CN113427320A - Multi-axis on-machine measurement planning method for reducing measurement uncertainty - Google Patents
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Abstract
The invention relates to a multi-axis on-machine measurement planning method for reducing measurement uncertainty, which converts a feasible probe axial set in a space into a rotation axis angle feasible graph and a contact point feasible graph on a ruby ball, and converts a space probe attitude optimization problem into a planning problem of a two-dimensional plane point set; establishing a relation between a touch point on the ruby ball and a machine tool rotating shaft, and providing optimization methods of different machine tool main shaft structures; the probe axial planning is carried out with the purposes of reducing the introduction of machine tool rotating shaft positioning errors and improving the pre-stroke error compensation precision in the detection, the uncertainty of on-machine measurement detection errors can be reduced, and the consistency and credibility of the measurement results are improved.
Description
Technical Field
The invention belongs to the technical field of precision measurement, and particularly relates to a multi-axis on-line measurement planning method for reducing measurement uncertainty.
Background
The on-machine measurement is a process method which takes a numerical control machine tool as a carrier and a measuring head as measuring equipment, measures the shape and position sizes of a workpiece clamped in the machine tool on line and feeds back the cutting quality in time. As a key technology of self-adaptive machining, secondary positioning and offline clamping can be avoided in on-machine measurement, the detection result can guide adjustment of a subsequent machining scheme, and the method has a wide application prospect in precision measurement. However, due to the influence of factors such as poor operating environment of the machine tool, cutting vibration, clamping of the measuring head and the workpiece, and the like, errors introduced in the measuring process by taking the machine tool, the measuring head and the workpiece as carriers can cause low precision and poor consistency of on-machine measurement results.
In modern measurement theory, according to the requirement of geometric error detection, uncertainty of a measurement result needs to be given while the measurement result is obtained. The magnitude of the measurement uncertainty determines the trustworthiness of the measurement. And the uncertainty of the on-machine measurement detection result is reduced, and the measurement process needs to be optimized. Among a plurality of error sources, the positioning error of a rotating shaft of a machine tool is a key factor influencing the working performance of the machine tool, and many scholars study the identification and compensation of the positioning error of the machine tool, but the influence caused by the positioning error of the rotating shaft is not considered in measurement, and the thinking of reducing the introduction of the positioning error and the uncertainty of measurement by using the axial direction of a probe is lacked. Furthermore, the pre-stroke error is another critical error factor in the on-machine measurement. The common pre-stroke error compensation method is to calibrate a series of position points on a standard ball to obtain corresponding pre-stroke amount, construct a clover error graph, and compensate the measurement result by the pre-stroke amount obtained by interpolation. The method has long time consumption and low compensation precision. Meanwhile, when the number of touch points on the ruby ball is large, the calculation process is complicated, and the compensation result is uncertain.
Disclosure of Invention
Technical problem to be solved
In order to reduce the uncertainty of the on-line measurement detection result and improve the consistency of the measurement result, the invention provides a multi-axis on-line measurement planning method for reducing the measurement uncertainty. Through converting the feasible probe axial direction in the space into a rotating shaft angle point set and a contact point set on the ruby ball, the probe axial direction is planned in a two-dimensional plane point set, and the number of contact points on the ruby ball and the number of times of change of the rotating shaft direction in the measuring process can be reduced.
Technical scheme
A multi-axis on-machine measurement planning method for reducing measurement uncertainty is characterized by comprising the following steps:
step 1: calculating feasible probe axial directions at measuring points
Establishing a local coordinate system O at the measurement pointsD-XDYDZDSetting a unit ball based on the local coordinate system, and constructing an inscribed polyhedron in the unit ball; according to a subdivision criterion, point sets which are uniformly distributed on a unit spherical surface in a discrete mode are used as initial probe axial directions, interference inspection is carried out by adopting a bounding box method, and a feasible probe axial direction set is obtained;
step 2: calculating a set of rotation axis angle points and a set of touch points on the ruby ball
1) Establishing a corresponding relation between the axial direction and the rotation angle of the probe based on a machine tool kinematics chain, and converting a feasible probe axial set after interference inspection into a rotation angle point set of a BC axis to form a rotation axis angle feasible diagram;
2) the positions of the measuring points on the ruby ball of the measuring head, which touch the measuring points, are all different when the probes are in the downward axial direction, and the method for calculating the positions of the feasible touch points on the ruby ball by the axial direction of the probes comprises the following steps: for a given probe axial unit vector (n)x,ny,nz) And the workpiece can rotate around the X axis of the workpiece coordinate system by an angle omega and rotate around the Z axis by an angle upsilon:
cos(υ)＝nz (2)
the transformation matrix M formed by the above rotation angles is:
in the formula (x)r，yr，zr) The coordinates of the center of the ruby sphere corresponding to the probe touching the measuring point;
the probe coordinate system O is obtained by the formula (4)P-XPYPZPLower red treasureSet m of corresponding touch point positions on stone balliThe coordinates are
mi＝M-1·Pi(i＝1,2,3...n) (4)
Wherein, PiThe coordinate of a theoretical measuring point under a workpiece coordinate system, and n is the number of the measuring points;
obtaining the parameterized representation theta of the touch point on the ruby ball under the ball coordinate system through the formula (5)i、
Forming a feasible diagram of touch points on the ruby ball, and selecting the same touch point on the ruby ball to measure when the feasible diagrams of touch points on the ruby ball corresponding to the plurality of measuring points are intersected;
in the formula, r is the radius of the ruby ball;
and step 3: establishing the relation between the touch point on the ruby ball and the rotating shaft of the machine tool
Selecting a point in the intersection of feasible graphs of touch points on the ruby ball corresponding to the multiple measuring points
Under the premise of ensuring that the position of the touch point is unchanged, the probe can rotate for a circle around the external normal vector of the measuring point, and an infinite number of probe axial directions can be generated, and are calculated by the formula (6):
wherein, κiThe angle of rotation of the probe about the outer normal vector, ((ii))xni，yni，zni) Probes produced for rotation of the probe about the external normal vectorAxial direction, N being a local coordinate system OD-XDYDZDTo the workpiece coordinate system OW-XWYWZWThe expression of the transformation matrix of (1) is represented by formula (7);
wherein (i)W,jW,kW) Is the three axial vector components of the workpiece coordinate system, (i)D,jD,kD) Representing the three axial vector components of the local coordinate system under the workpiece coordinate;
when the machine tool has a main shaft orientation function, the axial direction of the probe generated by the probe rotating around the outer normal vector at the measuring point is converted into a curve segment in a feasible diagram of the rotating shaft angle; when the machine tool has no main shaft orientation function, the probe rotates around the external normal vector at the measuring point by an angle kiIn the rotation axis angle feasible map is a fixed value.
Preferably: local coordinate system O described in step 1D-XDYDZDThe Z axis of the coordinate system coincides with the normal vector at the measuring point, the Y axis coincides with the V-direction tangent vector, and the X axis coincides with the U-direction tangent vector.
Preferably: and 2, converting the feasible probe axial set after the interference inspection into a rotation angle point set of the BC shaft to form a rotation shaft angle feasible diagram:
wherein (n)x,ny,nz) The axial direction of the probe is shown, and the rotation angles are shown in (B, C).
A method for calculating uncertainty of a multi-axis on-machine measurement planning method is characterized by comprising the following steps:
because the uncertainty component of repeated measurement is much greater than the resolution of the measurement device, only the uncertainty of measurement error due to the repeated accuracy is considered; for m repeated measurements of a certain measurement point,by using
The mean value of multiple measurement results in the X, Y, Z direction is shown, and the standard uncertainty u of the measurement results in the X, Y, Z direction is calculated by combining the Bessel formulax、uy、uz；
The detection result of the three-coordinate measuring machine is taken as the standard for evaluating the on-machine measurement precision, and the result of the three-coordinate measuring machine detecting the measurement point is (x)c,yc,zc) The measurement error in each direction of the measurement point is expressed as:
the total measurement error for this measurement point correspondence is expressed as:
from the uncertainty transfer principle, the uncertainty of the total measurement error is calculated as follows:
a multi-axis numerical control machine tool is characterized in that the multi-axis on-machine measurement planning method is adopted for progressive on-machine measurement.
Advantageous effects
The invention starts from the angle of probe attitude optimization in on-machine measurement, and provides a multi-axis on-machine measurement planning method for reducing measurement uncertainty, which converts a feasible probe axial set in space into a rotation axis angle feasible graph and a touch point feasible graph on a ruby ball, and converts the space probe attitude optimization problem into a planning problem of a two-dimensional plane point set; establishing a relation between a touch point on the ruby ball and a machine tool rotating shaft, and providing optimization methods of different machine tool main shaft structures; the probe axial planning is carried out with the purposes of reducing the introduction of machine tool rotating shaft positioning errors and improving the pre-stroke error compensation precision in the detection, the uncertainty of on-machine measurement detection errors can be reduced, and the consistency and credibility of the measurement results are improved. The calculation method has good stability, can be popularized and applied to on-machine measurement of other multi-axis machine tools, and has certain engineering application value.
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The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 local coordinate system at measurement points and feasible axial collection of probes
FIG. 2 is a view showing the rotation axis angle
FIG. 3 probe axial to workpiece coordinate system X, Z shaft included angle
FIG. 4 is a diagram of the feasible touch points on the ruby ball
FIG. 5 is a schematic view showing the probe axially rotating around the outer normal vector at the measuring point
FIG. 6 is a view showing the probe axis direction concentrated at the angle point of the rotation axis when the machine tool has the spindle orientation function
FIG. 7 is a diagram showing the probe axial direction concentrated at the angle point of the rotating shaft when the machine tool has no main shaft orientation function
FIG. 8 distribution of measurement points
FIG. 9 measurement error uncertainty contrast in example 1
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The implementation steps of the invention are as follows:
the method comprises the following steps:
to facilitate the discretization of the initial probe axis, it is necessaryEstablishing a local coordinate system O at the measurement pointsD-XDYDZDThe Z axis of the coordinate system coincides with the normal vector at the measuring point, the Y axis coincides with the V-direction tangent vector, and the X axis coincides with the U-direction tangent vector. A unit sphere is set based on the local coordinate system, and an inscribed regular icosahedron is constructed within the unit sphere. According to the subdivision rule, when the subdivision number is 3, point sets which are uniformly distributed on a unit spherical surface are discretely taken as initial probe axial directions, interference check is carried out by adopting a bounding box method, and a feasible probe axial direction set is obtained, as shown in fig. 1.
Step two:
Step1：
establishing the probe axial direction (n) by the post-processing formula (1)x,ny,nz) And (3) corresponding relation with the rotation angles (B and C), converting a feasible probe axial set after the interference inspection into a rotation angle point set of the BC axis to form a rotation axis angle feasible diagram, which is shown in FIG. 2.
Step2：
For a certain measuring point, different probes are downward axially, and the positions of the measuring points on the ruby ball of the measuring head are different. The method for axially calculating the position of the feasible touch point on the ruby ball by the probe comprises the following steps: given a probe axial unit vector of (n)x,ny,nz) It can be rotated around the X-axis of the workpiece coordinate system by an angle ω and around the Z-axis by an angle ν, as shown in fig. 3.
cos(υ)＝nz (3)
The transformation matrix M formed by the above rotation angles is:
in the formula (x)r，yr，zr) The coordinates of the center of the ruby sphere corresponding to the probe touching the measuring point.
The probe coordinate system O is obtained by the formula (5)P-XPYPZPSet m of corresponding touch point positions on lower ruby balliThe coordinates are
The origin of the probe coordinate system is positioned at the center of the ruby sphere, and the three axial vectors are respectively parallel to the machine tool coordinate system.
mi＝M-1·Pi(i＝1,2,3...n) (5)
Wherein, PiIs the theoretical measuring point coordinate under the workpiece coordinate system, and n is the number of the measuring points.
Obtaining the parameterized representation theta of the touch point on the ruby ball under the ball coordinate system through the formula (6)i、
A feasible diagram of the touch points on the ruby ball is formed, as shown in fig. 4. When the feasible images of the touch points on the ruby balls corresponding to the plurality of measuring points exist in an intersection, the same touch point on the ruby ball can be shared for measurement.
Wherein r is the radius of the ruby sphere.
Step three:
selecting a point in the intersection of feasible graphs of touch points on the ruby ball corresponding to the multiple measuring points
On the premise of ensuring that the position of the touch point is not changed, the probe can rotate around the external normal vector at the measuring point for a circle, and an infinite number of probe axial directions can be generated, as shown in fig. 5, and can be calculated by the formula (7):
wherein, κiThe angle of rotation of the probe about the outer normal vector, ((ii))xni，yni，zni) The probe axis generated by the probe rotating around the outer normal vector, N is a local coordinate system OD-XDYDZDTo the workpiece coordinate system OW-XWYWZWThe expression of (2) is shown by equation (8).
Wherein (i)W,jW,kW) Is the three axial vector components of the workpiece coordinate system, (i)D,jD,kD) Is a representation of the three axial vector components of the local coordinate system in the object coordinates.
When the machine tool has a spindle orientation function, the axial direction of the probe generated by the rotation of the probe around the outer normal vector at the measuring point is converted into a curve segment in a feasible diagram of the angle of the rotating shaft, as shown in fig. 6. The plurality of measuring points correspond to a plurality of curve segments in the feasible angle diagram of the rotating shaft, so that the rotating angle can be planned on the curve segments, and the rotating shaft always keeps unidirectional rotation in the measuring process.
When the machine tool has no main shaft orientation function, the probe rotates around the external normal vector at the measuring point by an angle kappaiIn the rotation axis angle feasible map is a fixed value, as shown in fig. 7. For a plurality of measurement points corresponding to a plurality of determined points in the rotation axis angle feasible map, the rotation direction of the rotation axis cannot be controlled.
Angle k of rotation of the probe around the outer normal vector at the measurement pointiThe calculation method of (2) is as follows: firstly, touching a point m on the ruby balliTo X under the probe coordinate systemPOPYPThe plane is used for projection, and the projection point is
Then, the machine tool kinematic chain is converted into a workpiece coordinate system
Finally, the transformation matrix N will
The point is converted into a local coordinate system and is recorded as
For calculating the rotation angle kiThe calculation formulas are shown in (9) to (10):
step four:
since the uncertainty component due to measurement repeatability is much larger than the resolution of the measurement device, only the uncertainty of the measurement error due to the accuracy of the repeatability is considered. For m repeated measurements of a certain measurement point, use
Represents the average value of multiple measurement results in the direction of X, Y, Z, and the calculation formula is shown as the formula (11):
the standard deviation in the X, Y, Z direction of the m measurements is calculated by the Bessel formula as:
the standard uncertainty of the measurement in the direction X, Y, Z is:
the mean value of m times of measurement results of the measurement point is
The detection result of the three-coordinate measuring machine is taken as the standard for evaluating the on-machine measurement precision, and the result of the three-coordinate measuring machine detecting the measurement point is (x)c,yc,zc) The measurement error in each direction of the measurement point is expressed as:
the total measurement error corresponding to the measurement point is expressed as
From the uncertainty transfer principle, the uncertainty of the total measurement error is calculated as follows:
the following description is given by way of example of an on-machine measurement of 16 measurement points on a centrifugal impeller:
the on-machine measuring system is a Beijing refined carving JD50 system, the adopted measuring head is an OMP400 trigger type measuring head of Renishaw company, and the diameter of the used centrifugal impeller is
Example 1: the two spline curves of the leaf back are distributed with 16 measuring points in total, as shown in fig. 8, and the corresponding three-coordinate measuring machine detection results are shown in table 1. Under the premise of only considering that a machine measuring head does not interfere with a workpiece and avoiding sudden change of a machine tool rotating shaft in the measuring process, the axial direction of a probe corresponding to each point is planned, when the selected probe is measured downwards, the touch positions on the ruby ball are different, 16 different pre-stroke amounts need to be compensated, and meanwhile, the rotating direction of the BC shaft is changed for 14 times in the measuring process. The experiment was repeated 50 times and the uncertainty of the measurement error obtained is shown in table 2.
TABLE 1 three-coordinate measuring machine test results of the measuring points
TABLE 2 measurement of error uncertainty before non-optimization
By adopting the on-machine measurement planning method in the application to optimize the posture of the probe, when the machine tool does not have the main shaft orientation function, the feasible images of the touch points on the ruby balls of the measuring points No. 1-8 exist in an intersection, and the feasible images of the touch points on the ruby balls of the measuring points No. 9-16 exist in an intersection, so that all the measuring points can be detected only by 2 touch positions on the ruby balls, the rotating direction of the BC axis is changed for 7 times in the measuring process, and the uncertainty of the measuring error obtained by 50 times of repeated experiments is shown in a table 3. When the machine tool has a main shaft orientation function, detection of 16 measurement points only needs two touch point positions on the ruby ball, meanwhile, the BC shaft always keeps unidirectional rotation in the whole measurement process, the experiment is repeated for 50 times, and the uncertainty of the obtained measurement error is shown in table 4.
TABLE 3 uncertainty of measurement error of machine tool without spindle orientation experiment
TABLE 4 machine tool measurement error uncertainty with spindle orientation experiment
The experimental measurement error uncertainty ratio in example 1 is shown in fig. 9, and it can be seen that by using the multi-axis on-machine measurement planning method in the present application, the measurement error uncertainty can be reduced by about 32% to 65% on average, the consistency and the reliability of the measurement result are improved, and the practicability and the effectiveness of the method are proved.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.
Claims (5)
1. A multi-axis on-machine measurement planning method for reducing measurement uncertainty is characterized by comprising the following steps:
step 1: calculating feasible probe axial directions at measuring points
Establishing a local coordinate system O at the measurement pointsD-XDYDZDSetting a unit ball based on the local coordinate system, and constructing an inscribed polyhedron in the unit ball; according to a subdivision criterion, point sets which are uniformly distributed on a unit spherical surface in a discrete mode are used as initial probe axial directions, interference inspection is carried out by adopting a bounding box method, and a feasible probe axial direction set is obtained;
step 2: calculating a set of rotation axis angle points and a set of touch points on the ruby ball
1) Establishing a corresponding relation between the axial direction and the rotation angle of the probe based on a machine tool kinematics chain, and converting a feasible probe axial set after interference inspection into a rotation angle point set of a BC axis to form a rotation axis angle feasible diagram;
2) the positions of the measuring points on the ruby ball of the measuring head, which touch the measuring points, are all different when the probes are in the downward axial direction, and the method for calculating the positions of the feasible touch points on the ruby ball by the axial direction of the probes comprises the following steps: for a given probe axial unit vector (n)x,ny,nz) And the workpiece can rotate around the X axis of the workpiece coordinate system by an angle omega and rotate around the Z axis by an angle upsilon:
cos(υ)＝nz (2)
the transformation matrix M formed by the above rotation angles is:
in the formula (x)r，yr，zr) The coordinates of the center of the ruby sphere corresponding to the probe touching the measuring point;
the probe coordinate system O is obtained by the formula (4)P-XPYPZPSet m of corresponding touch point positions on lower ruby balliThe coordinates are
mi＝M-1·Pi(i＝1,2,3...n) (4)
Wherein, PiThe coordinate of a theoretical measuring point under a workpiece coordinate system, and n is the number of the measuring points;
obtaining the parameterized representation theta of the touch point on the ruby ball under the ball coordinate system through the formula (5)i、
Form a feasible map of touch points on the ruby ball, when there are moreWhen the feasible images of the touch points on the ruby ball corresponding to each measuring point exist in an intersection, the same touch point on the ruby ball can be selected for measurement;
in the formula, r is the radius of the ruby ball;
and step 3: establishing the relation between the touch point on the ruby ball and the rotating shaft of the machine tool
Selecting a point in the intersection of feasible graphs of touch points on the ruby ball corresponding to the multiple measuring points
Under the premise of ensuring that the position of the touch point is unchanged, the probe can rotate for a circle around the external normal vector of the measuring point, and an infinite number of probe axial directions can be generated, and are calculated by the formula (6):
wherein, κiThe angle of rotation of the probe about the outer normal vector, ((ii))xni，yni，zni) The probe axis generated by the probe rotating around the outer normal vector, N is a local coordinate system OD-XDYDZDTo the workpiece coordinate system OW-XWYWZWThe expression of the transformation matrix of (1) is represented by formula (7);
wherein (i)W,jW,kW) Is the three axial vector components of the workpiece coordinate system, (i)D,jD,kD) Representing the three axial vector components of the local coordinate system under the workpiece coordinate;
when the machine tool is provided with a main shaftDuring the orientation function, the probe axial direction generated by the probe rotating around the external normal vector at the measuring point is converted into a feasible graph of the rotating shaft angle to form a curve section; when the machine tool has no main shaft orientation function, the probe rotates around the external normal vector at the measuring point by an angle kiIn the rotation axis angle feasible map is a fixed value.
2. A multi-axis on-machine measurement planning method for reducing measurement uncertainty as claimed in claim 1, wherein the local coordinate system O in step 1D-XDYDZDThe Z axis of the coordinate system coincides with the normal vector at the measuring point, the Y axis coincides with the V-direction tangent vector, and the X axis coincides with the U-direction tangent vector.
3. The method for planning multiaxial on-machine measurement for reducing measurement uncertainty as claimed in claim 1, wherein in step 2, the feasible probe axial set after the interference check is converted into a rotation angle point set of the BC axis, so as to form a rotation axis angle feasible map:
wherein (n)x,ny,nz) The axial direction of the probe is shown, and the rotation angles are shown in (B, C).
4. A method for calculating uncertainty of the multiaxis on-machine measurement planning method of claim 1, characterized by:
because the uncertainty component of repeated measurement is much greater than the resolution of the measurement device, only the uncertainty of measurement error due to the repeated accuracy is considered; for m repeated measurements of a certain measurement point, use
The mean value of multiple measurement results in the X, Y, Z direction is shown, and the standard uncertainty u of the measurement results in the X, Y, Z direction is calculated by combining the Bessel formulax、uy、uz；
The detection result of the three-coordinate measuring machine is taken as the standard for evaluating the on-machine measurement precision, and the result of the three-coordinate measuring machine detecting the measurement point is (x)c,yc,zc) The measurement error in each direction of the measurement point is expressed as:
the total measurement error for this measurement point correspondence is expressed as:
from the uncertainty transfer principle, the uncertainty of the total measurement error is calculated as follows:
5. a multi-axis numerically controlled machine tool, characterized by performing on-machine measurements using the method of claim 1.
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