CN111992909A - Three-dimensional laser drilling positioning method - Google Patents
Three-dimensional laser drilling positioning method Download PDFInfo
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- CN111992909A CN111992909A CN202011007259.0A CN202011007259A CN111992909A CN 111992909 A CN111992909 A CN 111992909A CN 202011007259 A CN202011007259 A CN 202011007259A CN 111992909 A CN111992909 A CN 111992909A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23K—SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- B23K26/00—Working by laser beam, e.g. welding, cutting or boring
- B23K26/36—Removing material
- B23K26/38—Removing material by boring or cutting
- B23K26/382—Removing material by boring or cutting by boring
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23K—SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- B23K26/00—Working by laser beam, e.g. welding, cutting or boring
- B23K26/08—Devices involving relative movement between laser beam and workpiece
- B23K26/083—Devices involving movement of the workpiece in at least one axial direction
- B23K26/0853—Devices involving movement of the workpiece in at least in two axial directions, e.g. in a plane
- B23K26/0861—Devices involving movement of the workpiece in at least in two axial directions, e.g. in a plane in at least in three axial directions
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23K—SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- B23K26/00—Working by laser beam, e.g. welding, cutting or boring
- B23K26/70—Auxiliary operations or equipment
- B23K26/702—Auxiliary equipment
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Abstract
The invention discloses a three-dimensional laser drilling positioning method, which comprises the following steps: initializing a three-dimensional five-axis motion platform, fixing a workpiece on the three-dimensional five-axis motion platform, and fixing a laser head above the three-dimensional five-axis motion platform; performing posture correction on the workpiece through a three-dimensional five-axis motion platform to enable a normal vector of a workpiece reference surface to be parallel to a Z axis of the three-dimensional five-axis motion platform; adjusting the distance from the workpiece reference surface to the laser head to be a preset value through a three-dimensional five-axis motion platform; searching mark points on the reference surface, and adjusting the posture of the workpiece through a three-dimensional five-axis motion platform to enable laser emitted by a laser head to fall on the center of a hole area to be processed of the workpiece; and sequentially extracting coordinate values of the hole to be machined in the workpiece coordinate system, and solving five-axis values (X, Y, Z, A and C) of the three-dimensional five-axis motion platform when the hole plane is vertical to the laser and the laser focus falls on the hole plane through coordinate transformation to complete the positioning of the hole to be machined.
Description
Technical Field
The invention belongs to the technical field of three-dimensional processing, and particularly relates to a three-dimensional laser drilling positioning method.
Background
The laser drilling machine is a simple and versatile form of three-dimensional machine, with two-dimensional motion in the horizontal plane, indicated at X, Y, with two coordinate axes perpendicular to each other and a third Z-axis perpendicular to the X-Y plane. Each dimension can drive the ball screw to run on the linear ball guide rail through the stepping motor, and the precision of the ball screw is determined by the precision of the screw and the precision of the ball guide rail. If a microprocessor system is matched, the three-dimensional machine tool can complete laser processing of various holes in a plane and a group of holes in a certain range. When a series of holes are to be machined in a tube or barrel of material, the machine tool should have a five dimensional function, the added two dimensions being, in addition to the three dimensions mentioned above, a 360 degree rotation of the X-Y plane, which we define as the a axis, and a 0-90 degree tilt of the X-Y plane in the Z direction, which we define as the C axis. The five-dimensional workbench can be used for various types of laser drilling processing.
The development of three-dimensional laser technology widens the application field of laser technology. At present, three-dimensional laser cutting and welding are widely applied to the industries of aerospace, automobile manufacturing and the like, compared with three-dimensional technologies in other industries, laser processing has special positioning requirements, and not only is the laser required to move on a workpiece according to a track, but also a processing point on the track is required to be perpendicular to the laser and be in a focus.
The existing three-dimensional laser drilling system generally has the problem that the positioning accuracy is low, and the positioning accuracy directly influences the laser processing effect, so that a three-dimensional laser drilling positioning method with high positioning accuracy needs to be provided urgently.
Disclosure of Invention
The invention aims to provide a three-dimensional laser drilling positioning method aiming at the problems in the prior art
In order to achieve the purpose, the invention adopts the technical scheme that:
a three-dimensional laser drilling positioning method comprises the following steps:
initializing a three-dimensional five-axis motion platform, fixing a workpiece on the three-dimensional five-axis motion platform, and fixing a laser head above the three-dimensional five-axis motion platform;
performing posture correction on the workpiece through a three-dimensional five-axis motion platform to enable a normal vector of a workpiece reference surface to be parallel to a Z axis of the three-dimensional five-axis motion platform;
adjusting the distance from the workpiece reference surface to the laser head to be a preset value through a three-dimensional five-axis motion platform;
searching mark points on the reference surface, and adjusting the posture of the workpiece through a three-dimensional five-axis motion platform to enable laser emitted by a laser head to fall on the center of a hole area to be processed of the workpiece to complete position alignment;
sequentially extracting coordinate values of holes to be machined in a workpiece coordinate system, solving five-axis values (X, Y, Z, A and C) of a three-dimensional five-axis motion platform when a hole plane is vertical to laser and a laser focus falls on the hole plane through coordinate transformation, and finishing the positioning of the holes to be machined;
the three-dimensional five-axis motion platform comprises three translation axes, namely an X axis, a Y axis and a Z axis, and two rotation axes, namely an A axis and a C axis, wherein the X axis, the Y axis and the Z axis are orthogonal in pairs; the A axis rotates around the X axis, and the C axis rotates around the Z axis.
Specifically, the method for performing posture correction on the workpiece comprises the following steps:
the coordinate A (X) of three non-collinear points on the reference surface of the workpiece on a three-dimensional five-axis motion platform is obtained through a vision and position sensorA，YA，ZA)、B(XB，YB，ZB)、C(XC，YC，ZC) By finding two vectors at three points
And
further, the normal vector of the plane of the reference plane is obtained
The calculation formula is as follows:
determining a normal vector
a＝(YA-YB)(ZC-ZB)-(YC-YB)(ZA-ZB)
b＝(ZA-ZB)(XC-XB)-(ZC-ZB)(XA-XB)
c＝(XA-XB)(YC-YB)-(XC-XB)(YA-YB)
Let normal vector
Included angle alpha and normal vector with Z axis
The included angle beta with the Y axis is as follows:
α＝acos(c/len)
β＝a tan(a/b)
and rotating the C-axis angle beta and the A-axis angle alpha through the three-dimensional five-axis motion platform, namely enabling the normal vector of the reference plane to be parallel to the Z axis.
Specifically, before performing the coordinate transformation, the following coordinate systems are first established:
a mechanical coordinate system, namely a coordinate system of a three-dimensional five-axis platform;
translating the original point of the mechanical coordinate system to the intersection point O of the A axis and the C axis, and clockwise rotating the translated mechanical coordinate system by 90 degrees around the Z axis to obtain a No. 0 coordinate system;
the No. 1 coordinate system has an original point of an intersection O of the A axis and the C axis, and a Z axis is superposed with the rotating axis of the A axis;
a No. 2 coordinate system, wherein the original point is an intersection O of the axis A and the axis C, and the axis Z is superposed with the rotation axis of the axis C;
the coordinate systems of No. 0, No. 1 and No. 2 are established according to the establishment mode of the kinematic linkage coordinate system of the mechanical arm;
the workpiece coordinate system, the origin O of the workpiece coordinate system is the central point of a region to be processed on the workpiece, the Z axis of the workpiece coordinate system is vertical to the workpiece reference plane, the X axis is vertical to the Y axis, and the XOY plane is parallel to the reference plane;
the fixture coordinate system, the origin of the fixture coordinate system is positioned at the intersection point of the A axis and the C axis, and the Z axis of the fixture coordinate system is superposed with the Z axis of the workpiece coordinate system;
and the origin of the laser coordinate system is the focal point of the laser, and the X axis, the Y axis and the Z axis of the laser coordinate system are respectively parallel to the X axis, the Y axis and the Z axis of the No. 0 coordinate system.
Further, the coordinate transformation method comprises the following steps:
according to the position relation among the coordinate system No. 0, the coordinate system No. 1 and the coordinate system No. 2, obtaining a conversion matrix as follows:
wherein the content of the first and second substances,
a transformation matrix representing coordinate system No. 1 relative to coordinate system No. 0;
a transformation matrix representing the coordinate system No. 2 relative to the coordinate system No. 1;
a transformation matrix representing coordinate system No. 2 relative to coordinate system No. 0; theta 1 is the rotation angle of the A shaft; theta 2 is the rotation angle of the C axis;
according to the position relation between the fixture coordinate system and the coordinate system No. 2, the following steps are carried out: the origin of the fixture coordinate system has a translation (dx, dy, dz) relative to the origin of the coordinate system No. 2, and the translation is a fixed value; then
Wherein the content of the first and second substances,
a transformation matrix representing the fixture coordinate system relative to coordinate system No. 0;
a transformation matrix representing the fixture coordinate system relative to coordinate system No. 2;
according to the coordinate value (X) of the laser focus in the mechanical coordinate systemlaser，Ylaser，Zlaser) The real-time coordinate of the three-dimensional five-axis is (X, Y, Z, A, C) for fixed value, then
Wherein the content of the first and second substances,
a transformation matrix representing the coordinate system 0 relative to the laser coordinate system;
according to the position relation between the laser coordinate system and the workpiece coordinate system, the Z axis of the laser coordinate system is coincident with the Z axis of the workpiece coordinate system, and the origin of the laser coordinate system and the origin of the workpiece coordinate system are inThe distance in the Z direction is r, and the included angle between the X/Y axis of the laser coordinate system and the X/Y axis of the workpiece coordinate system is thetad(ii) a Then
Wherein the content of the first and second substances,
the state 0 represents the state after the position alignment is finished, at the moment, the Z axis of the workpiece coordinate system is coincident with the Z axis of the laser coordinate system, and the distance between the origin of the workpiece coordinate system and the origin of the laser coordinate system in the Z direction is r;
a transformation matrix representing the fixture coordinate system relative to the workpiece coordinate system; c thetadRepresents cos θd；sθdDenotes sin θd。
Further, when the plane of the hole to be processed is perpendicular to the laser and the focus of the laser falls on the plane of the hole, the rotation angles theta 1 and theta 2 of the axis A and the axis C of the three-dimensional five-axis motion platform are calculated according to a coordinate transformation method; the method comprises the following steps:
according to a matrix transformation formula
Obtaining a transformation matrix of the workpiece coordinate system relative to the No. 0 coordinate system;
taking the coordinates of the hole to be processed in the workpiece coordinate system as4P(XHOLE，YHOLE，ZHOLE) Calculating the coordinate of the hole to be processed in the fixture coordinate system as
θ 1, θ 2 are calculated according to the following equations:
A3＝a cos(Z3/len)
C3＝a cos(X/Y)
where, a3 ═ θ 1, and C3 ═ θ 2.
Further, the method for calculating the X, Y and Z values of the three-dimensional five-axis motion platform when the plane of the hole to be processed is perpendicular to the laser and the laser focus falls on the plane of the hole comprises the following steps:
according to the values of theta 1 and theta 2, firstly calculating
Then according to
Calculate out
According to
Wherein the content of the first and second substances,0the coordinate of P is (Y)laser-Y，-Xlaser+X，Zlaser-Z)；
The X, Y, Z value is calculated according to the following formula:
Ylaser-Y＝r00*XHOLE+r01*YHOLE+r02*ZHOLE+r03
-Xlaser+X＝r10*XHOLE+r11*YHOLE+r12*ZHOLE+r13
Zlaser-Z＝r20*XHOLE+r21*YHOLE+r22*ZHOLE+r23
and combining the rotation angles of the axis A and the axis C to obtain five-axis values (X, Y, Z, A and C) of the three-dimensional five-axis motion platform when the hole plane is vertical to the laser and the laser focus falls on the hole plane, and finishing the positioning of the hole to be processed.
Compared with the prior art, the invention has the beneficial effects that: according to the invention, a workpiece to be processed is arranged on the three-dimensional five-axis motion platform, the laser processing head is fixed above the workpiece, the laser head is fixed in the process of positioning the workpiece, and the coordinate of the laser focus in a mechanical coordinate system is fixed, so that the coordinate conversion in the positioning process is facilitated; according to the invention, the coordinates of the hole to be processed on the workpiece coordinate system are converted into values of each axis of the three-dimensional five-axis motion platform through coordinate conversion, so that the positioning precision is in the same order of magnitude as the axis orthogonality of the three-dimensional five-axis motion platform, and the positioning precision in the workpiece processing process is improved.
Drawings
FIG. 1 is a block diagram illustrating a three-dimensional laser drilling positioning method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an embodiment of the present invention for determining a normal vector of a workpiece reference plane;
FIG. 3 is a schematic diagram of the position relationship of 7 coordinate systems in the embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a gesture correction for a workpiece according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating a relationship between a workpiece coordinate system and a laser coordinate system according to an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the present embodiment provides a three-dimensional laser drilling positioning method by taking machining of an oil outlet of an oil nozzle as an example, and the method includes the following steps:
initializing a three-dimensional five-axis motion platform, fixing a workpiece on the three-dimensional five-axis motion platform, and fixing a laser head above the three-dimensional five-axis motion platform;
performing posture correction on the workpiece through a three-dimensional five-axis motion platform to enable a normal vector of a workpiece reference surface to be parallel to a Z axis of the three-dimensional five-axis motion platform;
adjusting the distance from the top datum plane of the oil nozzle to the laser head to be a preset value (the preset value is the distance from the laser head to a laser focus) through a three-dimensional five-axis motion platform;
a mark point on a reference surface is searched, the posture of a workpiece is adjusted through a three-dimensional five-axis motion platform, so that laser emitted by a laser head falls on the center of a hole area to be processed of the workpiece (namely the top of a spherical surface of the center of the reference surface at the top of an oil nozzle), and position alignment is completed;
sequentially extracting coordinate values of holes to be machined in a workpiece coordinate system, solving five-axis values (X, Y, Z, A and C) of a three-dimensional five-axis motion platform when a hole plane is vertical to laser and a laser focus falls on the hole plane through coordinate transformation, and finishing the positioning of the holes to be machined;
the three-dimensional five-axis motion platform comprises three translation axes, namely an X axis, a Y axis and a Z axis, and two rotation axes, namely an A axis and a C axis, wherein the X axis, the Y axis and the Z axis are orthogonal in pairs; the A axis rotates around the X axis, and the C axis rotates around the Z axis.
Specifically, the method for performing posture correction on the workpiece comprises the following steps:
as shown in fig. 2, coordinates a (X) of three non-collinear points on the reference plane of the top of the fuel injector on the three-dimensional five-axis motion platform are obtained by the vision and position sensorA，YA，ZA)、B(XB，YB，ZB)、C(XC，YC，ZC) By finding two vectors at three points
And
further, the normal vector of the plane of the reference plane is obtained
The calculation formula is as follows:
determining a normal vector
a＝(YA-YB)(ZC-ZB)-(YC-YB)(ZA-ZB)
b＝(ZA-ZB)(XC-XB)-(ZC-ZB)(XA-XB)
c＝(XA-XB)(YC-YB)-(XC-XB)(YA-YB)
Let normal vectors as shown in FIG. 4
Included angle alpha and normal vector with Z axis
The included angle beta with the Y axis is as follows:
α＝acos(c/len)
β＝a tan(a/b)
and rotating the C-axis angle beta and the A-axis angle alpha through the three-dimensional five-axis motion platform, namely enabling the normal vector of the reference plane to be parallel to the Z axis.
Specifically, as shown in fig. 3, before performing coordinate transformation, the following 7 coordinate systems are first established:
mechanical coordinate system (X)w，Yw，Zw) Namely a coordinate system of the three-dimensional five-axis platform;
coordinate system No. 0 (X)0，Y0，Z0) Translating the original point of the mechanical coordinate system to the intersection point O of the A axis and the C axis, and clockwise rotating the translated mechanical coordinate system by 90 degrees around the Z axis to obtain a No. 0 coordinate system;
coordinate system No. 1 (X)1，Y1，Z1) The original point is the intersection point O of the A axis and the C axis, and the Z axis is superposed with the rotating axis of the A axis;
coordinate system No. 2 (X)2，Y2，Z2) The original point is the intersection point O of the axis A and the axis C, and the axis Z is superposed with the rotation axis of the axis C;
the coordinate systems of No. 0, No. 1 and No. 2 are established according to the establishment mode of the kinematic linkage coordinate system of the mechanical arm;
workpiece coordinate system (X)4，Y4，Z4) The origin O of the workpiece coordinate system is the central point of a region to be processed on the workpiece, the Z axis of the origin O is vertical to the workpiece datum plane, the X axis is vertical to the Y axis, and the XOY plane is parallel to the datum plane;
fixture coordinate system (X)3，Y3，Z3) The origin of the fixture coordinate system is positioned at the intersection point of the A axis and the C axis, and the Z axis of the fixture coordinate system is superposed with the Z axis of the workpiece coordinate system;
laser coordinate system (X)5，Y5，Z5) The origin of the laser coordinate system is the focal point of the laser, and the X axis, the Y axis and the Z axis of the laser coordinate system are respectively parallel to the X axis, the Y axis and the Z axis of the No. 0 coordinate system.
Further, the coordinate transformation method comprises the following steps:
according to the position relation among the No. 0 coordinate system, the No. 1 coordinate system and the No. 2 coordinate system, a D-H parameter table is listed as follows:
| i | ai-1 | ai-1 | di | θi |
| 1 | -90 | 0 | 0 | θ1 |
| 2 | 90 | 0 | 0 | θ2 |
obtaining a conversion matrix according to the D-H parameter table as follows:
wherein the content of the first and second substances,
a transformation matrix representing coordinate system No. 1 relative to coordinate system No. 0;
a transformation matrix representing the coordinate system No. 2 relative to the coordinate system No. 1;
a transformation matrix representing coordinate system No. 2 relative to coordinate system No. 0; theta 1 is the rotation angle of the A shaft; theta 2 is the rotation angle of the C axis;
according to the position relation between the fixture coordinate system and the coordinate system No. 2, the following steps are carried out: the origin of the fixture coordinate system has a translation (dx, dy, dz) relative to the origin of the coordinate system No. 2, and the translation is a fixed value; then
Wherein the content of the first and second substances,
a transformation matrix representing the fixture coordinate system relative to coordinate system No. 0;
a transformation matrix representing the fixture coordinate system relative to coordinate system No. 2;
according to the coordinate value (X) of the laser focus in the mechanical coordinate systemlaser，Ylaser，Zlaser) The real-time coordinate of the three-dimensional five-axis is (X, Y, Z, A, C) for fixed value, then
Wherein the content of the first and second substances,
a transformation matrix representing the coordinate system 0 relative to the laser coordinate system;
according to the position relation between the laser coordinate system and the workpiece coordinate system, the Z axis of the laser coordinate system is coincident with the Z axis of the workpiece coordinate system, the distance between the origin of the laser coordinate system and the origin of the workpiece coordinate system in the Z direction is the radius r of the sphere center (namely the sphere center of the central spherical surface of the reference surface of the oil nozzle), and the included angle between the X/Y axis of the laser coordinate system and the X/Y axis of the workpiece coordinate system is thetad(ii) a Then
Wherein the content of the first and second substances,
the state 0 represents the state after the position alignment is finished, at the moment, the Z axis of the workpiece coordinate system is coincident with the Z axis of the laser coordinate system, and the distance between the origin of the workpiece coordinate system and the origin of the laser coordinate system in the Z direction is r;
a transformation matrix representing the fixture coordinate system relative to the workpiece coordinate system; c thetadRepresents cos θd；sθdDenotes sin θd。
Further, when the plane of the hole to be processed is perpendicular to the laser and the focus of the laser falls on the plane of the hole, the rotation angles theta 1 and theta 2 of the axis A and the axis C of the three-dimensional five-axis motion platform are calculated according to a coordinate transformation method; the method comprises the following steps:
according to a matrix transformation formula
Obtaining a transformation matrix of the workpiece coordinate system relative to the No. 0 coordinate system;
taking the coordinates of the hole to be processed in the workpiece coordinate system as4P(XHOLE，YHOLE，ZHOLE) Calculating the coordinate of the hole to be processed in the fixture coordinate system as
θ 1, θ 2 are calculated according to the following equations:
A3＝a cos(Z3/len)
C3＝a cos(X/Y)
where, a3 ═ θ 1, and C3 ═ θ 2.
Further, the method for calculating the X, Y and Z values of the three-dimensional five-axis motion platform when the plane of the hole to be processed is perpendicular to the laser and the laser focus falls on the plane of the hole comprises the following steps:
according to the values of theta 1 and theta 2, firstly calculating
Then according to
Calculate out
According to
Wherein the content of the first and second substances,0the coordinate of P is (Y)laser-Y，-Xlaser+X，Zlaser-Z)；
The X, Y, Z value is calculated according to the following formula:
Ylaser-Y＝r00*XHOLE+r01*YHOLE+r02*ZHOLE+r03
-Xlaser+X＝r10*XHOLE+r11*YHOLE+r12*ZHOLE+r13
Zlaser-Z＝r20*XHOLE+r21*YHOLE+r22*ZHOLE+r23
and combining the rotation angles of the axis A and the axis C to obtain five-axis values (X, Y, Z, A and C) of the three-dimensional five-axis motion platform when the hole plane is vertical to the laser and the laser focus falls on the hole plane, and finishing the positioning of the hole to be processed.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (6)
1. A three-dimensional laser drilling positioning method is characterized by comprising the following steps:
initializing a three-dimensional five-axis motion platform, fixing a workpiece on the three-dimensional five-axis motion platform, and fixing a laser head above the three-dimensional five-axis motion platform;
performing posture correction on the workpiece through a three-dimensional five-axis motion platform to enable a normal vector of a workpiece reference surface to be parallel to a Z axis of the three-dimensional five-axis motion platform;
adjusting the distance from the workpiece reference surface to the laser head to be a preset value through a three-dimensional five-axis motion platform;
searching mark points on the reference surface, and adjusting the posture of the workpiece through a three-dimensional five-axis motion platform to enable laser emitted by a laser head to fall on the center of a hole area to be processed of the workpiece to complete position alignment;
sequentially extracting coordinate values of holes to be machined in a workpiece coordinate system, solving five-axis values (X, Y, Z, A and C) of a three-dimensional five-axis motion platform when a hole plane is vertical to laser and a laser focus falls on the hole plane through coordinate transformation, and finishing the positioning of the holes to be machined;
the three-dimensional five-axis motion platform comprises three translation axes, namely an X axis, a Y axis and a Z axis, and two rotation axes, namely an A axis and a C axis, wherein the X axis, the Y axis and the Z axis are orthogonal in pairs; the A axis rotates around the X axis, and the C axis rotates around the Z axis.
2. The three-dimensional laser drilling positioning method of claim 1, wherein the workpiece is subjected to posture correction by:
the coordinate A (X) of three non-collinear points on the reference surface of the workpiece on a three-dimensional five-axis motion platform is obtained through a vision and position sensorA，YA，ZA)、B(XB，YB，ZB)、C(XC，YC，ZC) By finding two vectors at three points
And
further, the normal vector of the plane of the reference plane is obtained
The calculation formula is as follows:
determining a normal vector
a＝(YA-YB)(ZC-ZB)-(YC-YB)(ZA-ZB)
b＝(ZA-ZB)(XC-XB)-(ZC-ZB)(XA-XB)
c＝(XA-XB)(YC-YB)-(XC-XB)(YA-YB)
Let normal vector
Included angle alpha and normal vector with Z axis
The included angle beta with the Y axis is as follows:
α＝acos(c/len)
β＝atan(a/b)
and rotating the C-axis angle beta and the A-axis angle alpha through the three-dimensional five-axis motion platform, namely enabling the normal vector of the reference plane to be parallel to the Z axis.
3. The three-dimensional laser drilling positioning method of claim 1, wherein before the coordinate transformation, the following coordinate systems are established:
a mechanical coordinate system, namely a coordinate system of a three-dimensional five-axis platform;
translating the original point of the mechanical coordinate system to the intersection point 0 of the A axis and the C axis, and clockwise rotating the translated mechanical coordinate system by 90 degrees around the Z axis to obtain a No. 0 coordinate system;
the No. 1 coordinate system has an original point of 0 at the intersection of the axis A and the axis C, and the axis Z is superposed with the rotation axis of the axis A;
a No. 2 coordinate system, wherein the original point is the intersection point 0 of the A axis and the C axis, and the Z axis is superposed with the rotating axis of the C axis;
the workpiece coordinate system, the origin O of the workpiece coordinate system is the central point of a region to be processed on the workpiece, the Z axis of the workpiece coordinate system is vertical to the workpiece reference plane, the X axis is vertical to the Y axis, and the XOY plane is parallel to the reference plane;
the fixture coordinate system, the origin of the fixture coordinate system is positioned at the intersection point of the A axis and the C axis, and the Z axis of the fixture coordinate system is superposed with the Z axis of the workpiece coordinate system;
and the origin of the laser coordinate system is the focal point of the laser, and the X axis, the Y axis and the Z axis of the laser coordinate system are respectively parallel to the X axis, the Y axis and the Z axis of the No. 0 coordinate system.
4. The three-dimensional laser drilling positioning method according to claim 3, wherein the coordinate transformation method comprises:
according to the position relation among the coordinate system No. 0, the coordinate system No. 1 and the coordinate system No. 2, obtaining a conversion matrix as follows:
wherein the content of the first and second substances,
representing the transformation of coordinate system No. 1 to coordinate system No. 0A matrix;
a transformation matrix representing the coordinate system No. 2 relative to the coordinate system No. 1;
a transformation matrix representing coordinate system No. 2 relative to coordinate system No. 0; theta 1 is the rotation angle of the A shaft; theta 2 is the rotation angle of the C axis;
according to the position relation between the fixture coordinate system and the coordinate system No. 2, the following steps are carried out: the origin of the fixture coordinate system has a translation (dx, dy, dz) relative to the origin of the coordinate system No. 2, and the translation is a fixed value; then
Wherein the content of the first and second substances,
a transformation matrix representing the fixture coordinate system relative to coordinate system No. 0;
a transformation matrix representing the fixture coordinate system relative to coordinate system No. 2;
according to the coordinate value (X) of the laser focus in the mechanical coordinate systemlaser，Ylaser，Zlaser) The real-time coordinate of the three-dimensional five-axis is (X, Y, Z, A, C) for fixed value, then
Wherein the content of the first and second substances,
a transformation matrix representing the coordinate system 0 relative to the laser coordinate system;
according to the laser coordinate systemThe position relation with the workpiece coordinate system can be known, the Z axis of the laser coordinate system is coincident with the Z axis of the workpiece coordinate system, the distance between the origin of the laser coordinate system and the origin of the workpiece coordinate system in the Z direction is r, and the included angle between the X/Y axis of the laser coordinate system and the X/Y axis of the workpiece coordinate system is thetad(ii) a Then
Wherein the content of the first and second substances,
the state 0 represents the state after the position alignment is finished, at the moment, the Z axis of the workpiece coordinate system is coincident with the Z axis of the laser coordinate system, and the distance between the origin of the workpiece coordinate system and the origin of the laser coordinate system in the Z direction is r;
a transformation matrix representing the fixture coordinate system relative to the workpiece coordinate system; c thetadRepresents cos θd；sθdDenotes sin θd。
5. The three-dimensional laser drilling positioning method according to claim 4, wherein angles θ 1 and θ 2 of rotation of the A axis and the C axis of the three-dimensional five-axis motion platform when the plane of the hole to be machined is perpendicular to the laser and the focus of the laser falls on the plane of the hole are calculated according to a coordinate transformation method; the method comprises the following steps:
according to a matrix transformation formula
Obtaining a transformation matrix of the workpiece coordinate system relative to the No. 0 coordinate system;
taking the coordinates of the hole to be processed in the workpiece coordinate system as4P(XHOLE，YHOLE，ZHOLE) Calculating the coordinate of the hole to be processed in the fixture coordinate system as
θ 1, θ 2 are calculated according to the following equations:
A3＝acos(Z3/len)
C3＝acos(X/Y)
where, a3 ═ θ 1, and C3 ═ θ 2.
6. The three-dimensional laser drilling positioning method of claim 5, wherein the method for calculating the X, Y and Z values of the three-dimensional five-axis motion platform when the plane of the hole to be machined is perpendicular to the laser and the focus of the laser falls on the plane of the hole comprises the following steps:
according to the values of theta 1 and theta 2, firstly calculating
Then according to
Calculate out
According to
Wherein the content of the first and second substances,0the coordinate of P is (Y)laser-Y，-Xlaser+X，Zlaser-Z)；
The X, Y, Z value is calculated according to the following formula:
Ylaser-Y＝r00*XHOLE+r01*YHOLE+r02*ZHOLE+r03-Xlaser+X＝r10*XHOLE+r11*YHOLE+r12*ZHOLE+r13Zlaser-Z＝r20*XHOLE+r21*YHOLE+r22*ZHOLE+r23
and combining the rotation angles of the axis A and the axis C to obtain five-axis values (X, Y, Z, A and C) of the three-dimensional five-axis motion platform when the hole plane is vertical to the laser and the laser focus falls on the hole plane, and finishing the positioning of the hole to be processed.
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