the forming segment i can be determined.
The invention has the following beneficial effects:
1) The invention can realize one-time accurate forming of the plane and space bending member with straight-bending characteristics, solves the difficult problems of determining the movement direction, the offset distance and the rotation angle of the bending die according to the space complex axis configuration, and avoids the defects of multiple trial and error and the like caused by the traditional human judgment error.
2) According to the invention, the spatial coordinates of the pipe in the global coordinate system are updated in real time, and the pose change of the active bending die in the forming process is obtained through analysis, so that the method has important significance for controlling the motion trail and preventing interference of active free bending equipment.
3) The method is simple and feasible, is beneficial to improving the processing precision of active three-dimensional free bending equipment such as five-axis equipment, six-axis equipment and the like, and has important engineering application value and obvious economic benefit in the engineering fields such as aerospace, nuclear power, automobiles and the like.
Drawings
FIG. 1 is a flow chart of a three-dimensional free bending active bending mode motion pose solving method;
FIG. 2 is a three-dimensional free bending active bending mode motion pose coordinate system transformation schematic diagram;
FIG. 3, schematic view of a planar "straight-curved" feature curved tubular member;
FIG. 4, schematic view of a spatial "straight-curved" feature curved tubular member;
FIG. 5, schematic view of a spatial "straight-curved" feature curved tube;
Detailed Description
The present invention will be described in detail with reference to specific examples.
As shown in fig. 1, a flow chart of a three-dimensional free bending active bending mode motion pose resolving method mainly comprises the following steps:
firstly, extracting a pipe axis according to the spatial configuration of a target bending piece 1 before bending and forming, dividing the pipe axis into forming sections according to geometric characteristics (straight line section-arc line section) in sequence, marking each forming section as i (the forming section i consists of a straight line part and an arc line part), and marking according to sequence: i= (1), (2), (3) … …, as shown in (a) of fig. 2;
secondly, establishing a global coordinate system O of the pipe axis at the starting point position of the first section of the pipe axis 0 -xyz, extracting the spatial coordinates of the line start point, the line-arc tangent point and the arc end point of each segment in turn according to the forming segment label order (1), (2), (3) … …:the end point of each forming section arc line coincides with the start point of the next forming section straight line, as shown in (a) of fig. 2;
thirdly, obtaining the linear part of the current forming section i at O 0 Direction vector in coordinate systemBy giving the direction vector->Respectively around O 0 Rotation alpha of x-axis and y-axis of coordinate system i 、β i Obtaining a conversion matrix->(taking the order of rotation about the x-axis and y-axis as an example) the linear part direction vector of the shaped section i>Rotate to and O 0 The z-axes of the coordinate system being parallel and according to a rotation matrix T i Calculating to obtain the positions of the rest segments in O 0 -new coordinates in xyz coordinate system, as shown in fig. 2 (b);
fourth, judging the movement direction of the bending die: for the straight line part of the forming section i, the pose corresponding to the bending die at the straight line starting point and the tangent point of the straight line and the arc line is kept unchanged; for the arc part of the forming section i, the space position coordinates of the front and rear points of the arc part are shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die (3):as shown in fig. 2 (c);
fifth step, calculating the bending die at O 0 Offset distance in x-y plane of coordinate system, motion process of straight line part of forming section i corresponding to bending die pose is unchanged, offset distance is 0, and pipe advancing length isWhereas for the arc part of the forming section i, according to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R i Corresponding bending die offset distance U i In combination with the bending die offset direction (m i-x ,m i-y ) Calculating the bending die at O 0 Offset distance of coordinate system along x-axis and y-axis: />Pipe advancing length->As shown in fig. 2 (c);
step six, calculating the rotation angle of the bending die, wherein the bending die of the linear part of the forming section i does not rotate; for the arc portion of the forming section i, the bending die offset distance U determined according to the fifth step is required i Determining the rotation angle of a bending die according to the guiding distance A of the three-dimensional free bending forming equipmentAs shown in fig. 2 (c);
as shown in FIG. 2, the three-dimensional free bending active bending die motion pose coordinate system transformation is schematically shown, and according to the calculation results of the fifth step and the sixth step, the bending die generates a combined motion of translation and rotation during the arc part of the forming section i, namely the bending die generates a motion along U i Translation and winding of direction and U i Rotation of the axis in a direction perpendicular to the direction.
The invention will be described in detail below with reference to specific examples of "flat 'straight-curved' signature curved pipe elements", "space 'straight-curved' signature curved pipe elements".
Example 1
FIG. 3 is a plan bending member with "straight-bend" characteristics, and the three-dimensional free bending active bending die motion pose analysis method for forming the part is as follows:
1) Before bending, extracting the pipe axis according to the configuration of a target bending piece (1), dividing the pipe axis into 2 forming sections and 1 linear section in turn according to geometric characteristics (linear section-arc section), marking each forming section as i, and marking according to the sequence: i= (1), (2), (3);
2) Establishing a global coordinate system O of the pipe axis at the starting point position of the first section of the pipe axis 0 -xyz, extracting the spatial coordinates of the line start point, the line-arc tangent point and the arc end point of each segment in turn according to the sequence of the shaped segment labels: (0, 0), (0,0,40), (0,10.05,77.5), (0,17.55,90.49), (0,27.54,166.37), (0,22.36,185.69), the end point of each forming section arc coinciding with the straight line start point of the next forming section;
3) The straight part of the forming section (1) is at O 0 Direction vector in coordinate systemAnd U i -R i The z-axis of the coordinate system is forward parallel and rotates the matrix T 1 The unit matrix is adopted, the coordinates of control points of the forming section 1 and the following forming sections are not changed, the offset distance of a bending die is 0mm, the rotation angle is 0 DEG, and the advancing length of the pipe is d 1-1 =40 mm. For the arc part of the forming section (1), the space position coordinates according to the tangent point of the straight line and the arc end point are shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: (m) 1-x ,m 1-y ) = (0,10.05), according to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R 1 Corresponding bending die offset distance U 1 Calculating the bending die at O by combining the bending die offset direction (0,10.05) 0 Offset distance of coordinate system along x-axis and y-axis: (U) 1-x ,U 1-y )＝(0,U 1 ) Angle of rotation of bending diePipe advance length d 1-2 = 36.27mm. The bending die generates composite conversion of translation and rotation when forming the arc line of the section (1);
4) The straight part of the forming section (2) is at O 0 Direction vector in coordinate systemBy giving the direction vector->Around O 0 The x-axis and the y-axis of the coordinate system are rotated by alpha respectively 2 = -30 ° and β 2 =0° make it and O 0 The z-axis of the coordinate system is parallel, and the transformation matrix can be calculated and obtained>And carrying out coordinate transformation on control points of the forming section (2) and the following forming sections through a transformation matrix. For the straight part of the forming section (2), the offset distance of the bending die is 0mm, the rotation angle is 0 DEG, and the advancing length of the pipe is d 2-1 =15 mm. For the arc part of the forming section (2), the spatial position coordinates of the tangent point and the arc end point of the straight line-arc after updating are shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: (m) 2-x ,m 2-y ) = (0, -29.29), according to the established U i -R i Relationship U 2 ＝f(R 2 ) Determining the current arc segment R 2 Corresponding bending die offset distance U 2 Calculating the bending die at O by combining the bending die offset direction (0, -29.29) 2 Offset distance of coordinate system along x-axis and y-axis: (U) 2-x ，U 2-y )＝(0，U 2 ) Bending die rotation angle->Pipe advance length d 2-2 =78.54 mm. The bending die generates composite conversion of translation and rotation when forming the arc line of the section (2);
5) The straight part of the forming section (3) is at O 0 Direction vector in coordinate systemBy giving the direction vector->Around O 0 Rotation alpha of x-axis and y-axis of coordinate system 3 =45° and β 3 =0°, let it be equal to O 0 The z-axis of the coordinate system being forward parallel, i.eAnd according to the rotation matrix T 3 Calculating to obtain the positions of the rest segments in O 0 -xyz coordinate system, bending die offset distance 0mm, rotation angle 0 °, tube advance length d 3-1 ＝20mm。
Example 2
FIG. 4 is a schematic view of a spatial bending member with "straight-bend" feature, and a method for resolving the pose of motion of a three-dimensional free bending active bending die during the formation of the part, as follows
1) Before bending, extracting the pipe axis according to the configuration of a target bending piece, dividing the pipe axis into 3 forming sections according to geometric characteristics (straight line section-arc line section), marking each forming section as i, and marking according to the sequence: i= (1), (2), (3);
2) Establishing a global coordinate system O of the pipe axis at the starting point position of the first section of the pipe axis 0 -xyz, extracting the spatial coordinates of the line start point, the line-arc tangent point and the arc end point of each segment in turn according to the sequence of the shaped segment labels: (0, 0), (0, 5), (0,10.74,21.44), (0,13.48,22.64), (-12.66,13.49,22.64), (-12.66,10.74,21.44), (-12.66, -2.43,26.56), each forming section arc end point coinciding with the next forming section straight line start point;
3) The straight part of the forming section (1) is at O 0 Direction vector in coordinate systemWith O 0 The z-axis of the coordinate system is forward parallel,rotation matrix T 1 The unit matrix is adopted, the coordinates of control points of the forming section 1 and the following forming sections are not changed, the offset distance of a bending die is 0mm, the rotation angle is 0 DEG, and the advancing length of the pipe is d 1-1 =5 mm. For the arc part of the forming section (1), the space position coordinates according to the tangent point of the straight line and the arc end point are shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: (m) 1-x ,m 1-y ) = (0,10.74), according to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R i Corresponding bending die offset distance U i Calculating the bending die at O by combining the bending die offset direction (0,10.74) 0 Offset distance of coordinate system along x-axis and y-axis: (U) 1-x ,U 1-y )＝(0,U 1 ) Angle of rotation of bending diePipe advance length d 1-2 =20.77 mm. The bending die generates composite conversion of translation and rotation when forming the arc line of the section (1);
4) The straight part of the forming section (2) is at O 0 Direction vector in coordinate systemBy giving the direction vector->Around O 0 Rotation alpha of x-axis and y-axis of coordinate system 2 = -66.32 ° and β 2 =0°, let it be equal to O 0 The z-axis of the coordinate system is forward parallel, and a rotation matrix can be obtained>And according to the rotation matrix T 2 Calculating to obtain the positions of the rest segments in O 0 -xyz coordinate system, bending die offset distance 0mm, rotation angle 0 °, tube advance length d 2-1 =3mm. For the arc part of the forming section (2), the space position of the tangent point of the straight line and the arc end point is based onPut the coordinates at O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: (m) 2-x ,m 2-y ) = (-12.66,0), according to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R 2 Corresponding bending die offset distance U 2 Calculating the bending die at O by combining the bending die offset direction (-12.66,0) 0 Offset distance of coordinate system along x-axis and y-axis: (U) 2-x ,U 2-y )＝(U 2 0), bending die rotation anglePipe advance length d 2-2 =19.88 mm. The curve of the bending die in the forming section (2) is a compound transformation which can generate translation and rotation;
6) The straight part of the forming section (3) is at O 0 Direction vector in coordinate systemBy vector the directionAround O 0 Rotation alpha of x-axis and y-axis of coordinate system 3 =180° and β 3 =0° make it and O 0 The z-axis of the coordinate system being forward parallel, i.eAnd according to the rotation matrix T 3 Calculating to obtain the positions of the rest segments in O 0 -xyz coordinate system, bending die offset distance 0mm, rotation angle 0 °, tube advance length d 3-1 =3mm. For the arc part of the forming section (3), the space position coordinates according to the tangent point of the straight line and the arc end point are shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: (m) 3-x ,m 3-y ) = (0, -10), according to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R 3 Corresponding bending die offset distance U 3 Combined with bending die deflectionCalculating the bending die at O according to the moving direction (0, -10) 0 Offset distance of coordinate system along x-axis and y-axis: (U) 3-x ,U 3-y )＝(0,U 3 ) Bending die rotation angle->Pipe advance length d 3-2 =15.69 mm. The bending die generates a composite transformation of translation and rotation when the forming section (2) arcs.
Example 3
FIG. 5 is a schematic view of a spatial bending member with "straight-bend" feature, and a method for resolving the pose of motion of a three-dimensional free bending active bending die during the formation of the part, as follows
1) Before bending, extracting the pipe axis according to the configuration of the target bending piece 1, dividing the pipe axis into 3 forming sections according to geometric characteristics (straight line section-arc line section), marking each forming section as i, and marking according to the sequence: i= (1), (2), (3);
2) Establishing a global coordinate system O of the pipe axis at the starting point position of the first section of the pipe axis 0 -xyz, extracting the spatial coordinates of the line start point, the line-arc tangent point and the arc end point of each segment in turn according to the sequence of the shaped segment labels: (0, 0), (0,0,25), (0,10,42.32), (0,18.66,47.32), (21.32,44.27,37.61), (30.40,42.36,25.90), (30.40,42.36, -3.20), the end point of each forming section arc coinciding with the straight start point of the next forming section;
3) The straight part of the forming section (1) is at O 0 Direction vector in coordinate systemWith O 0 The z-axis of the coordinate system is forward parallel and rotates the matrix T 1 The unit matrix is adopted, the coordinates of control points of the forming section 1 and the following forming sections are not changed, the offset distance of a bending die is 0mm, the rotation angle is 0 DEG, and the advancing length of the pipe is d 1-1 =5 mm. For the arc part of the forming section (1), the space position coordinates according to the tangent point of the straight line and the arc end point are shown as O 0 Determining motion of bending die based on projection direction of x-y plane in coordinate systemThe direction is: (m) 1-x ,m 1-y ) = (0, 10), according to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R 1 Corresponding bending die offset distance U 1 Calculating the bending die at O by combining the bending die offset directions (0, 10) 0 Offset distance of coordinate system along x-axis and y-axis: (U) 1-x ,U 1-y )＝(0,U 1 ) Bending die rotation angle->Pipe advance length d 1-2 =20.94 mm. The bending die generates composite conversion of translation and rotation when forming the arc line of the section (1);
4) The straight part of the forming section (2) is at O 0 Direction vector in coordinate systemBy giving the direction vector->Around O 0 Rotation alpha of x-axis and y-axis of coordinate system 2 = -60 ° and β 2 =0°, let it be equal to O 0 The z-axis of the coordinate system is forward parallel to obtain a rotation matrix +.>And according to the rotation matrix T 2 Calculating to obtain the positions of the rest segments in O 0 -xyz coordinate system, bending die offset distance 0mm, rotation angle 0 °, tube advance length d 2-1 =10mm. For the arc part of the forming section (2), the space position coordinates according to the tangent point of the straight line and the arc end point are shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: />According to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R 2 Corresponding bending die offset distance U 2 In combination with bending die offset direction->Calculating the bending die at O 0 Offset distance of coordinate system along x-axis and y-axis: />Bending die rotation angle>Pipe advance length d 2-2 =41.89 mm. The bending die generates composite conversion of translation and rotation when forming the arc line of the section (2);
6) The straight part of the forming section (3) is at O 0 Direction vector in coordinate systemBy giving the direction vector->First winding O 0 X-axis rotation alpha of coordinate system 3-1 = 50.77 ° and then rotated about the x-axis by α 3-2 = 129.23 ° bringing it into contact with O 0 The z-axis forward direction of the coordinate system, obtaining a rotation matrix +.>And according to the rotation matrix T 3 Calculating to obtain the positions of the rest segments in O 0 -xyz coordinate system, bending die offset distance 0mm, rotation angle 0 °, tube advance length d 3-1 =15 mm. For the arc part of the forming section (3), the space position coordinates according to the tangent point of the straight line and the arc end point are shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: (m) 3-x ,m 3-y ) = (0,18.2), according to the established U i -R i Relationship U i ＝f(R i ) Determining the current arc segment R 3 Corresponding bending die offset distance U 3 Calculating the bending die position by combining the bending die deflection direction (0,18.2)O 0 Offset distance of coordinate system along x-axis and y-axis: (U) 3-x ,U 3-y )＝(0,U 3 ) Bending die rotation angle->Pipe advance length d 3-2 =31.44 mm. The bending die generates a composite transformation of translation and rotation when the forming section (3) arcs.
It will be understood that modifications and variations will be apparent to those skilled in the art from the foregoing description, and it is intended that all such modifications and variations be included within the scope of the following claims.
Claims (8)
1. A three-dimensional free bending active bending die motion pose analysis method is characterized by comprising the following steps of: in the bending forming process, the axis of the pipe of each forming section is rotated to be parallel to the z axis of the global coordinate system, the coordinates of the characteristic points of the forming section under the global coordinate system are recalculated based on the rotation change matrix, the movement direction, the offset distance and the rotation angle of the bending die are judged according to the directions of the characteristic points in the x-y plane of the global coordinate system, and finally the position of the bending die in the bending forming process is analyzed; the method comprises the following steps:
extracting the pipe axis according to the spatial configuration of a target bending piece before bending and forming, dividing the pipe axis into forming sections according to geometric characteristics, marking each forming section as i, and marking according to the sequence: i= (1), (2), (3) … …; the division principle of the forming section is as follows: dividing each straight-curved member including straight-line segment-arc segment into a forming segment according to the configuration of the straight-curved member including straight-line segment-arc segment, and if all straight-line segment-arc segments are divided, leaving a single straight-line segment, then the straight-line segment is also regarded as a forming segment;
secondly, establishing a global coordinate system O of the pipe axis at the starting point position of the first section of the pipe axis 0 -xyz, sequentially extracting the spatial coordinates of the start point of the linear part, the tangent point of the linear-arc line and the end point of the arc line part of each forming section, wherein the end point of the arc line of each forming section is in heavy contact with the start point of the linear of the next forming sectionCombining;
thirdly, the axis of the current forming section i consists of a straight line part and an arc line part, and the current forming section i starts from the straight line part; calculating the position of the linear part at O according to the space coordinates of the starting point of the linear part and the point of tangency with the arc part 0 Direction vector in coordinate systemDirection vector +.>Respectively around O 0 Rotation alpha of x-axis and y-axis of coordinate system i And beta i Obtaining a rotation change matrix T i By rotating the change matrix T i Converting the space coordinates of the forming section i and the following forming sections so that the linear section direction of the converted forming section i is equal to O 0 The z-axis of the coordinate system is parallel;
fourthly, when analyzing the motion pose of the bending die, keeping the pose corresponding to the straight line part of the forming section i at the straight line starting point and the tangent point of the straight line and the arc line of the bending die unchanged; and for the arc part of the forming section i, the connecting line between the tangent point of the straight line and the arc part and the ending point of the arc part is at O 0 The projection direction of the x-y plane in the coordinate system is used for judging the offset direction and the rotation direction of the bending die;
fifthly, when calculating the offset distance of the bending die, the straight line part of the forming section i corresponds to the pose of the bending die and does not change, so the offset distance of the bending die is 0; for the arc part of the forming section i, the arc part is required to be changed according to the arc radius R i And U i -R i The relation obtains the offset distance U of the bending die corresponding to the arc line i Calculating the offset distance U of the bending die decomposition in the x and y directions by combining the offset direction of the bending die i-x And U i-y ；
Sixthly, when the rotation angle of the bending die is calculated, the linear part of the forming section i corresponds to the bending die and does not generate rotary motion, so the rotation angle is 0; for the arc part of the forming section i, the bending die offset distance U is determined according to the fifth step i And calculating the configuration size of the three-dimensional free bending equipment to obtain the bending die rotation angle.
2. The method for analyzing the motion pose of the three-dimensional free bending active bending die according to claim 1, which is characterized in that: in the second step, according to the established global coordinate system O of the pipe axis 0 -xyz, extracting the spatial coordinates of the line start point, the line-arc tangent point and the arc end point of each segment in turn according to the sequence of the shaped segment labels:
3. the method for analyzing the motion pose of the three-dimensional free bending active bending die according to claim 2, which is characterized in that: in the third step, the straight line part of the current forming section i is at O 0 Direction vector of coordinate systemBy giving the direction vector->Respectively around O 0 Rotation alpha of x-axis and y-axis of coordinate system i 、β i Obtaining a conversion matrix->By rotating the change matrix T i Changing coordinates of the forming section i to enable the linear part of the forming section i after conversion to be in contact with O 0 The z-axes of the coordinate system being parallel and according to a rotation matrix T i Calculating to obtain the positions of the rest segments in O 0 And (5) down-converting the coordinate system.
4. The three-dimensional free-bending active bending die motion of claim 2The pose analysis method is characterized in that: in the fourth step, the bending die is analyzed at O 0 When the gesture moves in the x-y plane of the coordinate system, the bending die does not generate offset motion for the straight line part of the forming section i, and the advancing length of the pipe is as followsFor the arc part of the forming section i, the coordinate of the space position of the tangent point of the straight line and the arc part and the termination point of the arc part is shown as O 0 The projection direction of the x-y plane in the coordinate system is used for judging the movement direction of the bending die: />Pipe advancing length during arc section forming>
5. The method for analyzing the motion pose of the three-dimensional free bending active bending die according to claim 2, which is characterized in that: in the fifth step, when the offset distance of the bending die is analyzed, the linear part of the forming section i is not offset due to the bending die, and the offset distance is 0; for the arc part of the forming section i, U is established according to experiments i -R i Relationship U i ＝f(R i ) Determining a current arc radius R i Corresponding bending die offset distance U i And according to the bending die movement direction (m i-x ,m i-y ) Calculating the offset distance of the bending die in the x and y directionsIn the sixth step, when the rotation angle of the bending die is analyzed, the linear part of the forming section i corresponds to the motion process that the bending die does not rotate, and the rotation angle is 0; for the arc portion of the forming section i, the bending die offset distance U determined according to the fifth step is required i And the guiding distance A of the three-dimensional free bending forming equipment to determine the bending die rotation angle +.>
6. The method for analyzing the motion pose of the three-dimensional free bending active bending die according to claim 1, which is characterized in that: the space pose of the bending die is actively adjusted in real time according to the axial configuration of the pipe, the bending die has four degrees of freedom which move along the x/y axis and rotate around the y/x axis in the moving process, and the four degrees of freedom are synthesized into the movement in the x-y plane and the rotation around any axis in the x-y plane, so that the requirements that the three-dimensional free bending active bending die can form components with any space bending direction and any bending angle and keep perpendicularity with the pipe axial line in real time in the forming process are met.
7. The method for analyzing the motion pose of the three-dimensional free bending active bending die according to claim 1, which is characterized in that: o when forming to the position of the tangent point of the straight line and the arc line of each section 0 The z-axis of the coordinate system is parallel to the tube feed direction, so that the subsequent arc portion of the forming section is at O 0 The projection directions in the x-y plane of the coordinate system are the offset direction and the rotation direction of the bending die.
8. The method for analyzing the motion pose of the three-dimensional free bending active bending die according to claim 1, which is characterized in that: according to the space coordinates of the tangent point of the straight line and the arc line in the forming section i and the space coordinates of the end point of the arc line, the tangential direction of the start point of the arc line, the length of the arc line section is calculated by combining the radius of the arc line, and the pipe feeding length of the forming section i is determined by combining the length of the straight line section.
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| CN113042838B (en) * | 2021-03-29 | 2022-07-29 | 贵阳航发精密铸造有限公司 | Method for determining machining angle of interference air film hole |
| CN113351704B (en) * | 2021-04-21 | 2022-09-16 | 南京航空航天大学 | Pipe bending robot track control and forming processing method |
| CN113059039A (en) * | 2021-05-19 | 2021-07-02 | 南京航空航天大学 | Method for avoiding interference by realizing three-dimensional free bending forming through bending die deflection |
| CN114570807B (en) * | 2022-01-25 | 2023-04-07 | 南京航空航天大学 | Six-axis bending device and method based on mandrel rotation |
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