CN112487615B - Method and device for calibrating main shaft head of five-shaft series-parallel machine tool - Google Patents

Method and device for calibrating main shaft head of five-shaft series-parallel machine tool Download PDF

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CN112487615B
CN112487615B CN202011288644.7A CN202011288644A CN112487615B CN 112487615 B CN112487615 B CN 112487615B CN 202011288644 A CN202011288644 A CN 202011288644A CN 112487615 B CN112487615 B CN 112487615B
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于广
李梦宇
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Abstract

The invention discloses a method and a device for calibrating a spindle head of a five-axis series-parallel machine tool, wherein the method comprises the following steps: establishing a kinematic model of an error item of a main shaft head of a five-axis series-parallel machine tool; establishing a kinematics positive solution equation of the center point of the cutter, and solving an error identification matrix of the position error of the center point of the cutter under corresponding input through a differential substitution differential method; driving a five-axis series-parallel machine tool through an RTCP function, enabling a main shaft head to move to different postures when the theoretical position of the center point of a cutter is unchanged, and measuring the position error of the center point of the cutter corresponding to each posture and the input vector of the corresponding main shaft head; solving an error identification matrix according to the measured input vector of the spindle head, and identifying geometric error parameters of the parallel spindle head of the five-axis series-parallel machine tool by combining the position error of the central point of the tool; 5) and substituting the geometric error parameters obtained by identification into the kinematic model with the error item to finish calibration. The invention solves the problems of high measurement cost and large time consumption in the calibration process, reduces the measurement cost and improves the calibration efficiency.

Description

Method and device for calibrating main shaft head of five-shaft series-parallel machine tool
Technical Field
The invention belongs to the field of machine tool manufacturing, and particularly relates to a method and a device for calibrating a spindle head of a five-axis series-parallel machine tool.
Background
Since the 21 st century, the parallel mechanism is more and more widely applied in the industry due to the advantages of high rigidity, high precision, bearing capacity and the like. The parallel-serial machine tool is an innovation of a machine tool structure, combines the advantages of a parallel mechanism and a serial mechanism, theoretically has better performance in the aspects of precision and rigidity compared with the traditional machine tool, has light weight and good processing flexibility, and has wide attention at home and abroad. However, the practical and industrialized products of the existing parallel-serial machine tool at home and abroad are very limited throughout the survey, and particularly in the aspect of precision, the actual precision of the parallel-serial machine tool is far lower than that obtained by theoretical analysis and simulation, and the precision requirement cannot be met. Therefore, how to ensure the geometric accuracy of the parallel-serial machine tool is a key technology which needs to be solved at present.
For a parallel-serial machine tool, a large number of passive joints exist in a parallel main shaft head, and a large number of geometric errors are brought in the manufacturing and assembling processes, so that the terminal (a parallel mechanism movable platform) of the main shaft head of the machine tool deviates from the originally designed terminal position, and the precision of the machine tool is greatly reduced. The kinematics calibration technology is a technology for identifying and obtaining error parameters in the kinematics of the machine tool to correct and control a model through measured actual errors of the machine tool after the machine tool is manufactured, so as to compensate errors of a machine tool terminal and improve the precision of the machine tool terminal. Therefore, it is necessary to perform kinematic calibration of the main spindle head of the parallel machine tool to improve the end precision of the machine tool.
The kinematics calibration is mainly divided into the following four steps: error modeling, error measurement, parameter identification and error compensation. The error measurement is the basis of identification and compensation, the higher the measurement precision is, the more the measurement information is, the more accurate the identification result is, and the higher the precision is after compensation.
At present, for the kinematics calibration of a five-axis series-parallel machine tool, because the rotation angle of a terminal around a cutter shaft does not influence the processing precision, three positions and two attitude angles need to be measured, the position measurement is easier to implement, but the attitude measurement is more difficult. If the attitude measurement is carried out by adopting a commercial measuring instrument, the measurement cost is higher, the measurement precision cannot reach the precision required by kinematics calibration, and if a self-made measuring tool is adopted for measurement, the steps are complicated, the efficiency is extremely low, and the measurable attitude is limited. When the measured position and attitude errors are used for identification, the identification result is influenced due to different dimensions of the position and the attitude.
Disclosure of Invention
Aiming at the problems of difficult attitude measurement and non-uniform position and attitude dimension in the identification process, the invention provides a method for calibrating a main shaft head of a five-axis hybrid machine tool by combining the structural form of the five-axis hybrid machine tool.
The technical scheme of the invention is as follows:
a method for calibrating a main shaft head of a series-parallel machine tool comprises the following steps:
1) establishing a kinematic model and a geometric error model of a main shaft head of a five-shaft series-parallel machine tool to form a kinematic model with an error term;
2) establishing a kinematics positive solution equation of the position of the center point of the cutter according to the length of the cutter, and obtaining an error identification matrix of the position error of the center point of the cutter under the input vector of the corresponding spindle head by a differential substitution differentiation method;
3) driving a five-axis series-parallel machine tool through an RTCP function, enabling a main shaft head to move to different postures when the theoretical position of the central point of a cutter is unchanged, and measuring the position error of the central point of the cutter corresponding to each posture and the input vector of the main shaft head corresponding to each posture;
4) substituting the measured input vector of the spindle head into an error identification matrix, and identifying the geometric error parameter of the parallel spindle head of the five-axis parallel machine tool by combining the measured position error of the central point of the tool;
5) and substituting the geometric error parameters obtained by identification into the kinematic model with the error item to realize error compensation and finish kinematic calibration.
Optionally, the establishing a kinematic positive solution equation of the position of the center point of the tool includes:
according to the length of the tool, reflecting the position and the posture of the main shaft head of the hybrid machine tool through the position of the center point of the tool, as shown in the following formula:
p＝H+RTT·[0 0 ld]T
wherein p represents a position vector of a center point of the toolH denotes the position vector of the center point of the spindle head moving platform, RTTAttitude matrix representing the main axis moving platform,/dIndicating the length of the tool.
Optionally, the obtaining an error identification matrix of the position error of the center point of the tool under the corresponding input vector of the spindle head by a differential-instead-differential method includes:
dp＝Jdr
Figure BDA0002783193500000031
wherein dp represents a position error column vector of a center point of the tool, q represents a spindle head input vector of the spindle head, dr represents a geometric error parameter column vector of the spindle head, J is an error identification matrix of the position error of the center point of the tool, and J is [ J ═ J1 J2…J33]，JiThe ith column vector of error identification matrix representing the error of the center point position of the tool, r represents the geometric parameter vector of the spindle head, riAnd taking a smaller value for the ith element, and keeping the error parameter difference vector with the elements all being 0.
Optionally, in step 2, measuring the position error of the center point of the corresponding tool in each posture includes:
the position error of the center point of the cutter is determined by the position of the sphere center of a ball head check rod arranged on a main shaft head, the position error is in contact with the outer wall of the ball head check rod along the radial direction through a plurality of dial indicators, after a main shaft head moving platform is changed from a first posture to a second posture, the control system is adjusted to perform linear motion in the direction X, Y, Z, the number of the dial indicators is the same as that of the dial indicators in the first posture, the change quantity in the direction X, Y, Z is read out from the control system to serve as the position error of the center point of the cutter in the direction X, Y, Z, wherein the direction X, Y, Z is along the three coordinate axes of a rectangular coordinate system.
Optionally, the number of the dial indicators is three, and the dial indicators correspond to the X, Y, Z directions respectively.
Optionally, the establishing a kinematic model and a geometric error model of a spindle head of a five-axis hybrid machine tool to form a kinematic model with an error term includes:
according to the closed-loop vector method, for each branch chain of the spindle head:
H+RTTRiai＝Ribi+RiRBiqi+RiRBiRCili
wherein, H, ai、bi、liAnd q isiRespectively representing the terminal position of the parallel spindle head, the structural parameters of the movable platform of the terminal, the structural parameters of the static platform, the structural parameters of the rod piece and the position of the slide block, RTT、Ri、RBiAnd RCiRespectively representing a rotation matrix from a movable platform to a static platform of the parallel spindle head terminal, a rotation matrix of each branched chain, a rotation matrix of a P pair and a rotation matrix of an R pair,
and (3) taking differential on two sides to obtain a geometric error model containing all error parameters:
H+RTTRi(ai+Δai)＝
Ri(bi+Δbi)+RiRBiRθBi(qi+Δqi)
+RiRBiRθBiRCiRθCi(li+Δli)
wherein Δ aiAnd Δ biRepresenting the geometric error vector of the moving platform and the geometric error vector of the stationary platform, Δ qiAnd Δ liRespectively representing the position error of each slide block and the length error of the connecting rod, RθBiAnd RθCiRepresenting a guide rail angle error matrix and a slide block angle error matrix, wherein i in the subscript corresponds to the ith branched chain,
rewriting the geometric error model into a kinematic model containing a geometric error term:
||H+RTTRi(ai+Δai)-Ri(bi+Δbi)-RiRBiRθBi(qi+Δqi)||2＝li+Δli
(H+RTTRi(ai+Δai)-Ri(bi+Δbi)-RiRBiRθBi(qi+Δqi))·RiRBiRθBiRCiRθCie2＝0。
optionally, substituting the measured input vector of the spindle head into an error identification matrix, and identifying geometric error parameters of the parallel spindle head of the five-axis parallel machine tool by combining the measured position error of the center point of the tool, includes:
1) obtaining a position error matrix dp after stacking according to the position error of the center point of the cutter and the corresponding input vector of the spindle head*3n×1And error identification matrix J*3n×33：
Figure BDA0002783193500000041
Wherein, dXn、dYnAnd dZnDenotes the positional deviation of the center point of the tool in the direction X, Y, Z, q, measured at the nth measurement attitudenRepresenting the spindle head input vector at the nth measurement attitude, r being a geometric parameter, JnRepresenting an error recognition matrix at the nth measurement attitude;
X0、Y0、Z0indicating X, Y, Z values in the control system at attitude zero;
Xn、Ynand ZnIndicating X, Y, Z values in the control system at the nth measurement attitude;
2) constructing an error identification equation:
dp*3n×1＝J*3n×33dr33×1 (7)；
3) iterative solution identification is carried out by using ridge estimation algorithm to obtain geometric error parameters dr of the parallel spindle heads33×1，
dr33×1＝(J*3n×33 TJ*3n×33+λI)-1J*3n×33 Tdp*3n×1 (8)
Where λ is the ridge estimation parameter.
I is a 33 th order identity matrix.
Note that dp is*3n×1、J*3n×33、dr33×1The subscripts of (a) are merely to illustrate the number of elements contained in the vector. E.g. dr and dr33×1Are identical in meaning, dr33×1The method is to show that the geometric error parameter column vector of the spindle head contains 33 elements.
The utility model provides a series-parallel connection lathe main shaft head calibration device which characterized in that includes:
the kinematic model establishing module is used for establishing a kinematic model and a geometric error model of a main shaft head of the five-shaft series-parallel machine tool to form a kinematic model with an error term;
the error identification matrix obtaining module is used for establishing a kinematic positive solution equation of the position of the center point of the cutter according to the length of the cutter, and obtaining an error identification matrix of the position error of the center point of the cutter under the corresponding main shaft head input vector by a differential substitution differentiation method;
the tool center point position error obtaining module is used for driving the five-axis series-parallel machine tool through an RTCP function, so that the spindle head moves to different postures when the theoretical position of the tool center point is not changed, and the corresponding tool center point position error and the corresponding spindle head input vector under each posture are measured;
the error identification module is used for substituting the measured input vector of the spindle head into an error identification matrix, and identifying the geometric error parameter of the spindle head of the five-axis series-parallel machine tool by combining the measured position error of the central point of the tool;
and the calibration module is used for substituting the geometric error parameters obtained by identification into the kinematic model with the error item to realize error compensation and finish kinematic calibration.
Compared with the prior art, the invention has the following advantages and prominent technical effects: the invention provides a kinematics calibration method which does not need to carry out attitude measurement and only needs to carry out position measurement, thereby greatly reducing the measurement cost. Secondly, the invention combines the RTCP function of the five-axis series-parallel machine tool, only needs to adjust the attitude and measure the position error of the corresponding center point of the cutter, only needs three dial indicators and only needs to be installed once to complete the measurement task, realizes the calibration, greatly simplifies the measurement steps and reduces the measurement time. In the identification process, the problem that the position and the attitude dimension are not uniform is avoided, so that the identification result is more favorable for improving the precision.
Drawings
FIG. 1 is a perspective view of a typical five-axis hybrid machine tool spindle head;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a schematic view of the mounting location of the dial gauge of the present invention;
FIG. 4 shows RTCP accuracy detection results before calibration of a five-axis series-parallel machine tool;
fig. 5 shows RTCP accuracy detection results after calibration of the five-axis series-parallel machine tool.
The calibration experiment in the figure verifies that a 3-PRRU mechanism based series-parallel machine tool is used.
Detailed Description
The principles, construction and embodiments of the present invention will be further explained with reference to the drawings.
Fig. 1 is a typical 3-PRRU parallel spindle head structure, in which a first slider 2, a second slider 6, and a third slider 8 of the parallel spindle head are mounted on a static platform 1, a first rod 3, a second rod 4, and a third rod 7 are connected to a terminal moving platform, the first slider 2, the second slider 6, and the third slider 8 respectively drive the first rod 3, the second rod 4, and the third rod 7, so as to drive the terminal moving platform 5 to move, and branched chains in which the first slider 2, the second slider 6, and the third slider 8 are respectively referred to as a first branch link, a second branched chain, and a third branched chain of the parallel spindle head.
Fig. 2 is a schematic flow chart of the method for calibrating a spindle head of a five-axis hybrid machine tool according to the present invention, and as shown in fig. 2, the method for calibrating a spindle head of a five-axis hybrid machine tool according to the present invention includes the following steps:
1) establishing a kinematic model and a geometric error model of a main shaft head of a five-shaft series-parallel machine tool;
taking the 3-PRRU spindle head as an example, the superposition of the revolute pair and the Hooke hinge is equivalent to a spherical hinge, so the 3-PRRU can be equivalent to a 3-PRS parallel structure in terms of operation.
According to the closed-loop vector method, for each branch of the spindle head there is:
H+RTTRiai＝Ribi+RiRBiqi+RiRBiRCili
wherein, H, ai、bi、liAnd q isiRespectively representing the terminal position of the parallel spindle head, the structural parameter of the movable platform of the terminal, the structural parameter of the static platform, the structural parameter of the rod piece and the position of the slide block, RTT、Ri、RBiAnd RCiAnd respectively showing a rotation matrix from the movable platform to the static platform of the parallel spindle head terminal, a rotation matrix of each branched chain, a rotation matrix of the P pair and a rotation matrix of the R pair.
The spindle head configuration is 3-PRRU, and the 3-PRRU can be simplified into 3-PRS when kinematic analysis is carried out. The kinematic pair of each branched chain connected with the fixed platform is a moving pair P, the kinematic pair connected with the moving platform is a ball pair S, and a revolute pair R is arranged between the moving pair and the ball pair. The expression of the rotation matrix of the P pair is the direction matrix of the moving pair guide rail, and the expression of the rotation matrix of the R pair is the direction matrix of the rod piece.
And taking differential on two sides to obtain a geometric error model containing all error parameters:
H+RTTRi(ai+Δai)＝Ri(bi+Δbi)+RiRBiRθBi(qi+Δqi)+RiRBiRθBiRCiRθCi(li+Δli)
wherein Δ aiAnd Δ biRepresenting the geometric error vector of the moving platform and the geometric error vector of the stationary platform, Δ qiAnd Δ liRespectively representing the position error of each slide and the length error of the connecting rod, RθBiAnd RθCiI pairs in subscript representing guide rail angle error matrix and slide block angle error matrixThis should be the ith branch.
The above equation can be rewritten as a kinematic equation and a constraint equation with geometric error terms:
||H+RTTRi(ai+Δai)-Ri(bi+Δbi)-RiRBiRθBi(qi+Δqi)||2＝li+Δli
(H+RTTRi(ai+Δai)-Ri(bi+Δbi)-RiRBiRθBi(qi+Δqi))·RiRBiRθBiRCiRθCie2＝0
2) establishing a kinematic positive solution equation of the position of the center point of the cutter according to the length of the cutter, and solving an error identification matrix function of the position error of the center point of the cutter under corresponding input through a differential substitution differentiation method;
firstly, the position of the center point of the cutter can be represented by the position and the posture of a movable platform of a parallel shaft head:
p＝H+RTT·[0 0 ld]T (1)
wherein p represents the position vector of the center point of the tool, H represents the position vector of the center point of the movable platform of the spindle head, and RTTAttitude matrix representing the main axis of the moving platform, ldIndicating the length of the tool.
The control model of the main spindle head of the parallel-serial machine tool can be written as the following functional form:
F(p,q,r)＝0 (2)
where q represents a spindle head input vector of the spindle head, r represents a geometric parameter of the spindle head, and derivation of equation (2) can be obtained:
Figure BDA0002783193500000071
since the spindle head input vector can be directly read from the control system, there is no error, and the formula (3) can be written as:
dp＝Jdr
Figure BDA0002783193500000072
wherein dp represents a position error column vector of a center point of the tool, dr represents a geometric error parameter column vector of the spindle head, J is a recognition matrix of the position error of the center point of the tool, and J is [ J ═ J1 J2…Jn]，JiI-th column vector, r, representing an error identification matrixiAnd taking a smaller value for the ith element, and obtaining the error parameter difference vector with all the remaining elements being 0.
3) Selecting a measurement attitude, driving a five-axis series-parallel machine tool through an RTCP function, enabling a main shaft head to move to different attitudes when the theoretical position of the center point of a tool is unchanged, and measuring the position error of the center point of the tool corresponding to each attitude and the input vector of the corresponding main shaft head;
the specific measurement method is shown in fig. 3:
in the actual measurement process, the position of the center point of the cutter is determined by the position of the sphere center of a ball head check rod arranged on a main shaft head, the measuring tool is three dial indicators 20, the three dial indicators 20 play a role in positioning, and the position of a ball with a known radius can be determined by any three points on the spherical surface, so that the dial indicators do not need to be strictly parallel to the coordinate axis direction and point to the sphere center in the installation process, and the difficulty in installing the dial indicators is reduced.
When the RTCP function is performed, the tool center point position is theoretically kept constant when the posture is changed, but the tool center point position is changed when the posture is changed due to the presence of geometric errors. Firstly, the attitude zero point of the spindle head is found, and the method is characterized in that a dial indicator is fixed at the front end of the spindle head, and the input of the spindle head is finely adjusted, so that the jitter of the dial indicator is less than 0.01mm when the spindle head rotates for one circle. Taking the attitude zero point (namely 0 th attitude) as a datum point, installing three dial indicators, and recording the reading of the dial indicators as [ x ]0 y0z0]The value X, Y, Z in the control system is [ X ]0 Y0 Z0]TChanging posture by RTCP functionThe state changes from the attitude Z1 to the attitude Z2, and the input vector q of the spindle head at the moment is recorded1i q2i q3i]TAnd (4) finely adjusting X, Y, Z value in the control system to enable the dial indicator reading to return to x0y0 z0]At this time, X, Y, Z value [ X ] in the control system is readi Yi Zi]TThen, it is determined that the input vector of the spindle head is [ q ]1i q2i q3i]TWhen the error of the center point position of the cutter is [ X ]i-X0 Yi-Y0 Zi-Z0]T。
The X, Y, Z value in the control system refers to the theoretical position of the center point of the tool calculated by the control system according to the input vectors of the spindle head (three input vectors of the spindle head and X, Y two tandem axes), and can be directly read from the panel of the control system. The main shaft head input vector is the driving vector of three main shaft heads of the main shaft head, and can also be directly read from the numerical control panel.
4) Solving an error identification matrix according to the measured input vector of the spindle head, and identifying geometric error parameters of the parallel spindle head of the five-axis parallel machine tool by combining the measured position error of the central point of the tool;
5) and substituting the identified geometric error parameters into the kinematic model with the error item to realize error compensation and finish kinematic calibration.
Fig. 4 shows the result of RTCP precision measurement performed by the five-axis parallel-serial machine tool before calibration in this example.
Fig. 5 shows the result of RTCP precision measurement performed by the five-axis parallel-serial machine tool after calibration in the present embodiment.
The calibration experiment platform is based on a five-axis hybrid machine tool containing a 3-PRRU main shaft head, and the maximum errors of the five-axis hybrid machine tool in the X, Y, Z direction before calibration are 2.4230mm, 1.1250mm and 3.9870mm respectively. After the calibration is carried out by using the provided calibration method of the main shaft head of the five-shaft series-parallel machine tool, the maximum errors of the five-shaft series-parallel machine tool in the X, Y, Z direction are respectively 0.0280mm, 0.0420mm and 0.0290 mm. The precision of the machine tool after calibration is greatly improved compared with that before calibration, and the accuracy of the method for calibrating the main shaft head of the five-shaft series-parallel machine tool is proved.
The invention provides a series-parallel machine tool spindle head calibration device, which comprises:
the kinematic model establishing module is used for establishing a kinematic model and a geometric error model of a main shaft head of the five-shaft series-parallel machine tool to form a kinematic model with an error item;
the error identification matrix obtaining module is used for establishing a kinematic positive solution equation of the position of the center point of the cutter according to the length of the cutter, and obtaining an error identification matrix of the position error of the center point of the cutter under the corresponding main shaft head input vector by a differential substitution differentiation method;
the tool center point position error obtaining module is used for driving the five-axis series-parallel machine tool through an RTCP function, so that the spindle head moves to different postures when the theoretical position of the tool center point is not changed, and the corresponding tool center point position error and the corresponding spindle head input vector under each posture are measured;
the error identification module is used for substituting the measured input vector of the spindle head into an error identification matrix, and identifying geometric error parameters of the spindle head of the five-axis series-parallel machine tool by combining the measured position error of the central point of the tool;
and the calibration module is used for substituting the geometric error parameters obtained by identification into the kinematic model with the error item to realize error compensation and finish kinematic calibration.

Claims (5)

1. A method for calibrating a main shaft head of a series-parallel machine tool is characterized by comprising the following steps:
1) establishing a kinematic model and a geometric error model of a main shaft head of a five-shaft series-parallel machine tool to form a kinematic model with an error term;
2) establishing a kinematic positive solution equation of the position of the center point of the tool according to the length of the tool, and obtaining an error identification matrix of the position error of the center point of the tool under the input vector of the corresponding spindle head by a differential substitution differential method;
3) driving a five-axis series-parallel machine tool through an RTCP function, enabling a main shaft head to move to different postures when the theoretical position of the central point of a cutter is unchanged, and measuring the position error of the central point of the cutter corresponding to each posture and the input vector of the main shaft head corresponding to each posture;
4) substituting the measured input vector of the spindle head into an error identification matrix, and identifying the geometric error parameter of the spindle head of the five-axis series-parallel machine tool by combining the measured position error of the central point of the tool;
5) substituting the geometric error parameters obtained by identification into the kinematic model with the error item to realize error compensation and finish kinematic calibration,
wherein, according to the length of the cutter, establishing a kinematic positive solution equation of the position of the center point of the cutter comprises the following steps:
according to the length of the tool, reflecting the position and the posture of the spindle head of the five-axis series-parallel machine tool through the position of the center point of the tool, as shown in the following formula:
p＝H+RTT·[0 0 ld]T
wherein p represents the position vector of the center point of the tool, H represents the position vector of the center point of the movable platform of the spindle head, and RTTAttitude matrix representing the main axis moving platform,/dIndicating the length of the tool;
wherein, the error identification matrix of the position error of the center point of the tool under the input vector of the corresponding spindle head obtained by the method of replacing differential by difference comprises:
dp＝Jdr
Figure FDA0003586581620000011
wherein dp represents a position error column vector of a center point of the tool, q represents a spindle head input vector of the spindle head, dr represents a geometric error parameter column vector of the spindle head, J is an error identification matrix of the position error of the center point of the tool, and J is [ J ═ J [ ]1 J2…J33]，JiI-th column vector of error identification matrix representing error of center point position of tool, r represents geometric parameter vector of spindle head, and r representsiTaking a smaller value for the ith element, and taking the error parameter difference vector with the remaining elements all being 0;
substituting the measured input vector of the spindle head into the error identification matrix, and identifying the geometric error parameter of the spindle head of the five-axis series-parallel machine tool by combining the measured position error of the central point of the tool, wherein the geometric error parameter comprises the following steps:
1) obtaining a position error matrix dp after stacking according to the position error of the center point of the cutter and the corresponding input vector of the spindle head*3n×1And error identification matrix J*3n×33：
Figure FDA0003586581620000021
Wherein, dXn、dYnAnd dZnDenotes the positional deviation of the center point of the tool in the direction X, Y, Z, q, measured at the nth measurement attitudenRepresenting the spindle head input vector at the nth measurement attitude, r being a geometric parameter, JnRepresenting an error recognition matrix at the nth measurement attitude;
X0、Y0、Z0indicating X, Y, Z values in the control system at attitude zero;
Xn、Ynand ZnIndicating X, Y, Z values in the control system at the nth measurement attitude;
2) constructing an error identification equation:
dp*3n×1＝J*3n×33dr33×1 (7)；
3) using ridge estimation algorithm to carry out iterative solution identification to obtain geometric error parameters dr of the parallel spindle heads33×1，
dr33×1＝(J*3n×33 TJ*3n×33+λI)-1J*3n×33 Tdp*3n×1 (8)
Wherein λ is a ridge estimation parameter;
i is a 33 th order identity matrix.
2. The method for calibrating the spindle head of the parallel-serial machine tool according to claim 1, wherein in step 3, the measuring the position error of the center point of the corresponding tool in each attitude comprises:
the position error of the center point of the cutter is determined by the position of the sphere center of a ball head detection rod arranged on a main shaft head, the position error is in contact with the outer wall of the ball head detection rod along the radial direction through a plurality of dial indicators, after a main shaft head moving platform is changed from a first posture to a second posture, the control system is adjusted to perform linear motion in the direction of X, Y, Z, the number of each dial indicator is the same as that of the dial indicator in the first posture, the change quantity in the direction of X, Y, Z is read out in the control system to serve as the position error of the center point of the cutter in the direction of X, Y, Z, wherein the direction of X, Y, Z is along three coordinate axes of a rectangular coordinate system.
3. The method for calibrating the spindle head of the series-parallel machine tool according to claim 2, wherein the number of the dial indicators is three, and the dial indicators correspond to X, Y, Z directions respectively.
4. The method for calibrating the main shaft head of the series-parallel machine tool according to claim 1, wherein the establishing of the kinematic model and the geometric error model of the main shaft head of the five-shaft series-parallel machine tool to form the kinematic model with the error term comprises:
according to the closed-loop vector method, for each branch chain of the spindle head:
H+RTTRiai＝Ribi+RiRBiqi+RiRBiRCili
wherein, H, ai、bi、liAnd q isiRespectively representing the terminal position of the parallel spindle head, the structural parameter of the movable platform of the terminal, the structural parameter of the static platform, the structural parameter of the rod piece and the position of the slide block, RTT、Ri、RBiAnd RCiRespectively representing a rotation matrix from a movable platform to a static platform of the parallel spindle head terminal, a rotation matrix of each branched chain, a rotation matrix of a P pair and a rotation matrix of an R pair,
and (3) taking differential on two sides to obtain a geometric error model containing all error parameters:
H+RTTRi(ai+Δai)＝Ri(bi+Δbi)+RiRBiRθBi(qi+Δqi)+RiRBiRθBiRCiRθCi(li+Δli)
wherein Δ aiAnd Δ biRepresenting the geometric error vector of the moving platform and the geometric error vector of the stationary platform, Δ qiAnd Δ liRespectively representing the position error of each slide and the length error of the connecting rod, RθBiAnd RθCiShowing a guide rail angle error matrix and a slide block angle error matrix, wherein i in the subscript corresponds to the ith branched chain,
rewriting the geometric error model into a kinematic model containing a geometric error term:
||H+RTTRi(ai+Δai)-Ri(bi+Δbi)-RiRBiRθBi(qi+Δqi)||2＝li+Δli
(H+RTTRi(ai+Δai)-Ri(bi+Δbi)-RiRBiRθBi(qi+Δqi))·RiRBiRθBiRCiRθCie2＝0。
5. the utility model provides a series-parallel connection lathe main shaft head calibration device which characterized in that includes:
the kinematic model establishing module is used for establishing a kinematic model and a geometric error model of a main shaft head of the five-shaft series-parallel machine tool to form a kinematic model with an error term;
the error identification matrix obtaining module is used for establishing a kinematic positive solution equation of the position of the center point of the tool according to the length of the tool and obtaining an error identification matrix of the position error of the center point of the tool under the input vector of the corresponding spindle head by a differential substitution differentiation method;
the tool center point position error obtaining module is used for driving the five-axis series-parallel machine tool through an RTCP function, so that the spindle head moves to different postures when the theoretical position of the tool center point is unchanged, and the corresponding tool center point position error and the corresponding spindle head input vector under each posture are measured;
the error identification module is used for substituting the measured input vector of the spindle head into an error identification matrix, and identifying geometric error parameters of the spindle head of the five-axis series-parallel machine tool by combining the measured position error of the central point of the tool;
the calibration module is used for substituting the geometric error parameters obtained by identification into the kinematic model with the error item to realize error compensation and finish kinematic calibration,
wherein, according to the length of the cutter, establishing a kinematic positive solution equation of the position of the center point of the cutter comprises the following steps:
according to the length of the cutter, reflecting the position and the posture of the main shaft head of the five-shaft series-parallel machine tool through the position of the central point of the cutter, as shown in the following formula:
p＝H+RTT·[0 0 ld]T
wherein p represents the position vector of the center point of the tool, H represents the position vector of the center point of the movable platform of the spindle head, and RTTAttitude matrix representing the main axis moving platform,/dIndicating the length of the tool;
wherein, the error identification matrix of the position error of the center point of the tool under the input vector of the corresponding spindle head obtained by the method of replacing differential by difference comprises:
dp＝Jdr
Figure FDA0003586581620000041
wherein dp represents a position error column vector of a center point of the tool, q represents a spindle head input vector of the spindle head, dr represents a geometric error parameter column vector of the spindle head, J is an error identification matrix of the position error of the center point of the tool, and J is [ J ═ J1 J2…J33]，JiI-th column vector of error identification matrix representing error of center point position of tool, r represents geometric parameter vector of spindle head, and r representsiIs the ith elementTaking a smaller value, and obtaining an error parameter difference vector with the remaining elements of 0;
substituting the measured input vector of the spindle head into the error identification matrix, and identifying the geometric error parameter of the spindle head of the five-axis series-parallel machine tool by combining the measured position error of the central point of the tool, wherein the geometric error parameter comprises the following steps:
1) obtaining a position error matrix dp after stacking according to the position error of the central point of the cutter and the corresponding input vector of the spindle head*3n×1And error identification matrix J*3n×33：
Figure FDA0003586581620000042
Wherein, dXn、dYnAnd dZnDenotes the positional deviation of the center point of the tool in the direction X, Y, Z, q, measured at the nth measurement attitudenRepresenting the spindle head input vector at the nth measurement attitude, r being a geometric parameter, JnRepresenting an error recognition matrix at the nth measurement attitude;
X0、Y0、Z0x, Y, Z values in the control system at attitude zero;
Xn、Ynand ZnIndicating X, Y, Z values in the control system at the nth measurement attitude;
2) constructing an error identification equation:
dp*3n×1＝J*3n×33dr33×1 (7)；
3) iterative solution identification is carried out by using ridge estimation algorithm to obtain geometric error parameters dr of the parallel spindle heads33×1，
dr33×1＝(J*3n×33 TJ*3n×33+λI)-1J*3n×33 Tdp*3n×1 (8)
Wherein λ is a ridge estimation parameter;
i is a 33 th order identity matrix.
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