CN109732401B - Detection method for position-independent errors of double rotating shafts of five-axis numerical control machine tool - Google Patents
Detection method for position-independent errors of double rotating shafts of five-axis numerical control machine tool Download PDFInfo
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Abstract
The invention discloses a detection method for position-independent errors of double rotating shafts of a five-axis numerical control machine tool, which is characterized in that a ball rod instrument is used as experimental equipment to identify position-independent geometric errors (PIGEs) in a swinging shaft B shaft and a rotating shaft C shaft in the five-axis numerical control machine tool, a new measurement track is provided, the asynchrony between the synthetic speed when the swinging shaft B shaft and the rotating shaft C shaft move coordinately and the capturing speed of the ball rod instrument is solved, a simulation model is established by combining a homogeneous transformation matrix in rigid body kinematics, and the identification and measurement of the position-independent geometric errors of the double rotating shafts of the five-axis numerical control machine tool are realized by combining the simulation model with experiments.
Description
Technical Field
The invention belongs to the technical field of numerical control machine tool detection, and particularly relates to a detection method for position-independent errors of double rotary shafts of a five-axis numerical control machine tool.
Technical Field
The five-axis numerical control machine tool is widely used for machining parts with complex geometric characteristics, and has the advantages of improving the surface finish degree, improving the removal rate of materials and the like. In most machining conditions, the orientation of the tool relative to the workpiece is changed by means of the double rotating shafts of the machine tool, so that the tool path is generated with greater flexibility than that of the traditional three-axis machining. However, the swinging axis B and the rotating axis C introduce more geometric error elements during machining, and the machined parts have defects and defects.
The research on the inherent errors of the B axis of the swing axis and the C axis of the rotating shaft is crucial to the control of the precision of a five-axis numerical control machine tool, and measuring devices such as a ball bar instrument, a laser interferometer, an R-test and the like are available at present. Because the characteristics of convenient operation, less time consumption and the like of the cue instrument are widely adopted. However, how to solve the asynchronism between the synthetic speed when the swing axis B and the rotating axis C move coordinately and the capturing speed of the ball rod instrument, and accurately identify the geometric error of the double rotating shafts which is irrelevant to the position by using the ball rod instrument, so that the method for quickly and simply detecting the irrelevant error of the position of the double rotating shafts of the five-axis numerical control machine tool is particularly important.
Disclosure of Invention
In order to solve the above problems, an object of the present invention is to provide a method for detecting a position-independent error of a double-rotation axis of a five-axis numerical control machine tool, in which a ball bar instrument is used to detect a position-independent geometric error of a swing axis B and a rotation axis C. The invention can simply and accurately measure the error, thereby greatly improving the processing quality. The specific measurement steps are as follows:
step 1, building an experimental measuring device according to the specific structure of the five-axis numerical control machine tool and the positions of a swing shaft B shaft and a rotating shaft C shaft.
And 2, combining an experimental device, and providing a track for measuring 8 items of position-independent geometric errors of the swing axis B and the rotating axis C of the five-axis numerical control machine tool.
Step 3, solving the asynchronism between the synthetic speed and the ball rod instrument capturing speed when the swing shaft B shaft and the rotating shaft C shaft move coordinately
And 4, combining the theory of a multi-body motion system of the machine tool with homogeneous coordinate transformation to identify errors.
And in the step 1, determining the measurement position of the ball arm instrument according to the structure of the five-axis numerical control machine tool, the B axis of the swing axis and the C axis of the rotating shaft. The two balls of the cue stick apparatus are magnetically attached to two tool cups that are attached to the spindle and to a fixture located on the table, comprising the steps of:
step 1.1, setting a measured coordinate system, wherein a Z axis is overlapped with an original Z axis of the machine tool, and an X axis and a Y axis of the measured coordinate system are parallel to the movement directions of the X axis and the Y axis of the machine tool.
Step 1.2, installing a rotating shaft C-axis tool cup on a clamp at the top of a rotating table, lifting an XOY plane of a measuring coordinate system on the rotating table, setting the size of a distance O-XYZ between a B axis of a swing shaft and an original point to be 400mm, adjusting the center from a main shaft tool cup to the B axis of the swing shaft to be 400mm by using a touch probe, meanwhile, adjusting the distance from a workpiece tool cup on the rotating table to the center of the rotating shaft C axis to be 400mm, expanding a ball bar instrument by using an extension rod, converting the nominal length of the ball bar instrument to be 400mm, and calibrating an experimental tool.
In the step 2, a corresponding program is utilized to control the swinging shaft B and the rotating shaft C of the five-axis numerical control machine tool to be linked, and the geometric error of the double revolving shafts of the five-axis numerical control machine tool, which is irrelevant to the position, is measured in the process, and the method comprises the following steps:
step 2.1, in the measuring path, firstly, the axis of the ball bar instrument is aligned with the Y axis of O-XYZ, one end of the ball bar instrument is arranged at the origin of the O-XYZ, and the other end of the ball bar instrument is arranged at the position 400mm away from the Y axis. The swing axis B axis and the rotation axis C axis are rotated from 0 DEG to-90 DEG and 90 DEG to 0 DEG, respectively.
Step 2.2, the distance between the two tool cups in the spindle and the rotary table is not constant, which may cause the cue stick instrument to fall from the magnetic center base, so that the coordinated movement of the swing axis B and the rotation axis C should ensure that the distance between the points P and Q in fig. 3 is kept constant at 400 mm.
Step 2.3, fig. 4, projects the point P in fig. 3 onto the XOY plane to obtain the relationship between the rotation angles of the swing axis B axis and the rotation axis C axis:
according to the Pythagorean theorem:
in the XOY plane according to the law of cosines:
by measuring means RB＝RC＝LDBBThe relationship between the rotation angles can be found in equation (1) and equation (2) at 400 mm:
and 3, solving the asynchronism between the synthetic speed and the club instrument capturing speed when the swing axis B and the rotating axis C move in a coordinated manner.
Step 3.1, the swing axis B axis and the rotation axis C axis rotate from 0 ° to-90 ° and 90 ° to 0 ° respectively, the swing axis B axis rotates at a constant speed, and the position of the rotation axis C axis angle corresponding to a step size of 0.1 ° can be given as:
and the angular positions of the swing axis B and the rotation axis C are:
step 3.2, each step of the experimental measurement is shown in fig. 5, forming a semicircular track.
Step 3.3 and fig. 6 show that adjacent step lengths are not equidistant, the fluctuation of the step length along the track causes the problem that the movement of the machine tool and the sampling of the cue instrument are not synchronous, and because the acquisition rate of the cue instrument is constant, it is important to ensure that the movement is uniform, and the analysis can be effective.
Step 3.4, the trace in fig. 6 represents the tool cup center position. The spindle tool cup is arranged on the spindle shell of the swing shaft B shaft, so that the axis of the tool cup and the center of the tool cup form a semi-right cone as shown in figure 7, thereby obtaining the parameters of a cone, and the radius of the bottom circle of the cone is
The aperture of the cone is 90 deg., and the generatrix length of the cone is 400 mm.
Step 3.5, in order to ensure that the distance between adjacent step lengths is constant, the cone is spread on a two-dimensional plane, as shown in fig. 8(a), if the distance | | OO' | is r,
in the figure
Can also be obtained in the unfolding plane
The available flare angle:
step 3.6, the central angle enclosed by OB and BP' is denoted as φ, which can be given as:
the central angle enclosed by OO ' and O ' P ' in step 3.7, fig. 8(c) can be given as Θ, in the bottom circle of the cone:
step 3.8, in fig. 8(c) where N is the midpoint of | | | OP' | |, based on the trigonometric relationship, the following equation can be given:
step 3.9, hence θBThe relationship with Θ can be obtained based on equations 5-9:
step 3.10, as long as the central positions of the tool cups are uniformly distributed in phi, uniform motion can be realized, 900 steps with equal distance are selected in the middle, and the steps are substituted into a formula of equation 5-10 to form uniformly distributed motion tracks as shown in fig. 9.
In step 4, an error measurement model is established according to a multi-body system theory and homogeneous coordinate transformation, and although the proposed method is performed on a swing axis and rotating table type five-axis machine tool, the method can be applied to any five-axis machine tool with a similar topological structure. To simplify the modeling process, current multi-axis NC systems are able to compensate for linear axis errors, thus assuming that only the PIGE of the rotating axis is considered to compensate for the geometric error of the linear axis before all tests.
And 4.1, PIGE of the C axis of the rotating shaft is according to ISO230-1, each rotating shaft has 4 PIGE, and a zero error can be ignored in consideration of the zero compensation function of CNC. 4 PIGE are two linear position error components E in the XOY plane in the X and Y axesXOCAnd EYOCAnd two components of orientation error E about the X-axis and Y-axis, respectivelyAOCAnd EBOC. A similar error contribution for the B-axis of the wobble axis can be obtained based on IOS 230-1.
Step 4.2, the total error of the motion axis can be evaluated by sequential multiplication of the basic homogeneous transformation matrix. According to multi-body system theory, the feature transformation matrix from the workpiece coordinate system to the reference coordinate system can be given as follows:
the cutting tool branch may be given similarly to the above expression:
the ideal transformation matrix from the tool center point to the workpiece coordinate system can be given as follows:
under the influence of PIGE in the contact, the actual posture of the transformation matrix is represented as:
where E is an identity matrix of order 4 × 4, due to geometric errors,
represents a given deviation matrix:
the actual transformation from the cutting tool center point to the workpiece can then be given by:
where the letters R, W, T and i denote the reference coordinate system, the workpiece coordinate system, the cutting tool coordinate system and the coordinate system of the i-th rigid body in the kinematic chain of the target machine tool. DidealAnd DactualRepresenting an ideal and actual homogeneous transformation matrix, representing a transformation from its left-subscripted coordinate system to one of its left-superscripts. Rot and Trans describe the transformation of rotation and translation, respectively, from its lower left-hand coordinate system to one of its upper left-hand corners in a homogeneous transformation matrix.
And 4.3, combining the experimental measurement data and the model provided in the step 4, and obtaining the geometric position-independent errors of the eight items of the swing shaft and the rotating shaft of the five-axis numerical control machine tool by using a pseudo-inverse method.
The method completes the analysis of the geometric errors of the five-axis numerical control machine tool with double revolving shafts irrelevant to the position, and comprises 8 geometric errors irrelevant to the geometric position.
The invention effectively solves the problem of identification and detection of geometric errors of double rotating shafts in a five-axis numerical control machine tool, which are irrelevant to the position, provides an effective detection path, solves the asynchrony of the ball arm instrument in the detection process, and finally obtains a measurement result.
Drawings
FIG. 1 is a structural diagram of a five-axis numerical control machine tool
FIG. 2 is a schematic diagram of the position of the experimental apparatus in the embodiment of the method of the present invention
FIG. 3 is a diagram illustrating measurement paths taken by experimental measurements in an embodiment of the method of the present invention
FIG. 4 is an XOY plane projection of the measurement path in an embodiment of the method of the present invention
FIG. 5 is a diagram illustrating a semicircular track formed by each step of the track according to an embodiment of the present invention
FIG. 6 is a flowchart of an embodiment of a method of the present invention for measuring path step size non-uniformity
FIG. 7 is a semi-circular cone formed by a B-axis measurement path tool cup in accordance with an embodiment of the present invention
FIG. 8 is a developed plan view of a semi-circular vertebral body formed in an embodiment of the method of the present invention
FIG. 9 is a diagram illustrating the step size uniformity of the measurement paths in the embodiment of the method of the present invention
Detailed Description
The following describes embodiments of the present invention in conjunction with experimental measurement methods and the accompanying drawings.
Fig. 1 is a structural view of a five-axis numerical control machine tool used in the present invention, and the measurement method will be described based on this.
And in the step 1, determining the measurement position of the ball arm instrument according to the structure of the five-axis numerical control machine tool and the types of the swing axis B and the rotating axis C. The two balls of the cue stick apparatus are magnetically attached to two tool cups that are attached to the spindle and to a fixture located on the table, comprising the steps of:
step 1.1, setting a measurement coordinate system conforming to the experimental measurement method, and enabling a Z axis of the coordinate system to coincide with an original Z axis of a machine tool, wherein an X axis and a Y axis of the coordinate system are parallel to the movement directions of the X axis and the Y axis of the machine tool.
Step 1.2, as shown in fig. 2, mounting the tool cup of the rotating shaft C axis on the top fixture of the rotating table, lifting the XOY plane of the measurement coordinate system on the rotating table, setting the distance between the swing axis B axis and the origin O-XYZ to 400mm, using the touch probe to adjust the center from the main shaft tool cup to the swing axis B axis to 400mm, and at the same time, extending the workpiece tool cup on the rotating table to 400mm from the center of the rotating shaft C axis, using the extension rod to extend the ball bar instrument, converting the nominal length of the ball bar instrument to 400mm, and calibrating the experimental tool.
In the step 2, a corresponding program is utilized to control the swinging shaft B and the rotating shaft C of the five-axis numerical control machine tool to be linked, and the geometric error of the double rotating shafts of the five-axis numerical control machine tool, which is irrelevant to the position, is measured in the process, and the method comprises the following steps:
step 2.1, the measurement path is as shown in FIG. 3, first aligning the shaft of the ball bar apparatus with the Y-axis of O-XYZ, with one end of the ball bar apparatus set at the origin of O-XYZ and the other end set at a position 400mm from Y. The swing axis B axis and the rotation axis C axis are rotated from 0 DEG to-90 DEG and 90 DEG to 0 DEG, respectively. Meanwhile, the ball arm instrument collects data.
Step 2.2, because the distance between the two tool cups on the main shaft and in the rotating table is not constant, the ball arm instrument falls off from the magnetic center base, so that the coordinated movement of the B axis of the swinging shaft and the C axis of the rotating shaft ensures that the distance between the P point and the Q point in the figure 3 is kept constant at 400 mm.
Step 2.3, fig. 4 projects the point P in fig. 3 to the XOY plane to obtain the relationship between the rotation angles of the B-axis and the C-axis:
according to the Pythagorean theorem:
in the XOY plane according to the law of cosines:
by measuring means RB＝RC＝LDBBThe relationship between the rotation angles can be found in equation (1) and equation (2) at 400 mm:
further, the problem of asynchronous movement of the swing axis B axis and the rotating axis C axis during data acquisition is solved in step 3.
Step 3.1, the swing axis B axis and the rotation axis C axis rotate from 0 ° to-90 ° and 90 ° to 0 ° respectively, the swing axis B axis rotates at a constant speed, and the position of the rotation axis C axis angle corresponding to a step size of 0.1 ° can be given as:
and the angular positions of the swing axis B and the rotation axis C are:
the semicircular track formed for each step of the experimental measurement is shown in step 3.2, fig. 5.
Step 3.3 and fig. 6 show that adjacent step lengths are not equidistant, the fluctuation of the step length along the track causes the problem that the movement of the machine tool and the sampling of the cue instrument are not synchronous, and because the acquisition rate of the cue instrument is constant, it is important to ensure that the movement is uniform, and the analysis can be effective.
Step 3.4, the trace in fig. 6 represents the tool cup center position. The spindle tool cup is arranged on the spindle shell of the swing shaft B shaft, so that the axis of the tool cup and the center of the tool cup form a semi-right cone as shown in figure 7, thereby obtaining the parameters of a cone, and the radius of the bottom circle of the cone is
The aperture of the cone is 90 deg., and the generatrix length of the cone is 400 mm.
Step 3.5, in order to ensure that the distance between adjacent step lengths is constant, the cone is spread on a two-dimensional plane, as shown in fig. 8(a), if the distance | | OO' | is r,
in the figure
Can also be obtained in the unfolding plane
The available flare angle:
step 3.6, the central angle enclosed by OB and BP' is denoted as φ, which can be given as:
the central angle enclosed by OO ' and O ' P ' in fig. 8(c), step 3.7, can be given as Θ, in the bottom circle of the cone:
step 3.8, N is the midpoint of | | OP' | in fig. 8(c), and based on the trigonometric relationship, the following equation can be given:
step 3.9, hence θBThe relationship with Θ can be obtained based on equations 5-9:
step 3.10 and fig. 9 show the motion tracks which are uniformly distributed, as long as the central positions of the tool cup are uniformly distributed in phi, uniform motion can be realized, 900 steps with equal distance are selected in the middle, and the steps are substituted into a formula 5-10 to form the motion tracks which are uniformly distributed.
Further, in step 4, an error measurement model is established according to the multi-body system theory and homogeneous coordinate transformation, and although the proposed method is performed on a five-axis machine tool of a swing axis B axis and a rotating table C axis type, the method can be applied to any five-axis machine tool with a similar topological structure. To simplify the modeling process, current multi-axis NC systems are able to compensate for linear axis errors, thus assuming that only the PIGE of the rotating axis is considered to compensate for the geometric error of the linear axis before all tests.
Step 4.1, rotating shaft C shaftPIGE according to ISO230-1, with 4 PIGE per axis of rotation, one zero error can be neglected in view of the zero compensation function of CNC. 4 PIGE are two linear position error components E in the XOY plane in the X and Y axesXOCAnd EYOCAnd two components of orientation error E about the X-axis and Y-axis, respectivelyAOCAnd EBOC. A similar error contribution for the B-axis of the wobble axis can be obtained based on IOS 230-1.
Step 4.2, the total error of the motion axis can be evaluated by sequential multiplication of the basic homogeneous transformation matrix. According to multi-body system theory, the feature transformation matrix from the workpiece coordinate system to the reference coordinate system can be given as follows:
the cutting tool branch may be given similarly to the above expression:
the ideal transformation matrix from the tool center point to the workpiece coordinate system can be given as follows:
under the influence of PIGE in the contact, the actual posture of the transformation matrix is represented as:
where E is an identity matrix of order 4 × 4, due to geometric errors,
represents a given deviation matrix:
the actual transformation from the cutting tool center point to the workpiece can then be given by:
where the letters R, W, T and i denote the reference coordinate system, the workpiece coordinate system, the cutting tool coordinate system and the coordinate system of the i-th rigid body in the kinematic chain of the target machine tool. DidealAnd DactualRepresenting an ideal and actual homogeneous transformation matrix, representing a transformation from its left-subscripted coordinate system to one of its left-superscripts. Rot and Trans describe the transformation of rotation and translation, respectively, from its lower left-hand coordinate system to one of its upper left-hand corners in a homogeneous transformation matrix.
Step 4.3, combining the experimental measurement data and the model provided in step 4, obtaining eight errors of the five-axis numerical control machine tool with independence of the geometric positions by using a pseudo-inverse method, wherein the errors are shown in table one:
Claims (1)
1. a detection method for position-independent errors of double rotating shafts of a five-axis numerical control machine is characterized by comprising the following steps:
step 1, building an experimental measuring device according to the specific structure of the five-axis numerical control machine tool and the positions of a swing shaft B shaft and a rotating shaft C shaft:
step 1.1, setting a measured coordinate system, wherein a Z axis is overlapped with an original Z axis of a machine tool, and an X axis and a Y axis of the measured coordinate system are parallel to the movement directions of the X axis and the Y axis of the machine tool;
step 1.2, installing a rotating shaft C-axis tool cup on a clamp at the top of a rotating table, lifting an XOY plane of a measuring coordinate system on the rotating table, setting the size of a distance O-XYZ between a B axis of a swing shaft and an original point to be 400mm, adjusting the center from a main shaft tool cup to the B axis of the swing shaft to be 400mm by using a touch probe, meanwhile, adjusting the distance from a workpiece tool cup on the rotating table to the center of the rotating shaft C axis to be 400mm, expanding a ball bar instrument by using an extension rod, converting the nominal length of the ball bar instrument to be 400mm, and calibrating an experimental tool;
and 2, combining an experimental measurement device, providing a track for measuring 8 position-independent geometric errors of an oscillating shaft B and a rotating shaft C of the five-axis numerical control machine tool:
step 2.1, in the measuring path, firstly, aligning the axis of a ball rod instrument with the Y axis of O-XYZ, arranging one end of the ball rod instrument at the origin of the O-XYZ, arranging the other end of the ball rod instrument at a position 400mm away from the Y axis, rotating the B axis of a swinging axis from 0 degree to-90 degrees, and simultaneously rotating the C axis of a rotating axis from 90 degrees to 0 degrees;
step 2.2, the distance between the two tool cups in the main shaft and the rotating table is not constant, so that the ball arm instrument falls off from the magnetic center seat, and therefore the coordinated movement of the B axis of the swinging shaft and the C axis of the rotating shaft ensures that the distance between the two bases of the ball arm instrument is kept constant at 400 mm;
and 2.3, projecting the measurement track to an XOY plane to obtain the relationship between the rotation angles of the swing axis B and the rotation axis C:
according to the Pythagorean theorem:
in the XOY plane according to the law of cosines:
by experimental measuring devices RB＝RC＝LDBBThe relationship between the rotation angles can be found in equation (1) and equation (2) at 400 mm:
and 3, solving the asynchronism between the synthetic speed and the club instrument capturing speed when the swing shaft B shaft and the rotating shaft C shaft move in a coordinated manner:
step 3.1, rotating the swing axis B from 0 degree to-90 degrees, simultaneously rotating the rotating axis C from 90 degrees to 0 degrees, rotating the swing axis B at a constant speed, and setting the position of the rotating axis C corresponding to the step length of 0.1 degree as follows:
and the angular positions of the B and C axes are:
step 3.2, each step measured in experiments shows that a semicircular track is formed, the adjacent steps of the formed semicircular track are not equidistant, and the fluctuation of the step along the track causes the problem that the movement of a machine tool and the sampling of the cue instrument are not synchronous;
and 3.3, representing the central position of the tool cup by the track, and installing the main shaft tool cup on a main shaft shell of the B-axis oscillating shaft, so that the axis of the tool cup and the center of the tool cup form a semi-right cone, and parameters of a cone can be obtained, wherein the radius of the bottom circle of the cone is
The aperture of the cone is 90 degrees, and the length of the generatrix of the cone is 400 mm;
step 3.4, in order to ensure that the distance between the adjacent step lengths is constant, the cone is spread on a two-dimensional plane, if the distance | | | OO' | | is r,
can be obtained in the unfolding plane
Therefore, the flare angle:
step 3.5, the central angle enclosed by OB and BP' is denoted as φ, so we derive:
step 3.6, the central angle enclosed by OO ' and O ' P ' is Θ, given in the bottom circle of the cone:
step 3.7, where N is the midpoint of | | | OP' | |, based on the trigonometric relationship, the following equation is derived:
step 3.8, hence θBThe relationship with Θ is obtained based on equation (5) -equation (9):
3.9, as long as the central positions of the tool cup are uniformly distributed in phi, uniform motion can be realized, 900 steps with equal distance are selected in the middle and substituted into equation (5) -equation (10) to form uniformly distributed motion tracks;
and 4, combining the theory of a multi-body motion system of the machine tool with homogeneous coordinate transformation to carry out error identification:
step 4.1, rotating shaft C axis PIGE according to ISO230-1, each rotating shaft has 4 PIGE, considering that zero compensation function of CNC ignores a zero error, so 4 PIGE is two linear position error components E on X axis and Y axis in XOY planeXOCAnd EYOCAnd two components of orientation error E about the X-axis and Y-axis, respectivelyAOCAnd EBOCThe error component of the B axis of the swing axis can also be obtained based on IOS 230-1;
and 4.2, evaluating the total error of the motion axis by sequential multiplication of a homogeneous transformation matrix, and according to the theory of a multi-body system, giving out the following characteristic transformation matrix from a workpiece coordinate system to a reference coordinate system:
the feature transformation matrix for the cutting tool branch is given by:
the ideal transformation matrix from the tool center point to the workpiece coordinate system is as follows:
under the influence of PIGE in the contact, the actual posture of the transformation matrix is represented as:
where E is an identity matrix of order 4 × 4, due to geometric errors,
represents a given deviation matrix:
the actual transformation from the cutting tool center point to the workpiece is represented as:
wherein the letters R, W, T and i denote the reference coordinate system, the workpiece coordinate system, the cutting tool coordinate system and the coordinate system of the i-th rigid body in the kinematic chain of the target machine tool, DidealAnd DactualRepresenting an ideal and actual homogeneous transformation matrix, representing the transformation from its left-lower coordinate system to one of its left superscripts, Rot and Trans, respectively, describing the transformation of rotation and translation in the homogeneous transformation matrix from its left-lower coordinate system to one of its upper left corners;
and 4.3, combining the experimental measurement data and the model provided in the step 4, and obtaining eight errors of the five-axis numerical control machine tool with the double rotating shafts, which are irrelevant to the geometric position, by using a pseudo-inverse method.
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| CN114012507B (en) * | 2021-12-09 | 2023-06-02 | 天津工业大学 | Identification method for position independent errors of double rotating shafts of cradle type five-axis machine tool |
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