Modeling method for error from tolerance to tooth surface of key part of forming gear grinding machine

Abstract

The invention discloses a modeling method from tolerance to tooth surface error of key parts of a forming gear grinding machine, which comprises the following steps of: 1, analyzing a kinematic chain and the key tolerance: analyzing a five-axis kinematic chain structure of the forming gear grinding machine, and identifying tolerance items of the key parts which have obvious influence on geometric error of each kinematic axis; step 2, tolerance-geometric error mapping modeling: establishing a mapping model from the tolerance of the key part to the geometric error of the motion axis; 3, geometric error-pose error transfer modeling: according to the kinematic chain structure, constructing a transfer model from the motion axis geometric error to the tool / workpiece pose error based on homogeneous coordinate transformation; step 4, integration of a comprehensive precision prediction model: establishing a comprehensive precision prediction model from key part tolerance to tooth surface pose error; and 5, model solving and precision prediction: solving the comprehensive precision prediction model by adopting a Monte Carlo simulation method, simulating and generating a motion axis geometric error and a tooth surface pose error, and realizing machining precision prediction.

Description

Technical Field

[0001] This invention belongs to the field of tooth surface error modeling technology for forming gear grinding machines. Specifically, it is a modeling method for the tolerance of key parts of forming gear grinding machines to tooth surface error, which is applied to the positive error modeling and machining accuracy prediction of forming gear grinding machines. Background Technology

[0002] High-precision gears are core components of transmission systems in major equipment, and their machining accuracy directly determines the overall performance and reliability of high-end equipment. As a key piece of equipment for achieving precision gear machining, the technological level of form grinding machines is an important indicator of a nation's high-end manufacturing capabilities. Currently, the research and development of existing high-end gear grinding equipment in China has long faced a technological bottleneck, relying primarily on imitation and experience-based adjustments. The fundamental problem lies in the unclear mapping mechanism between the manufacturing tolerances of machine tool components and the overall machine motion accuracy. This leads to a lack of precise theoretical guidance in machine tool design, a heavy reliance on trial and error, and consequently, high manufacturing costs and excessively long development cycles.

[0003] To improve machine tool accuracy, existing technologies mainly focus on modeling the propagation of geometric errors, that is, establishing a mathematical model from the geometric errors of the motion axes to the spatial errors at the end of the machine tool. These methods are typically based on multibody system theory or the principle of homogeneous coordinate transformation, aiming to describe and compensate for the errors of existing machine tools.

[0004] However, the aforementioned existing technologies have a fundamental flaw: their modeling premise assumes that the geometric errors of each motion axis are known quantities, failing to reveal how the geometric errors of the motion axes themselves are induced by the design tolerances and manufacturing deviations of the underlying components. In other words, the existing models are "posterior" models, unable to predict the overall machine accuracy and performance based on component tolerances during the design phase. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a modeling method for the tolerance of key components of a forming gear grinding machine to the tooth surface error, which can realize the complete accuracy prediction from component tolerance to shaft error to machine tool machining error, so as to realize the accuracy forward design of the machine tool.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for modeling the tolerances of key components in a forming gear grinding machine to the tooth surface error includes the following steps: Step 1: Kinematic Chain and Critical Tolerance Analysis: Analyze the five-axis kinematic chain structure of the forming gear grinding machine, which includes three linear axes and two rotary axes; using the machine bed as the reference coordinate system, establish the workpiece chain from the bed to the workpiece and the tool chain from the bed to the cutting tool; based on the kinematic chain, identify the critical component tolerance items that have a significant impact on the geometric error of each kinematic axis; Step 2: Tolerance-Geometric Error Mapping Modeling: Based on screw theory and homogeneous coordinate transformation, a mapping model is established from the tolerances of the key components to the geometric errors of the motion axis. For linear axes, a local coordinate system is defined for each component, and the influence of each key tolerance item is represented as an independent error screw. The actual pose model from the guide rail mounting surface to the slider is constructed through linear superposition and coordinate transformation. For rotary axes, the same method is used to establish a mapping model from the tolerances of their key components to the geometric errors. Step 3: Geometric error-pose error propagation modeling: Based on the kinematic chain structure, construct a propagation model from the geometric error of the motion axis to the tool / workpiece pose error based on homogeneous coordinate transformation; Step 4: Integration of comprehensive accuracy prediction model: Combining the principle of forming gear grinding, the tolerance-geometric error mapping model and the geometric error-pose error transfer model are integrated to establish a comprehensive accuracy prediction model from the tolerance of key parts to the pose error of the tooth surface. Step 5: Model Solving and Accuracy Prediction: The comprehensive accuracy prediction model is solved using the Monte Carlo simulation method; the scaling factor is sampled to meet its constraints; the sampling results are substituted into the comprehensive accuracy prediction model to simulate and generate the geometric error of the motion axis and the tooth surface pose error, thereby realizing the prediction of machining accuracy.

[0007] Furthermore, in step one, the key component tolerances of the linear shaft include: guide rail mounting surface height tolerance. and flatness tolerance Guide rail height tolerance and flatness tolerance Guide rail straightness error , and Slider height tolerance and flatness tolerance ; The key component tolerances of the rotary shaft include: bed top surface height tolerance. and flatness tolerance mandrel diameter tolerance Workbench height tolerance and flatness tolerance ; The linear axis geometric error terms include: positioning errors of the X-axis, Y-axis, and Z-axis. , and Roll error around the X-axis Yaw error around the Y-axis pitch error around the Z-axis ; The geometric error elements of the rotating shaft include six position-related geometric errors and four position-independent installation errors.

[0008] Furthermore, in step two, the actual pose model of the guide rail mounting surface to the slider... Represented as: in: This is the actual pose error matrix of the guide rail mounting surface; This is the actual pose error matrix of the guide rail; This is the actual pose error matrix of the slider; The coordinate transformation matrix is ​​used to transfer the pose error of the guide rail mounting surface in the bed coordinate system to the guide rail coordinate system; This is the transformation matrix from the coordinate system of the guide rail starting point to the coordinate system of the slider mounting point; This is the transformation matrix from the coordinate system at the slider mounting point to the slider coordinate system.

[0009] Furthermore, the total error rotation of the guide rail mounting surface Represented as: in: This represents the total error rotation of the guide rail mounting surface; For the height tolerance of the guide rail mounting surface The error spinor; For the flatness tolerance of the guide rail mounting surface The error spinor; and The guide rail mounting surface is respectively and Length in the direction; It is a scaling factor, and ,in , These are the upper and lower limit deviations, respectively. , and These represent the overall translation components of the plane, the degree of tilt around the x-direction, and the degree of tilt around the y-direction, respectively. Actual pose error matrix of guide rail mounting surface Total error rotation through the guide rail mounting surface Obtained through conversion; Total error spin of the guide rail Represented as: in: The total error rotation of the guide rail; For guide rail height tolerance The error spinor; For the flatness tolerance of the guide rail The error spinor; The rotation of the pose error caused by the straightness error of the guide rail; For the flatness tolerance of the guide rail exist Displacement error in direction; and These are the flatness tolerances of the guide rails. exist and Angular error in direction; )and These respectively represent the axis of the guide rail as... Direction and Straightness error in direction; Actual pose error matrix of the guide rail Total error spin of the guide rail Obtained through conversion; Total error spin of the slider's own manufacturing tolerance Represented as: in: This represents the total error rotation of the slider's own manufacturing tolerance; Indicates slider height tolerance The error spinor; For slider flatness tolerance The error spinor; For slider flatness tolerance exist Displacement error in direction; and These are the flatness tolerances of the slider. exist and Angular error in direction; Actual pose error matrix of the slider The total error spin of the slider itself to manufacture tolerances Obtained through conversion.

[0010] Furthermore, in step two, the mapping model between the tolerance and geometric error of the key component X of the linear axis is expressed as follows: in: Indicates the first Group Proportion Factor Under this value, the linear axis Move from the initial position to A mapping model between the tolerances and geometric errors of key components at location; , and This indicates the positioning error of the linear axis in the X, Y, and Z axes. This refers to the roll error of the linear axis around the X-axis. This refers to the yaw error of the linear axis around the Y-axis. The pitch error of the linear axis about the Z-axis; It is a translation vector; It is the corner vector; For the tolerances of key components; Furthermore, in step two, the actual pose model of the rotation axis Represented as: in: Represents the actual pose model of the rotation axis; This is the actual pose matrix of the top surface of the bed; This is the actual pose matrix of the mandrel; This represents the actual pose matrix of the worktable surface. This is the transformation matrix from the bed coordinate system to the mandrel coordinate system; This is the transformation matrix from the mandrel coordinate system to the table coordinate system; Mapping model between tolerances and geometric errors of key components of a rotating shaft Represented as: in: A mapping model representing the relationship between tolerances and geometric errors of key components of a rotating shaft; An ideal pose model representing the rotation axis; Indicates the first Group proportion factor.

[0011] Furthermore, the total pose deviation caused by the bed plane height tolerance and flatness tolerance is expressed as: in: The total positional deviation of the top surface of the bed; For the height tolerance of the top surface of the bed The error spinor; For the flatness tolerance of the top surface of the bed The error spinor; and The top surface of the bed is respectively and Length in the direction; It is a scaling factor, and ,in , These are the upper and lower limit deviations, respectively. , and These represent the overall translation components of the plane, the degree of tilt around the x-direction, and the degree of tilt around the y-direction, respectively. Actual pose model of the rotation axis Total error spin through the top surface of the bed Obtained through conversion; Mandrel error spindle Represented as: in: Indicates the error spindle; For the mandrel diameter tolerance; The length of the mandrel; and This indicates translation along the x and y directions; and These represent the degree of tilt controlled around the x and y directions, respectively; actual pose matrix of mandrel spindle error spindle Obtained through conversion; Total positional deviation of the worktable Represented as: in: Indicates the total positional deviation of the worktable; Indicates the workbench height tolerance The error spinor; Indicates the flatness tolerance of the worktable surface The error spinor; Indicates the radius of the working frustum; and This represents the translation component of the plane along the z-direction; and These represent the degree of tilt controlled around the x and y directions, respectively; Actual pose matrix of the worktable Total deviation of worktable posture Obtained through conversion.

[0012] Furthermore, in step three, the geometric error of the motion axis is transformed into the actual pose model of the tool. for: From the geometric error of the motion axis to the actual pose model of the workpiece for: in: This represents the pose transformation matrix between the i-axis and the j-axis. and These represent the ideal transformation matrix of the installation pose, the installation pose error matrix, the ideal transformation matrix of the motion pose, and the motion pose error transformation matrix between the motion axes i and j, respectively. Tool / Workpiece Actual Position Model for: in: An error propagation model from the machine base coordinate system to the workpiece coordinate system; This is an error propagation model from the machine base coordinate system to the tool coordinate system; Model of motion axis geometric error to tool / workpiece pose error for: in: An ideal pose model for the tool / workpiece; The transfer model from motion axis geometric error to tool / workpiece pose error. Represented as: in: This represents the tolerance-geometric error model for linear shaft parts. This represents the tolerance-geometric error model for rotating shaft parts.

[0013] Furthermore, in step four, the method for establishing a comprehensive accuracy prediction model from key component tolerances to tooth surface pose error includes: Establish a model of the pose error of the grinding wheel under the influence of tolerances of key components. for: in: This is the actual position vector of the grinding wheel surface; This is the actual attitude vector of the grinding wheel surface; This is a model for the transfer of motion axis geometric errors to tool / workpiece pose errors; This is the grinding wheel position vector; This is the attitude vector; Based on grinding wheel pose error model Obtain the gear tooth surface pose error model : in: Indicates the positional error of the tooth surface; This indicates the tooth surface attitude error.

[0014] Furthermore, in step five, the specific implementation of the Monte Carlo simulation is as follows: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Uniformly distributed sampling is performed within the range (-1, 1) to ensure that the sampling results meet the tolerance constraints; n sampling simulations are conducted, where N is the total sample size, and each group... Substituting these values ​​into the model, the various pose errors generated by the motion axes during actual motion are simulated, resulting in comprehensive error models for both the linear and rotational axes. and : in: Indicates the first Group Proportion Factor Under this value, the linear axis Move from the initial position to A mapping model between the tolerances and geometric errors of key components at location; A mapping model representing the relationship between tolerances and geometric errors of key components of a rotating shaft.

[0015] The beneficial effects of this invention are as follows: This invention presents a modeling method for the transformation of tolerances to tooth surface errors in key components of a gear grinding machine. By constructing a complete predictive model from component tolerances to tooth surface errors, it achieves three major technological breakthroughs: (1) Established positive design capability: Through kinematic chain analysis and key tolerance identification, positive prediction from part-level tolerance to system-level accuracy was realized for the first time, breaking through the traditional experience-based design mode that relies on trial and error; (2) Multi-scale precision transfer is realized: Based on the screw theory and coordinate transformation, the error mapping model accurately reveals the transmission mechanism of manufacturing tolerance in the machine tool space and solves the problem of unclear coupling relationship between part tolerance and overall machine precision; (3) Improved prediction accuracy and efficiency: The Monte Carlo simulation method was adopted, and statistically accurate prediction was achieved through proportional factor sampling, which not only ensured the reliability of the prediction results, but also significantly reduced the computational complexity.

[0016] In summary, the modeling method for key component tolerances and tooth surface errors of the forming gear grinding machine of this invention can realize complete accuracy prediction from component tolerances to shaft errors and then to machine tool machining errors. It transforms accuracy design from "post-compensation" to "pre-prediction" to achieve positive accuracy design of machine tools. It provides theoretical basis and technical support for the accuracy design and optimization of high-end CNC machine tools, and is of great significance to improving my country's independent high-end equipment R&D capabilities. Attached Figure Description

[0017] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a technical roadmap for the modeling method of key component tolerances to tooth surface errors in the forming gear grinding machine of the present invention; Figure 2 For forming the kinematic chain of the gear grinding machine; Figure 3 The assembly and motion relationships of the components of a linear shaft; Figure 4 The assembly and motion relationships of the components of the rotating shaft; Figure 5 Constraint scaling factor The sampling test process. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0019] like Figure 1 As shown in the figure, the modeling method for the tolerance of key parts of the forming gear grinding machine to the tooth surface error in this embodiment includes the following steps.

[0020] Step 1: Kinematic Chain and Critical Tolerance Analysis: Analyze the five-axis kinematic chain structure of the forming gear grinding machine, which includes three linear axes and two rotary axes; using the machine bed as the reference coordinate system, establish the workpiece chain from the bed to the workpiece and the tool chain from the bed to the cutting tool; based on the kinematic chain, identify the critical component tolerance items that have a significant impact on the geometric error of each kinematic axis.

[0021] (1) Kinematic chain analysis of forming gear grinding machine The profile gear grinding machine is a five-axis machine tool with three linear axes (X, Y, Z) and two rotary axes (A, C). To clarify the transmission relationship between manufacturing errors of machine tool parts and tool / workpiece pose errors, this embodiment is based on multibody kinematics, separating each motion axis as an independent system. By analyzing the component composition of each axis, its key components are constructed into local kinematic chains according to assembly relationships and motion sequences. Then, based on the motion relationships between axes, using the machine tool bed as a reference coordinate system, two kinematic chain branches are established from the bed to the workpiece (workpiece chain) and the tool (tool chain). Furthermore, by integrating the local kinematic chains of each axis, the machine tool's workpiece chain, and the tool chain through coordinate transformation, a kinematic chain describing the motion from machine tool parts to the tool / workpiece is constructed. The specific motion relationships of the profile gear grinding machine are as follows: Figure 2 As shown.

[0022] (2) Tolerance analysis of key components Based on a clear understanding of the machine tool's kinematic chain structure, this paper further analyzes the tolerances of key components that affect motion accuracy. Manufacturing tolerances of machine tool components are crucial factors leading to machine tool geometric errors, primarily including dimensional tolerances and geometrical tolerances. These manifest as deviations in the length, width, and height of parts, as well as flatness errors in mating surfaces. Multiple types of manufacturing errors are coupled together, jointly affecting the machine tool's motion accuracy. However, due to the large number of machine tool components, analyzing all tolerances is time-consuming and computationally expensive. Therefore, selecting the tolerances of key components that significantly influence the geometric errors of motion axes helps reduce the complexity of tolerance analysis and improve design efficiency.

[0023] Clarifying the causes of geometric errors in machine tool motion axes is a prerequisite for identifying tolerance items of key components. Since linear and rotary axes in machine tools have different structures, they can be discussed separately during tolerance analysis. Key component tolerance items are selected based on the degree of influence of component tolerances on the geometric errors of the motion axes during the motion process.

[0024] First, the geometric errors and their manifestations of linear shafts are defined. The geometric errors of a linear shaft originate from the manufacturing tolerances of components such as the guide rail mounting surface, the guide rail, and the slider, and are manifested as displacement and angular errors in the six degrees of freedom of space. Among these, displacement errors include the shaft's positioning error. Horizontal straightness error Straightness error in the vertical direction Angular error includes roll. sway and pitch error In addition, the perpendicularity error between straight axes is also a geometric error.

[0025] Based on the geometric errors of linear axes, this paper considers the assembly and motion relationships between the components of the linear axis and analyzes the key tolerances that significantly affect the geometric errors. Taking the X-axis as an example, the dimensions and geometric tolerances of the guide rail mounting surface, the guide rail and slider assembly surface, and the slider and motion platform assembly surface will cause straightness errors of the axis, and generate angular errors through coupling effects, such as... Figure 3 As shown. However, not all tolerance factors have a significant impact on the geometric error of the moving axis. For example, dimensional deviations in the parallel direction of the guide rail mounting surface have a negligible impact on the geometric error; furthermore, the perpendicularity error between linear axes mainly originates from the installation process rather than manufacturing tolerances. Therefore, the aforementioned tolerance items are all non-critical factors.

[0026] Compared to linear axes, rotary axes, in addition to having the same six geometric errors, also have four position-independent installation errors, including two radial errors and two axial perpendicularity errors. To determine the critical tolerances of rotary axes, the assembly and motion relationships between the component parts are considered, and the influence of component tolerances on the geometric errors of the rotary axis is analyzed. Taking the C-axis as an example, the height and form / position tolerances of the workpiece mounting surface directly affect the workpiece's positional accuracy. Simultaneously, the dimensional tolerances of the worktable drive shaft cause radial runout of the worktable, which in turn leads to radial displacement errors during the rotation of the rotary axis, such as... Figure 4 As shown. Therefore, these tolerance types are critical component tolerances. Furthermore, dimensional tolerances parallel to the worktable surface only affect the size of that plane and do not directly affect the workpiece pose; these are non-critical component tolerances. Radial error and and verticality error and It is mainly affected by assembly errors rather than part manufacturing tolerances. Therefore, the influence of part tolerances on this type of geometric error is not considered.

[0027] In summary, the 41 geometric error elements of the five motion axes of the forming gear grinding machine, as well as the tolerances of key components that may have a significant impact on them, can be summarized in Table 1. The tolerances of key components for the Y and Z axes are similar to those for the X axis, and the tolerances of key components for the A axis are similar to those for the C axis; therefore, they are not repeated in the table.

[0028] In this embodiment, the key component tolerances of the linear shaft include: guide rail mounting surface height tolerance. and flatness tolerance Guide rail height tolerance and flatness tolerance Guide rail straightness error , and Slider height tolerance and flatness tolerance The key tolerances for the rotary shaft include: bed top surface height tolerance. and flatness tolerance mandrel diameter tolerance Workbench height tolerance and flatness tolerance The linear axis geometric error term includes the positioning errors of the X, Y, and Z axes. , and Roll error around the X-axis Yaw error around the Y-axis pitch error around the Z-axis The geometric error elements of the rotating shaft include six position-related geometric errors and four position-independent installation errors.

[0029] Step 2: Tolerance-Geometric Error Mapping Modeling: Based on screw theory and homogeneous coordinate transformation, a mapping model is established from the tolerance of the key components to the geometric error of the motion axis. For linear axes, a local coordinate system is defined for each component, and the influence of each key tolerance item is represented as an independent error screw. The actual pose model from the guide rail mounting surface to the slider is constructed through linear superposition and coordinate transformation. For rotary axes, the same method is used to establish a mapping model from the tolerance of the key components to the geometric error.

[0030] Taking a linear shaft as an example, the kinematic chain of the linear shaft in a gear grinding machine can be described as guide rail mounting base → guide rail → slider. To accurately describe its kinematic relationship, the local coordinate systems of each part are defined as follows: system B is fixed to the mounting base surface; systems G1 and G2 are located at the top center of the left and right guide rails respectively; systems S1 and S2 are fixed at the top center of the front and rear sliders on the left guide rail respectively; and systems S3 and S4 are fixed at the top center of the front and rear sliders on the right guide rail. Figure 3 As shown in the figure. Among them, the B system is located at the center position between the initial points of the two guide rails, and the coordinate systems of each guide rail and slider are established based on its geometric characteristics.

[0031] To quantitatively analyze the impact of tolerances on geometric errors, based on the established part coordinate system, screw theory is used to describe the actual and ideal pose deviations of the guide rail mounting base, guide rail, and slider caused by manufacturing deviations. This deviation can be expressed as: in: This indicates the deviation of the actual surface position from the nominal position; This represents the deviation of the actual surface attitude from the nominal attitude.

[0032] Therefore, the influence of each critical tolerance on the part pose can be expressed as an independent error screw. : in: , and These represent the displacement errors along the x, y, and z coordinate directions, respectively. , and These represent the rotational errors along the x, y, and z coordinates, respectively.

[0033] Based on the above method, a geometric error model for the tolerances of key components of the linear shaft to the motion shaft is established. For ease of subsequent description, the relevant tolerance items of the linear shaft are numbered as shown in Table 2.

[0034] (1) Total error rotation of the guide rail mounting surface First, the influence of the height tolerance of the guide rail mounting surface on the mounting surface pose is studied. This is because the height tolerance of the mating surface... Only affects the plane Positional deviation in direction, height tolerance The error spinor can be expressed as: To simulate the variation in actual part manufacturing tolerances, a scaling factor is introduced. Therefore, the error screw of the height tolerance can be expressed as: in: It is a scaling factor, and ,in , These are the upper and lower limit deviations, respectively, ensuring... Variations are within the tolerance range.

[0035] The flatness tolerance of the assembly surface belongs to Class I planar positioning dimension tolerance zone. The plane can move in three degrees of freedom, including one translation and two rotations. For the guide rail mounting base surface, the flatness tolerance... It can be decomposed into along Translation and rotation in direction and The rotation of direction. Therefore, The error screw of the tolerance term can be expressed as: in: , and The ranges of the three error parameters can be determined based on the following tolerance domain boundary conditions: in: Install the plane equation for the guide rail; This represents the maximum height difference between the planes; and The guide rail mounting surface is respectively and Length in the direction.

[0036] Set the scaling factor , and Let represent the overall translation component of the plane, the degree of tilt about the x-direction, and the degree of tilt about the y-direction, respectively. From the above equation, we can obtain the expressions for the three spinor parameters: In the formula, the scaling factor , and Constraint inequalities must be satisfied .

[0037] Since the height tolerance and flatness tolerance are located in the same coordinate system, the error screws of the two types of tolerances can be linearly superimposed, thereby allowing the total error screw of the guide rail mounting surface to be calculated. Represented as: in: This represents the total error rotation of the guide rail mounting surface; For the height tolerance of the guide rail mounting surface The error spinor; For the flatness tolerance of the guide rail mounting surface The error spinor; and The guide rail mounting surface is respectively and Length in the direction; It is a scaling factor, and ,in , These are the upper and lower limit deviations, respectively. , and These represent the overall translation components of the plane, the degree of tilt around the x-direction, and the degree of tilt around the y-direction, respectively.

[0038] Actual pose error matrix of guide rail mounting surface Total error rotation through the guide rail mounting surface The result is obtained through conversion. Specifically, considering the extremely small manufacturing error of high-precision machine tools, the actual pose error matrix of the guide rail mounting surface is... It can be simplified to: (2) Total error screw of the guide rail Similar to the critical tolerances of the guide rail mounting surfaces on the machine bed, height tolerance and flatness tolerance also significantly affect the guide rail's positional accuracy. Taking a guide rail arranged along the x-direction as an example, similar to the method for establishing the error rotation of the guide rail mounting surface, the guide rail height tolerance... and flatness tolerance The error spinor can be expressed as: Furthermore, the straightness error of the guide rail is also a significant factor affecting motion accuracy. A guide rail arranged in the x-direction exhibits straightness errors in the y and z directions, leading to displacement errors in the y and z directions of the motion axis. This error is also highly dependent on the load position height. Therefore, the pose error and screw error caused by the guide rail straightness error are significant factors. It can be represented as: in: and These represent the straightness errors in the y and z directions when the guide rail is at position x.

[0039] Total error spin of the guide rail Represented as: in: The total error rotation of the guide rail; For guide rail height tolerance The error spinor; For the flatness tolerance of the guide rail The error spinor; The rotation of the pose error caused by the straightness error of the guide rail; For the flatness tolerance of the guide rail exist Displacement error in direction; and These are the flatness tolerances of the guide rails. exist and Angular error in direction; )and These respectively represent the axis of the guide rail as... Direction and Straightness error in direction.

[0040] Actual pose error matrix of the guide rail Total error spin of the guide rail Obtained through conversion.

[0041] (3) Total error of slider manufacturing tolerance The aforementioned manufacturing errors of the guide rail directly affect the pose of the slider mounted on it, thus causing motion deviations. To obtain the total pose deviation of the slider, in addition to the guide rail error, the influence of the slider's own manufacturing tolerances (height tolerance and flatness) must also be considered. Therefore, it is necessary to construct the slider's own pose error matrix.

[0042] Similar to the method for establishing the error rotation of the guide rail mounting surface, the slider height tolerance... and flatness tolerance Error spinor and It can be represented as: Therefore, the total error screw of the slider's own manufacturing tolerance Represented as: in: This represents the total error rotation of the slider's own manufacturing tolerance; Indicates slider height tolerance The error spinor; For slider flatness tolerance The error spinor; For slider flatness tolerance exist Displacement error in direction; and These are the flatness tolerances of the slider. exist and Angular error in direction.

[0043] Actual pose error matrix of the slider The total error spin of the slider itself to manufacture tolerances Obtained through conversion.

[0044] (4) Mapping model of tolerance of key components of linear shaft to geometric error of moving shaft Based on the error screws of each part, a pose error matrix is ​​constructed. Considering the machine tool kinematic chain structure, a mapping relationship between part tolerances and geometric errors of motion axes is established through homogeneous coordinate transformation.

[0045] Assuming the guide rail is in an ideal position on the mounting surface, the pose error of the guide rail mounting surface in the bed coordinate system B is transferred to the guide rail coordinate system G through coordinate transformation. This coordinate transformation matrix... It can be represented as: In the formula, This refers to the installation distance between the two guide rails; This refers to the guide rail height.

[0046] Therefore, the transformation matrix from the guide rail starting coordinate system G to the slider mounting point coordinate system I is... It can be represented as: Based on the motion relationship between the guide rail and the slider, the transformation matrix from coordinate system I at the slider mounting point to coordinate system S of the slider is... It can be represented as: in: Indicates the height of the slider.

[0047] By multiplying the pose matrices in the order of the kinematic chain, the actual pose model from the guide rail mounting surface to the slider can be constructed. : in: This is the actual pose error matrix of the guide rail mounting surface; This is the actual pose error matrix of the guide rail; This is the actual pose error matrix of the slider; The coordinate transformation matrix is ​​used to transfer the pose error of the guide rail mounting surface in the bed coordinate system to the guide rail coordinate system; This is the transformation matrix from the coordinate system of the guide rail starting point to the coordinate system of the slider mounting point; This is the transformation matrix from the coordinate system at the slider mounting point to the slider coordinate system.

[0048] Without considering manufacturing errors, the ideal pose matrices between each coordinate system are multiplied sequentially to obtain the ideal pose model from the guide rail mounting surface to the slider. It can be represented as: The linear shaft guide system of the gear grinding machine has four sliders. Therefore, based on the above-mentioned modeling method from the mounting surface to the sliders, it is necessary to construct the pose models of the four sliders respectively.

[0049] The pose of each slider varies due to its own tolerance and position, and the motion platform is supported by all sliders. Therefore, the differences in slider pose will cause a deviation between the actual pose and the ideal pose of the motion platform. Based on the poses of the four sliders, the pose error of the motion platform can be obtained by solving the rigid body motion equations.

[0050] First, the transformation matrix from the ideal pose to the actual pose coordinates of the motion platform. It can be represented as: In the formula: It is a rotation matrix; For translation vectors; for small errors, the rotation matrix is... It can be approximated as: in: It is the identity matrix; , and These represent the rotational errors around x, y, and z, respectively; It is the antisymmetric matrix of the transformation of the rotation error vector.

[0051] Secondly, the ideal position vector of the platform and actual position vector It can be obtained through the following formula: Based on the pose transformation between the ideal and actual positions of the motion platform, the relationship between the ideal and actual positions of the platform can be expressed as: For each slider, three position transformation equations in the x, y, and z directions can be obtained, thus establishing a solution model for the motion platform's pose. The platform's pose error is reflected in six terms of displacement and rotation; therefore, solving this model is an overdetermined problem, which can be solved using the least squares method.

[0052] Will Substituting into the position transformation equation, we get: The error at each point is then the difference between the actual and the ideal pose: in: Indicates by Construct an antisymmetric matrix.

[0053] Apply the equation to the standard matrix operation form The conversion yields: The actual pose vector of the motion platform can be obtained by solving the problem using the least squares method. : Since the pose change of the motion platform actually reflects the geometric error of the linear axis X, the mapping model between the tolerance of the key component of the linear axis X and the geometric error can be expressed as: in: Indicates the first Group Proportion Factor Under this value, the linear axis Move from the initial position to A mapping model between the tolerances and geometric errors of key components at location; , and This indicates the positioning error of the linear axis in the X, Y, and Z axes. This refers to the roll error of the linear axis around the X-axis. This refers to the yaw error of the linear axis around the Y-axis. The pitch error of the linear axis about the Z-axis; It is a translation vector; It is the corner vector; For tolerances of critical components.

[0054] Based on a similar method, mapping models between part tolerances and linear axis Y and Z errors can be established respectively.

[0055] (5) Mapping model of key component tolerances to geometric error of rotating shaft For a rotational axis, the poses of its key components can be described using the same method. Taking rotational axis C as an example, its kinematic chain is as follows: Figure 4 As shown, it can be described as bed-drive shaft-worktable, and the tolerances and numbers of the key parts involved are shown in Table 3.

[0056] First, the rotary axis is mounted on the top surface of the bed, which is on the same plane as the linear axis guide rail mounting surface. Therefore, the total positional deviation caused by the bed plane height tolerance and flatness tolerance can be established similarly. , represented as: in: The total positional deviation of the top surface of the bed; For the height tolerance of the top surface of the bed The error spinor; For the flatness tolerance of the top surface of the bed The error spinor; and The top surface of the bed is respectively and Length in the direction; It is a scaling factor, and ,in , These are the upper and lower limit deviations, respectively. , and These represent the overall translation components of the plane, the degree of tilt around the x-direction, and the degree of tilt around the y-direction, respectively.

[0057] Actual pose model of the rotation axis Total error spin through the top surface of the bed Obtained through conversion.

[0058] Errors on the top surface of the machine bed are transmitted to the workpiece mounting table via the mandrel. Therefore, the manufacturing accuracy of the mandrel has a significant impact on the accuracy of the rotary axis. Based on tolerance analysis of key components, manufacturing deviations in the mandrel diameter will cause radial displacement of the rotary axis and angular errors perpendicular to the axis of rotation. A mandrel error rotation parameter can be established. : in: Indicates the error spindle; For the mandrel diameter tolerance; The length of the mandrel; and This indicates translation along the x and y directions; and These represent the degree of tilt controlled around the x and y directions, respectively.

[0059] actual pose matrix of mandrel spindle error spindle Obtained through conversion.

[0060] Manufacturing errors of the worktable directly affect the workpiece's positional accuracy. The height and flatness tolerances of the worktable contribute to the total deviation in worktable positional accuracy. It can be represented as: in: Indicates the total positional deviation of the worktable; Indicates the workbench height tolerance The error spinor; Indicates the flatness tolerance of the worktable surface The error spinor; Indicates the radius of the working frustum; and This represents the translation component of the plane along the z-direction; and This indicates the degree of tilt around the x-direction and around the y-direction.

[0061] Actual pose matrix of the worktable Total deviation of worktable posture Obtained through conversion.

[0062] In summary, since the table pose accuracy directly affects machining accuracy, this embodiment uses the total pose deviation of the table under the influence of manufacturing deviations of key components to characterize the geometric error of the rotary axis. Therefore, based on the error propagation chain of the key components of the rotary axis, the actual pose model of the rotary axis can be obtained. : The ideal pose of the rotation axis can be expressed as: : in: Represents the actual pose model of the rotation axis; This is the actual pose matrix of the top surface of the bed; This is the actual pose matrix of the mandrel; This represents the actual pose matrix of the worktable surface. This is the transformation matrix from the bed coordinate system to the mandrel coordinate system; This is the transformation matrix from the mandrel coordinate system to the table coordinate system.

[0063] Combining the above two equations, a mapping model from the tolerances of key components to the geometric errors of the rotating shaft can be constructed. : in: A mapping model representing the relationship between tolerances and geometric errors of key components of a rotating shaft; An ideal pose model representing the rotation axis; Indicates the first Group proportion factor.

[0064] Step 3: Modeling the transfer of geometric error to pose error: Based on the kinematic chain structure, construct a transfer model from the geometric error of the motion axis to the pose error of the tool / workpiece based on homogeneous coordinate transformation.

[0065] The forming gear grinding machine uses the machine base as a reference to construct the tool chain (R→X→Z→A→Y→T) and the workpiece chain (R→C→W). Based on homogeneous coordinate transformation, the mapping relationship between the tool coordinate system T and the workpiece coordinate system W and the machine base coordinate system R is established, and finally the relative pose of the tool and the workpiece is determined.

[0066] Establishing a model for the machine tool's motion axes to the tool / workpiece pose error requires considering both the installation and motion stages. Installation errors primarily stem from inaccurate fit relationships between axes during the installation phase. During the motion stage, geometric errors arise from the movement of axes along parts with manufacturing defects. First, the ideal installation pose matrix is ​​defined. And the actual installation matrix considering geometric errors Define the ideal motion matrix. and actual motion matrix Based on the toolchain and workpiece chain, error propagation from the bed to the tool and workpiece is achieved by multiplying each pose matrix by the position in sequence according to the motion order. Taking the transformation from the machine base R to the linear axis X as an example, the pose matrix of the motion axis X is established as follows.

[0067] Ideal mounting position of motion axis X relative to the base R during installation It can be represented as: In the formula: Represents the identity matrix.

[0068] The X-axis is fixedly mounted on the machine base, therefore the error mounting pose matrix relative to the machine base R is... It can be represented as: The ideal motion pose matrix after the X-axis moves x under control command. It can be represented as: Considering the geometric error elements along the X-axis, the error motion pose matrix T relative to the base R is... meRX It can be represented as: In summary, a geometric error module can be established from the base R to the linear axis X. : Similarly, the ideal mounting pose, error mounting pose, ideal motion pose, and error motion pose matrix of the other motion axes of the forming gear grinding machine can be established using the above method.

[0069] Then, assuming the tool is fixed to the Y-axis by a fixture and the workpiece table is fixedly mounted on the machine base, the pose matrices between the Y-axis and the tool, and between the C-axis and the machine base, are considered as identity matrices, as shown in Table 4.

[0070] Based on the above analysis of the geometric error modules of each motion axis, positional error models from the machine tool motion axis to the tool and workpiece are constructed according to the tool chain and workpiece chain of the forming gear grinding machine.

[0071] For the toolchain, establish the pose mapping relationship from coordinate system T to R under the influence of geometric errors, and the model from the geometric error of the motion axis to the actual pose of the tool. It can be constructed as: Similarly, based on the pose transformation relationship between the workpiece coordinate system W and the reference coordinate system R in the toolchain, a model of the motion axis geometric error to the actual pose of the workpiece can be established. for: in: This represents the pose transformation matrix between the i-axis and the j-axis. and These represent the ideal transformation matrix of the installation pose, the installation pose error matrix, the ideal transformation matrix of the motion pose, and the motion pose error transformation matrix between the i-axis and the j-axis, respectively.

[0072] Tool / Workpiece Actual Position Model for: in: An error propagation model from the machine base coordinate system to the workpiece coordinate system; This is an error propagation model from the machine base coordinate system to the tool coordinate system.

[0073] To compare with the actual pose and reflect the influence of motion axis geometric errors on tool / workpiece pose, it is necessary to establish an ideal tool / workpiece pose model without considering the influence of geometric errors.

[0074] Ideal pose model of the tool coordinate system relative to the reference coordinate system It can be represented as: Ideal pose model of workpiece coordinate system relative to reference coordinate system It can be represented as: By combining the ideal pose models of the toolchain and workpiece chain, an ideal pose model from the motion axis to the tool / workpiece can be established. for: By subtracting the actual pose from the ideal pose, a model can be constructed to represent the geometric error of the motion axis to the tool / workpiece pose error. for: in: This is the ideal pose model for the tool / workpiece.

[0075] Furthermore, the geometric error of the motion axis can be reflected by the tolerances of key components. Therefore, a mapping model from component tolerances to tool / workpiece pose errors exists. It can be established as: in: This represents the tolerance-geometric error model for linear shaft parts. This represents the tolerance-geometric error model for rotating shaft parts.

[0076] This embodiment establishes a complete mapping model based on screw theory and homogeneous coordinate transformation, from the tolerances of key components to the geometric errors of motion axes, and then to the tool / workpiece pose errors. This model clearly reveals the transmission mechanism of manufacturing tolerances within the machine tool space. Furthermore, Monte Carlo simulation is introduced to simulate and solve for the geometric errors of motion axes under the influence of component tolerances.

[0077] Step 4: Integration of Comprehensive Accuracy Prediction Model: Combining the principle of forming gear grinding, the tolerance-geometric error mapping model and the geometric error-pose error transfer model are integrated to establish a comprehensive accuracy prediction model from the tolerance of key parts to the pose error of the tooth surface.

[0078] In practical engineering, the positional error between the tool and the workpiece alone is insufficient to fully reflect the overall machining accuracy of a machine tool. Therefore, this patent, based on the machining principle of a forming gear grinding machine, extends the accuracy of the end of the kinematic chain in the error model E to the machining accuracy of the machine tool.

[0079] To reflect the impact of key component tolerances on tooth surface pose, it is first necessary to consider the influence of component tolerances on the cutting tool. Therefore, based on the forming grinding wheel model, considering the pose error from component tolerances to the cutting tool / workpiece, a pose error model of the grinding wheel under the influence of key component tolerances is established. for: in: This is the actual position vector of the grinding wheel surface; This is the actual attitude vector of the grinding wheel surface; This is a model for the transfer of motion axis geometric errors to tool / workpiece pose errors; This is the grinding wheel position vector; This is the attitude vector.

[0080] Based on the principle of form grinding, it can be assumed that in the gear coordinate system, the rotating surface of the forming grinding wheel has the same shape as the tooth surface of the gear to be machined. Therefore, it can be based on the grinding wheel pose error model. Obtain the gear tooth surface pose error model : in: Indicates the positional error of the tooth surface; This indicates the tooth surface attitude error.

[0081] Solving this model can realize the mapping from part manufacturing deviations to workpiece machining errors, providing theoretical support for the precision design and prediction of machine tools.

[0082] Step 5: Model Solving and Accuracy Prediction: The comprehensive accuracy prediction model is solved using the Monte Carlo simulation method; the scaling factor is sampled to meet its constraints; the sampling results are substituted into the comprehensive accuracy prediction model to simulate and generate the geometric error of the motion axis and the tooth surface pose error, thereby realizing the prediction of machining accuracy.

[0083] In this embodiment, Monte Carlo simulation is used to obtain a sufficient number of solutions that satisfy the constraints. ,like Figure 5 As shown, the solution process is as follows: (1) Take The constraint scaling factor satisfies a uniform distribution in (-1,1) and meets the tolerance constraint conditions; (2) for Sampling was used to conduct a simulation experiment, where n was the number of samplings and N was the total sample size. The sampling process is shown in XX below; (3) Each group was divided into groups Substituting these values ​​into the model, the various pose errors generated by the motion axes during actual motion are simulated, resulting in comprehensive error models for both the linear and rotational axes. and : in: Indicates the first Group Proportion Factor Under this value, the linear axis Move from the initial position to A mapping model between the tolerances and geometric errors of key components at location; A mapping model representing the relationship between tolerances and geometric errors of key components of a rotating shaft.

[0084] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A modeling method for the tolerance to tooth surface error of key components in a forming gear grinding machine, characterized in that: Includes the following steps: Step 1: Kinematic Chain and Critical Tolerance Analysis: Analyze the five-axis kinematic chain structure of the forming gear grinding machine, which includes three linear axes and two rotary axes; using the machine bed as the reference coordinate system, establish the workpiece chain from the bed to the workpiece and the tool chain from the bed to the cutting tool; based on the kinematic chain, identify the critical component tolerance items that have a significant impact on the geometric error of each kinematic axis; Step 2: Tolerance-Geometric Error Mapping Modeling: Based on screw theory and homogeneous coordinate transformation, a mapping model is established between the tolerances of the key components and the geometric errors of the motion axis. For linear axes, a local coordinate system is defined for each component, and the influence of each key tolerance item is represented as an independent error screw. The actual pose model from the guide rail mounting surface to the slider is constructed through linear superposition and coordinate transformation. For rotary axes, the same method is used to establish a mapping model between the tolerances of their key components and the geometric errors. Step 3: Geometric error-pose error propagation modeling: Based on the kinematic chain structure, construct a propagation model from the geometric error of the motion axis to the tool / workpiece pose error based on homogeneous coordinate transformation; Step 4: Integration of comprehensive accuracy prediction model: Combining the principle of forming gear grinding, the tolerance-geometric error mapping model and the geometric error-pose error transfer model are integrated to establish a comprehensive accuracy prediction model from the tolerance of key parts to the pose error of the tooth surface. Step 5: Model Solving and Accuracy Prediction: The comprehensive accuracy prediction model is solved using the Monte Carlo simulation method; the scaling factor is sampled to meet its constraints; the sampling results are substituted into the comprehensive accuracy prediction model to simulate and generate the geometric error of the motion axis and the tooth surface pose error, thereby realizing the prediction of machining accuracy.

2. The modeling method for the tolerance to tooth surface error of key components of a forming gear grinding machine according to claim 1, characterized in that: In step one, the key component tolerances of the linear shaft include: guide rail mounting surface height tolerance. and flatness tolerance Guide rail height tolerance and flatness tolerance Guide rail straightness error , and Slider height tolerance and flatness tolerance ; The key component tolerances of the rotary shaft include: bed top surface height tolerance. and flatness tolerance mandrel diameter tolerance Workbench height tolerance and flatness tolerance ; The linear axis geometric error term includes: the positioning error of the X-axis along the x-direction of the coordinate system. and straightness error along the y and z directions and X-axis roll error around the coordinate system Yaw error around the y-direction pitch error around the z-direction ; The geometric error elements of the rotating shaft include six position-related geometric errors and four position-independent installation errors.

3. The modeling method for the tolerance to tooth surface error of key components of a forming gear grinding machine according to claim 1, characterized in that: In step two, the actual pose model from the guide rail mounting surface to the slider... Represented as: in: This is the actual pose error matrix of the guide rail mounting surface; This is the actual pose error matrix of the guide rail; This is the actual pose error matrix of the slider; The coordinate transformation matrix is ​​used to transfer the pose error of the guide rail mounting surface in the bed coordinate system to the guide rail coordinate system; This is the transformation matrix from the coordinate system of the guide rail starting point to the coordinate system of the slider mounting point; This is the transformation matrix from the coordinate system at the slider mounting point to the slider coordinate system.

4. The modeling method for the tolerance to tooth surface error of key components of a forming gear grinding machine according to claim 3, characterized in that: Total error rotation of guide rail mounting surface Represented as: in: This represents the total error rotation of the guide rail mounting surface; For the height tolerance of the guide rail mounting surface The error spinor; For the flatness tolerance of the guide rail mounting surface The error spinor; and The guide rail mounting surface is respectively and Length in the direction; It is a scaling factor, and ,in , These are the upper and lower limit deviations, respectively. , and These represent the overall translation components of the plane, the degree of tilt around the x-direction, and the degree of tilt around the y-direction, respectively. Actual pose error matrix of guide rail mounting surface Total error rotation through the guide rail mounting surface Obtained through conversion; Total error spin of the guide rail Represented as: in: The total error rotation of the guide rail; For guide rail height tolerance The error spinor; For the flatness tolerance of the guide rail The error spinor; The rotation of the pose error caused by the straightness error of the guide rail; For the flatness tolerance of the guide rail exist Displacement error in direction; and These are the flatness tolerances of the guide rails. exist and Angular error in direction; )and These respectively represent the axis of the guide rail as... Direction and Straightness error in direction; Actual pose error matrix of the guide rail Total error spin of the guide rail Obtained through conversion; Total error spin of the slider's own manufacturing tolerance Represented as: in: This represents the total error rotation of the slider's own manufacturing tolerance; Indicates slider height tolerance The error spinor; For slider flatness tolerance The error spinor; For slider flatness tolerance exist Displacement error in direction; and These are the flatness tolerances of the slider. exist and Angular error in direction; Actual pose error matrix of the slider The total error spin of the slider itself to manufacture tolerances Obtained through conversion.

5. The modeling method for the tolerance to tooth surface error of key components of a forming gear grinding machine according to claim 3 or 4, characterized in that: In step two, the mapping model between the tolerance and geometric error of the key component X of the linear axis is expressed as follows: in: Indicates the first Group Proportion Factor Under this value, the linear axis Move from the initial position to A mapping model between the tolerances and geometric errors of key components at location; , and This indicates the positioning error of the linear axis in the X, Y, and Z axes. This represents the roll error of the linear axis around the X-axis. This refers to the yaw error of the linear axis around the Y-axis. The pitch error of the linear axis about the Z-axis; It is a translation vector; It is the corner vector; For tolerances of critical components.

6. The modeling method for the tolerance to tooth surface error of key components of a forming gear grinding machine according to claim 1, characterized in that: In step two, the actual pose model of the rotation axis Represented as: in: Represents the actual pose model of the rotation axis; This represents the actual pose matrix of the top surface of the bed; This is the actual pose matrix of the mandrel; This represents the actual pose matrix of the worktable surface. This is the transformation matrix from the bed coordinate system to the mandrel coordinate system; This is the transformation matrix from the mandrel coordinate system to the table coordinate system; Mapping model between tolerances and geometric errors of key components of a rotating shaft Represented as: in: A mapping model representing the relationship between tolerances and geometric errors of key components of a rotating shaft; A model representing the ideal pose of the rotation axis; Indicates the first Group proportion factor.

7. The modeling method for the tolerance to tooth surface error of key components of a forming gear grinding machine according to claim 6, characterized in that: The total pose deviation caused by the bed plane height tolerance and flatness tolerance is expressed as: in: The total positional deviation of the top surface of the bed; For the height tolerance of the top surface of the bed The error spinor; For the flatness tolerance of the top surface of the bed The error spinor; and The top surface of the bed is respectively and Length in the direction; It is a scaling factor, and ,in , These are the upper and lower limit deviations, respectively. , and These represent the overall translation components of the plane, the degree of tilt around the x-direction, and the degree of tilt around the y-direction, respectively. Actual pose model of the rotation axis Total error spin through the top surface of the bed Obtained through conversion; Mandrel error spindle Represented as: in: Indicates the error spindle; For the mandrel diameter tolerance; The length of the mandrel; and This indicates translation along the x and y directions; and These represent the degree of tilt controlled around the x and y directions, respectively; actual pose matrix of mandrel Through spindle error spindle Obtained through conversion; Total positional deviation of the worktable Represented as: in: Indicates the total positional deviation of the worktable; Indicates the workbench height tolerance The error spinor; Indicates the flatness tolerance of the worktable surface The error spinor; Indicates the radius of the working frustum; and This represents the translation component of the plane along the z-direction; and These represent the degree of tilt controlled around the x and y directions, respectively; Actual pose matrix of the worktable Total deviation of worktable posture Obtained through conversion.

8. The modeling method for the tolerance of key components of a forming gear grinding machine to tooth surface error according to claim 1, characterized in that: In step three, the geometric error of the motion axis is transformed into the actual pose model of the tool. for: From the geometric error of the motion axis to the actual pose model of the workpiece for: in: This represents the pose transformation matrix between the i-axis and the j-axis. and Represents the ideal transformation matrix of the installation pose, the error matrix of the installation pose, the ideal transformation matrix of the motion pose, and the error transformation matrix of the motion pose between the i-axis and the j-axis; Tool / Workpiece Actual Position Model for: in: An error propagation model from the machine base coordinate system to the workpiece coordinate system; This is an error propagation model from the machine base coordinate system to the tool coordinate system; Model of motion axis geometric error to tool / workpiece pose error for: in: An ideal pose model for the tool / workpiece; The transfer model from motion axis geometric error to tool / workpiece pose error. Represented as: in: This represents the tolerance-geometric error model for linear shaft parts. This represents the tolerance-geometric error model for rotating shaft parts.

9. The modeling method for the tolerance of key components of a forming gear grinding machine to tooth surface error according to claim 1, characterized in that: In step four, the method for establishing a comprehensive accuracy prediction model from key component tolerances to tooth surface pose error includes: Establish a model of the pose error of the grinding wheel under the influence of tolerances of key components. for: in: This is the actual position vector of the grinding wheel surface; This is the actual attitude vector of the grinding wheel surface; This is a model for the transfer of motion axis geometric errors to tool / workpiece pose errors; This is the grinding wheel position vector; This is the attitude vector; Based on grinding wheel pose error model Obtain the gear tooth surface pose error model : in: Indicates the positional error of the tooth surface; This indicates the tooth surface attitude error.

10. The modeling method for the tolerance to tooth surface error of key components of a forming gear grinding machine according to claim 8, characterized in that: In step five, the specific implementation of the Monte Carlo simulation is as follows: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Uniformly distributed sampling is performed within the range (-1, 1) to ensure that the sampling results meet the tolerance constraints; n sampling simulations are conducted, where N is the total sample size, and each group... Substituting these values ​​into the model, the various pose errors generated by the motion axes during actual motion are simulated, resulting in comprehensive error models for both the linear and rotational axes. and : in: Indicates the first Group Proportion Factor Under this value, the linear axis Move from the initial position to A mapping model between the tolerances and geometric errors of key components at location; A mapping model representing the relationship between tolerances and geometric errors of key components of a rotating shaft.

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