Analysis method for geometric error of linear feeding system under any attitude

Abstract

The invention discloses a method for analyzing geometric errors of a linear feeding system under any attitude. The method comprises the following steps of: constructing a representation method of the linear feeding system under any attitude; testing and decomposing guide rail assembly errors, and establishing a stress balance equation of the linear feeding system; the geometric error of the moving part is solved; performing geometric error traceability analysis, and determining main factors influencing the geometric error of the moving part; the method for analyzing the geometric error under any attitude is developed for different linear feeding system configurations, a stress balance equation of the linear feeding system under any attitude is established, the geometric error of a moving part is solved, traceability is achieved by comparing the influence degrees of different factors on the geometric error, and the accuracy of the geometric error analysis is improved. In order to solve the problems of assembly precision verification, structure optimization, active precision design and the like of the linear feeding system, the invention further comprises a system, equipment and a medium for realizing the method.

Description

Technical Field

[0001] The present invention relates to the technical field of geometric accuracy analysis of linear feed systems of high-end CNC machine tools, and in particular to a method for analyzing the geometric errors of linear feed systems under arbitrary postures, a method for modeling the geometric errors of spatial linear feed systems, and an active design method for the geometric accuracy of linear feed systems. Background Art

[0002] The linear feed system is an important functional component of high-end CNC equipment. Its geometric accuracy directly affects the machining accuracy of parts in high-end CNC equipment. At present, domestic and foreign scholars have carried out a lot of research on the geometric accuracy of linear feed systems, including measurement method development, measurement device development, modeling method research, error identification, error tracing, reliability analysis, active design, and analysis of the generation and degradation mechanism of single accuracy such as straightness. The above research is mainly carried out on linear feed systems with specific configurations and arrangements. Patent application number 201510974996.0 discloses a method for constructing a geometric error model for a rolling guide feed system. Considering the load and guide contact stiffness, the geometric error of the workbench is solved through the static equilibrium equation of the workbench. This method only considers the influence of the deformation of the guide rail itself when external load is applied, and does not consider the influence of the assembly error of the guide rail and the spatial posture of the feed axis. The invention with application number 202211218760.0 discloses a method for predicting the vertical straightness and angular error of a machine tool linear axis. It analyzes the manufacturing and assembly errors of the guide rail reference surface and realizes the prediction of the vertical straightness and angular error of the linear axis through geometric relationships. This method only considers the errors of the guide rail itself and does not consider the influence of the flexibility and spatial posture of functional components such as the guide rail and lead screw on the accuracy of the linear axis. The invention with application number 202410965088.4 discloses a method for rapid parameterized modeling of geometric errors for multi-configuration five-axis machine tools. When analyzing the geometric errors of five-axis machine tools with different configurations, the influence of spatial posture on the geometric error of the feed axis is characterized by a local transfer matrix and a transfer vector table. However, this method only considers the overall geometric error of the feed axis and does not analyze the quantitative relationship between the performance of each component functional component and the geometric error of the feed axis, which is not conducive to error tracing analysis.

[0003] In summary, the actual structure of linear feed systems varies widely, and the structural form, configuration, and assembly process of components such as guide rails and lead screws vary significantly, limiting the applicability of the aforementioned research. More importantly, the assembly and operational postures of linear feed systems often differ. For example, the precision adjustment of the vertical axis is often performed in a horizontal position. The varying effects of gravity and other loads in different postures mean that the precision design indicators for qualified assembly may not necessarily meet the requirements for qualified operation. These factors make it difficult for engineers to calculate and verify the various precision requirements during assembly and operation during design. Summary of the Invention

[0004] In order to overcome the defects of the above-mentioned prior art, the purpose of the present invention is to provide a method for analyzing the geometric error of a linear feed system under arbitrary posture. For different linear feed system configurations, a geometric error model of the linear feed system under arbitrary posture is established, and the influence of different factors on the geometric error is compared to solve the problems of precision design, assembly precision verification and optimization of the linear feed system, providing a basis for precision calibration, active design and assembly process optimization.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for analyzing geometric errors of a linear feed system under arbitrary postures includes the following steps:

[0007] Step 1: Parameter construction of components in the linear feed system under arbitrary postures, including the construction of basic parameters and layout parameters of the guide rail pair, the construction of screw parameters, and the construction of moving component parameters;

[0008] Step 2: Measure and decompose the assembly errors of each component in the linear feed system, including measuring the assembly error of the reference guide rail; measuring the assembly errors of multiple other guide rails along the normal and side surfaces of the reference guide rail; measuring the installation and positioning surface errors of multiple guide rail sliders on the moving component with the working surface of the moving component as the reference; and the relative error of the installation and positioning surface of the slider in the guide rail coordinate system with the slider on the reference guide rail as the reference.

[0009] Step 3: Establish the force balance equation at a certain position of the linear feed system based on the parameters of step 1 and the error of step 2;

[0010] Step 4: Similarly to the force balance equation at a certain position, establish the force balance equation under any stroke of the moving part and solve the geometric error of the moving part;

[0011] Step 5: Based on the change in geometric error, obtain the error change rate and determine the factors affecting the geometric error of the moving part.

[0012] The step 1 is specifically as follows:

[0013] Step 1.1: Construction of basic parameters of guide rail pair, including geometric parameters, structural parameters, performance parameters and motion parameters; geometric parameters include guide rail length L G and width W G , slider length L S and width W S And the total height of the guide rail H GS ; Structural parameters include the number of sliders N S , initial position S0 and spacing D Sk (k=1,,2,…,NS -1); performance parameters include normal stiffness K szj and tangential stiffness K syj ; The motion parameter refers to the displacement S of the slider; the center position of each slider in the guide rail coordinate system O-x1y1z1 is N S ),have The stiffness matrix of the guide rail slider at j is expressed as:

[0014]

[0015] Step 1.2: The construction of the guide rail layout parameters is determined according to the function and structure of the linear feed system. The layout parameters of the guide rail under the global coordinate system O-x0y0z0 include the number of guide rails N G and the spatial posture of the guide rail, guide rail i (i=1,,2,…,N G )'s spatial posture q Gi =[r Gi θ Gi ] T Including the position r of one end Gi (x Gi ,y Gi ,z Gi ) and angular attitude θ Gi (θ Gxi ,θ Gyi ,θ Gzi ), then the spatial posture transformation matrix of guide rail i is:

[0016]

[0017] The relative posture transformation matrix between rail i and any other rail k is:

[0018]

[0019] The coordinates of the center position of each slider of the guide rail i after assembly are r Sij (x Sij ,y Sij ,z Sij ),have:

[0020]

[0021] Step 1.3: Construction of screw parameters, including the center position r of the screw nut under O-x0y0z0 BN (x BN ,y BN ,z BN ), angle posture θ BN (θ BNx ,θ BNy ,θBNz ), axial stiffness K of the screw coordinate system O-x2y2z2 bsa and radial stiffness K bsr1 , K bsr2 , the stiffness matrix at the center of the screw nut is expressed as:

[0022]

[0023] Then the spatial attitude transformation matrix of the screw nut is obtained

[0024]

[0025] Step D: Construction of moving part parameters, mainly referring to mass m T and the position r of the center of mass MC under O-x0y0z0 TC (x TC ,y TC ,z TC ).

[0026] The step 2 is specifically as follows:

[0027] Step 2.1: After all guide rails are installed, measure the assembly error of the reference guide rail Including normal surface error and lateral error

[0028] Step 2.2: Using the reference rail as a reference, measure the assembly errors of multiple rails i along the normal and side surfaces of the reference rail. and The assembly error of each guide rail i in the guide rail coordinate system O-x1y1z1 is:

[0029]

[0030] Step 2.3: Using the working surface of the moving part as a reference, measure the installation positioning surface errors of multiple guide rail sliders on the moving part. Includes errors along the normal and lateral directions and Taking the slider on the reference guide rail as the reference, the relative error of the slider's installation positioning surface in the guide rail coordinate system O-x1y1z1 is:

[0031]

[0032] The step three is specifically as follows:

[0033] Step 3.1: Force analysis of the guide rail pair, the displacement q of the moving part under the action of external load in the global coordinate system O-x0y0z0 T =[u Tx ,uTy ,u Tz ,θ Tx ,θ Ty ,θ Tz ] T When , the displacement of slider j on guide rail i is:

[0034] q GSij =TS GSij q T (9)

[0035] Where,

[0036]

[0037] The displacement of slider j on guide rail i in the guide rail coordinate system O-x1y1z1 is:

[0038]

[0039] The force exerted by slider j on the guide rail i on the moving part is:

[0040]

[0041] The resultant force of all guide rail pairs on the moving parts is:

[0042]

[0043] Step 3.2: Force analysis of the screw pair. The displacement of the center of the screw nut in the global coordinate system O-x0y0z0 is:

[0044] q BN =TS BN q T (16)

[0045] Where,

[0046]

[0047]

[0048] Then, the displacement of the center of the screw nut in the screw coordinate system O-x2y2z2 is The force exerted by the screw pair on the moving parts is

[0049] Step 3.3: There are gravity, cutting force, etc. N under O-x0y0z0 F External loads act on the moving parts, and the kth (k=1,2,…,N F ) The magnitude of the external load is F k =[F xi ,F yi ,Fzi ,M xi ,M yi ,M zi ] T , the action point is r Fk (x Fk ,y Fk ,z Fk ), then the resultant force of the external load is:

[0050]

[0051] Where,

[0052]

[0053] Step 3.4: The force balance equation of the moving part in the global coordinate system O-x0y0z0 is:

[0054] K T q T =F T (twenty three)

[0055] Where,

[0056]

[0057]

[0058] Then, the geometric error q of the moving part is T for:

[0059] q T =(K T ) -1 F T (26)

[0060] The step 4 is specifically as follows:

[0061] According to the structural parameters, processing accuracy, assembly process and service conditions of the linear feed system, the travel of the moving part is divided into N equal parts, and the moving part is moved to any travel S j Similarly, in step 3, the arbitrary travel S of the moving part is established j The force balance equation at the position and solve the current stroke S j The geometric error q Tj Repeat the above steps to get the geometric error variation law of the moving part in the full stroke q T (S); Check the geometric errors of the linear feed system according to the design indicators of various geometric errors to find out the accuracy indicators that exceed the tolerance.

[0062] The step five is specifically as follows:

[0063] For the structure and precision parameters of the linear feed system, i , when the parameter increment ratio is r, the change in the geometric error of the moving part is:

[0064] Δq T (P i )=K T (P i (1+r)) -1 F T (P i (1+r))-K T (P i ) -1 F T (P i ) (27)

[0065] Similarly, the above formula (25) is used to calculate the change in geometric error when the various parameters of the guide rail pair, screw pair, moving part parameters and machining accuracy index change, and then the error change rate S(P i )=Δq T (P i ) / q T , according to the error change rate S(P i ) can determine the main factors affecting the geometric errors of moving parts, which serve as key variables in precision design.

[0066] The present invention also includes:

[0067] A system includes a processor capable of running a method for analyzing geometric errors of a linear feed system under arbitrary postures.

[0068] A device comprising:

[0069] Memory: used for storing a computer program of the method for analyzing geometric errors of a linear feed system under arbitrary postures;

[0070] Processor: used to implement the method for analyzing the geometric error of a linear feed system under arbitrary posture when executing the computer program.

[0071] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a method for analyzing geometric errors of a linear feed system under arbitrary postures.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] 1. Step 1 of the present invention realizes the parameterization of the linear axis feed system in spatial posture through parametric characterization of the geometry and performance of functional components such as guide rail pairs, lead screws, and moving parts. It can be used to analyze the performance of linear axis feed systems in spatial posture under different configurations, external dimensions, and assembly processes. It has a wide range of applications and strong versatility.

[0074] 2. In step 2 of the present invention, the measured value of the guide rail assembly error is introduced to decompose and solve the installation positioning surface error. The measured error data decomposition algorithm expands the application scope of the theoretical analysis model and improves the accuracy of the calculation results.

[0075] 3. Steps three and four of the present invention analyze the spatial force state of the guide rail pair, lead screw, and moving parts through the spatial posture relationship transformation matrix of force and displacement, establish the force balance equation of the linear feed system in the spatial posture when subjected to external loads such as gravity and cutting force, and realize the solution of the geometric error of the moving parts in any posture, providing a basis for the development of active design tool software for the geometric error of the linear axis feed system under different configurations and assembly states.

[0076] 4. Step five of the present invention characterizes the degree of influence of changes in various parameters such as the guide pair, the screw pair, the moving part parameters and the processing accuracy index on the geometric error of the moving part through the error change rate, which is conducive to quantitative analysis of the main factors affecting the geometric error of the moving part and provides a basis for geometric error tracing analysis and key variable selection during precision design.

[0077] In summary, the present invention utilizes the established geometric error model to calculate the degree to which the dimensions and precision of different components affect the geometric error of a moving part. This allows the primary influencing factors of the moving part's geometric error to be determined, allowing for the rational allocation of precision ranges for each component, thereby reducing the manufacturing difficulty and production costs of the component. This method is highly versatile and has a wide range of applications. It can be applied to the precision analysis of linear feed systems of varying configurations during design, assembly, and operational posture, providing a foundation for the development of software tools for the active geometric error design of linear feed systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a typical structural diagram of a linear feed system.

[0079] Figure 2 This is a schematic diagram of the vertical arrangement of double guide rails.

[0080] Figure 3 This is a schematic diagram of the three-rail space layout.

[0081] Figure 4 It is a schematic diagram of the guide rail pair structural parameters.

[0082] Figure 5 This is a schematic diagram of the spatial layout of the guide rail

[0083] Figure 6 This is a schematic diagram of the guide rail assembly error test results.

[0084] Figure 7 This is a schematic diagram of the guide rail slider installation surface error.

[0085] Figure 8 It is a schematic diagram of the geometric error calculation process of the linear feed system.

[0086] Figure 9 It is a schematic diagram comparing the geometric errors of the horizontal and vertical axes.

[0087] Among them: 1-guide rail base; 2-guide rail pair; 21-guide rail; 22-slider; 3-moving part; 4-ball screw; 5-bearing seat; 6-drive motor. DETAILED DESCRIPTION

[0088] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0089] The typical structural type of the linear feed system analyzed in this invention is as follows Figure 1 As shown in the figure, it mainly consists of a guide rail base 1, a guide rail 21 mounted thereon, a guide rail pair 2, a moving part 3, a ball screw 4, a bearing seat 5 and a drive motor 6. The drive motor 6 drives the moving part 3 to different positions through the ball screw 4. Among them, the number of guide rail pairs 2 and the spatial posture relationship vary greatly in different linear feed systems. Figure 1 The middle one has double guide rails arranged horizontally. Figure 2 The middle one has double guide rails arranged vertically. Figure 3 It is a three-rail space layout.

[0090] The present invention is based on the above linear feed system and provides a method for analyzing the geometric error of the linear feed system under arbitrary postures, which specifically includes the following steps:

[0091] Step 1: Construct the representation method of the linear feed system under arbitrary posture;

[0092] The method for representing the linear feed system under any posture in this embodiment specifically includes the following:

[0093] Step 1.1: Construction of basic parameters of guide rail pair 2. The basic parameters mainly include geometric parameters, structural parameters, performance parameters and motion parameters, such as Figure 4 As shown. The geometric parameters include the length L of the guide rail 21 G and width W G , the length of the slider 22 is L S and width WS And the total height of the guide rail H GS The structural parameters include the number of sliders N S , initial position S0 and spacing D Sk (k=1,,2,…,N S -1). Performance parameters include normal stiffness K szj and tangential stiffness K syj The operating parameter refers to the displacement S of the slider. The center position of each slider in the guide rail coordinate system O-x1y1z1 is have The stiffness matrix of the guide rail slider at j can be expressed as

[0094]

[0095] Step 1.2: The construction of the guide rail layout parameters is mainly determined according to the function and structure of the linear feed system. Figure 5 The layout parameters of the guide rails in the global coordinate system O-x0y0z0 include the number of guide rails N G and the spatial posture of the guide rail, guide rail i (i=1,,2,…,N G )'s spatial posture q Gi =[r Gi θ Gi ] T Including the position r of one end Gi (x Gi ,y Gi ,z Gi ) and angular attitude θ Gi (θ Gxi ,θ Gyi ,θ Gzi ). Then, the spatial posture transformation matrix of guide rail i is

[0096]

[0097] Multiple guide rails are often used in parallel, so the relative posture transformation matrix between guide rail i and any other guide rail k is

[0098]

[0099] The coordinates of the center position of each slider of the guide rail i after assembly are r Sij (x Sij ,y Sij ,z Sij ),have

[0100]

[0101] Step 1.3: Construction of screw parameters, including the center position r of the screw nut under O-x0y0z0 BN(x BN ,y BN ,z BN ), angle posture θ BN (θ BNx ,θ BNy ,θ BNz ) and the axial stiffness K under the screw coordinate system O-x2y2z2 bsa and radial stiffness K bsr1 , K bsr2 The stiffness matrix at the center of the screw nut can be expressed as

[0102]

[0103] Then, the same method as the guide rail is used to obtain the spatial posture transformation matrix of the screw nut

[0104]

[0105] Step 1.4: Construction of moving part parameters, mainly referring to mass m T and the position r of the center of mass MC under O-x0y0z0 TC (x TC ,y TC ,z TC ).

[0106] Step 2: Testing and decomposition of guide rail assembly errors;

[0107] The implementation of the guide rail assembly error test and decomposition in this embodiment specifically includes the following steps:

[0108] Step 2.1: After all rails are installed, measure them using a level or other tool. Figure 6 Assembly error of the middle reference guide rail 211 Including normal surface error and lateral error

[0109] Step 2.2: Using the reference rail 211 as a reference, measure the assembly errors of the other rails 21i along the normal and side surfaces of the reference rail 211. and The assembly error of each guide rail i in the guide rail coordinate system O-x1y1z1 is

[0110]

[0111] Step 2.3: Using the working surface of the moving part as a reference, measure Figure 7 The installation positioning surface error of multiple guide rail sliders 22ij on the moving parts Includes errors along the normal and lateral directions and Taking the slider 2211 on the guide rail 211 as the reference, the relative error of the installation positioning surface of the slider 22ij in the guide rail coordinate system O-x1y1z1 is

[0112]

[0113] Step 3: Establish the force balance equation of the linear feed system;

[0114] The implementation of establishing the force balance equation of the linear feed system in this embodiment specifically includes the following steps:

[0115] Step 3.1: Force analysis of the guide rail pair, the displacement q of the moving part under the action of external load in the global coordinate system O-x0y0z0 T =[u Tx ,u Ty ,u Tz ,θ Tx ,θ Ty ,θ Tz ] T When , the displacement of slider j on guide rail i is

[0116] q GSij =TS GSij q T (9)

[0117] Where,

[0118]

[0119] The displacement of slider j on guide rail i in the guide rail coordinate system O-x1y1z1 is

[0120]

[0121] The force exerted by slider j on the guide rail i on the moving part is

[0122]

[0123] The resultant force of all guide rail pairs acting on the moving parts is

[0124]

[0125] Step 3.2: Force analysis of the screw pair, the center of the screw nut in the global coordinate system O-x0y0z0

[0126] q BN =TS BN q T (16)

[0127] Where,

[0128]

[0129] The displacement of the center of the screw nut in the screw coordinate system O-x2y2z2 is:

[0130]

[0131] The force exerted by the screw pair on the moving parts is:

[0132]

[0133] Step 3.3: There are gravity, cutting force, etc. N under O-x0y0z0 F External loads act on the moving parts, and the kth (k=1,2,…,N F ) The magnitude of the external load is F k =[F xi ,F yi ,F zi ,M xi ,M yi ,M zi ] T , the action point is r Fk (x Fk ,y Fk ,z Fk ). The magnitude of gravity is F TCG =[0,0,-m TC g,0,0,0] T , the action point is r TC (x TC ,y TC ,z TC ). Then the resultant force of the external load is:

[0134]

[0135] Where,

[0136]

[0137] Step D: The force balance equation of the moving part in the global coordinate system O-x0y0z0 is:

[0138]

[0139] After finishing, we can get:

[0140] K T q T =F T (26)

[0141] Where,

[0142]

[0143] Then, the geometric error q of the moving part is T for:

[0144] q T =(K T ) -1 F T (28)

[0145] Step 4: Solve the geometric error of the moving parts;

[0146] The implementation of solving the geometric error of the moving part in this embodiment specifically includes the following steps:

[0147] like Figure 8 According to the structural parameters, processing accuracy, assembly process and service conditions of the linear feed system, the travel of the moving part is divided into N equal parts, and the moving part is moved to any travel S j Similarly, the formula (26) in step 3 is used to establish the arbitrary travel S of the moving part j The force balance equation at , and solve the current stroke S according to formula (28) j The geometric error q Tj , solve to get the current itinerary S j The geometric error q Tj Repeat the above steps to get the geometric error variation law of the moving part in the full stroke q T Based on this, the straightness and other precision indicators of the moving parts are calculated. The geometric errors of the linear feed system are verified according to the design indicators of various geometric errors. The out-of-tolerance precision indicators are found, providing a basis for structural optimization design and assembly process improvement.

[0148] Step 5: Geometric error tracing analysis.

[0149] The implementation of geometric error tracing analysis in this embodiment specifically includes the following steps:

[0150] For the structure, accuracy and other parameters of the linear feed system P i , when the parameter increment ratio is r, the change in the geometric error of the moving part is

[0151] Δq T (P i )=K T (P i (1+r)) -1 F T (P i (1+r))-K T (P i ) -1 F T (P i ) (4)

[0152] The above formula is used to calculate the change of geometric error when various parameters such as guide rail pair, screw pair, moving part parameters and processing accuracy index change, and then obtain the error change rate S(P i )=Δq T (P i ) / q T , according to the error change rate S(P i ) can determine the main factors affecting the geometric errors of moving parts, which serve as key variables in precision design.

[0153] The present invention also includes:

[0154] A system includes a processor capable of running a method for analyzing geometric errors of a linear feed system under arbitrary postures.

[0155] A device comprising:

[0156] Memory: used for storing a computer program of the method for analyzing geometric errors of a linear feed system under arbitrary postures;

[0157] Processor: used to implement the method for analyzing the geometric error of a linear feed system under arbitrary posture when executing the computer program.

[0158] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a method for analyzing geometric errors of a linear feed system under arbitrary postures.

[0159] Example effect verification:

[0160] Vertical use of linear feed system assembly accuracy calibration and guide rail accuracy index calculation, the implementation effect is as follows Figure 9 As shown. Before assembly, the linear feed system was placed horizontally to adjust the guide rail mounting surface and the slider mounting surface precision. The maximum geometric error in the z direction was 4.9μm, which was less than the design value of 5.0μm. After passing the inspection, it was hoisted to a vertical use state. Due to the change in the direction of gravity, the geometric error of the moving parts changed. The maximum geometric error in the z direction increased to 7.5μm, exceeding the design value of 5.0μm. For this out-of-tolerance precision, the main influencing factors were found through traceability analysis to be the guide rail lateral stiffness, guide rail surface accuracy, etc. The adjustment amount of the above factors was calculated based on the overshoot of the geometric error to achieve active design of precision.

[0161] In summary, the present invention provides a geometric error analysis model for a linear feed system under arbitrary spatial postures. By comprehensively considering the combined effects of guide rails, lead screws, moving parts and external forces under spatial postures, a geometric error model for a linear feed system under arbitrary postures is established. During the design phase, the accuracy indicators of the assembly and use phases are accurately calculated and verified, and the accuracy differences under different guide rail configurations and external dimensions are compared, providing technical means for the structural design of the linear feed system and the improvement and active design of the accuracy of its components.

Claims

1. A method for analyzing geometric errors of a linear feed system under arbitrary postures, characterized in that: The following steps are involved: Step 1: Parameter construction of components in the linear feed system under arbitrary postures, including the construction of basic parameters and layout parameters of the guide rail pair, the construction of screw parameters, and the construction of moving component parameters; Step 2: Measure and decompose the assembly errors of each component in the linear feed system, including measuring the assembly error of the reference guide rail; measuring the assembly errors of multiple other guide rails along the normal and side surfaces of the reference guide rail; measuring the installation and positioning surface errors of multiple guide rail sliders on the moving component with the working surface of the moving component as the reference; and the relative error of the installation and positioning surface of the slider in the guide rail coordinate system with the slider on the reference guide rail as the reference. Step 3: Establish the force balance equation at a certain position of the linear feed system based on the parameters of step 1 and the error of step 2; Step 4: Similarly to the force balance equation at a certain position, establish the force balance equation under any stroke of the moving part and solve the geometric error of the moving part; Step 5: Based on the change in geometric error, obtain the error change rate and determine the factors affecting the geometric error of the moving part.

2. The method for analyzing geometric errors of a linear feed system under arbitrary postures according to claim 1 is characterized in that: The step 1 is specifically as follows: Step 1.1: Construction of basic parameters of guide rail pair, including geometric parameters, structural parameters, performance parameters and motion parameters; geometric parameters include guide rail length L G and width W G , slider length L S and width W S And the total height of the guide rail H GS ; Structural parameters include the number of sliders N S , initial position S0 and spacing D Sk (k=1,,2,…,N S -1); performance parameters include normal stiffness K szj and tangential stiffness K syj ; The motion parameter refers to the displacement S of the slider; the center position of each slider in the guide rail coordinate system O-x1y1z1 is have The stiffness matrix of the guide rail slider at j is expressed as: Step 1.2: The construction of the guide rail layout parameters is determined according to the function and structure of the linear feed system. The layout parameters of the guide rail under the global coordinate system O-x0y0z0 include the number of guide rails N G and the spatial posture of the guide rail, guide rail i (i=1,,2,…,N G )'s spatial posture q Gi =[r Gi θ Gi ] T Including the position r of one end Gi (x Gi ,y Gi ,z Gi ) and angle attitude θ Gi (θ Gxi ,θ Gyi ,θ Gzi ), then the spatial attitude transformation matrix of rail i is: The relative posture transformation matrix between rail i and any other rail k is: The coordinates of the center position of each slider of the guide rail i after assembly are r Sij (x Sij ,y Sij ,z Sij ),have: Step 1.3: Construction of screw parameters, including the center position r of the screw nut under O-x0y0z0 BN (x BN ,y BN ,z BN ), angle posture θ BN (θ BNx ,θ BNy ,θ BNz ), axial stiffness K of the screw coordinate system O-x2y2z2 bsa and radial stiffness K bsr1 , K bsr2 , the stiffness matrix at the center of the screw nut is expressed as: Then the spatial attitude transformation matrix of the screw nut is obtained Step D: Construction of moving part parameters, mainly referring to mass m T and the position r of the center of mass MC under O-x0y0z0 TC (x TC ,y TC ,z TC ).

3. The method for analyzing geometric errors of a linear feed system under arbitrary postures according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1: After all guide rails are installed, measure the assembly error of the reference guide rail Including normal surface error and lateral error Step 2.2: Using the reference rail as a reference, measure the assembly errors of multiple rails i along the normal and side surfaces of the reference rail. and The assembly error of each guide rail i in the guide rail coordinate system O-x1y1z1 is: Step 2.3: Using the working surface of the moving part as a reference, measure the installation positioning surface errors of multiple guide rail sliders on the moving part. Includes errors along the normal and lateral directions and Taking the slider on the reference guide rail as the reference, the relative error of the slider's installation positioning surface in the guide rail coordinate system O-x1y1z1 is:

4. The method for analyzing geometric errors of a linear feed system under arbitrary postures according to claim 1, characterized in that: The step three is specifically as follows: Step 3.1: Force analysis of the guide rail pair, the displacement q of the moving part under the action of external load in the global coordinate system O-x0y0z0 T =[u Tx ,u Ty ,u Tz ,θ Tx ,θ Ty ,θ Tz ] T When , the displacement of slider j on guide rail i is: q GSij =TS GSij q T (9) Where, The displacement of slider j on guide rail i in the guide rail coordinate system O-x1y1z1 is: The force exerted by slider j on the guide rail i on the moving part is: The resultant force of all guide rail pairs on the moving parts is: Step 3.2: Force analysis of the screw pair. The displacement of the center of the screw nut in the global coordinate system O-x0y0z0 is: q BN =TS BN q T (16) Where, Then, the displacement of the center of the screw nut in the screw coordinate system O-x2y2z2 is The force exerted by the screw pair on the moving parts is Step 3.3: There are gravity, cutting force, etc. N under O-x0y0z0 F External loads act on the moving parts, and the kth (k=1,2,…,N F ) The magnitude of the external load is F k =[F xi ,F yi ,F zi ,M xi ,M yi ,M zi ] T , the action point is r Fk (x Fk ,y Fk ,z Fk ), then the resultant force of the external load is: Where, Step 3.4: The force balance equation of the moving part in the global coordinate system O-x0y0z0 is: K T q T =F T (23) Where, Then, the geometric error q of the moving part is T for q T =(K T ) -1 F T (26) 。 5. The method for analyzing geometric errors of a linear feed system under arbitrary postures according to claim 1, characterized in that: The step 4 is specifically as follows: According to the structural parameters, processing accuracy, assembly process and service conditions of the linear feed system, the travel of the moving part is divided into N equal parts, and the moving part is moved to any travel S j Similarly, in step 3, the arbitrary travel S of the moving part is established j The force balance equation at the position and solve the current stroke S j The geometric error q Tj Repeat the above steps to get the geometric error variation law of the moving part in the full stroke q T (S); Check the geometric errors of the linear feed system according to the design indicators of various geometric errors to find out the accuracy indicators that exceed the tolerance.

6. The method for analyzing geometric errors of a linear feed system under arbitrary postures according to claim 1, characterized in that: The step five is specifically as follows: For the structure and precision parameters of the linear feed system, i , when the parameter increment ratio is r, the change in the geometric error of the moving part is: Δq T (P i )=K T (P i (1+r)) -1 F T (P i (1+r))-K T (P i ) -1 F T (P i ) (27) Similarly, the above formula (25) is used to calculate the change in geometric error when the various parameters of the guide rail pair, screw pair, moving part parameters and machining accuracy index change, and then the error change rate S(P i )=Δq T (P i ) / q T , according to the error change rate S(P i ) can determine the main factors affecting the geometric errors of moving parts, which serve as key variables in precision design.

7. A system comprising a processor, characterized in that: A method for analyzing geometric errors of a linear feed system under arbitrary postures capable of running any of claims 1-6.

8. A device, characterized in that include: Memory: a computer program for storing a method for analyzing geometric errors of a linear feed system under arbitrary postures as described in any of claims 1-6; Processor: used to implement the method for analyzing the geometric error of a linear feed system under arbitrary posture as described in any of claims 1-6 when executing the computer program.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the method for analyzing the geometric error of a linear feed system under arbitrary posture described in any of claims 1-6.

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