CN112487615B - A five-axis hybrid machine tool spindle head calibration method and device - Google Patents

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 spindle head of five-axis hybrid machine tool

technical field

The invention belongs to the field of machine tool manufacturing, in particular to a method and a device for calibrating a spindle head of a five-axis hybrid machine tool.

Background technique

Since the 21st century, parallel mechanisms have been more and more widely used in the industry due to their advantages of high stiffness, high precision, and bearing capacity. As an innovation of machine tool structure, hybrid machine tool combines the advantages of parallel mechanism and series mechanism. In theory, compared with traditional machine tools, it has better performance in terms of accuracy and rigidity, and is lighter in weight and better in processing flexibility. It has received extensive attention at home and abroad. However, looking at the existing hybrid machine tools at home and abroad, the products that can be practical and industrialized are very limited, especially in terms of accuracy, the actual accuracy of the hybrid machine tool is far lower than the accuracy obtained by theoretical analysis and simulation, and cannot meet the accuracy requirements. . Therefore, how to ensure the geometric accuracy of the hybrid machine tool is the key technology that needs to be solved at present.

For a hybrid machine tool, there are a large number of passive joints in the parallel spindle head, which will bring a large number of geometric errors in the manufacturing and assembly process, resulting in the terminal of the machine tool spindle head (parallel drive platform) will deviate from the original designed terminal position, Machine tool accuracy is greatly reduced. The kinematics calibration technology is a technology that corrects the control model by identifying the error parameters in the machine tool kinematics through the measured actual error of the machine tool after the machine tool is manufactured, thereby compensating for the machine tool terminal error and improving the machine tool terminal accuracy. Therefore, it is necessary to kinematically calibrate the spindle head of the hybrid machine tool to improve the terminal accuracy of the machine tool.

The kinematic calibration is mainly divided into the following four steps: error modeling, error measurement, parameter identification, and error compensation. Among them, error measurement is the basis of identification and compensation. The higher the measurement accuracy, the more measurement information, the more accurate the identification result, and the higher the accuracy after compensation.

At present, for the kinematics calibration of five-axis hybrid machine tools, since the rotation angle of the terminal around the tool axis does not affect the machining accuracy, it is necessary to measure three positions and two attitude angles. The position measurement is relatively easy to implement, but the attitude measurement is more difficult. If a commercial measuring instrument is used for attitude measurement, the measurement cost is high, and the measurement accuracy cannot reach the accuracy required for kinematic calibration. If a self-made measuring instrument is used for measurement, the steps are cumbersome, the efficiency is extremely low, and the measurable attitude is limited. When using the measured position and attitude errors for identification at the same time, the identification results will also be affected due to the different position and attitude dimensions.

SUMMARY OF THE INVENTION

Aiming at the above problems of difficulty in attitude measurement and the inconsistency of position and attitude dimensions in the identification process, the present invention proposes a method for calibrating the spindle head of a five-axis hybrid machine tool in combination with the structure of a five-axis hybrid machine tool. The position of the center point reflects the position and attitude of the parallel spindle head, and no attitude measurement is required. Combined with a small number of devices and simple operation steps, the calibration can be achieved only by measuring the position deviation of each attitude when the RTCP moves, and avoids the identification process. The problem of non-uniform dimensions improves the identification accuracy and greatly reduces the measurement cost.

The technical scheme of the present invention is as follows:

A method for calibrating a spindle head of a hybrid machine tool, comprising the following steps:

1) Establish the kinematic model and geometric error model of the spindle head of the five-axis hybrid machine tool, and form a kinematic model with an error term;

2) According to the tool length, establish the kinematics positive solution equation of the position of the tool center point, and obtain the error identification matrix of the position error of the tool center point under the corresponding spindle head input vector by the method of differential substitution of differentiation;

3) Drive the five-axis hybrid machine tool through the RTCP function, so that when the theoretical position of the tool center point remains unchanged, the spindle head moves to different attitudes, and the position error of the corresponding tool center point under each attitude and the corresponding spindle head input vector are measured;

4) Substitute the measured input vector of the spindle head into the error identification matrix, and combine the measured position error of the tool center point to identify the geometric error parameters of the parallel spindle head of the five-axis hybrid machine tool;

5) Substitute the identified geometric error parameters into the kinematics model with an error term to realize error compensation and complete kinematic calibration.

Optionally, the kinematic positive solution equation for establishing the position of the tool center point includes:

According to the length of the tool, the position and attitude of the spindle head of the hybrid machine tool are reflected by the position of the center point of the tool, as shown in the following formula:

p=H+R _TT ·[0 0 l _d ] ^T

Among them, p represents the position vector of the tool center point, H represents the position vector of the center point of the spindle head moving platform, R _TT represents the attitude matrix of the spindle moving platform, and _ld represents the length of the tool.

Optionally, the error identification matrix that obtains the position error of the tool center point under the corresponding spindle head input vector by using the method of differential substitution for differential includes:

dp=Jdr

Among them, dp represents the position error column vector of the tool center point, q represents the spindle head input vector of the spindle head, dr represents the geometric error parameter column vector of the spindle head, J is the error identification matrix of the tool center point position error, J=[J ₁ J ₂ …J ₃₃ ], J _i represents the i-th column vector of the error identification matrix of the tool center point position error, r represents the geometric parameter vector of the spindle head, ri _i is the i-th element taking the smaller value, and the remaining elements are all An error parameter difference vector of 0.

Optionally, in step 2, measuring the position error of the tool center point corresponding to each attitude includes:

The position error of the tool center point is determined by the position of the ball head inspection baseball center installed on the spindle head, and is in contact with the outer wall of the ball head inspection rod in the radial direction through a plurality of dial indicators. After the second posture, adjust the control system to perform linear motion in the X, Y, and Z directions, so that the indication of each dial indicator is the same as the indication in the first posture, and the control system reads out the X, Y, and Z directions. The change amount of is taken as the position error of the tool center point in the X, Y, and Z directions, wherein the X, Y, and Z directions are directions along the three coordinate axes of the Cartesian coordinate system.

Optionally, there are three dial indicators, and they correspond to the X, Y, and Z directions respectively.

Optionally, the kinematic model and geometric error model of the spindle head of the five-axis hybrid machine tool are established to form a kinematic model with an error term, including:

According to the closed-loop vector method, for each branch of the spindle head there are:

H+R _TT R _i a _i =R _i b _i +R _i R _Bi q _i +R _i R _Bi R _Ci l _i

Among them, H, a _i , b _i , _li and qi _represent the terminal position of the parallel spindle head, the structural parameters of the terminal moving platform, the structural parameters of the static platform, the structural parameters of the rod and the position of the slider, respectively, R _TT , R _i , R _Bi and R _Ci respectively represent the rotation matrix from the moving platform at the end of the parallel spindle head to the static platform, the rotation matrix of each branch chain, the rotation matrix of the P pair and the rotation matrix of the R pair,

Differentiate both sides to obtain a geometric error model containing all error parameters:

H+R _TT R _i (a _i +Δa _i )=

R _i (b _i +Δb _i )+R _i R _Bi R _θBi (q _i +Δq _i )

+R _i R _Bi R _θBi R _Ci R _θCi (l _i +Δl _i )

where Δa _i and Δb _i represent the geometric error vector of the moving platform and the geometric error vector of the static platform, Δq _i and Δli _i represent the position error of each slider and the length error of the connecting rod, respectively, R _θBi and R _θCi represent the guide rail angle error matrix and slider angle error matrix, i in the subscript corresponds to the i-th branch,

The geometric error model is rewritten as a kinematic model with geometric error terms:

||H+R _TT R _i (a _i +Δa _i )-R _i (b _i +Δb _i )-R _i R _Bi R _θBi (q _i +Δq _i )|| ₂ =l _i +Δl _i

(H+R _TT R _i (a _i +Δa _i )-R _i (b _i +Δb _i )-R _i R _Bi R _θBi (q _i +Δq _i )) R _i R _Bi R _θBi R _Ci R _θCi e ₂ =0.

Optionally, the measured input vector of the spindle head is substituted into the error identification matrix, and the geometric error parameters of the parallel spindle head of the five-axis hybrid machine tool are identified in combination with the measured position error of the tool center point, including:

1) According to the position error of the tool center point and the corresponding input vector of the spindle head, the stacked position error matrix dp _*3n×1 and the error identification matrix J _*3n×33 are obtained:

Among them, dX _n , dY _n and dZ _n represent the positional deviation of the tool center point in the X, Y and Z directions measured at the nth measurement attitude, and q _n represents the spindle head spindle head at the nth measurement attitude Input vector, r is the geometric parameter, J _n represents the error identification matrix at the nth measurement attitude;

X ₀ , Y ₀ , Z ₀ represent the values of X, Y, and Z in the control system at attitude zero;

X _n , Y _n and Z _n represent the X, Y and Z values in the control system at the nth measurement attitude;

2) Construct the error identification equation:

dp _*3n×1 =J _*3n×33 dr _33×1 (7);

3) Use the ridge estimation algorithm to iteratively solve the identification to obtain the geometric error parameter dr _33×1 of the parallel spindle head,

dr _33×1 = (J _*3n×33 ^T J _*3n×33 +λI) ^-1 J _*3n×33 ^T dp _*3n×1 (8)

where λ is the ridge estimation parameter.

I is an identity matrix of order 33.

It should be noted that the subscripts of dp _*3n×1 , J _*3n×33 , and dr _33×1 are only used to describe the number of elements contained in the vector. For example, dr and dr _33×1 have the same meaning, and dr ₃₃ ×1 means that the column vector of geometric error parameters of the spindle head contains 33 elements.

A device for calibrating a spindle head of a hybrid machine tool, comprising:

The kinematic model building module is used to establish the kinematic model and geometric error model of the spindle head of the five-axis hybrid machine tool, and form a kinematic model with an error term;

The error identification matrix acquisition module is used to establish the kinematics positive solution equation of the position of the tool center point according to the tool length, and obtain the error identification matrix of the position error of the tool center point under the corresponding spindle head input vector by the method of difference instead of differential;

The tool center point position error acquisition module is used to drive the five-axis hybrid machine tool through the RTCP function, so that when the theoretical position of the tool center point remains unchanged, the spindle head moves to different attitudes, and the corresponding tool center point position errors and Corresponding spindle head input vector;

The error identification module is used to substitute the measured input vector of the spindle head into the error identification matrix, and combine the measured position error of the tool center point to identify the geometric error parameters of the spindle head of the five-axis hybrid machine tool;

The calibration module is used for substituting the identified geometric error parameters into the kinematics model with an error term to realize error compensation and complete kinematics calibration.

Compared with the prior art, the present invention has the following advantages and prominent technical effects: 1. The present invention proposes a kinematic calibration method that does not require attitude measurement but only needs to measure the position, which greatly reduces the measurement cost . ②The present invention combines the RTCP function of the five-axis hybrid machine tool, only needs to adjust the posture, and measure the position error of the corresponding tool center point, only three dial indicators are required, and only one installation is required to complete the measurement task, achieve calibration, and extremely It greatly simplifies the measurement steps and reduces the measurement time. ③In the process of identification, the present invention avoids the problem that the dimensions of the position and the attitude are not unified, so that the identification result is more conducive to the improvement of the accuracy.

Description of drawings

Fig. 1 is a three-dimensional schematic diagram of a typical five-axis hybrid machine tool spindle head;

Fig. 2 is the flow chart of the method of the present invention;

Fig. 3 is the schematic diagram of the installation position of the dial indicator of the present invention;

Figure 4 shows the RTCP accuracy test results before the calibration of the five-axis hybrid machine tool;

Figure 5 shows the RTCP accuracy test results after the calibration of the five-axis hybrid machine tool.

The calibration experiment in the figure verifies the use of a hybrid machine tool based on the 3-PRRU mechanism.

Detailed ways

The principle, structure and implementation of the present invention will be further described below with reference to the accompanying drawings.

Figure 1 is a typical 3-PRRU parallel spindle head structure. The first slider 2, the second slider 6, and the third slider 8 of the parallel spindle head are mounted on the static platform 1, and the first rod 3 , The second rod 4 and the third rod 7 are connected to the terminal moving platform, and the first slide 2, the second slide 6 and the third slide 8 drive the first rod 3, the second rod 4 and the third slide respectively. The three rods 7 drive the terminal moving platform 5 to move. The branches where the first sliding block 2, the second sliding block 6 and the third sliding block 8 are located are respectively called the first branch connection and the second branch chain of the parallel spindle head. and the third branch.

Fig. 2 is a schematic flowchart of the method for calibrating the spindle head of a five-axis hybrid machine tool in the present invention. As shown in Fig. 2, the method for calibrating a spindle head of a five-axis hybrid machine tool provided by the present invention includes the following steps:

1) Establish the kinematic model and geometric error model of the spindle head of the five-axis hybrid machine tool;

Taking the 3-PRRU spindle head as an example, the superposition of the rotating 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 transportation.

According to the closed-loop vector method, for each branch of the spindle head there are:

H+R _TT R _i a _i =R _i b _i +R _i R _Bi q _i +R _i R _Bi R _Ci l _i

Among them, H, a _i , b _i , _li and qi _represent the terminal position of the parallel spindle head, the structural parameters of the terminal moving platform, the structural parameters of the static platform, the structural parameters of the rod and the position of the slider, respectively, R _TT , R _i , R _Bi and R _Ci respectively represent the rotation matrix from the moving platform at the end of the parallel spindle head to the static platform, the rotation matrix of each branch chain, the rotation matrix of the P pair and the rotation matrix of the R pair.

The configuration of the spindle head is 3-PRRU, which can be simplified to 3-PRS for kinematic analysis. The kinematic pair connected with the fixed platform of each branch chain is the moving pair P, the kinematic pair connected with the moving platform is the ball pair S, and the rotating pair R is between the moving pair and the ball pair. Here, the rotation matrix of the P pair expresses the direction matrix of the moving auxiliary guide rail, and the rotation matrix of the R pair expresses the direction matrix of the rod.

Differentiating both sides, the geometric error model containing all error parameters can be obtained:

H+R _TT R _i (a _i +Δa _i )=R _i (b _i +Δb _i )+R _i R _Bi R _θBi (q _i +Δq _i )+R _i R _Bi R _θBi R _Ci R _θCi (l _i +Δl _i )

where Δa _i and Δb _i represent the geometric error vector of the moving platform and the geometric error vector of the static platform, Δq _i and Δli _i represent the position error of each slider and the length error of the connecting rod, respectively, R _θBi and R _θCi represent the guide rail angle error Matrix and slider angle error matrix, i in the subscript corresponds to the ith branch.

The above equation can be rewritten as the motion equation and constraint equation with geometric error terms:

||H+R _TT R _i (a _i +Δa _i )-R _i (b _i +Δb _i )-R _i R _Bi R _θBi (q _i +Δq _i )|| ₂ =l _i +Δl _i

(H+R _TT R _i (a _i +Δa _i )-R _i (b _i +Δb _i )-R _i R _Bi R _θBi (q _i +Δq _i )) R _i R _Bi R _θBi R _Ci R _θCi e ₂ =0

2) According to the tool length, establish the kinematics positive solution equation of the position of the tool center point, and obtain the error identification matrix function of the position error of the tool center point under the corresponding input by using the method of difference instead of differential;

First of all, the position of the tool center point can be represented by the position and attitude of the parallel shaft head moving platform:

p=H+R _TT ·[0 0 l _d ] ^T (1)

Among them, p represents the position vector of the tool center point, H represents the position vector of the center point of the spindle head moving platform, R _TT represents the attitude matrix of the spindle moving platform, and _ld represents the length of the tool.

The control model of the spindle head of the hybrid machine tool can be written in the following functional form:

F(p,q,r)=0 (2)

Among them, q represents the spindle head input vector of the spindle head, and r represents the geometric parameters of the spindle head. The derivation of formula (2) can be obtained:

Since the input vector of the spindle head can be directly read from the control system, there is no error, equation (3) can be written as:

dp=Jdr

Among them, dp represents the position error column vector of the tool center point, dr represents the geometric error parameter column vector of the spindle head, J is the tool center point position error error identification matrix, J=[J ₁ J ₂ …J _n ], J _i represents The ith column vector of the error error identification matrix, ri is the _ith element taking the smaller value, and the remaining elements are all 0 error parameter difference vectors.

3) Select the measurement attitude, drive the five-axis hybrid machine tool through the RTCP function, so that when the theoretical position of the tool center point remains unchanged, the spindle head moves to different attitudes, and measure the position error of the tool center point corresponding to each attitude and the corresponding spindle head input vector;

The specific measurement method is shown in Figure 3:

In the actual measurement process, the position of the center point of the tool is determined by the position of the ball head inspection baseball center installed on the spindle head. The measuring tool is three dial indicators 20, and the three dial indicators Determine the position of a ball with a known radius, so the dial indicator does not need to be strictly parallel to the coordinate axis and point to the center of the ball during the installation process, which reduces the difficulty of dial indicator installation.

When the RTCP function is executed, theoretically, when the attitude changes, the position of the tool center point remains unchanged, but due to the existence of geometric errors, when the attitude changes, the position of the tool center point will change. First, find the zero point of the spindle head attitude. The method is to fix the dial indicator at the front end of the spindle head and fine-tune the input of the spindle head so that the dial indicator jumps less than 0.01mm when the spindle head rotates once. Take the attitude zero point (that is, the 0th attitude) as the reference point, install three dial indicators, record the reading of the dial indicators as [x ₀ y ₀ z ₀ ], and the X, Y, and Z values in the control system are [X ₀ Y ₀ Z ₀ ] ^T , change the attitude through the RTCP function, from the attitude Z1 to the attitude Z2, record the input vector [q _1i q _2i q _3i ] ^T of the spindle head at this time, fine-tune the X, Y, Z values in the control system, so that the The reading of the sub-meter returns to [x ₀ y ₀ z ₀ ], and the X, Y, Z values [X _i Y _i Z _i ] ^T in the control system are read at this time, and the input vector of the spindle head is measured as [q _1i q _2i q _3i ] ^T , the tool center point position error is [X _i -X ₀ Y _i -Y ₀ Z _i -Z ₀ ] ^T .

Among them, the X, Y, Z values in the control system refer to the theoretical position of the tool center point calculated by the control system according to the input vectors of the spindle head (the input vectors of the three spindle heads of the spindle head and the two series axes of X and Y). Read from the control system panel. The input vector of the spindle head refers to the driving vector of the three driving axes of the spindle head, which can also be read directly from the CNC panel.

4) Obtain the error identification matrix according to the measured input vector of the spindle head, and identify the geometric error parameters of the parallel spindle head of the five-axis hybrid machine tool in combination with the measured position error of the tool center point;

5) Substitute the geometric error parameters obtained by identification into the kinematics model with error terms to realize error compensation and complete kinematics calibration.

Figure 4 shows the results of the RTCP accuracy test performed on the first five-axis hybrid machine tool calibrated in this example.

Figure 5 shows the results of RTCP accuracy detection on the five-axis hybrid machine tool after calibration in this example.

The calibration experimental platform is based on a five-axis hybrid machine tool with a 3-PRRU spindle head. Before calibration, the maximum errors of the five-axis hybrid machine tool in the X, Y, and Z directions are 2.4230mm, 1.1250mm, and 3.9870mm, respectively. After calibration using the proposed five-axis hybrid machine tool spindle head calibration method, the maximum errors of the five-axis hybrid machine tool in the X, Y, and Z directions are 0.0280mm, 0.0420mm, and 0.0290mm, respectively. The accuracy of the machine tool after calibration has been greatly improved compared with that before the calibration, which proves the accuracy of the calibration method of the spindle head of the five-axis hybrid machine tool.

The invention provides a spindle head calibration device for a hybrid machine tool, comprising:

The kinematic model building module is used to establish the kinematic model and geometric error model of the spindle head of the five-axis hybrid machine tool, and form a kinematic model with an error term;

The error identification matrix acquisition module is used to establish the kinematics positive solution equation of the position of the tool center point according to the tool length, and obtain the error identification matrix of the position error of the tool center point under the corresponding spindle head input vector by the method of difference instead of differential;

The tool center point position error acquisition module is used to drive the five-axis hybrid machine tool through the RTCP function, so that when the theoretical position of the tool center point remains unchanged, the spindle head moves to different attitudes, and the corresponding tool center point position errors and Corresponding spindle head input vector;

The error identification module is used to substitute the measured input vector of the spindle head into the error identification matrix, and combine the measured position error of the tool center point to identify the geometric error parameters of the spindle head of the five-axis hybrid machine tool;

The calibration module is used for substituting the identified geometric error parameters into the kinematics model with an error term to realize error compensation and complete kinematics 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+R_TT·[0 0 l_d]^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 R_TTAttitude 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

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]，J_iI-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 represents_iTaking 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：

Wherein, dX_n、dY_nAnd dZ_nDenotes the positional deviation of the center point of the tool in the direction X, Y, Z, q, measured at the nth measurement attitude_nRepresenting the spindle head input vector at the nth measurement attitude, r being a geometric parameter, J_nRepresenting an error recognition matrix at the nth measurement attitude;

X₀、Y₀、Z₀indicating X, Y, Z values in the control system at attitude zero;

X_n、Y_nand Z_nIndicating X, Y, Z values in the control system at the nth measurement attitude;

2) constructing an error identification equation:

dp_*3n×1＝J_*3n×33dr_33×1 (7)；

3) using ridge estimation algorithm to carry out iterative solution identification to obtain geometric error parameters dr of the parallel spindle heads_33×1，

dr_33×1＝(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+R_TTR_ia_i＝R_ib_i+R_iR_Biq_i+R_iR_BiR_Cil_i

wherein, H, a_i、b_i、l_iAnd q is_iRespectively 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, R_TT、R_i、R_BiAnd R_CiRespectively 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+R_TTR_i(a_i+Δa_i)＝R_i(b_i+Δb_i)+R_iR_BiR_θBi(q_i+Δq_i)+R_iR_BiR_θBiR_CiR_θCi(l_i+Δl_i)

wherein Δ a_iAnd Δ b_iRepresenting the geometric error vector of the moving platform and the geometric error vector of the stationary platform, Δ q_iAnd Δ l_iRespectively representing the position error of each slide and the length error of the connecting rod, R_θBiAnd R_θCiShowing 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+R_TTR_i(a_i+Δa_i)-R_i(b_i+Δb_i)-R_iR_BiR_θBi(q_i+Δq_i)||₂＝l_i+Δl_i

(H+R_TTR_i(a_i+Δa_i)-R_i(b_i+Δb_i)-R_iR_BiR_θBi(q_i+Δq_i))·R_iR_BiR_θBiR_CiR_θCie₂＝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+R_TT·[0 0 l_d]^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 R_TTAttitude 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

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]，J_iI-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 represents_iIs 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：

Wherein, dX_n、dY_nAnd dZ_nDenotes the positional deviation of the center point of the tool in the direction X, Y, Z, q, measured at the nth measurement attitude_nRepresenting the spindle head input vector at the nth measurement attitude, r being a geometric parameter, J_nRepresenting an error recognition matrix at the nth measurement attitude;

X₀、Y₀、Z₀x, Y, Z values in the control system at attitude zero;

X_n、Y_nand Z_nIndicating X, Y, Z values in the control system at the nth measurement attitude;

2) constructing an error identification equation:

dp_*3n×1＝J_*3n×33dr_33×1 (7)；

3) iterative solution identification is carried out by using ridge estimation algorithm to obtain geometric error parameters dr of the parallel spindle heads_33×1，

dr_33×1＝(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.

Images