A method for modeling milling machine geometric error of microsphere target considering clamping deformation

Abstract

The application provides a microsphere target milling machine tool geometric error modeling method considering clamping deformation, relates to the error analysis technical field of high-precision machining machine tools, and aims to solve the problems of the existing method, i.e., a complex modeling process, great difficulty in model simplification, no consideration of the influence of workpiece clamping deformation, and low model precision. The method comprises the following steps: S1, constructing a microsphere target milling machine tool geometric error model according to the rigid body theory and the multi-body system theory, using a homogeneous coordinate transformation matrix to represent the pose conversion relationship between adjacent topological structures of the machine tool, and solving the geometric error of the machine tool; S2, constructing a microsphere target clamping deformation model and solving the clamping deformation of the microsphere target; and S3, constructing a microsphere target milling machine tool geometric error model considering clamping deformation and solving the microsphere target milling machine tool geometric error considering clamping deformation. The model has high precision and can further improve the machining precision of the machine tool.

Description

Technical Field

[0001] This invention relates to the field of error analysis technology for high-precision machine tools, and more specifically, to a geometric error modeling method for microspherical target milling machine tools that takes into account clamping deformation. Background Technology

[0002] The world today is facing unprecedented major changes. Industries such as military equipment, aerospace, and electronic medical devices are booming, and the demand for various precision, miniaturized, and integrated complex micro-components is increasing. The requirements for the manufacturing precision and surface quality of characteristic structures are becoming higher and higher, which promotes the rapid development of the precision and ultra-precision manufacturing industry, especially ultra-precision machine tools.

[0003] For example, thin-walled spherical shell microspherical targets with diameters of 1–5 mm and shell thicknesses of 20–120 μm are widely used in energy research. These targets require milling to create dozens to hundreds of micro-pit structures with depths of 0.5–20 μm and widths of 50–200 μm across their entire surface, with a contour error better than 0.3 μm and a surface roughness R... a With a precision better than 20nm and pit spacing error reaching the micrometer level, high requirements are placed on the geometric errors and machining accuracy of milling machine tools. Microspheres are complex micro-components of thin-walled spherical shells, and the machining accuracy of ultra-precision milling machines directly affects the surface quality of the micro-pit structure across the entire surface. In actual machining, the machine tool is subject to several errors, leading to positional deviations in the machining trajectory. External factors such as temperature, relative humidity, and human influence can be kept within a small range through strict control of natural environmental conditions. Among internal causes such as milling principle deviations, machine tool geometric errors, tool friction and wear, and thermal deformation errors, geometric errors account for a large proportion and significantly affect the machining accuracy. Simultaneously, the brittle polymer microspheres constrained by micro-scale have small wall thicknesses and relatively low stiffness. Under the influence of minute surface defects, non-uniform materials, and vacuum negative pressure during adsorption clamping, the microspheres will deform during clamping, directly affecting machining accuracy. Therefore, it is urgent to model and characterize the geometric errors of the microspherical target milling machine tool under clamping deformation in order to achieve high-quality machining of the micro-pit structure on the surface of the microspherical target.

[0004] Common methods for modeling machine tool geometric errors include the quadratic relation method, the error matrix method, rigid body kinematics, multibody system theory, and helical theory. These methods are complex in their modeling processes, difficult to simplify, and only consider the motion errors of each axis of the machine tool, neglecting the impact of workpiece clamping deformation on the surface quality of the machined microstructures. Therefore, they cannot achieve high-precision modeling and characterization of the geometric errors of machine tools used in micro-spherical target milling. Key performance indicators such as the uniformity of micro-pit structure distribution, contour accuracy, and surface roughness fall far short of requirements. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] Existing methods have a complex modeling process, are difficult to simplify, do not consider the impact of workpiece clamping deformation on the surface quality of the feature microstructure, and have low model accuracy.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] This invention provides a method for modeling geometric errors in a microsphere target milling machine tool, taking into account clamping deformation. The method includes the following steps:

[0009] S1. Construct a geometric error model for the microsphere target milling machine tool based on rigid body theory and multibody system theory. Use a homogeneous coordinate transformation matrix to characterize the pose transformation relationship between adjacent topological structures of the machine tool, and solve for the geometric error of the machine tool. The steps include:

[0010] S11. Divide the topology of the micro-spherical target milling machine tool into workpiece branches and tool branches. The workpiece branches are the motion chains that are transmitted from the machine tool bed to the workpiece, and the tool branches are the motion chains that are transmitted from the machine tool bed to the tool.

[0011] S12. Starting with the machine tool bed as the initial sequence, sequentially number the workpiece branches and tool branches along the kinematic chain direction, construct the relationship between each typical body, and obtain the low-order body sequence of the micro-spherical target milling machine tool topology;

[0012] S13. Determine the homogeneous transformation of the coordinate systems of each axis of the microsphere target milling machine tool;

[0013] Translation, rotation, and scaling operations between coordinate systems are represented using matrices. Matrix addition is used to express translation transformations between coordinate systems, while matrix multiplication is used to represent rotation and scaling transformations. The calculation is performed from the source coordinate system O... s To the target coordinate system O g The comprehensive transformation matrix;

[0014] S14. Geometric error source analysis of microsphere milling machine tool, and determination of machine tool geometric error terms;

[0015] S15. Analyze the errors of the linear axis system and calculate the motion deviation matrix generated by each linear axis during actual motion;

[0016] S16. Analyze the error of the rotating shaft system and calculate the motion deviation matrix generated by each rotating shaft during actual motion;

[0017] S17. Construct a geometric error model for the microsphere target milling machine tool and solve for the geometric error of the machine tool;

[0018] S2. Construct a model of the microsphere target clamping deformation and solve for the clamping deformation of the microsphere target;

[0019] S3. Construct a geometric error model for the micro-spherical target milling machine tool that considers clamping deformation, and solve for the geometric error of the micro-spherical target milling machine tool when considering clamping deformation.

[0020] Furthermore, the specific transmission process of the workpiece branch in S11 is as follows: machine tool bed, X-axis, Y-axis, C-axis, clamping system, workpiece; the specific transmission process of the tool branch is as follows: machine tool bed, Z-axis, B-axis, milling axis, tool.

[0021] Furthermore, the low-order body sequence described in S12 is represented as follows:

[0022] L m (j)=i (1)

[0023] Where m represents the number of typical bodies in the multibody system; j represents the nth-order higher-order body of typical body i;

[0024] To ensure the constraint relationships between the various typical entities, the typical entities must also satisfy:

[0025]

[0026] From formulas (1) and (2), we obtain

[0027] L(j)=i (3)

[0028] Based on the relationships between the typical bodies obtained, the low-order body sequence of the topology of the microsphere target milling machine tool is obtained.

[0029] Furthermore, in S14, the machine tool geometric error term is determined, including:

[0030] X-axis: δxx, δxy, δxz, θxx, θxy, θxz;

[0031] Y axis: δyx, δyy, δyz, θyx, θyy, θyz;

[0032] Z axis: δzx, δzy, δzz, θzx, θzy, θzz;

[0033] C axis: δcx, δcy, δcz, θcx, θcy, θcz;

[0034] B axis: δbx, δby, δbz, θbx, θby, θbz;

[0035] Verticality error includes: βyx, βyz, βcy, βcx, βzx, βbz, βbx, βay, βaz, βvx, βvy;

[0036] δmn, θmn, and βmn represent translation error, motion angle error, and perpendicularity error, respectively. The first subscript represents the direction of motion, and the second subscript represents the direction of error.

[0037] Furthermore, S15 includes the following steps:

[0038] Let the initial homogeneous coordinates of the X-axis linear guide in the source coordinate system be [x0, y0, z0, 1]. T When there are no geometric errors, after the X-axis linear guide moves a distance x along the X direction, its coordinates in the target coordinate system are [x0+x,y0,z0,1]. T The coordinate system transformation matrix T at this time x-u for:

[0039]

[0040] Under the influence of linear error, the actual motion trajectory of the X-axis linear guide rail deviates (δ). xx ,δ xy ,δ xz The coordinate system transformation matrix is:

[0041]

[0042] Under the influence of angular error, the actual deflection angle of the X-axis linear guide rail deviates (θ). xx ,θ xy ,θ xz The homogeneous coordinate transformation matrix corresponding to the angular deviation is:

[0043]

[0044] From formulas (5) and (6), we can obtain the homogeneous coordinate transformation matrix corresponding to the actual movement of the X-axis linear guide rail under the combined effects of positioning error and linearity error:

[0045]

[0046] From formulas (4) and (7), the error matrix ΔTx = Tx-r - Tx-u generated by the X-axis linear guide during actual motion can be obtained as:

[0047]

[0048] Using the same method, the error matrices generated by the Y-axis and Z-axis during actual motion are determined as follows:

[0049]

[0050]

[0051] Furthermore, S16 includes the following steps;

[0052] Let the initial coordinates of the B-axis in the source coordinate system be [x0, y0, z0, 1]. T When there is no geometric error, the coordinate transformation matrix T from the source coordinate system to the target coordinate system when rotating the B-axis by an angle θ is... B-u for:

[0053]

[0054] Under the influence of linear error, the actual motion of the B-axis will produce a linear deviation (δ). bx ,δ by ,δ bz The coordinate transformation matrix is:

[0055]

[0056] Under the influence of angular error, the actual deflection angle of the B-axis guide rail will deviate (θ). bx ,θ by ,θ bz The homogeneous transformation matrix corresponding to the angular deviation is:

[0057]

[0058] From formulas (12) and (13), the homogeneous coordinate transformation matrix corresponding to the actual motion of the B-axis under the combined effects of linear error and angular error can be obtained as follows:

[0059]

[0060] From formulas (11) and (14), the motion error matrix ΔT generated by the B-axis during actual motion can be obtained. B =T B -rT B -u means:

[0061]

[0062] Using the same method, the error matrix generated by the C-axis during actual motion can be obtained as follows:

[0063]

[0064] Furthermore, S17 includes the following steps:

[0065] S171, Transform the matrix between adjacent objects Represented as:

[0066]

[0067] in, It is an error-free static transformation matrix. This is the actual static transformation matrix. The transformation matrix of adjacent bodies in error-free motion. This is the transformation matrix of the actual moving adjacent bodies;

[0068] The homogeneous coordinate transformation form of the workpiece branch error-free motion / actual motion is:

[0069]

[0070] The homogeneous coordinate transformation form of the error-free motion / actual motion of the tool branch is:

[0071]

[0072]

[0073] S172. When the micro-spherical target milling machine tool has no geometric errors, the spatial position of the apex of the ball end mill on the milling axis coincides with the spatial position of the micro-pit structure to be machined on the micro-spherical target; therefore, the spatial position of the ball end mill tip obtained by transforming the tool coordinate system to the global coordinate system coincides with the spatial position obtained by transforming the micro-pit structure from the workpiece coordinate system to the global coordinate system, i.e.

[0074]

[0075] Among them, P w =[P wx ,P wy ,P wz ,1] T P represents the position of the microstructure to be machined in the workpiece coordinate system. t =[P tx ,P ty ,P tz ,1] T This represents the coordinates of the milling cutter tip in the tool coordinate system, where P is taken. t =[0,0,0,1] T ;

[0076] The trajectory of the milling cutter tip in the workpiece coordinate system, without considering machine tool geometric errors, is as follows:

[0077] P wu =P1 -1 P2P t (19)

[0078] in,

[0079]

[0080] From formula (17), the actual motion trajectory of the milling cutter tip in the workpiece coordinate system can be obtained as follows:

[0081]

[0082] From formulas (19) and (20), the actual machining error of the microsphere target milling machine tool can be obtained as follows:

[0083] E = P wu -P wr (twenty one)

[0084] By substituting the numerical value of the geometric error of the machine tool into formula (21), the actual error of the micro-spherical target milling machine tool can be obtained.

[0085] Furthermore, S2 includes the following process: Considering that under vacuum negative pressure, the microsphere target and the vacuum adsorption fixture form a circumferential contact, that is, the supporting force is distributed on the circumference passing through the contact point, and local contact stress will be generated in the contact area, causing overall deformation and local deformation of the microsphere target during clamping; the local characteristics of the contact stress are relatively obvious, and it will rapidly decrease as the distance between the contact point of the microsphere target and the fixture increases; a micro-element segment of the microsphere target-fixture contact area is selected for analysis to obtain the central angle β. va The radial force dF of the corresponding infinitesimal segment is:

[0086] dF=qRdβ va 2πRcos(α va +β va sin(α) va +β va ) (twenty two)

[0087] Where, β va α represents the central angle corresponding to the infinitesimal segment, in degrees. va represents the cone angle, °; R represents the microsphere target radius; q represents the vacuum negative pressure, kPa;

[0088] The radial pressure in the contact area between the microsphere target and the fixture is:

[0089]

[0090] Within the contact area between the microsphere target and the clamp, due to the vacuum negative pressure, the endpoint of the microsphere target along the clamp axis is the position of maximum static deformation after adsorption and clamping. The deformation v2 of the microsphere target clamping is:

[0091]

[0092] Among them, E laδ represents the GDP elastic modulus of the microsphere target material, MPa; δ represents the thickness of the microsphere target shell, μm; μ represents the Poisson's ratio of the microsphere target material.

[0093] Furthermore, S2 also includes verifying the deformation v2 of the obtained microspherical target clamping by finite element simulation of the deformation of the microspherical target adsorption clamping, and jointly determining the magnitude of the microspherical target clamping deformation.

[0094] Furthermore, S3 includes the following steps:

[0095] The geometric error E of the microspherical target milling machine tool is mainly composed of E x E y E z The combination of errors in three directions results in the maximum static deformation v2 of the microsphere target during adsorption and clamping along the axis of the suction device, which is consistent with the Z-axis movement direction of the microsphere target milling machine. Therefore, the error E along the Z-axis movement direction of the microsphere target milling machine is... z2 for:

[0096] E z2 =E z +v2 (25)

[0097] Therefore, the geometric error E of the microsphere target milling machine tool considering workpiece clamping deformation is... final for:

[0098]

[0099] Compared with the prior art, the beneficial effects of the present invention are:

[0100] This invention uses rigid body kinematics and multibody system theory to model and characterize the geometric error of a micro-spherical target milling machine tool. Through theoretical calculation and simulation analysis, the deformation of the micro-spherical target during actual adsorption and clamping is obtained. Thus, a geometric error model of a micro-spherical target milling machine tool considering the workpiece adsorption and clamping deformation is established, which has high accuracy.

[0101] This method has a certain degree of universality. It is not only suitable for establishing geometric error models of machine tools for ultra-precision micro-milling of complex micro-components such as micro-spherical targets, but can also be further extended to the calibration of geometric errors of conventional multi-axis machine tools under workpiece deformation. It can be used to guide the design of key functional components and machining processes of machine tools, so as to further improve the machining accuracy of machine tools. Attached Figure Description

[0102] Figure 1 This is a flowchart of a geometric error modeling method for a microspherical target milling machine tool that considers clamping deformation, as described in an embodiment of the present invention.

[0103] Figure 2 This is a schematic diagram of the microsphere target milling machine tool structure in an embodiment of the present invention;

[0104] Figure 3 This is a schematic diagram of the topology of the microsphere target milling machine tool in an embodiment of the present invention;

[0105] Figure 4 This is a schematic diagram of the coordinate system translation transformation of the microsphere target milling machine tool in an embodiment of the present invention;

[0106] Figure 5 This is a schematic diagram of the coordinate system rotation transformation of the microsphere target milling machine tool in an embodiment of the present invention;

[0107] Figure 6 This is a schematic diagram of the microsphere target under force and deformation in an embodiment of the present invention.

[0108] Figure 7 This is a schematic diagram of the deformation of the microsphere target adsorption clamping in an embodiment of the present invention.

[0109] Explanation of reference numerals in the attached figures:

[0110] 1-Machine bed, 2-Z-axis motion unit, 3-B-axis rotary table, 4-Milling axis, 5-Y-axis motion unit, 6-Workpiece axis C-axis, 7-X-axis motion unit. Detailed Implementation

[0111] In the description of this invention, it should be noted that the terms used in the various embodiments, such as "upper," "lower," "front," "rear," "left," and "right," which indicate orientation, are only used to simplify the description of the positional relationships based on the accompanying drawings and do not mean that the components and devices referred to must be operated in accordance with the specific orientations and defined operations, methods, and structures in the specification. Such directional terms do not constitute a limitation of this invention.

[0112] In the description of this invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0113] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0114] Specific Implementation Plan 1: Combining Figures 1 to 7 As shown, this invention provides a method for modeling geometric errors in a microsphere target milling machine tool that considers clamping deformation, such as... Figure 2As shown, the method is based on an ultra-precision five-axis linkage machine tool. The machine tool adopts a "T"-shaped layout, including three linear motion axes: X-axis motion unit 7, Y-axis motion unit 5, and Z-axis motion unit 2; two rotary axes: B-axis rotary table 3 and workpiece axis C-axis 6; and a machine bed 1. The X-axis motion unit 7 and Z-axis motion unit 2 are mounted on the machine bed 1 and arranged perpendicularly to each other. The Y-axis motion unit 5 is arranged vertically on the X-axis guide rail. The three linear motion axes are driven by linear motion motors. The workpiece axis C-axis 6 is arranged in the middle of the Y-axis slide and uses a gas hydrostatic bearing and circular grating feedback control. The B-axis rotary table 3 is arranged on the guide rail of the Z-axis motion unit 2 and is driven by a liquid hydrostatic bearing. A horizontal CCD camera is mounted on a transition plate on the B-axis rotary table 3. A vertical CCD camera is mounted on the Y-axis transition plate and can move with the Y-axis motion unit 5. The milling axis 4 is mounted on the B-axis rotary table 3.

[0115] The method includes the following steps:

[0116] S1. Construct a geometric error model for the microsphere target milling machine tool based on rigid body theory and multibody system theory. Use a homogeneous coordinate transformation matrix to characterize the pose transformation relationship between adjacent topological structures of the machine tool, and solve for the geometric error of the machine tool. The steps include:

[0117] S11. Divide the topology of the micro-spherical target milling machine tool into workpiece branches and tool branches. The workpiece branches are the motion chains that are transmitted from the machine tool bed to the workpiece, and the tool branches are the motion chains that are transmitted from the machine tool bed to the tool.

[0118] S12. Starting with the machine tool bed as the initial sequence, sequentially number the workpiece branches and tool branches along the kinematic chain direction, construct the relationship between each typical body, and obtain the low-order body sequence of the micro-spherical target milling machine tool topology.

[0119] S13. Determine the homogeneous transformation of the coordinate systems of each axis of the microsphere target milling machine tool;

[0120] Translation, rotation, and scaling operations between coordinate systems are represented using matrices. Matrix addition is used to express translation transformations between coordinate systems, while matrix multiplication is used to represent rotation and scaling transformations. The calculation is performed from the source coordinate system O... s To the target coordinate system O g The comprehensive transformation matrix;

[0121] S14. Geometric error source analysis of microsphere milling machine tool, and determination of machine tool geometric error terms;

[0122] S15. Analyze the errors of the linear axis system and calculate the motion deviation matrix generated by each linear axis during actual motion;

[0123] S16. Analyze the error of the rotating shaft system and calculate the motion deviation matrix generated by each rotating shaft during actual motion;

[0124] S17. Construct a geometric error model for the microsphere target milling machine tool and solve for the geometric error of the machine tool;

[0125] S2. Construct a model of the microsphere target clamping deformation and solve for the clamping deformation of the microsphere target;

[0126] S3. Construct a geometric error model for the micro-spherical target milling machine tool that considers clamping deformation, and solve for the geometric error of the micro-spherical target milling machine tool when considering clamping deformation.

[0127] Specific Implementation Plan Two: (e.g.) Figure 3 As shown, based on rigid body kinematics and multibody system theory, each moving part of the micro-spherical target milling machine tool is abstracted into an independent rigid body, and the various errors existing in each moving part of the machine tool are separated. Each rigid body corresponds to a functional component system, thus establishing the topology of the micro-spherical target milling machine tool.

[0128] The specific transfer process of the workpiece branch in S11 is as follows: machine tool bed, X-axis, Y-axis, C-axis, clamping system, workpiece; the specific transfer process of the tool branch is as follows: machine tool bed, Z-axis, B-axis, milling axis, tool. All other aspects of this implementation scheme are the same as in Specific Implementation Scheme One.

[0129] Specific Implementation Scheme 3: Define the machine bed as body 0 in the above micro-spherical target milling machine tool topology, which is stationary relative to the bottom surface. Starting with body 0, sequentially number the workpiece and tool branches along the motion chain direction.

[0130] The low-order sequence starting with bed 0 in S12 is represented as follows:

[0131] L m (j)=i (1)

[0132] Where m represents the number of typical bodies in the multibody system; j represents the nth-order higher-order body of typical body i;

[0133] To ensure the constraint relationships between the various typical entities, the typical entities must also satisfy:

[0134]

[0135] From formulas (1) and (2), we obtain

[0136] L(j)=i (3)

[0137] Based on the relationships between the typical volumes obtained, the low-order volume sequence of the microsphere target milling machine tool topology is acquired. This implementation scheme is otherwise identical to specific implementation scheme two.

[0138] Based on the relationships between the typical volumes obtained, the low-order volume sequence of the microsphere target milling machine tool topology can be obtained, as shown in Table 1.

[0139] Table 1

[0140]

[0141] Specific implementation plan four: In S13, the transformation matrix for transferring the position of any set of points in a plane or space from the original coordinate system to the target coordinate system is:

[0142] F1=F0M1+M2 (4)

[0143] Where F0 represents the original coordinates of the coordinate system to be transformed, F1 represents the coordinates after the coordinate system transformation, M1 represents the rotation transformation matrix, and M2 represents the translation matrix;

[0144] Formula (4) simplifies to:

[0145] F1=F0M (5)

[0146] Where M represents the combined matrix of rotation and translation transformations;

[0147] like Figure 4 As shown, for coordinate system translation transformation, when the source coordinate system O s The target coordinate system O is obtained by translating the coordinate axes X, Y, and Z by distances a, b, and c. g Based on the homogeneous coordinate transformation, the coordinate transformation matrix corresponding to the distance 'a' that the microsphere target milling machine tool moves along the X-axis can be obtained:

[0148]

[0149] The coordinate transformation matrix corresponding to the distance b that the microspherical target milling machine tool moves along the Y-axis can be obtained as follows:

[0150]

[0151] The coordinate transformation matrix corresponding to the distance c that the microspherical target milling machine tool moves along the Y-axis can be obtained as follows:

[0152]

[0153] From equations (6), (7) and (8), we can obtain the equations from the source coordinate system O. s To the target coordinate system O g The comprehensive translation transformation matrix:

[0154]

[0155] like Figure 5 As shown, for coordinate system rotation transformation, the target coordinate system Og is obtained by rotating the source coordinate system Os around the coordinate axes X, Y and Z by angles αβ and θ respectively;

[0156] According to the theory of homogeneous coordinate transformation, the coordinate transformation matrix corresponding to a rotation of α around the X-axis can be obtained:

[0157]

[0158] We can obtain the coordinate transformation matrix corresponding to the rotation around the Y-axis by an angle β:

[0159]

[0160] We can obtain the coordinate transformation matrix corresponding to the rotation around the Z-axis by an angle θ:

[0161]

[0162] From equations (10), (11), and (12), the comprehensive rotation transformation matrix from the source coordinate system Os to the target coordinate system Og can be obtained:

[0163]

[0164] Among them, m1=sinαsinβcosθ-cosαsinθ, m2=cosαsinβcosθ+sinαsinθ, m3=sinαsinβsinθ-cosαcosθ, m4=cosαsinβsinθ+sinαcosθ, m5=sinαcosθ; m6=cosαcosβ;

[0165] Since the angular deviations α, β, and θ are relatively small during actual motion, formula (13) is further approximated to obtain:

[0166]

[0167] This implementation plan is otherwise the same as Specific Implementation Plan 1.

[0168] Specific implementation plan five: Based on rigid body kinematics and multibody system theory, each motion unit of the micro-spherical target milling machine tool contains six geometric errors, including linear error and angular error.

[0169] For milling linear motion units, the above six geometric errors mainly include position movement error, two straightness offset errors, and three angle errors: pitch, roll, and yaw.

[0170] The geometric error terms for milling rotary motion units mainly consist of one axial linear error, two radial linear errors, and three angular errors, including angular positioning and tilting errors.

[0171] Considering the installation characteristics of the milling axis, its tilt angle is expressed as a certain angle of rotation of the milling axis around the X-axis, defined as the A-axis.

[0172] S14 defines the machine tool geometric error terms, including:

[0173] X-axis: δ xx ,δ xy ,δ xz ,θ xx ,θ xy ,θ xz ;

[0174] Y-axis: δ yx ,δ yy ,δ yz ,θ yx ,θ yy ,θ yz ;

[0175] Z-axis: δ zx ,δ zy ,δ zz ,θ zx ,θ zy ,θ zz ;

[0176] C-axis: δ cx ,δ cy ,δ cz ,θ cx ,θ cy ,θ cz ;

[0177] B-axis: δ bx ,δ by ,δ bz ,θ bx ,θ by ,θ bz ;

[0178] Verticality error includes: β yx ,β yz ,β cy ,β cx ,β zx ,β bz ,β bx ,β ay ,β az ,β vx ,β vy ;

[0179] Using δ mn θmn ,β mn These represent translation error, motion angle error, and perpendicularity error, respectively. The first subscript indicates the direction of motion, and the second subscript indicates the direction of error. This implementation scheme is otherwise identical to Specific Implementation Scheme Four.

[0180] Specific implementation plan six: S15 includes the following steps:

[0181] Let the initial homogeneous coordinates of the X-axis linear guide in the source coordinate system be [x0, y0, z0, 1]. T When there are no geometric errors, after the X-axis linear guide moves a distance x along the X direction, its coordinates in the target coordinate system are [x0+x,y0,z0,1]. T The coordinate system transformation matrix T at this time x-u for:

[0182]

[0183] Under the influence of linear error, the actual motion trajectory of the X-axis linear guide rail deviates (δ). xx ,δ xy ,δ xz The coordinate system transformation matrix is:

[0184]

[0185] Under the influence of angular error, the actual deflection angle of the X-axis linear guide rail deviates (θ). xx ,θ xy ,θ xz From formula (14), we know that the homogeneous coordinate transformation matrix corresponding to the angle deviation is:

[0186]

[0187] From formulas (16) and (17), the homogeneous coordinate transformation matrix corresponding to the actual movement of the X-axis linear guide rail under the combined effect of six errors, including positioning error and linearity error, can be obtained as follows:

[0188]

[0189] From formulas (15) and (18), the error matrix ΔT generated by the X-axis linear guide during actual motion can be obtained. x =T x-r -T x-u for:

[0190]

[0191] Using the same method, the error matrices generated by the Y-axis and Z-axis during actual motion are determined as follows:

[0192]

[0193]

[0194] This implementation plan is otherwise the same as Specific Implementation Plan Five.

[0195] Specific implementation plan seven: S16 includes the following steps;

[0196] Let the initial coordinates of the B-axis in the source coordinate system be [x0, y0, z0, 1]. T When there is no geometric error, the coordinate transformation matrix T from the source coordinate system to the target coordinate system when rotating the B-axis by an angle θ is... B-u for:

[0197]

[0198] During actual movement, the B-axis will deviate in its actual rotation position due to the combined effects of six errors, including linearity error and angular error. Under the influence of linearity error, the actual movement of the B-axis will produce a linear deviation (δ). bx ,δ by ,δ bz The coordinate transformation matrix is:

[0199]

[0200] Under the influence of angular error, the actual deflection angle of the B-axis guide rail will deviate (θ). bx ,θ by ,θ bz The homogeneous transformation matrix corresponding to the angular deviation is:

[0201]

[0202] From formulas (23) and (24), the homogeneous coordinate transformation matrix corresponding to the actual motion of the B-axis under the combined effects of linear error and angular error can be obtained as follows:

[0203]

[0204] From formulas (22) and (25), the motion error matrix ΔT generated by the B-axis during actual motion can be obtained. B =T B-r -T B-u for:

[0205]

[0206] Using the same method, the error matrix generated by the C-axis during actual motion can be obtained as follows:

[0207]

[0208] This implementation plan is otherwise the same as Specific Implementation Plan Six.

[0209] Specific implementation plan eight: S17 includes the following steps:

[0210] S171, Transform the matrix between adjacent objects Represented as:

[0211]

[0212] in, It is an error-free static transformation matrix. This is the actual static transformation matrix. The transformation matrix of adjacent bodies in error-free motion. This is the transformation matrix of the actual moving adjacent bodies;

[0213] Table 2 shows the coordinate transformation relationships between adjacent topologies. The homogeneous coordinate transformation forms of the error-free motion / actual motion of the workpiece branch W are shown in Table 3.

[0214] Table 3

[0215]

[0216]

[0217] The homogeneous coordinate transformation forms of the error-free motion / actual motion of the tool branch are shown in Table 4.

[0218] Table 4

[0219]

[0220] S172. When the micro-spherical target milling machine tool has no geometric errors, the spatial position of the vertex of the ball end mill on the milling axis coincides with the spatial position of the micro-pit structure to be machined on the micro-spherical target; therefore, the spatial position of the ball end mill tip obtained by transforming the tool coordinate system to the global coordinate system coincides with the spatial position obtained by transforming the micro-pit structure from the workpiece coordinate system to the global coordinate system, i.e.

[0221]

[0222] Among them, P w =[P wx ,P wy ,P wz ,1] T P represents the position of the microstructure to be machined in the workpiece coordinate system. t =[P tx ,P ty ,P tz ,1]T This represents the coordinates of the milling cutter tip in the tool coordinate system, where P is taken. t =[0,0,0,1] T ;

[0223] The trajectory of the milling cutter tip in the workpiece coordinate system, without considering machine tool geometric errors, is as follows:

[0224] P wu =P1 -1 P2P t (30)

[0225] in,

[0226]

[0227] From formula (28), the actual motion trajectory of the milling cutter tip in the workpiece coordinate system can be obtained as follows:

[0228]

[0229] From formulas (30) and (31), the actual machining error of the micro-spherical target milling machine tool can be obtained as follows:

[0230] E = P wu -P wr (32)

[0231] The range of 41 geometric errors present in the microsphere milling machine tool is shown in Table 5.

[0232] Table 5

[0233]

[0234]

[0235] Substituting the geometric error values ​​in Table 5 into formula (32), the actual achievable machining accuracy of the microsphere target milling machine tool is obtained, and the error results are shown in Table 6.

[0236] Table 6

[0237]

[0238] This implementation plan is otherwise the same as specific implementation plan seven.

[0239] Based on the dynamics theory of multibody systems, this implementation scheme uses a fourth-order homogeneous coordinate transformation matrix to parametrically characterize the pose transformation relationship between adjacent topological structures of the machine tool. For both static and dynamic cases, the corresponding error-free transformation matrix and the actual motion transformation matrix are given respectively, and the comprehensive error-free transformation matrix and the comprehensive actual motion transformation matrix are calculated respectively.

[0240] Specific Implementation Plan Nine: (e.g.) Figure 6 As shown, S2 includes the following process: Considering the formation of circumferential contact between the microsphere target and the vacuum adsorption fixture under vacuum negative pressure, the supporting force is distributed on the circumference passing through the contact point. Local contact stress is generated in the contact area, causing overall and local deformation of the microsphere target during clamping; the local characteristics of the contact stress are relatively obvious, and it decreases rapidly as the distance between the contact point of the microsphere target and the fixture increases; a micro-element segment of the microsphere target-fixture contact area is selected for analysis to obtain the central angle β. va The radial force dF of the corresponding infinitesimal segment is:

[0241] dF=qRdβ va 2πRcos(α va +β va sin(α) va +β va (33)

[0242] Where, β va α represents the central angle corresponding to the infinitesimal segment, in degrees. va The cone angle is represented in °; q represents vacuum pressure in kPa.

[0243] The radial pressure in the contact area between the microsphere target and the fixture is:

[0244]

[0245] Within the contact area between the microsphere target and the clamp, due to the vacuum negative pressure, the endpoint of the microsphere target along the clamp axis is the position of maximum static deformation after adsorption and clamping. The deformation v2 of the microsphere target clamping is:

[0246]

[0247] Among them, E la δ represents the GDP elastic modulus of the microsphere target material, MPa; δ represents the thickness of the microsphere target shell, μm; μ represents the Poisson's ratio of the microsphere target material.

[0248] Based on the mechanical properties of the GDP material in the microsphere target and the applied experimental conditions (vacuum negative pressure q = -77.98 kPa, elastic modulus E = 5 GPa, shell thickness = 50 μm, Poisson's ratio of GDP material = 0.3, and cone angle α = 37°), the maximum static deformation of the microsphere target under a vacuum negative pressure of -77.98 kPa, v2 = 9.26 nm, can be obtained. Other aspects of this implementation scheme are the same as in specific implementation scheme one.

[0249] Specific implementation plan ten: S2 also includes verifying the deformation v2 of the microsphere target clamping by finite element simulation of the deformation of the microsphere target adsorption clamping, and jointly determining the magnitude of the microsphere target clamping deformation.

[0250] like Figure 7 As shown, finite element simulation of microsphere target adsorption and clamping was conducted using Abaqus software to verify the theoretical analysis results and jointly determine the deformation of the microsphere target during adsorption and clamping. The cone angle α was selected as 37°, the vacuum negative pressure q as -77.98 kPa, and the elastic modulus E... la With a pressure of 5 GPa, a shell thickness of 50 μm, and a Poisson's ratio of 0.3 for the GDP material, finite element adsorption simulation was conducted. As shown in the figure, the maximum static deformation of the microsphere target along the axial direction of the suction device is only on the order of several nanometers, which is consistent with the theoretical analysis results.

[0251] Based on theoretical analysis and finite element simulation results, the maximum static clamping deformation of the microsphere target is selected as 9.26 nm. The rest of this implementation scheme is the same as specific implementation scheme nine.

[0252] Specific implementation plan eleven: Based on the geometric error model of the micro-spherical target milling machine tool and the deformation of the micro-spherical target during adsorption and clamping, establish a geometric error model of the micro-spherical target milling machine tool that takes into account the workpiece clamping deformation.

[0253] S3 includes the following steps:

[0254] The geometric error E of the microspherical target milling machine tool is mainly composed of E x E y E z The combination of errors in three directions results in the maximum static deformation v2 of the microsphere target during adsorption and clamping along the axis of the suction device, which is consistent with the Z-axis movement direction of the microsphere target milling machine. Therefore, the error E along the Z-axis movement direction of the microsphere target milling machine is... z2 for:

[0255] E z2 =E z +v2 (36)

[0256] Therefore, the geometric error E of the microsphere target milling machine tool considering workpiece clamping deformation is... final for:

[0257]

[0258] From Table 6, combined with formulas (35) and (37), the geometric error of the microsphere target milling machine tool considering clamping deformation can be obtained.

[0259]

[0260] Within a 10mm stroke, the geometric error of the microspherical target milling machine, considering clamping deformation, is 0.4816μm. When the stroke range is less than 2mm, it meets the processing requirements and can achieve dozens to hundreds of micro-pit structures with depths of 0.5-20μm and widths of 50-200μm on the entire surface of thin-walled spherical shell microspherical targets with diameters of 1-5mm and shell thicknesses of 20-120mm. The contour error is better than 0.3μm, and the surface roughness R is [not specified]. a The processing requirements are better than 20nm. This implementation scheme is otherwise the same as Specific Implementation Scheme One.

[0261] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for modeling geometric errors in a microsphere target milling machine tool considering clamping deformation, characterized in that, The method includes the following steps: S1. Construct a geometric error model for the microsphere target milling machine tool based on rigid body theory and multibody system theory. Use a homogeneous coordinate transformation matrix to characterize the pose transformation relationship between adjacent topological structures of the machine tool, and solve for the geometric error of the machine tool. The steps include: S11. Divide the topology of the micro-spherical target milling machine tool into workpiece branches and tool branches. The workpiece branches are the motion chains that are transmitted from the machine tool bed to the workpiece, and the tool branches are the motion chains that are transmitted from the machine tool bed to the tool. S12. Starting with the machine tool bed as the initial sequence, sequentially number the workpiece branches and tool branches along the kinematic chain direction, construct the relationship between each typical body, and obtain the low-order body sequence of the micro-spherical target milling machine tool topology; S13. Determine the homogeneous transformation of the coordinate systems of each axis of the microsphere target milling machine tool; Translation, rotation, and scaling operations between coordinate systems are represented using matrices. Matrix addition is used to express translation transformations between coordinate systems, while matrix multiplication is used to represent rotation and scaling transformations. The calculation is performed from the source coordinate system O... s To the target coordinate system O g The comprehensive transformation matrix; S14. Geometric error source analysis of microsphere milling machine tool, and determination of machine tool geometric error terms; S15. Analyze the errors of the linear axis system and calculate the motion deviation matrix generated by each linear axis during actual motion; S16. Analyze the error of the rotating shaft system and calculate the motion deviation matrix generated by each rotating shaft during actual motion; S17. Construct a geometric error model for the microsphere target milling machine tool and solve for the geometric error of the machine tool; S2. Construct a model of the microsphere target clamping deformation and solve for the clamping deformation of the microsphere target; S3. Construct a geometric error model for the micro-spherical target milling machine tool that considers clamping deformation, and solve for the geometric error of the micro-spherical target milling machine tool when considering clamping deformation; S3 includes the following steps: The geometric error E of the microspherical target milling machine tool is mainly composed of E x E y E z The combination of errors in three directions results in the maximum static deformation v2 of the microsphere target during adsorption and clamping along the axis of the suction device, which is consistent with the Z-axis movement direction of the microsphere target milling machine. Therefore, the error E along the Z-axis movement direction of the microsphere target milling machine is... z2 for: Yes z2 =Yes z +v2(25) Therefore, the geometric error E of the microsphere target milling machine tool considering workpiece clamping deformation is... final for: (26)。 2. The method according to claim 1, characterized in that, The specific transmission process of the workpiece branch in S11 is as follows: machine tool bed, X-axis, Y-axis, C-axis, clamping system, workpiece; the specific transmission process of the tool branch is as follows: machine tool bed, Z-axis, B-axis, milling axis, tool.

3. The method according to claim 2, characterized in that, The low-order body sequence described in S12 is represented as follows: (1) Where m represents the number of typical bodies in the multibody system; j represents the nth-order higher-order body of typical body i; To ensure the constraint relationships between the various typical entities, the typical entities must also satisfy: (2) From formulas (1) and (2), we get (3) Based on the relationships between the typical bodies obtained, the low-order body sequence of the topology of the microsphere target milling machine tool is obtained.

4. The method according to claim 1, characterized in that, S14 defines the machine tool geometric error terms, including: X axis:d xx , d xy , d xz , θ xx , θ xy , θ xz ; Y axis:d yx , d yy , d yz , θ yx , θ yy , θ yz ; Z axis:d zx , d zy , d zz , θ zx , θ zy , θ zz ; C axis: d cx , d cy , d cz , θ cx , θ cy , θ cz ; B axis: d bx , d by , d bz , θ bx , θ by , θ bz ; vertical error including: b yx , b yz , b cy , b cx , b zx , b bz , b bx , b ay , b az , b vx , b vy ; Using δ mn θ mn ,β mn These represent translation error, motion angle error, and perpendicularity error, respectively. The first subscript represents the direction of motion, and the second subscript represents the direction of error.

5. The method according to claim 4, characterized in that, S15 includes the following steps: Let the initial homogeneous coordinates of the X-axis linear guide in the source coordinate system be [x0, y0, z0, 1]. T When there are no geometric errors, after the X-axis linear guide moves a distance x along the X direction, its coordinates in the target coordinate system are [x0+x, y0, z0,1]. T The coordinate system transformation matrix T at this time x-u for: (4) Under the influence of linear error, the actual motion trajectory of the X-axis linear guide rail deviates (δ). xx , δ xy , δ xz The coordinate system transformation matrix is: (5) Under the influence of angular error, the actual deflection angle of the X-axis linear guide rail deviates (θ). xx , θ xy , θ xz The homogeneous coordinate transformation matrix corresponding to the angular deviation is: (6) From formulas (5) and (6), we can obtain the homogeneous coordinate transformation matrix corresponding to the actual movement of the X-axis linear guide rail under the combined effects of positioning error and linearity error: (7) From formulas (4) and (7), the error matrix ΔT generated by the X-axis linear guide during actual motion can be obtained. x =T x-r -T x-u for: (8) Using the same method, the error matrices generated by the Y-axis and Z-axis during actual motion are determined as follows: (9) (10)。 6. The method according to claim 5, characterized in that, S16 includes the following steps; Let the initial coordinates of the B-axis in the source coordinate system be [x0, y0, z0, 1]. T When there is no geometric error, the coordinate transformation matrix T from the source coordinate system to the target coordinate system when rotating the B-axis by an angle θ is... B-u for: (11) Under the influence of linear error, the actual motion of the B-axis will produce a linear deviation (δ). bx , δ by , δ bz The coordinate transformation matrix is: (12) Under the influence of angular error, the actual deflection angle of the B-axis guide rail will deviate (θ). bx , θ by , θ bz The homogeneous transformation matrix corresponding to the angular deviation is: (13) From formulas (12) and (13), the homogeneous coordinate transformation matrix corresponding to the actual motion of the B-axis under the combined effects of linear error and angular error can be obtained as follows: (14) From formulas (11) and (14), the motion error matrix ΔT generated by the B-axis during actual motion can be obtained. B =T B-r -T B-u for: (15) Using the same method, the error matrix generated by the C-axis during actual motion can be obtained as follows: (16)。 7. The method according to claim 6, characterized in that, S17 includes the following steps: S171, Transform the matrix between adjacent objects Represented as: (17) in, It is an error-free static transformation matrix. This is the actual static transformation matrix. The transformation matrix of adjacent bodies in error-free motion. This is the transformation matrix of the actual moving adjacent bodies; The homogeneous coordinate transformation form of the workpiece branch error-free motion / actual motion is: The homogeneous coordinate transformation form of the error-free motion / actual motion of the tool branch is: S172. When the micro-spherical target milling machine tool has no geometric errors, the spatial position of the apex of the ball end mill on the milling axis coincides with the spatial position of the micro-pit structure to be machined on the micro-spherical target; therefore, the spatial position of the ball end mill tip obtained by transforming the tool coordinate system to the global coordinate system coincides with the spatial position obtained by transforming the micro-pit structure from the workpiece coordinate system to the global coordinate system, i.e. (18) Among them, P w = [P wx , P wy , P wz ,1] T P represents the position of the microstructure to be machined in the workpiece coordinate system. t = [P tx , P ty ,P tz ,1] T This represents the coordinates of the milling cutter tip in the tool coordinate system, where P is taken. t =[0,0,0,1] T ; The trajectory of the milling cutter tip in the workpiece coordinate system, without considering machine tool geometric errors, is as follows: （19） in, , ； From formula (17), the actual motion trajectory of the milling cutter tip in the workpiece coordinate system can be obtained as follows: (20) From formulas (19) and (20), the actual machining error of the micro-spherical target milling machine tool can be obtained as follows: (21) By substituting the numerical value of the geometric error of the machine tool into formula (21), the actual error of the micro-spherical target milling machine tool can be obtained.

8. The method according to claim 1, characterized in that, S2 includes the following process: Under vacuum negative pressure, the microsphere target and the vacuum adsorption fixture form a circumferential contact, meaning the supporting force is distributed on the circumference passing through the contact point. Local contact stress is generated in the contact area, leading to overall and local deformation of the microsphere target during clamping. The local characteristics of the contact stress are quite obvious and decrease rapidly as the distance between the contact point of the microsphere target and the fixture increases. A micro-element segment of the microsphere target-fixture contact area is selected for analysis to obtain the central angle β. va The radial force dF of the corresponding infinitesimal segment is: (22) Where, β va α represents the central angle corresponding to the infinitesimal segment, in degrees. va represents the cone angle, °; R represents the microsphere target radius; q represents the vacuum negative pressure, kPa; The radial pressure in the contact area between the microsphere target and the fixture is: (23) Within the contact area between the microsphere target and the clamp, due to the vacuum negative pressure, the endpoint of the microsphere target along the clamp axis is the position of maximum static deformation after adsorption and clamping. The deformation v2 of the microsphere target clamping is: (24) Among them, E la δ represents the GDP elastic modulus of the microsphere target material, MPa; δ represents the thickness of the microsphere target shell, μm; μ represents the Poisson's ratio of the microsphere target material.

9. The method according to claim 8, characterized in that, S2 also includes verifying the deformation v2 of the microspherical target clamping by finite element simulation of the deformation of the microspherical target adsorption clamping, and jointly determining the magnitude of the microspherical target clamping deformation.

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