CN113359609B - Key geometric error optimization proportioning compensation method for five-axis numerical control machine tool - Google Patents

Key geometric error optimization proportioning compensation method for five-axis numerical control machine tool Download PDF

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CN113359609B
CN113359609B CN202110763788.1A CN202110763788A CN113359609B CN 113359609 B CN113359609 B CN 113359609B CN 202110763788 A CN202110763788 A CN 202110763788A CN 113359609 B CN113359609 B CN 113359609B
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CN113359609A (en
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项四通
张海南
孙江浩
虞奔
钱博增
陈茂雷
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Ningbo University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The optimization proportioning compensation method for the key geometric errors of the five-axis numerical control machine tool comprises the following steps: firstly, establishing a spatial error model; establishing a space error model of the five-axis numerical control machine tool by using a homogeneous coordinate matrix; secondly, identifying key geometric errors based on a quasi-Monte Carlo method; measuring a key geometric error of a machine tool motion axis, and calculating a workpiece dimension error caused by the key geometric error based on a spatial error model; fourthly, cutting the workpiece, calibrating the overall dimension error, and calculating the proportion of the dimension error of the workpiece caused by the critical geometric error and the non-critical geometric error; and fifthly, determining the optimal proportion of the key geometric errors according to the coupling relation between the key geometric errors and the non-key geometric errors and the total sensitivity, and compensating in real time. The invention only measures and compensates the key geometric error to the optimized proportion value, thereby achieving the effect of compensating all errors and improving the machining precision of the machine tool.

Description

Key geometric error optimization proportioning compensation method for five-axis numerical control machine tool
Technical Field
The invention belongs to the technical field of machining precision of numerical control machines, and relates to a key geometric error optimization proportioning compensation method for a five-axis numerical control machine.
Background
The numerical control machine tool is one of the most important tools in industrial production as a 'machine tool for working mother machines' in the manufacturing industry. The five-axis numerical control machine tool is a representative of high-grade numerical control machine tools, can process various complex curve curved surfaces, has high production efficiency, good flexibility and short clamping time, plays an important role in important fields such as aerospace and the like, and plays a significant role in improving the national manufacturing level.
However, the numerical control machine tool forms a machining error on a workpiece when machining the workpiece due to a combination of an internal organization structure of the numerical control machine tool and an external environment. Among various errors of the machine tool, geometric errors and thermal errors of the machine tool are main errors of machine tool machining, and the machining precision of the numerical control machine tool is seriously influenced. Because the manufacturing and assembling errors of the motion axis are difficult to avoid, the geometric error is an important factor influencing the precision of the machine tool. They map directly onto the workpiece dimensions, which severely affects the machining accuracy and therefore it is necessary to compensate for this.
The most common geometric error compensation method for the five-axis machine tool at present is to measure 41 geometric errors of the five-axis machine tool through equipment such as a laser interferometer and a ball bar instrument, and then obtain an inverse kinematics solution of the five-axis machine tool through calculating a Jacobian matrix, so that a new G code is generated to perform spatial error compensation on the five-axis machine tool. The method does not consider the coupling relation among the geometric errors, measures and compensates all the geometric errors item by item, has long compensation period and great workload and cost, and cannot meet the increasing manufacturing requirements. How to realize the high-efficiency high-precision compensation of the geometric errors of the five-axis numerical control machine tool for the machining of workpieces with complex structures becomes an urgent neck problem.
Disclosure of Invention
The invention provides a five-axis numerical control machine tool key geometric error optimization proportioning compensation method for overcoming the prior art. According to the method, the coupling relation among the geometric errors is considered, the key geometric errors are subjected to proportion compensation, and finally, the effect of compensating all the geometric errors can be achieved only by measuring and optimizing the proportion compensation key geometric errors, so that efficient and high-precision compensation is realized.
The optimization proportioning compensation method for the key geometric errors of the five-axis numerical control machine tool comprises the following steps:
firstly, establishing a spatial error model; establishing a space error model of the five-axis numerical control machine tool by using a homogeneous coordinate matrix, and determining a position error and a direction error;
secondly, identifying the key geometric errors based on a quasi-Monte Carlo method, and determining the main sensitivity and the total sensitivity of the key geometric errors;
measuring a key geometric error of a machine tool motion axis, and calculating a workpiece dimension error caused by the key geometric error based on a spatial error model;
fourthly, cutting the workpiece, calibrating the overall dimension error, and calculating the proportion of the dimension error of the workpiece caused by the critical geometric error and the non-critical geometric error;
and fifthly, determining the optimal proportion of the key geometric errors according to the coupling relation between the key geometric errors and the non-key geometric errors and the total sensitivity, and compensating in real time.
Compared with the prior art, the invention has the beneficial effects that:
according to the method for optimizing, proportioning and compensating the geometric errors of the machine tool, the geometric errors are not directly compensated after the critical geometric errors are identified according to different space transfer rules of the errors and the coupling relation exists between the critical geometric errors and non-critical geometric errors, and the optimized proportioning and compensation are carried out on the critical geometric errors according to the main sensitivity proportion. The method only measures and compensates the key geometric errors to the optimized proportion value, and achieves the effect of compensating all the errors, thereby solving the problem that the existing method needs to measure and compensate all the geometric errors, improving the working efficiency, fundamentally improving the machining precision of the machine tool, and having important significance for improving the universality of an error model and the overall machining precision of a five-axis numerical control machine.
The technical scheme of the invention is further explained by combining the drawings and the embodiment:
drawings
FIG. 1 is a route diagram of a key geometric error optimization proportioning compensation technology of a five-axis numerical control machine tool;
FIG. 2 is a schematic view of the processing of the test piece S in the example;
FIG. 3 is a three-coordinate calibration specimen size chart;
FIG. 4 is a graph of the results of the calculation of the main sensitivity to coupling sensitivity for the geometric errors in three directions X, Y, Z at the measured points in the machining area;
FIG. 5 is a total error plot of three-coordinate measuring machine calibration at the measurement point;
FIG. 6 is a graph of the spatial error caused by the critical geometric error at the measurement point;
FIG. 7 is a graph of spatial errors caused by non-critical geometric errors at measurement points;
FIG. 8 is a graph of optimized match values for five key errors at various points in the processing trajectory;
FIG. 9 is a graph of X, Y and Z dimensional errors of an "S" specimen in zone four before compensation;
FIG. 10 is a chart of X, Y and Z dimensional errors of the directly compensated "S" specimen in zone four;
FIG. 11 is a graph of the X, Y and Z dimensional errors of the "S" specimen in zone four after optimization compensation.
Detailed Description
Referring to fig. 1, the method for optimizing the proportion of the key geometric error of the five-axis numerical control machine tool according to the embodiment includes the following steps:
firstly, establishing a spatial error model; establishing a space error model of the five-axis numerical control machine tool by using a homogeneous coordinate matrix, and determining a position error and a direction error;
secondly, identifying the key geometric errors based on a quasi-Monte Carlo method, and determining the main sensitivity and the total sensitivity of the key geometric errors;
measuring a key geometric error of a machine tool motion axis, and calculating a workpiece dimension error caused by the key geometric error based on a spatial error model;
fourthly, cutting the workpiece, calibrating the overall dimension error, and calculating the proportion of the dimension error of the workpiece caused by the critical geometric error and the non-critical geometric error;
and fifthly, determining the optimal proportion of the key geometric errors according to the coupling relation between the key geometric errors and the non-key geometric errors and the total sensitivity, and compensating in real time.
And obtaining the workpiece dimension error caused by the non-critical geometric error according to the overall dimension error and the workpiece dimension error caused by the critical geometric error. And optimizing and proportioning spatial errors caused by all key geometric errors according to the coupling relation between the two, after determining the compensation quantity of the spatial errors, optimizing and proportioning compensation according to the main sensitivity proportion aiming at all key geometric errors, wherein the size error of a workpiece caused by the compensated key geometric errors is the same as that caused by non-keys, and the sizes and the directions of the workpiece caused by the compensated key geometric errors are opposite, so that the workpiece is offset, and the machine tool achieves higher precision.
In the above, the first step of establishing the spatial error model is performed according to the following steps:
firstly, based on small angle errors, giving a geometric error transfer matrix of a motion axis:
Figure GDA0003605638980000031
the kinematic transfer matrix of the motion axis is determined by the theoretical motion amount and the geometric error together, and is as follows:
H＝Motion·Error
in the formula, MotionRepresenting an ideal motion matrix, ErrorRepresenting a geometric error matrix;
establishing a space error model of the five-axis numerical control machine tool based on positive kinematics homogeneous coordinate transformation, wherein the space error model comprises the following formula:
Figure GDA0003605638980000032
WTTa motion transfer matrix representing the motion of the tool relative to the workpiece is a 4 x 4 homogeneous coordinate matrix representing the position and direction of the tool relative to the workpiece, and a position P representing the positionWTTIn the fourth column, direction O is shown asWTTThe third column of (a), the position error Δ P (Δ x, Δ y, Δ z) and the direction error Δ O (Δ i, Δ j, Δ k) are obtained as follows:
Figure GDA0003605638980000033
WTTactuala motion transfer matrix in case of an error is indicated,WTTidealrepresenting the motion transfer matrix without error in the ideal case. In the spatial error model, the position error Δ P is divided into two parts: the part caused by the translational error of the moving shaft and the part caused by the angular error of the moving shaft. Because the translational error of the moving shaft does not influence the direction of the tool, the direction error delta O of the tool nose relative to the workpiece is only caused by the angle error of the moving shaft.
The identification of the key geometric errors in the second step is carried out by the following steps:
let the machine space error equation be f (x), y be the model output,i.e. the pose error of the tip relative to the workpiece, including a position error and an orientation error, where x ═ x (x ═ x)1,x2,…,xn) For n geometric error input variables, the five-axis numerical control machine tool has 41 geometric errors, so that n is 41;
then, according to the known geometric error xiThe distribution function of (2) is sampled for N times in each input variable definition domain by using a quasi-Monte Carlo method, so that 2N x N matrixes are constructed; usually, N is 10000;
Figure GDA0003605638980000041
replacing ith column of matrix A with ith column of matrix B to obtain new matrix Ci；
Figure GDA0003605638980000042
Will be the above matrix A, B, CiSubstituting the space error equation y ═ f (x) as the model input to obtain the output response: y isA＝f(A),yBF (b) and yCi＝f(Ci)；
Geometric error variable xiMain sensitivity S ofiAnd coupling sensitivity STiThe following formula is calculated, wherein SiRepresents the error xiCritical degree of (1), STiIndicating the degree of different orders of integration between the error and other errors;
Figure GDA0003605638980000051
wherein x is～iDenotes dividing by xiGeometric error other than, xiRepresenting the geometric error of the i-th term.
And step three, calculating the workpiece dimension error caused by the key geometric error based on the spatial error model, namely substituting all key geometric errors into the spatial error model to obtain a spatial error A1 caused by all key geometric errors.
The calculation in the fourth step is that the proportion of the workpiece dimension error caused by the key geometric error and the non-key geometric error is obtained according to the spatial error model and the sensitivity analysis of the quasi-Monte Carlo method: the total dimensional error C1 is the spatial error a1+ the spatial error B1 due to the non-critical geometric errors.
The above is that the overall dimension error is calibrated by the three-coordinate measuring machine and the spatial error A1 caused by the key error obtained in the third step is obtained, and the spatial error B1 caused by the non-key error can be obtained.
Further, the optimal ratio of the key geometric errors is determined in the step five: optimizing and proportioning spatial error A1 caused by all key geometric errors, and firstly, dividing the optimizing and proportioning proportion into seven categories according to the positive and negative of the spatial error A1 caused by the key geometric errors of points on a cutter path during workpiece processing, the spatial error B1 caused by non-key errors and the total workpiece size error C1, as shown in the following table 1;
then, classifying according to the size of the overall size error C1, and when C1 is less than 3 μm, judging that the error is in an allowable range without compensation; when C1 > 3 μm, compensation is needed, and the optimal proportion p represents compensating the spatial error a1 to p times of the original error total, i.e. the compensation amount is a1 · (1-p), wherein for category one and category two, subdivision is performed according to the absolute value of a1 and B1, wherein the proportion p is negative to represent compensation to error reversal, for example: if the original error total amount is 20 μm, the current error needs to be compensated to-10 μm;
for class three and class five, the amount of compensation for spatial error a1 is reduced and less than spatial error a1, for example: if the original error total amount is 20 μm, the error total amount is compensated to 10 μm;
for the category four and the category six, the spatial error A1 is increased, for example, the original error total amount is 20 μm, and now is compensated to 30 μm;
for class seven, when the non-critical geometric error causes spatial error B1 to be 0, then the proportioning ratio of a1 is 1, i.e., no compensation is performed. Of these, the categories one, two, three and five are the four most common.
TABLE 1
Figure GDA0003605638980000061
After space errors A1 caused by all key geometric errors are optimally matched, the optimal matching ratio of the single key geometric errors is set as piTrue value e of the associated key geometric erroriCalculating the coupling sensitivity S of the key geometric error by a quasi-Monte Carlo methodTiThe key geometric error is matched according to the optimized ratio piSubstituting the following formula, making the size of the spatial error caused by the key geometric error after the proportioning compensation equal to the spatial error caused by the non-key error, but the direction is opposite, and then obtaining the optimized proportioning ratio p of m key geometric errorsi；
ΔE＝f(E1,…,Em)＝f(p1e1,…,pmem)＝-B1
p1:…:pm＝S1:…:Sm
Wherein eiIs the true magnitude of the critical geometric error of item i, EiSpatial error, p, due to i-th geometric error after compensation for optimal proportioningiFor the optimal ratio of the ith error, i is in the range of [1, m]，
For example: by using the optimized ratio of the single key geometric errors, the optimized ratio p of the four key geometric errors can be obtainedi。
ΔE＝f(E1,E5,E10,E20)＝f(p1e1,p5e5,p10e10,p20e20)＝-B1
p1:p5:p10:p20＝S1:S5:S10:S20
Examples
In the experiment, the cutting machining of an S test piece is carried out on a five-axis numerical control machine tool with the model number of JDGR400, so that the effectiveness of the proposed geometric error optimization compensation is verified. The tool path is programmed by NX12.0 and the machining steps are performed according to the procedures in ISO-10794 of 2020. As shown in FIGS. 2 and 3, an "S" part is cut on a JDGR400 five-axis numerical control machine tool, and the dimensional error is calibrated by using three coordinates.
And (3) taking a complete processing track with the length of z being 14.5mm as an example to carry out optimized proportioning compensation. 30 data points are uniformly taken in the processing track, and every 5 points form a group. First, the main sensitivity S of the geometric errors in the X, Y and Z directions of each measuring point in each group is calculatediAnd a multi-step coupling sensitivity STiAnd the critical geometric error is determined as shown in figure 4.
The workpiece is cut and three-coordinate calibration is completed and the total dimensional error C1 is obtained, fig. 5, and any one group is taken as a test, and the group is called area four. Measuring the key error obtained by sensitivity analysis through a laser interferometer and a ball rod instrument, bringing the measured value into a space error model to obtain a space error A1 caused by the key error at the measured point, as shown in FIG. 6, and finally, subtracting a part A1 caused by the key geometric error from the total size error C1 to obtain a part caused by the non-key geometric error, as shown in FIG. 7.
Calculating an optimized ratio p value:
as shown in fig. 8, the optimal matching values of the five key geometric errors at each point are respectively solved according to the error optimal matching method. The optimized proportion ratio p represents that the error A1 is compensated to be p times of the original error value, namely, the compensation amount is A1 (1-p). p ═ 1 indicates that compensation is not performed; p-0 means that the error is compensated to zero, i.e. all are compensated; p < 0 indicates that the error is compensated to the opposite direction, such as from 20 μm to-10 μm; 0< P < 1 means that the error is compensated small, e.g., from 20 μm to 5 μm, P is 0.25; p > 1 indicates that the error is made large, and if the error is compensated from 20 μm to 30 μm, p is 1.5. For locations where the total dimensional error in X, Y and Z directions is less than 3 μm, such as the Y and Z direction errors of data point set 1 on the abscissa in fig. 8a, no error compensation is required, and therefore the geometric error optimization ratio at these points is 1.
And calculating error compensation quantities of five motion axes along the data points according to the geometric error optimization ratio values at the data points, and transmitting the error compensation quantities to a numerical control system through an error compensator for real-time error compensation.
The reference group is to compensate the key error to 0, calculate the error compensation amount of five motion axes, and perform real-time error compensation, wherein the dimensional errors of the 'S' test piece in the X, Y and Z directions in the area four before compensation are shown in FIG. 9; the size errors of the compensated 'S' test piece in the X, Y and Z directions in the area four are shown in FIG. 10, and the machining precision of the overall workpiece is improved by 71%; the dimensional errors of the 'S' test piece in three directions of X, Y and Z in the area four after the experimental group optimization compensation are shown in FIG. 11, and the machining precision of the overall workpiece is improved by 90%. The feasibility and the superiority of the geometric error optimization proportioning compensation method are verified.
The present invention is not limited to the above embodiments, and those skilled in the art can make various changes and modifications without departing from the scope of the invention.

Claims (4)

1. The optimization proportioning compensation method for the key geometric errors of the five-axis numerical control machine tool is characterized by comprising the following steps of: comprises the following steps:
firstly, establishing a spatial error model; establishing a space error model of the five-axis numerical control machine tool by using a homogeneous coordinate matrix, and determining a position error and a direction error;
secondly, identifying the key geometric errors based on a quasi-Monte Carlo method, and determining the main sensitivity and the total sensitivity of the key geometric errors;
measuring a key geometric error of a machine tool motion axis, and calculating a workpiece dimension error caused by the key geometric error based on a spatial error model;
fourthly, cutting the workpiece, calibrating the overall dimension error, and calculating the proportion of the dimension error of the workpiece caused by the critical geometric error and the non-critical geometric error; the calculation in the fourth step is that the proportion of the workpiece dimension error caused by the key geometric error and the non-key geometric error is obtained according to the spatial error model and the sensitivity analysis of the quasi-Monte Carlo method: overall dimensional error C1 — all critical geometric errors cause spatial error a1+ non-critical geometric errors cause spatial error B1;
fifthly, determining the optimal proportion of the key geometric errors according to the coupling relation between the key geometric errors and the non-key geometric errors and the total sensitivity, and compensating in real time;
determining the optimal proportion of the key geometric errors: optimizing and proportioning spatial error A1 caused by all key geometric errors, and firstly, dividing the optimizing and proportioning proportion into seven categories according to the positive and negative of the spatial error A1 caused by the key geometric errors of points on a cutter path during workpiece processing, the spatial error B1 caused by non-key errors and the total workpiece size error C1;
the category I and the category II show that the space error A1 caused by the key geometric error is consistent with the space error B1 caused by the non-key geometric error in positive and negative, and show a consistent relation in the same direction; category three and category five indicate that the space error A1 caused by the key geometric error is inconsistent with the space error B1 caused by the non-key geometric error in positive and negative directions and show a repellent relationship in the opposite directions; the category four and the category six represent that the space error A1 caused by the key geometric error is inconsistent with the positive and negative of the space error B1 caused by the non-key geometric error and show a repellent relation in the opposite directions; category seven indicates that the non-critical geometric error causes spatial error B1 to be 0;
then, classifying according to the size of the overall size error C1, and when C1 is less than 3 μm, judging that the error is in an allowable range without compensation; when C1 is more than 3 μm, compensation is needed, the optimization proportion P represents that the spatial error A1 is compensated to P times of the total error amount, namely the compensation amount is A1(1-P), wherein, for category one and category two, subdivision is carried out according to the absolute value of A1 and B1, wherein the proportion P is negative number to represent that the compensation is carried out until the error is reversed, when | A1| ≧ | B1| is used as category one, and is represented as P ≧ -1; when | A1| < | B1|, it is of category two, and is represented by P < -1; for category three and category five, the compensation amount of the spatial error A1 is reduced, and the compensation amount is smaller than the spatial error A1, which is represented as 0< P < 1; for category four and category six, increasing the spatial error A1, denoted as P > 1;
determining optimal proportioning for critical geometric errorsCarrying out optimized proportioning by including a single key geometric error; after space errors A1 caused by all key geometric errors are optimally matched, the optimal matching ratio of the single key geometric errors is set as piTrue value e of the associated key geometric erroriCalculating the coupling sensitivity S of the key geometric error by a quasi-Monte Carlo methodTiThe key geometric error is matched according to the optimized ratio piSubstituting the formula into the formula, making the size of the spatial error caused by the key geometric error after proportioning compensation equal to the spatial error caused by the non-key error, but the direction is opposite, and then solving the optimized proportioning ratio p of m key geometric errorsi；
ΔE＝f(E1,…,Em)＝f(p1e1,…,pmem)＝-B
p1:…:pm＝S1:…:Sm
Wherein eiIs the true magnitude of the critical geometric error of item i, EiSpatial error, p, caused by i-th geometric error after compensation for optimal proportioningiFor the optimal ratio of the ith error, i is in the range of [1, m]。
2. The five-axis numerical control machine tool key geometric error optimization proportioning compensation method of claim 1, wherein: the first step of establishing a spatial error model is carried out according to the following steps:
firstly, a geometric error transfer matrix of a motion axis is given based on a small angle error:
Figure FDA0003605638970000021
the kinematic transfer matrix of the motion axis is determined by the theoretical motion amount and the geometric error together, and is as follows:
H＝Motion·Error
in the formula, MotionRepresenting an ideal motion matrix, ErrorRepresenting a geometric error transfer matrix;
establishing a space error model of the five-axis numerical control machine tool based on positive kinematics homogeneous coordinate transformation, wherein the space error model comprises the following formula:
Figure FDA0003605638970000022
WTTa motion transfer matrix representing the motion of the tool relative to the workpiece, a 4 x 4 homogeneous coordinate matrix representing the position and direction of the tool relative to the workpiece, and a position P representing the positionWTTIn the fourth column, direction O is shown asWTTThe third column of (a), the position error Δ P (Δ x, Δ y, Δ z) and the direction error Δ O (Δ i, Δ j, Δ k) are obtained as follows:
Figure FDA0003605638970000023
WTTactuala motion transfer matrix in case of an error is indicated,WTTidealrepresenting the motion transfer matrix without error in the ideal case.
3. The five-axis numerical control machine tool key geometric error optimization proportioning compensation method of claim 2, wherein: the identification of the key geometric errors in the second step is carried out by the following steps:
and (f) (x) and y is output of a model, namely the pose error of the tool nose relative to the workpiece, wherein x (x) is the position error and the direction error, and x (x) is the position error and the direction error1,x2,…,xn) For n geometric error input variables, the five-axis numerical control machine tool has 41 geometric errors, so that n is 41;
then, according to the known geometric error xiThe distribution function of (2) is sampled for N times in each input variable definition domain by using a quasi-Monte Carlo method, so that 2N x N matrixes are constructed;
Figure FDA0003605638970000031
replacing ith column of matrix A with ith column of matrix B to obtain new matrix Ci；
Figure FDA0003605638970000032
Will be the above matrix A, B, CiSubstituting the space error equation y ═ f (x) as the model input to obtain the output response: y isA＝f(A),yBF (B) and
Figure FDA0003605638970000033
geometric error variable xiMain sensitivity S ofiAnd coupling sensitivity STiThe following formula is calculated, wherein SiRepresenting the error xiCritical degree of (1), STiIndicating the degree of different orders of integration between the error and other errors;
Figure FDA0003605638970000034
wherein x is～iDenotes dividing by xiGeometric error other than, xiRepresenting the geometric error of the i-th term.
4. The five-axis numerical control machine tool key geometric error optimization proportioning compensation method of claim 2, characterized in that: and step three, calculating the workpiece dimension error caused by the key geometric error based on the spatial error model, namely substituting all key geometric errors into the spatial error model to obtain all key geometric errors causing spatial error A1.
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