CN115755770A - Distance error-based double-rotation axis position-independent geometric error identification method - Google Patents
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Abstract
The invention discloses a distance error-based double-rotating-shaft position-independent geometric error identification method, which comprises the following steps of: based on dual quaternions, unified representation of rotation and translation motion of the machine tool is realized, and a coordinate system model of the machine tool cutter relative to a workpiece is established; measuring distance error between target balls through coordinated movement of two rotating shafts, wherein a shaft B performs 0-90-degree rotating motion during measurement, a shaft C performs 0-360-degree rotating motion to completely cover the moving stroke of a rotating shaft of a machine tool, and the same laser tracker is used for measuring the coordinates of the target balls at the cutter end and the coordinates of the target balls at the workpiece end; and (3) considering the geometric error definition irrelevant to the position, representing the geometric error based on dual quaternion, establishing a dual-rotation-axis geometric error model, and decoupling the machine tool error based on a Levenberg-Marquardt algorithm. The method provided by the invention can completely cover the movement strokes of the two rotating shafts, and is favorable for realizing the comprehensive measurement of geometric errors; the coordinate system does not need to be transformed in the identification process, so that the precision loss caused by the transformation of the coordinate system of the measuring point is avoided.
Description
Technical Field
The invention relates to the technical field of machine tool error measurement, in particular to a distance error-based method for identifying a position-independent geometric error of double rotating shafts.
Technical Field
With the development of modern manufacturing industry, the position of the five-axis machine tool in the manufacturing industry of automobiles, medical equipment and molds becomes more and more important due to the fact that the five-axis machine tool has greater flexibility and processing efficiency. Due to the complexity of its structure and operating conditions, the five-axis machine tool machining process is subject to various errors, with geometric errors being one of the largest sources of error. If the identification of geometric errors is lacked, the machining precision is greatly influenced.
Numerous measurement instruments are used to identify geometric errors. The laser tracker has the advantages of high measuring speed and wide range, and can perform three-dimensional measurement in a working space. Compared with other instruments, the laser tracker is not limited by a fixed distance, can measure geometric errors more comprehensively, but the existing method is difficult to realize error identification of the full stroke of the double-rotating-shaft.
Disclosure of Invention
The invention aims to provide a method for identifying a position-independent geometric error of a double-rotating shaft based on a distance error, which can identify the position-independent geometric error of the double-rotating shaft based on the measured distance error. The invention is beneficial to realizing the error identification of the full stroke of the double-rotating-shaft.
The method for identifying the position-independent geometric errors of the double rotating shafts based on the distance errors comprises the following steps:
step 1, realizing unified representation of rotation and translation motion of a machine tool based on dual quaternions, and constructing a coordinate system model of the machine tool cutter relative to a workpiece:
wherein
And with
Which represent the position of the tool and the workpiece, respectively, in the ideal case with respect to the machine coordinate system.
A dual quaternion form representing the ith axis,
to represent
Conjugation of (2):
step 2, measuring distance errors between the target balls through coordinated movement of the two rotating shafts, wherein the two target balls are needed in the measuring process, and the X axis, the Y axis and the Z axis are kept still in the measuring process; the same laser tracker is used for measuring the coordinates of the target ball at the cutter end and the coordinates of the target ball at the workpiece end, and the distance value between the two target balls is calculated according to the measurement result, which comprises the following steps:
and 2.1, measuring distance errors between the target balls through the coordinated movement of the two rotating shafts, keeping the X, Y and Z shafts still in the measuring process, and establishing the origin of a machine tool coordinate system at the intersection point of the axes of the two rotating shafts. The measuring process needs two target balls, and the length L of the target ball at the cutter end t The design parameters of the tool setting gauge and the machine tool are determined, the target ball at the end of the workpiece is adjusted to a known position through the pan-tilt and the probe of the machine tool, and the position of the target ball at the end of the workpiece is t relative to the position of a C-axis coordinate system w 。
And 2.2, performing 0-90-degree rotary motion on the axis B during measurement, and performing 0-360-degree rotary motion on the axis C to completely cover the motion stroke of the rotating shaft of the machine tool. The same laser tracker is used to measure the coordinates (x) of the target ball at the end of the tool bi ，y bi ，z bi ) And the coordinates (x) of the target sphere at the end of the workpiece ci ，y ci ，z ci ). In order to avoid the light interruption and the continuous connection in the measuring process, the same machine tool code is repeatedly operated twice in the measuring process, the tracker is operated each time to track and measure one target ball in real time, and the distance value L between the two target balls is calculated according to the measuring result BC ：
The geometric error model of the rotation axis is defined in the machine coordinate system, but the distance value does not change in either the machine coordinate system or the measurement coordinate system of the laser tracker, and is therefore based on the distance value L BC And identifying the geometric error of the machine tool. Distance value L BC The difference from the ideal distance value is the distance error.
Step 3, considering the geometric error definition irrelevant to the position, representing the geometric error based on dual quaternion, and establishing a dual-rotation-axis geometric error model, wherein an upper mark e represents the error influence:
wherein
And
respectively representing the positions of the tool and the workpiece relative to the machine coordinate system under the influence of the geometric errors,
and
a dual quaternion form representing the ISO-defined C-axis 4 geometric error,
and
a dual quaternion form representing the ISO defined B-axis 4 geometric error.
Based on the error model, obtaining the position relation of the tool relative to the workpiece coordinate system under the influence of geometric errors:
wherein dual quaternion
Indicating the position of the tool relative to the coordinate system of the workpiece under the influence of geometrical errors,
i.e. coordinate values of the tool relative to the coordinate system of the workpiece, based on which L is established BC And
error identification function of (1):
the optimization function is solved based on a Levenberg-Marquardt algorithm, machine tool error decoupling is achieved, geometric errors of eight items of double rotating shafts and irrelevant positions are obtained, and the value of f (x) is the residual error between the calculated value and the measured value of the error model. So far all parameters in the error model are known.
The invention relates to a distance error-based method for identifying a position-independent geometric error of double rotating shafts, which has the following specific beneficial effects:
the method provided by the invention can completely cover the movement strokes of the two rotating shafts, and is favorable for realizing the comprehensive measurement of geometric errors; the coordinate system does not need to be transformed in the identification process, so that the precision loss caused by the transformation of the coordinate system of the measuring point is avoided.
Drawings
FIG. 1 is a diagram of a five-axis machine tool.
Fig. 2 is a schematic diagram of dual-axis rotation measurement.
FIG. 3 is a schematic diagram of the distance between two target balls in the embodiment of the method of the present invention.
FIG. 4 is a graph of distance and residual data in an embodiment of the method of the present invention.
FIG. 5 is a schematic view of a rotation axis error.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
FIG. 1 is a schematic diagram of a five-axis machine tool, which is taken as an example to illustrate the method of the present invention.
Step 1, realizing unified representation of rotation and translation motion of a machine tool based on dual quaternions, and constructing a model of a machine tool cutter relative to a workpiece coordinate system:
wherein
And
which represent the position of the tool and the workpiece, respectively, in the ideal case, relative to the machine coordinate system.
A dual quaternion form representing the ith axis,
to represent
Conjugation of (a):
step 2, measuring distance errors between target balls through coordinated movement of two rotating shafts, wherein two target balls are needed in the measuring process, and X, Y and Z axes are kept still in the measuring process; the same laser tracker is used for measuring the coordinates of the target ball at the cutter end and the coordinates of the target ball at the workpiece end, and the distance value between the two target balls is calculated according to the measurement result, which comprises the following steps:
step 2.1, coordinating and transporting through two rotating shaftsAnd (3) measuring distance errors dynamically, wherein the measuring process is as shown in figure 2, X, Y and Z axes are kept still, and the origin of a machine tool coordinate system is established at the intersection point of the axes of the two rotating shafts. The measuring process needs two target balls, and the length L of the target ball at the cutter end t Determined by the design parameters of the tool setting gauge and the machine tool, the target ball at the workpiece end is adjusted to a known position through the pan-tilt-percentage and the probe of the machine tool, and the position of the target ball at the workpiece end is t relative to the position of a C-axis coordinate system w . In this example L t Is 400mm, t w Is (400, 0).
And 2.2, during measurement, the B axis performs 0-90-degree rotary motion, the C axis performs 0-360-degree rotary motion, the motion stroke of the rotating shaft of the machine tool is completely covered, and ideally, the distance between the two target balls is shown in figure 3. The same laser tracker is used to measure the coordinates (x) of the target sphere at the tool end bi ，y bi ，z bi ) And the coordinates (x) of the target sphere at the end of the workpiece ci ，y ci ，z ci ). In order to avoid the light interruption and the continuous connection in the measuring process, the same machine tool code is repeatedly operated twice in the measuring process, the tracker is operated each time to track and measure one target ball in real time, and the actual distance value L of the two target balls is calculated according to the measuring result BC ：
The geometric error model of the rotation axis is defined in the machine tool coordinate system, but the distance value does not change no matter in the machine tool coordinate system or in the measurement coordinate system of the laser tracker, so that the distance value L is based on BC Identifying geometrical errors of machine tool, distance value L BC The difference from the ideal distance value, which is the distance error, is shown in fig. 4.
Step 3, geometric error definition irrelevant to the position is considered, the geometric error definition is shown in figure 5, geometric errors are represented based on dual quaternions, and a dual-rotation-axis geometric error model is established:
wherein
And
respectively representing the positions of the tool and the workpiece relative to the machine coordinate system under the influence of the geometric errors,
and
denotes ISO definition C axis E X0C 、E Y0C 、E A0C And E B0C A dual quaternion form of the 4-term geometric error,
and
denotes ISO definition B axis E X0B 、E Z0B 、E A0B And E C0B Dual quaternion form of 4 term geometric error.
Based on the error model, obtaining the position relation of the tool relative to the workpiece coordinate system under the influence of the geometric error:
wherein dual quaternion
Indicating the position of the tool relative to the coordinate system of the workpiece under the influence of geometrical errors,
i.e. the coordinates of the tool relative to the coordinate system of the workpieceThe value:
wherein theta is c And theta b Respectively representing the rotation angles of the C-axis and the B-axis, on the basis of which L is established BC And
error identification function of (1):
the optimization function is solved based on a Levenberg-Marquardt algorithm, machine tool error decoupling is achieved, geometric errors of eight items of double rotating shafts and irrelevant positions are obtained, the value of f (x) is the residual error between the calculated value and the measured value of the error model, and the residual error value is shown in figure 4. So far all parameters in the error model are known.
The invention finally obtains 8 items of geometric errors irrelevant to the position of the double rotating shafts of the machine tool. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention, as any modifications, equivalent substitutions, improvements and the like, which are within the spirit and principle of the invention, are intended to be covered by the scope of the invention.
Claims (2)
1. A method for identifying a position-independent geometric error of double rotating shafts based on a distance error is characterized by comprising the following steps: based on dual quaternions, unified representation of rotation and translation motion of the machine tool is realized, and a coordinate system model of the machine tool cutter relative to a workpiece is established; measuring distance errors between the target balls through coordinated movement of the two rotating shafts, wherein the two target balls are needed in the measuring process, and calculating distance values of the two target balls according to the measuring result; a dual-rotation axis geometric error model is established based on dual quaternion, and error decoupling is carried out based on a Levenberg-Marquardt algorithm, and the method comprises the following steps:
step 1, realizing unified representation of rotation and translation motion of a machine tool based on dual quaternions, and constructing a coordinate system model of the machine tool cutter relative to a workpiece:
wherein
And
respectively representing the positions of the tool and the workpiece relative to the machine coordinate system under the ideal condition;
a dual quaternion form representing the ith axis,
to represent
Conjugation of (2):
step 2, measuring distance errors between target balls through coordinated movement of two rotating shafts, wherein two target balls are needed in the measuring process, and X, Y and Z axes are kept still in the measuring process; the same laser tracker is used for measuring the coordinates of the target balls at the cutter end and the coordinates of the target balls at the workpiece end, and the distance value between the two target balls is calculated according to the measurement result;
step 3, considering the geometric error definition irrelevant to the position, representing the geometric error based on dual quaternion, and establishing a dual-rotation-axis geometric error model:
wherein
And with
Respectively representing the positions of the tool and the workpiece relative to the machine coordinate system under the influence of the geometric errors,
and with
Is C axis E X0C 、E Y0C 、E A0C And E B0C A dual quaternion form of the 4-term geometric error,
and
is B axis E X0B 、E Z0B 、E A0B And E C0B Dual quaternion form of 4 geometric errors;
based on the error model, obtaining the position relation of the tool relative to the workpiece coordinate system under the influence of geometric errors:
wherein dual quaternion
Indicating the position of the tool relative to the coordinate system of the workpiece under the influence of geometrical errors,
and
i.e. coordinate values of the tool in the X, Y, Z directions relative to the workpiece coordinate system, based on which L is established BC And
error identification function of (2):
the optimization function is solved based on a Levenberg-Marquardt algorithm, machine tool error decoupling is achieved, and geometric errors of the double-rotation-axis 8 item independent of the position are obtained, wherein the value of f (x) is a residual error between an error model calculation value and a measured value.
2. The method for identifying the position-independent geometric errors of the double rotating shafts based on the distance errors as claimed in claim 1, wherein in the step 2, the distance errors between the target balls are measured through the coordinated movement of the two rotating shafts, two target balls are required in the measuring process, and the X, Y and Z axes are kept still in the measuring process; the same laser tracker is used for measuring the coordinates of the target ball at the cutter end and the coordinates of the target ball at the workpiece end, and the distance value between the two target balls is calculated according to the measurement result, which comprises the following steps:
step 2.1, measuring distance errors between target balls through coordinated movement of the two rotating shafts, keeping X, Y and Z axes still in the measuring process, and establishing an original point of a machine tool coordinate system at an intersection point of the axes of the two rotating shafts; the measuring process needs two target balls, and the length L of the target ball at the cutter end t Determined by the design parameters of the tool setting gauge and the machine tool, the target ball at the workpiece end is adjusted to a known position through the pan-tilt-percentage and the probe of the machine tool, and the position of the target ball at the workpiece end is t relative to the position of a C-axis coordinate system w ；
2.2, during measurement, the B shaft rotates by 0-90 degrees, and the C shaft rotates by 0-360 degrees, so that the motion stroke of the rotating shaft of the machine tool is completely covered; the same laser tracker is used to measure the coordinates (x) of the target sphere at the tool end bi ，y bi ，z bi ) And the coordinates (x) of the target ball at the end of the workpiece ci ，y ci ，z ci ) (ii) a In order to avoid the light interruption and the continuous connection in the measuring process, the same machine tool code is repeatedly operated twice in the measuring process, the tracker is operated each time to track and measure one target ball in real time, and the actual distance value L of the two target balls is calculated according to the measuring result BC ：
The geometric error model of the rotation axis is defined in the machine tool coordinate system, but the distance value does not change no matter in the machine tool coordinate system or in the measurement coordinate system of the laser tracker, so that the distance value L is based on BC Identifying geometrical errors of the machine, the distance value L BC The difference from the ideal distance value is the distance error.
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