Method for identifying sensitive geometric errors of a gear forming grinding machine tool facing gear evaluation errors

Abstract

The application discloses a forming gear grinding machine sensitive geometric error identification method for gear evaluation error, which comprises the following steps: establishing a grinding wheel rotary surface parameter model based on gear parameters to be machined; establishing a quantitative mapping analytical model of machine tool geometric error-gear tooth profile / helical line deviation; and identifying sensitive geometric errors affecting the evaluation deviation of the gear tooth profile / helical line. The application can identify key errors affecting the gear surface precision, provide a theoretical basis for subsequent machining compensation, and improve the forming gear grinding error compensation efficiency.

Description

Technical Field

[0001] This invention relates to the field of grinding error analysis technology for CNC forming gear grinding machines, and in particular to a method for identifying sensitive geometric errors in forming gear grinding machines for evaluating gear errors. Background Technology

[0002] With the rapid development of the manufacturing industry, CNC profile grinding machines have been widely used in the precision gear machining industry due to their high production efficiency, high grinding accuracy, and ease of profile modification. Unlike traditional machining methods, profile grinding is a line contact machining process. Inaccurate relative positional relationship between the grinding wheel and gear caused by machine tool geometric errors will result in changes in the shape and posture of the contact line, exacerbating the impact of machine tool geometric errors on the machining and grinding accuracy.

[0003] To reduce the impact of machine tool geometric errors on machining results and improve the efficiency of geometric error compensation, it is crucial to accurately identify the sensitive geometric error sources of various tooth surface deviations. The foundation for identifying these sensitive geometric error sources lies in establishing a quantitative mapping model between machine tool geometric errors and various tooth surface deviations. Traditional modeling methods use the spatial pose error of the tool to replace machining errors as the model's output variable for analysis. However, the line contact machining method of form grinding dictates that tool spatial errors cannot characterize tooth surface deviations. Furthermore, the evaluation parameters for tooth surface deviations are already given in national standards; further research is needed to determine the quantitative mapping relationship between machine tool geometric error sources and tooth surface error evaluation parameters. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the problems existing in the above and / or existing machine tool error analysis, the present invention is proposed.

[0006] Therefore, the purpose of this invention is to provide a method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors. This method can analyze the influence of various geometric error sources of the machine tool on tooth surface deviations, thereby identifying key geometric errors that have a significant impact on standard tooth surface deviation parameters such as total tooth profile deviation and total tooth direction deviation. This provides a theoretical basis for subsequent modeling and compensation of machine tool geometric errors, thereby improving the compensation efficiency of machine tool geometric errors.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors, comprising the following steps:

[0008] Establish a parameter model of the grinding wheel's rotating surface based on the parameters of the gear to be processed;

[0009] Establish a quantitative mapping analytical model for machine tool geometric errors—tooth profile / helix deviation;

[0010] Identify sensitive geometric errors that affect the evaluation deviation of tooth profile / helix.

[0011] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors according to the present invention, the step of establishing the parametric model of the grinding wheel's rotating surface is as follows:

[0012] Establish a digital model of the tooth surface;

[0013] The contact line on the tooth surface is calculated based on the principle of forming gear grinding, and then transformed into a grinding wheel coordinate system to establish a grinding wheel rotation surface model by rotating around the axis.

[0014] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors according to the present invention, the method includes: establishing a standard tooth surface digital model, taking an involute gear as an example, and comprising the following steps.

[0015] Establish a coordinate system O with the center of the lower end face of the gear as the origin. f1 In coordinate system O f1 Establish a standard involute tooth profile equation, and then define the involute tooth profile... Sweep along the spiral, x f1 (u) represents the x-coordinate of the involute tooth profile, y f1 (u) represents the y-coordinate of the involute tooth profile in the gear coordinate system O. G Establish a standard involute tooth surface model In the formula Represents from coordinate system O f1 To O G The homogeneous coordinate transformation, where θ is the rotation parameter about the Z-axis, for the involute tooth surface model. and the normal vector model of any point on the tooth surface as follows;

[0016] (1);

[0017] (2);

[0018] In the formula r b Let be the base circle radius of the involute gear, σ0 be the base circle tooth groove half angle, u be the involute parameter, and θ be the rotation parameter about the Z-axis. u max and u min These are the upper and lower limits of the involute parameter u, respectively, and β. b n is the base circle helix angle. g1Let nx be the normal vector of a point on the tooth surface. g1 ny is the x-direction component of the normal vector of a point on the tooth surface. g1 Let nz be the y-direction component of the normal vector at a point on the tooth surface. g1 Let z be the z-direction component of the normal vector at a point on the tooth surface.

[0019] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors according to the present invention, the specific steps for establishing the grinding wheel revolution surface model are as follows:

[0020] Transform the involute tooth surface model and the tooth surface normal vector model into the grinding wheel coordinate system O. w In the homogeneous coordinate transformation matrix as follows;

[0021] (3);

[0022] γ is the grinding wheel mounting angle, φ is the gear rotation angle, and D x D is the center distance between the grinding wheel and the gear. z Let φ and D be the z-axis distance between the grinding wheel shaft and the gear end face. z Assign a value of 0, and set the grinding wheel coordinate system O. w The lower involute tooth surface model and tooth surface normal vector model are as follows.

[0023] (4);

[0024] x w Let x and y be the coordinates of points on the tooth surface in the grinding wheel coordinate system. w Let y be the y-coordinate of a point on the tooth surface in the grinding wheel coordinate system, and z be the z-co w nx is the z-coordinate of a point on the tooth surface in the grinding wheel coordinate system. w Let ny be the x-component of the normal vector on the tooth surface in the grinding wheel coordinate system. w Let nz be the y-direction component of the normal vector on the tooth surface in the grinding wheel coordinate system. w Let z be the z-direction component of the normal vector on the tooth surface in the grinding wheel coordinate system;

[0025] Based on the principle of profile grinding, the contact condition between the grinding wheel and the gear is that the normal vectors of the grinding wheel and the gear at the common point are the same and pass through the axis of the grinding wheel. Therefore, the contact equation between the grinding wheel and the gear is established as follows;

[0026] (5),

[0027] Solving the equation yields the explicit expression of the unknown θ with respect to the unknown u. Substituting this into equation (4) gives the contact line model with respect to only one unknown u. and contact line unit normal vector model ;

[0028] x q1 Let x and y be the x-coordinates of points on the contact line in the grinding wheel coordinate system. q1 Let y be the y-coordinate of a point on the contact line in the grinding wheel coordinate system, and z be the z-coordinate of the point on the contact line. q1 nx is the z-coordinate of a point on the contact line in the grinding wheel coordinate system. q1 Let ny be the x-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system. q1 Let nz be the y-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system. q1 Let z be the z-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system;

[0029] In the grinding wheel coordinate system O w Rotate the contact line along the y-direction to establish a grinding wheel revolution surface model r. s (u, and the unit normal vector model n at any point on the surface s (u, )as follows;

[0030] (6);

[0031] Let be the rotation angle around the y-direction.

[0032] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors according to the present invention, the method includes the following steps when establishing machine tool geometric errors:

[0033] Define geometric errors and establish a machine tool geometric error-contact line spatial pose error model;

[0034] Based on the gear deviation evaluation method, the contact conditions of the forming gear grinding are redefined, and a machine tool geometric error-tooth profile / helix error model is further established.

[0035] A machine tool geometric error evaluation deviation model—tooth profile / helix evaluation deviation model—is established based on gear error evaluation standards.

[0036] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors according to the present invention, the specific steps for establishing the machine tool geometric error-contact line spatial pose error model are as follows:

[0037] The kinematic chain of the grinding system of a CNC forming gear grinding machine includes two linear axes, X and Z, and two rotary axes, A and C. The position-related error caused by manufacturing defects in the moving parts of the machine tool is defined.

[0038] Define position-independent error caused by inaccurate relative positional relationships between motion axes during machine tool assembly;

[0039] The machine tool kinematic chain is divided into two parts: the tool chain and the workpiece chain. The coordinate transformation between two adjacent coordinate systems is obtained by multiplying three matrices: a position-independent error transformation matrix, a motion transformation matrix, and a position-dependent error transformation matrix. Let X, Z, A, and C represent the motion quantities of the X-axis, Y-axis, A-axis, and C-axis, respectively, and M... ij Represents the coordinate transformation from coordinate system i to coordinate system j; the comprehensive motion transformation matrix of the workpiece chain. M RX M is the comprehensive motion transformation matrix from the X-axis coordinate system to the workpiece coordinate system. XZ M is the comprehensive motion transformation matrix from the Z-axis coordinate system to the X-axis coordinate system. ZA M is the comprehensive motion transformation matrix from the A-axis coordinate system to the Z-axis coordinate system. AW The comprehensive motion transformation matrix from the grinding wheel coordinate system to the A-axis coordinate system, and the comprehensive motion transformation matrix of the tool chain. M RC M is the comprehensive motion transformation matrix from the C-axis coordinate system to the machine tool coordinate system. CG This represents the comprehensive motion transformation matrix from the gear coordinate system to the C-axis coordinate system, and the transformation matrix from the grinding wheel coordinate system to the gear coordinate system affected by geometric errors. as follows;

[0040] (6);

[0041] M RW M is the comprehensive motion transformation matrix of the workpiece chain. RG This is the comprehensive motion transformation matrix of the toolchain;

[0042] During profile grinding, the motion quantities X and A along the X and A axes remain constant and are related to the grinding wheel parameters and the parameters of the gear being machined. X=D x A=γ, Z=-p·C, where p is the gear helix parameter. Equation (6) is simplified. There is only one variable, C, in the model of the rotating surface of the grinding wheel r. s and surface unit normal model n s The process of transforming to the gear coordinate system is as follows;

[0043] (7);

[0044] The point on the tooth surface where the dot product of the relative velocity and the unit normal vector is zero is the point of contact, which satisfies the identity. Therefore, the following equation is established;

[0045] (8);

[0046] Equation (8) is a transcendental equation. For each input parameter u and parameter C, combined with formula (7), the points on the contact line are obtained. x cl Let x and y be the x-coordinates of points on the contact line in the gear coordinate system. cl Let be the y-coordinate of a point on the contact line in the gear coordinate system, and z be the z-coordinate of the point on the contact line. cl Let z be the z-coordinate of a point on the contact line in the gear coordinate system, and the actual machined tooth surface is obtained by the envelope of a series of contact lines.

[0047] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors according to the present invention, the specific steps for establishing the machine tool geometric error—tooth profile curve / helix curve error model are as follows:

[0048] The point on the contact line passing through the end section satisfies z=z es , z es The z-coordinate represents the end section. To establish a quantitative mapping model for gear evaluation deviation, the contact conditions are modified, resulting in contact condition one, as follows.

[0049] (9);

[0050] Solve the system of equations (9) and substitute r q The tooth profile curve model with respect to the number u is obtained. x tpl (u) represents the x-coordinate of a point on the tooth profile at the lower end of the gear coordinate system, and y-coordinate of... tpl (u) is the y-coordinate of a point on the tooth profile at the lower end of the gear coordinate system, z tpl (u) is the z-coordinate of the point on the tooth profile at the lower end of the gear coordinate system, and the machine tool geometric error-tooth profile curve error model is established accordingly.

[0051] Take the contact line to meet the requirements The points are used to construct the helical curve, where r is the pitch circle radius of the gear. The contact conditions are modified to obtain contact condition two, as follows.

[0052] (10);

[0053] Solve the system of equations (10) and substitute r q The spiral curve model is obtained from it. ;

[0054] x hl (u) represents the x-coordinate of a point on the pitch circle helix in the gear coordinate system, and y-coordinate of the point on the pitch circle helix. hl (u) is the y-coordinate of a point on the pitch circle helix in the gear coordinate system, and z is the z-coordinate of the point. hl (u) is the z-coordinate of a point on the pitch circle helix in the gear coordinate system, and the machine tool geometric error-helix curve error model is established accordingly.

[0055] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors according to the present invention, the specific steps include: establishing a machine tool geometric error—tooth profile / helix evaluation deviation model.

[0056] The error ff between the actual tooth profile and the theoretical tooth profile in the normal vector direction of the standard involute tooth profile is calculated as follows.

[0057] (11);

[0058] Calculate the theoretical involute development length fb tpl as follows,

[0059] (12);

[0060] x tpl Let x and y be the coordinates of points on the tooth profile at the lower end of the gear coordinate system. tpl Let y be the y-coordinate of a point on the tooth profile at the lower end of the gear coordinate system;

[0061] With tooth profile error ff tpl The x-axis represents the length fb of the theoretical involute. tpl Plot the tooth profile error curve on the ordinate and perform least-squares fitting as follows;

[0062] (13);

[0063] The optimal solutions for a1 and b1 are given by the following equation;

[0064] (14);

[0065] Total tooth profile deviation F of the gear α Tooth profile shape deviation f fα Tooth profile tilt deviation f Hα The calculation is as follows;

[0066] (15);

[0067] In the formula Therefore, a model based on machine tool geometric error and gear tooth profile deviation can be established to determine the quantitative mapping relationship from machine tool geometric error to the three tooth profile deviations. The same applies to helical deviation. First, the helical deviation ff is calculated. hl as follows;

[0068] (16);

[0069] x hl Let x and y be the coordinates of a point on the pitch circle helix in the gear coordinate system. hlLet y be the y-coordinate of a point on the pitch circle helix in the gear coordinate system;

[0070] With spiral error ff hl The x-axis is the z-coordinate of a point on the spiral curve. hl Using the vertical axis as the ordinate, plot the spiral error curve and perform a least-squares fit as follows:

[0071] (17);

[0072] Similarly, the optimal solutions for a2 and b2 are given by the following equations.

[0073] (18);

[0074] Gear 3-term helical deviation F β (total deviation of the spiral), f fβ (helix shape deviation), f Hβ The (helix tilt deviation) is calculated as follows;

[0075] (19);

[0076] max(ff hl (u)) represents the maximum spiral error, min(ff) hl (u)) represents the minimum spiral error, and max(z) hl (u) is the z-coordinate of the endpoint of the helix, min(z) hl (u) is the z-coordinate of the lower end of the helix. From this, a model of machine tool geometric error-gear helix deviation can be established to determine the quantitative mapping relationship from machine tool geometric error to three helix deviations.

[0077] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors according to the present invention, the specific steps for identifying sensitive geometric errors affecting the evaluation deviation of tooth profile / helix are as follows:

[0078] Based on the machine tool geometric error-tooth profile / helix error model, the sensitivity index is used to represent the degree of influence of a single error term change on gear error, and the coupling index is used to represent the degree of correlation between a single error term and other errors;

[0079] Based on the multi-contact line correlation characteristics of the evaluation of tooth surface deviation in forming grinding, the improved Morris method is used to calculate the sensitivity index and coupling index of each geometric error;

[0080] Obtain the form grinding machine tool sensitive geometric error terms that affect the deviation of gear tooth profile / helix.

[0081] As a preferred embodiment of the method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors according to the present invention, the specific steps for using a coupling index to represent the degree of correlation between a single error term and other errors are as follows:

[0082] The machine tool geometric error-tooth profile deviation model is simplified as follows:

[0083] (20);

[0084] Construct a randomized matrix F with respect to the variables. * as follows;

[0085] (twenty one);

[0086] Construct the randomized sampling matrix S * as follows;

[0087] (twenty two);

[0088] Set the lower limit of all input parameters to E. min =[ , , , ..., ], the upper limit is E max =[ , , , ..., ], Input parameter value range matrix = repmat (E max -E min If m1+1,1), then the random error matrix ER is derived from the randomized sampling matrix S. * get:

[0089] (twenty three);

[0090] S * If only one variable changes between two adjacent rows, with a difference of ∆, then the basic effect EE caused by the change in only the element in the i-th column between two adjacent rows is as follows: i for,

[0091] (twenty four);

[0092] S * Using adjacent rows of elements as model input variables, we obtain the basic effects of m variables. We repeat this process SN times to obtain the SN basic effects of a single variable.

[0093] Calculate the mean μ of the basic effect for each error term.i and standard deviation σ i As a sensitivity index and coupling index

[0094] (25);

[0095] Where D* is a diagonal matrix constructed based on the number of variables, with diagonal elements randomly generated with equal probability, and S 34×33 To generate a strictly lower triangular matrix where all elements are 1, F is a 34×33 dimensional identity matrix;

[0096] The sensitivity index and coupling index of each geometric error are calculated using the improved Morris method, including the following steps:

[0097] A novel method for constructing the random error matrix ER is presented. First, the range of input parameter values ​​R is modified. E For R E *, vector R E The structure is as follows:

[0098] (26);

[0099] X max Y max Z max A max C max Represent the maximum travel distance of each motion axis and construct a random matrix. The matrix elements are 1 or -1 with equal probability distribution. The random error ER in equation (23) is reconstructed as follows:

[0100] (27);

[0101] The basic effects of the variables are calculated using the reconstructed random error matrix ER, and the sensitivity index and coupling index of each error term are calculated according to Equation (25).

[0102] Obtaining the form grinding machine tool sensitive geometric error terms that affect gear tooth profile / helix deviation includes the following steps.

[0103] A sensitivity index greater than the average value is considered a sensitive geometric error, while a coupling index greater than the average value is considered a strong coupling error.

[0104] Compared with the prior art, the present invention has the following technical effects: using the present invention can identify the key errors that affect the accuracy of the tooth surface, provide a theoretical basis for subsequent processing compensation, and improve the efficiency of error compensation in forming and grinding. Attached Figure Description

[0105] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0106] Figure 1 This is a simplified three-dimensional structural diagram of the gear grinding machine tool in this invention.

[0107] Figure 2 This is a schematic diagram of the forming grinding process.

[0108] Figure 3 This is a schematic diagram illustrating the calculation principle of the end section profile.

[0109] Figure 4 The total deviation of the tooth profile F α The results of the sensitivity analysis are shown in the figure.

[0110] Figure 5 For tooth profile shape deviation f fα The results of the sensitivity analysis are shown in the figure.

[0111] Figure 6 For the tooth profile tilt deviation f Hα The results of the sensitivity analysis are shown in the figure.

[0112] Figure 7 The total deviation F of the spiral β The results of the sensitivity analysis are shown in the figure.

[0113] Figure 8 The deviation of the spiral shape f fβ The results of the sensitivity analysis are shown in the figure.

[0114] Figure 9 The deviation of the spiral inclination f Hβ The results of the sensitivity analysis are shown in the figure.

[0115] In the diagram, 1 is the connecting seat, 2 is the connecting plate, 3 is the sliding block, R is the machine tool base, G is the gear, and W is the grinding wheel. Detailed Implementation

[0116] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0117] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0118] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0119] Example 1

[0120] Reference Figures 1-3 This is the first embodiment of the present invention. This embodiment provides a method for identifying sensitive geometric errors of forming grinding machine tools for gear evaluation errors. It can identify key geometric errors that have a significant impact on standard tooth surface deviation parameters such as total tooth profile deviation and total helix deviation, providing a theoretical basis for subsequent modeling and compensation of machine tool geometric errors, thereby improving the compensation efficiency of machine tool geometric errors.

[0121] A brief description of a gear grinding machine tool: The gear grinding machine tool includes a machine tool base R, on which a gear G is rotatably connected. A connecting seat 1 is also slidably connected to the machine tool base R. The connecting seat 1 can move in the direction of gear G or away from the direction of gear G. Figure 1 The X direction is parallel to the moving direction of the connecting seat 1. A sliding block 3 that can slide in the height direction is connected to the connecting seat 1. A connecting plate 2 is rotatably connected to the sliding block 3. A grinding wheel W is connected to the connecting plate 2. The structure for realizing the rotation of the gear G, the movement of the connecting seat 1 and the sliding of the sliding plate are all existing technologies and are not the focus of this invention, so they will not be described in detail here.

[0122] A method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors includes the following steps:

[0123] S1: Establish a parameter model of the grinding wheel's rotating surface based on the parameters of the gear to be processed;

[0124] S1.1 Establishing a digital model of the tooth surface, taking an involute gear as an example, includes the following steps:

[0125] Establish a coordinate system O with the center of the lower end face of the gear as the origin. f1 Let the positive direction of the machine tool's X-axis movement be the x-direction of the coordinate system, the positive direction of the machine tool's Y-axis movement be the y-direction of the coordinate system, and the positive direction of the machine tool's Z-axis movement be the z-direction of the coordinate system. In coordinate system O... f1 Establish a standard involute tooth profile equation, and then define the involute tooth profile... Sweep along the spiral, x f1 (u) represents the x-coordinate of the involute tooth profile, y f1 (u) represents the y-coordinate of the involute tooth profile; establish a gear coordinate system O. G Coordinate system O at zero position GWith coordinate system O f1 Coincident; in gear coordinate system O G Establish a standard involute tooth surface model In the formula Represents from coordinate system O f1 To O G The homogeneous coordinate transformation, where θ is the rotation parameter about the Z-axis, for the involute tooth surface model. and the normal vector model of any point on the tooth surface as follows;

[0126] (1);

[0127] (2);

[0128] In the formula r b Let be the base circle radius of the involute gear, σ0 be the base circle tooth groove half angle, u be the involute parameter, and θ be the rotation parameter about the Z-axis. u max and u min These are the upper and lower limits of the involute parameter u, respectively, and β. b n is the base circle helix angle. g1 Let nx be the normal vector of a point on the tooth surface. g1 ny is the x-direction component of the normal vector of a point on the tooth surface. g1 Let nz be the y-direction component of the normal vector at a point on the tooth surface. g1 The z-direction component of the normal vector at a point on the tooth surface;

[0129] S1.2 Calculate the contact line on the tooth surface based on the principle of gear grinding, and transform it into the grinding wheel coordinate system to establish a grinding wheel revolution surface model by rotating it around the axis. The specific steps for establishing the grinding wheel revolution surface model are as follows:

[0130] S1.2.1 Establish the grinding wheel coordinate system O w The origin of the coordinate system is defined at the center of the grinding wheel's rotation axis, and the x-direction of the coordinate system is parallel to the gear coordinate system O. G The x-direction coincides, and other directions are determined using the right-hand rule; the involute tooth surface model and the tooth surface normal vector model are transformed to the grinding wheel coordinate system O. w In the homogeneous coordinate transformation matrix as follows;

[0131] (3);

[0132] γ is the grinding wheel mounting angle, φ is the gear rotation angle, and D x D is the center distance between the grinding wheel and the gear. z The distance in the z-direction between the grinding wheel shaft and the gear end face; φ and D z Assign a value of 0, and set the grinding wheel coordinate system O. wThe lower involute tooth surface model and tooth surface normal vector model are as follows.

[0133] (4);

[0134] x w Let x and y be the coordinates of points on the tooth surface in the grinding wheel coordinate system. w Let y be the y-coordinate of a point on the tooth surface in the grinding wheel coordinate system, and z be the z-co w nx is the z-coordinate of a point on the tooth surface in the grinding wheel coordinate system. w Let ny be the x-component of the normal vector on the tooth surface in the grinding wheel coordinate system. w Let nz be the y-direction component of the normal vector on the tooth surface in the grinding wheel coordinate system. w Let z be the z-direction component of the normal vector on the tooth surface in the grinding wheel coordinate system;

[0135] S1.2.2 Based on the principle of profile grinding, the contact condition between the grinding wheel and the gear is that the normal vectors of the grinding wheel and the gear at the common point are the same and pass through the axis of the grinding wheel. Therefore, the contact equation between the grinding wheel and the gear is established as follows;

[0136] (5),

[0137] S1.2.3 Solving the equation yields an explicit expression for only one unknown, u. Substituting this expression into equation (4) yields the contact line model for only one unknown, u. Contact line unit normal vector model ;

[0138] x q1 Let x and y be the x-coordinates of points on the contact line in the grinding wheel coordinate system. q1 Let y be the y-coordinate of a point on the contact line in the grinding wheel coordinate system, and z be the z-coordinate of the point on the contact line. q1 nx is the z-coordinate of a point on the contact line in the grinding wheel coordinate system. q1 Let ny be the x-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system. q1 Let nz be the y-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system. q1 Let z be the z-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system;

[0139] S1.2.4 in the grinding wheel coordinate system O w Rotate the contact line along the y-direction to establish a grinding wheel revolution surface model r. s (u, and the unit normal vector model n at any point on the surface s (u, )as follows;

[0140] (6);

[0141] Let be the rotation angle around the y-direction;

[0142] S2: Establish a quantitative mapping analytical model for machine tool geometric error—tooth profile / helix deviation;

[0143] S2.1 Define geometric errors and establish a machine tool geometric error—contact line spatial pose error model, specifically including the following steps.

[0144] S2.1.1 The kinematic chain of the grinding system of a CNC forming gear grinding machine includes two linear axes, X and Z, and two rotary axes, A and C. Position-related errors caused by manufacturing defects in the moving parts of the machine tool are defined, including 24 items, as follows:

[0145] δ x (X) - Positioning error of the X-axis in the x-direction, δ y (X) - Straightness error of the X-axis in the y-direction.

[0146] δ z (X) - Straightness error of the X-axis in the z-direction, ε x (X) - Roll error of the X-axis about the x-direction

[0147] ε y (X) - X-axis pitch error about the y-direction, ε z (X) - X-axis yaw error about the z-direction

[0148] δ x (Z) - Straightness error of the Z-axis in the x-direction, δ y (Z) - Straightness error of the Z-axis in the y-direction.

[0149] δ z (Z) - Z-axis positioning error in the z-direction, ε x (Z) - Z-axis pitch error about the x-direction

[0150] ε y (Z) - Z-axis y-axis y-axis y-axis y-axis y-axis ε z (Z) - Roll error of the Z-axis about the z-direction

[0151] δ x (A) - Straightness error of A-axis in the x-direction, δ y (A) - Straightness error of A-axis in the y-direction.

[0152] δ z (A) - Straightness error of the A-axis in the z-direction, ε x (A) - Positioning error of A-axis around the x-direction

[0153] ε y(A) - A-axis rotation angle error around the y-direction, ε z (A) - A-axis rotation angle error around the z-direction

[0154] δ x (C) - Straightness error of C-axis in the x-direction, δ y (C) - Straightness error of the C-axis in the y-direction;

[0155] δ z (C) - Straightness error of the C-axis in the z-direction, ε x (C) - C-axis rotation angle error around the x-direction

[0156] ε y (C) - C-axis rotation angle error around the y-direction, ε z (C) - Positioning error of C-axis around the z-direction;

[0157] S2.1.2 defines position-independent errors caused by inaccurate relative positions between motion axes during machine tool assembly, including 9 items:

[0158] β ZX - Perpendicularity error between Z-axis and X-axis, β AZ - Angle error between the A-axis and the Z-axis coordinate system in the z-direction, δ Az - A-axis position offset error in the z-direction, γ AY -Angle error between the A-axis and the Z-axis coordinate system in the y-direction, δ Ay - A-axis position offset error in the y-direction, α CY - Angle error between the C-axis and the machine tool coordinate system in the y-direction, δ Cy - C-axis position offset error in the y-direction, β CX - Angle error between the C-axis and the machine tool coordinate system in the x-direction, δ Cx - C-axis position offset error in the x direction;

[0159] S2.1.3 The machine tool kinematic chain is divided into two parts: the tool chain (R - X - Z - A - W) and the workpiece chain (R - C - G). The coordinate transformation between two adjacent coordinate systems is obtained by multiplying three matrices: the position-independent error transformation matrix, the motion transformation matrix, and the position-dependent error transformation matrix. The geometric error transformation matrix between two adjacent coordinate systems is as follows.

[0160] (37)

[0161] (38),

[0162] (39)

[0163] (40),

[0164] (41),

[0165] (42),

[0166] In the formula, X, Z, A, and C represent the motion quantities along the X-axis, Y-axis, A-axis, and C-axis, respectively, and M represents the motion quantities along the M-axis. ij Represents the coordinate transformation from coordinate system i to coordinate system j; the motion transformation matrix of the workpiece chain. M RX M is the comprehensive motion transformation matrix from the X-axis coordinate system to the workpiece coordinate system. XZ M is the comprehensive motion transformation matrix from the Z-axis coordinate system to the X-axis coordinate system. ZA M is the comprehensive motion transformation matrix from the A-axis coordinate system to the Z-axis coordinate system. AW The comprehensive motion transformation matrix from the grinding wheel coordinate system to the A-axis coordinate system, and the comprehensive motion transformation matrix of the tool chain. M RC M is the comprehensive motion transformation matrix from the C-axis coordinate system to the machine tool coordinate system. CG This represents the combined motion transformation matrix from the gear coordinate system to the C-axis coordinate system, and the combined motion transformation matrix from the grinding wheel coordinate system to the gear coordinate system, which is affected by geometric errors. as follows;

[0167] (6);

[0168] M RW M is the comprehensive motion transformation matrix of the workpiece chain. RG This is the comprehensive motion transformation matrix of the toolchain;

[0169] During the S2.1.4 form grinding process, the motion quantities X and A along the X and A axes remain constant and are related to the grinding wheel parameters and the parameters of the gear to be machined. X=D x A=γ, Z=-p·C, where p is the gear helix parameter. Equation (6) is simplified. There is only one variable, C, in the model of the rotating surface of the grinding wheel r. s and surface unit normal model n s The process of transforming to the gear coordinate system is as follows;

[0170] (7);

[0171] The point on the tooth surface where the dot product of the relative velocity and the unit normal vector is zero is the contact point, i.e., satisfying the identity. Therefore, the following equation is established;

[0172] (8);

[0173] Equation (8) is a transcendental equation. Each input parameter u and parameter C represents the number of points on a single contact line, and C represents the number of contact lines. Combining with formula (7), the points on the contact line are obtained. x cl Let x and y be the x-coordinates of points on the contact line in the gear coordinate system. cl Let be the y-coordinate of a point on the contact line in the gear coordinate system, and z be the z-coordinate of the point on the contact line. cl Let z be the z-coordinate of a point on the contact line in the gear coordinate system, and the actual machined tooth surface is obtained by the envelope of a series of contact lines;

[0174] S2.2 Extending the contact conditions for form grinding, further establishing the machine tool geometric error—tooth profile curve / helix curve error model, specifically including the following steps.

[0175] S2.2.1 The point on the contact line passing through the end section satisfies z=z es , z es The z-coordinate represents the end section. To establish a quantitative mapping model for gear evaluation deviation, the contact conditions are modified, resulting in contact condition one, as follows.

[0176] (9);

[0177] S2.2.2 Solve the system of equations (9) and substitute r q The tooth profile curve model with respect to the number u is obtained; x tpl (u) represents the x-coordinate of a point on the tooth profile at the lower end of the gear coordinate system, and y-coordinate of the point on the gear tooth profile. tpl (u) is the y-coordinate of a point on the tooth profile at the lower end of the gear coordinate system, z tpl (u) is the z-coordinate of the point on the tooth profile of the lower section of the gear coordinate system, and the machine tool geometric error-helix error model is established accordingly.

[0178] S2.2.3 Take the contact line that satisfies The points are used to construct the helical curve, where r is the pitch circle radius of the gear. The contact conditions are modified to obtain contact condition two, as follows.

[0179] (10);

[0180] Solve the system of equations (10) and substitute r q The spiral curve model is obtained from it. x hl (u) represents the x-coordinate of a point on the pitch circle helix in the gear coordinate system, and y-coordinate of the point on the pitch circle helix. hl (u) is the y-coordinate of a point on the pitch circle helix in the gear coordinate system, z hl(u) is the z-coordinate of a point on the pitch circle helix in the gear coordinate system, and thus a machine tool geometric error-helix curve error model is established.

[0181] S2.3 Establish a machine tool geometric error—tooth profile / helix error model based on the gear error evaluation standard, specifically including the following steps:

[0182] The error ff between the actual tooth profile and the theoretical tooth profile in the normal vector direction of the standard involute tooth profile S2.3.1 is calculated as follows:

[0183] (11);

[0184] S2.3.2 Calculate the theoretical involute development length fb tpl as follows,

[0185] (12);

[0186] x tpl Let x and y be the coordinates of points on the tooth profile at the lower end of the gear coordinate system. tpl Let y be the y-coordinate of a point on the tooth profile at the lower end of the gear coordinate system;

[0187] S2.3.3 with tooth profile error ff tpl The x-axis represents the length fb of the theoretical involute. tpl Plot the tooth profile error curve on the ordinate and perform least-squares fitting as follows;

[0188] (13);

[0189] The optimal solutions for a1 and b1 are given by the following equation;

[0190] (14);

[0191] S2.3.4 Total tooth profile deviation F of the gear α Tooth profile shape deviation f fα Tooth profile tilt deviation f Hα The calculation is as follows;

[0192] (15);

[0193] In the formula Therefore, a model based on machine tool geometric error and gear tooth profile deviation can be established to determine the quantitative mapping relationship from machine tool geometric error to the three tooth profile deviations. The same applies to helical deviation. First, the helical deviation ff is calculated. hl as follows;

[0194] (16);

[0195] x hl Let x and y be the coordinates of a point on the pitch circle helix in the gear coordinate system. hl Let y be the y-coordinate of a point on the pitch circle helix in the gear coordinate system;

[0196] S2.3.5 uses the spiral error ff hl The x-axis is the z-coordinate of a point on the spiral curve. hl Using the vertical axis as the ordinate, plot the spiral error curve and perform a least-squares fit as follows:

[0197] (17);

[0198] Similarly, the optimal solutions for a2 and b2 are given by the following equations.

[0199] (18);

[0200] S2.3.6 Gear 3-term helical deviation F β (total deviation of the spiral), f fβ (helix shape deviation), f Hβ The (helix tilt deviation) is calculated as follows;

[0201] (19);

[0202] max(ff hl (u)) represents the maximum spiral error, min(ff) hl (u)) represents the minimum spiral error, and max(z) hl (u) is the z-coordinate of the endpoint of the helix, min(z) hl (u)) is the z-coordinate of the lower end of the helix. From this, a model of machine tool geometric error-gear helix deviation can be established to determine the quantitative mapping relationship from machine tool geometric error to the three helix deviations.

[0203] S3: Improve the Morris global sensitivity analysis method to identify sensitive geometric errors affecting the evaluation deviation of tooth profile / helix, specifically including the following steps.

[0204] S3.1 Based on the machine tool geometric error—tooth profile / helix error model, a sensitivity index is used to represent the degree of influence of a single error term change on gear error, and a coupling index is used to represent the degree of correlation between a single error term and other errors. Specifically, this includes the following steps:

[0205] S3.1.1 The machine tool geometric error-tooth profile deviation model is simplified as follows:

[0206] (20);

[0207] S3.1.2 Constructing a randomized matrix F with respect to the variables * as follows;

[0208] (twenty one);

[0209] S3.1.3 Constructing the randomized sampling matrix S * as follows;

[0210] (twenty two);

[0211] S3.1.4 Set the lower limit of all input parameters to E. min =[ , , , ..., ], the upper limit is E max =[ , , , ..., ], Input parameter value range matrix = repmat (E max -E min If m1+1,1), then the random error matrix ER is obtained from the random matrix S*:

[0212] (twenty three);

[0213] S3.1.5 S * Given a random matrix where only one variable changes between any two adjacent rows, with a difference of ∆, what is the fundamental effect EE caused if only the element in the i-th column changes between any two adjacent rows? i for,

[0214] (twenty four);

[0215] S3.1.6 will S * Using adjacent rows of elements as model input variables, we obtain the basic effects of m variables. We repeat this process SN times to obtain the SN basic effects of a single variable.

[0216] S3.1.7 Calculate the mean μ of the basic effect for each error term. i and standard deviation σ i As a sensitivity index and coupling index

[0217] (25);

[0218] Where D* is a diagonal matrix constructed based on the number of variables, with diagonal elements randomly generated with equal probability, and S 34×33To generate a strictly lower triangular matrix where all elements are 1, F is a 34×33 dimensional identity matrix;

[0219] S3.2 Based on the multi-contact line correlation characteristics of the evaluation of tooth surface deviation in forming grinding, the improved Morris method is used to calculate the sensitivity index and coupling index of each geometric error, including the following steps:

[0220] S3.2.1 presents a new method for constructing the random error matrix ER. First, the range of input parameter values ​​R is modified. E For R E *, vector R E The structure is as follows:

[0221] (26);

[0222] X max Y max Z max A max C max Represent the maximum travel distance of each motion axis and construct a random matrix. The matrix elements are 1 or -1 with equal probability distribution. The random error ER in equation (23) is reconstructed as follows:

[0223] (27);

[0224] S3.2.2 The basic effects of the variables are calculated using the reconstructed random error matrix ER, and the sensitivity index and coupling index of each error term are calculated according to Equation (25);

[0225] When obtaining the sensitive geometric error terms of the forming grinding machine tool that affect the deviation of gear tooth profile / helix in S3.3, it is determined that the sensitivity index is greater than the average value and the coupling index is greater than the average value and the coupling error is stronger.

[0226] This invention first determines the sand profile and establishes a revolution surface model based on the parameters of the gear to be processed. Second, it analyzes the machine tool kinematic chain, establishing the pose transformation relationship between the coordinate systems of various machine tool components based on multibody system theory and homogeneous coordinate transformation, thus establishing a machine tool geometric error-tool spatial pose error model. Then, based on the principle of form grinding, the model is extended to establish a machine tool geometric error-contact line spatial pose error model. Next, according to the tooth surface deviation standard evaluation method specified in national standards, a parameter mapping for machine tool geometric error-tooth surface deviation is established. Finally, based on an improved Morris global sensitivity analysis method, the sensitivity index and coupling index of each error term are analyzed, thereby identifying the key errors affecting tooth surface accuracy, providing a theoretical basis for subsequent machining compensation, and improving the efficiency of form grinding error compensation.

[0227] Example 2

[0228] refer to Figures 3-9 The difference between this embodiment and Embodiment 1 is that, using a specific embodiment as an example, the present invention can identify key geometric errors that have a significant impact on standard tooth surface deviation parameters such as total tooth profile deviation and total helix deviation.

[0229] The proposed number of cyclic samplings is SN=50. In position-independent errors, the displacement error range is 0~20μm, and the rotation error range is 0~20mdeg. In position-related errors, the error value is replaced by the sine function of the coordinate axis motion, with the displacement error range being -10~10μm and the rotation error range being -10~10mdeg. Combined with step S3.1, the sensitivity index and coupling index of each machine tool geometric error source are calculated. The geometric error term with a sensitivity index greater than the average value is taken as the sensitive geometric error source of the tooth surface deviation, i.e., the key geometric error.

[0230] For ease of analysis, the geometric errors of the machine tool are numbered as follows;

[0231] 1~6: ε x (X), ε y (X), ε z (X), δ x (X), δ y (X), δ z (X);

[0232] 7~12: ε x (Z), ε y (Z), ε z (Z), δ x (Z), δ y (Z), δ z (Z);

[0233] 13~18: ε x (A), ε y (A), ε z (A), δ x (A), δ y (A), δ z (A);

[0234] 19~24: ε x (C), ε y (C), ε z (C), δ x (C), δ y (C), δ z (C);

[0235] 25~33: β ZX β AZ γAY δ Az δ Ay α CY β CX δ Cy δ Cx ;

[0236] Sensitivity error analysis was performed on the three tooth profile deviations and the three helix deviations respectively. The analysis results are as follows: Figures 4-9 As shown.

[0237] Sensitive geometric errors were defined as those with a sensitivity index greater than the average value, while strong coupling errors were defined as those with a coupling index greater than the average value. The final identified sensitive geometric errors and strong coupling errors for the three tooth profile deviations and three helical deviations are shown in Table 1.

[0238] Table 1

[0239] Tooth surface deviation parameters Sensitive geometric error Strong coupling error <![CDATA[Total profile deviation F α > <![CDATA[ε z (X)、e y (Z)、e z (Z)、e z (A)、b AZ 、c AY ]]> <![CDATA[ε x (X)、e y (X)、e z (X)、e x (Z)、e z (Z)、e x (A)、e z (A)、e x (C)、e y (C)、b ZX 、c AY ,a CY 、b CX ]]> <![CDATA[Tooth profile shape deviation f fα > <![CDATA[ε z (X)、e x (Z)、e y (Z)、e z (Z)、e x (A)、e z (A)、b AZ 、c AY ]]> <![CDATA[ε x (X)、e y (X)、e z (X)、e x (Z)、e y (Z)、e z (Z)、e x (A)、e z (A)、e x (C)、e y (C)、b AZ 、c AY ,a CY 、b CX ]]> <![CDATA[Tooth profile inclination deviation f Hα > <![CDATA[ε y (X)、e z (X)、e y (Z)、e z (Z)、e z (A)、b AZ 、c AY ]]> <![CDATA[ε x (X)、e y (X)、e z (X)、e x (Z)、e z (Z)、e x (A)、e z (A)、e x (C)、e y (C)、b ZX 、c AY ,a CY 、b CX ]]> <![CDATA[Total deviation of helix F β > <![CDATA[ε x (C)、e y (C)、e z (C)、d y (C)、b ZX ]]> <![CDATA[ε z (Z)、e x (C)、e y (C)、e z (C)、d y (C)、b ZX ]]> <![CDATA[Helical shape deviation f fβ > <![CDATA[ε z (Z)、δ y (Z)、e x (C)、e y (C)、e z (C)、d x (C)、d y (C)]]> <![CDATA[εε y (Z)、e z (Z)、e x (C)、e y (C)、e z (C)、d x (C)、d y (C)、b ZX ]]> <![CDATA[Helical line tilt deviation f Hβ > <![CDATA[ε x (C)、e y (C)、e z (C)、d y (C)、b ZX ]]> <![CDATA[ε x (C)、e y (C)、e z (C)、d x (C)、d y (C)、b ZX ]]>

[0240] Among the 33 machine tool geometric errors, 12 sensitive geometric errors were selected, and the following patterns were observed: all sensitive geometric error sources were angular errors; tooth profile deviations were more sensitive to the geometric errors of the tool chain; angular deviations around the z-direction on the tool chain were all sensitive geometric errors; and helical deviations were more sensitive to the geometric errors of the workpiece chain.

[0241] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors, characterized in that: It includes the following steps, Establish a parameter model of the grinding wheel's rotating surface based on the parameters of the gear to be processed; A quantitative mapping analytical model for machine tool geometric error—tooth profile / helix deviation is established, specifically as follows: Define geometric errors and establish a machine tool geometric error-contact line spatial pose error model; Based on the gear deviation evaluation method, the contact conditions of the forming gear grinding are redefined, and a machine tool geometric error-tooth profile / helix error model is further established. Establish a machine tool geometric error evaluation deviation model based on gear error evaluation standards; The specific steps for establishing a machine tool geometric error evaluation deviation model—tooth profile / helix—are as follows: The error ff between the actual and theoretical tooth profiles in the normal vector direction of the standard involute tooth profile tpl (u) is calculated as follows. （11）； Calculate the theoretical involute development length fb tpl (u) is as follows, （12）； x tpl Let x and y be the coordinates of points on the tooth profile at the lower end of the gear coordinate system. tpl Let y be the y-coordinate of a point on the tooth profile at the lower end of the gear coordinate system; With tooth profile error ff tpl The x-axis represents the length fb of the theoretical involute. tpl Plot the tooth profile error curve on the ordinate and perform least-squares fitting to obtain the least-squares equation fb for the tooth profile error curve. a (u) is as follows; （13）； The optimal solutions for a1 and b1 are given by the following equation; （14）； Total tooth profile deviation F of the gear α Tooth profile shape deviation f fα Tooth profile tilt deviation f Hα The calculation is as follows; （15）； In the formula Therefore, a model based on machine tool geometric error and gear tooth profile deviation can be established to determine the quantitative mapping relationship from machine tool geometric error to the three tooth profile deviations. The same applies to helical deviation. First, the helical deviation ff is calculated. hl (u) is as follows; (16)； x hl Let x and y be the coordinates of a point on the pitch circle helix in the gear coordinate system. hl Let y be the y-coordinate of a point on the pitch circle helix in the gear coordinate system; With spiral error ff hl (u) is the x-coordinate, and z is the z-coordinate value of a point on the spiral curve. hl Plot the helical error curve with the vertical axis as the ordinate, and perform least-squares fitting to obtain the least-squares equation fb for the tooth profile error curve. b (u) is as follows, （17）； Similarly, the optimal solutions for a2 and b2 are given by the following equations. （18）； Total deviation F of gear helix β Spiral shape deviation f fβ Spiral tilt deviation f Hβ The calculation is as follows; （19）； max(ff hl (u)) represents the maximum spiral error, min(ff) hl (u)) represents the minimum spiral error, and max(z) hl (u) is the z-coordinate of the endpoint of the helix, min(z) hl (u) is the z-coordinate of the lower end of the helix. From this, a model of machine tool geometric error-gear helix deviation can be established to determine the quantitative mapping relationship from machine tool geometric error to three helix deviations.

2. The method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors as described in claim 1, characterized in that: The steps to establish a parametric model of the rotating surface of a grinding wheel are as follows: Establish a digital model of the tooth surface; The contact line on the tooth surface is calculated based on the principle of forming gear grinding, and then transformed into a grinding wheel coordinate system to establish a grinding wheel rotation surface model by rotating around the axis.

3. The method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors as described in claim 2, characterized in that: Establishing a standard digital model of the tooth surface, taking an involute gear as an example, includes the following steps: Establish a coordinate system O with the center of the lower end face of the gear as the origin. f1 In coordinate system O f1 Establish a standard involute tooth profile equation, and then define the involute tooth profile... Sweep along the spiral, x f1 (u) represents the x-coordinate of the involute tooth profile, y f1 (u) represents the y-coordinate of the involute tooth profile in the gear coordinate system O. G Establish a standard involute tooth surface model In the formula Represents from coordinate system O f1 To O G The homogeneous coordinate transformation, where θ is the rotation parameter about the Z-axis, for the involute tooth surface model. and the normal vector model of any point on the tooth surface as follows; (1)； (2)； In the formula r b Let be the base circle radius of the involute gear, σ0 be the base circle tooth groove half angle, u be the involute parameter, and θ be the rotation parameter about the Z-axis. u max and u min These are the upper and lower limits of the involute parameter u, respectively, and β. b n is the base circle helix angle. g1 Let nx be the normal vector of a point on the tooth surface. g1 ny is the x-direction component of the normal vector of a point on the tooth surface. g1 Let nz be the y-direction component of the normal vector at a point on the tooth surface. g1 Let z be the z-direction component of the normal vector at a point on the tooth surface.

4. The method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors as described in claim 2, characterized in that: The specific steps for establishing a model of a grinding wheel's rotating surface are as follows: Transform the involute tooth surface model and the tooth surface normal vector model into the grinding wheel coordinate system O. w In the homogeneous coordinate transformation matrix as follows; （3）； γ is the grinding wheel mounting angle. D is the gear rotation angle. x D is the center distance between the grinding wheel and the gear. z Let φ and D be the z-axis distance between the grinding wheel shaft and the gear end face. z Assign a value of 0, and set the grinding wheel coordinate system O. w The lower involute tooth surface model and tooth surface normal vector model are as follows. （4）； x w Let x and y be the coordinates of points on the tooth surface in the grinding wheel coordinate system. w Let y be the y-coordinate of a point on the tooth surface in the grinding wheel coordinate system, and z be the z-co w nx is the z-coordinate of a point on the tooth surface in the grinding wheel coordinate system. w Let ny be the x-component of the normal vector on the tooth surface in the grinding wheel coordinate system. w Let nz be the y-direction component of the normal vector on the tooth surface in the grinding wheel coordinate system. w Let z be the z-direction component of the normal vector on the tooth surface in the grinding wheel coordinate system; Based on the principle of profile grinding, the contact condition between the grinding wheel and the gear is that the normal vectors of the grinding wheel and the gear at the common point are the same and pass through the axis of the grinding wheel. Therefore, the contact equation between the grinding wheel and the gear is established as follows; （5）， Solving the equation yields an explicit expression for only one involute parameter u, which, when substituted into equation (4), gives the contact line model. and contact line unit normal vector model ; x q1 Let x and y be the x-coordinates of points on the contact line in the grinding wheel coordinate system. q1 Let y be the y-coordinate of a point on the contact line in the grinding wheel coordinate system, and z be the z-coordinate of the point on the contact line. q1 nx is the z-coordinate of a point on the contact line in the grinding wheel coordinate system. q1 Let ny be the x-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system. q1 Let nz be the y-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system. q1 Let z be the z-direction component of the normal vector of a point on the contact line in the grinding wheel coordinate system; In the grinding wheel coordinate system O w Rotate the contact line along the y-direction to establish a grinding wheel revolution surface model r. s (u, and the unit normal vector model n at any point on the surface. s (u, )as follows; （6）； Let be the rotation angle around the y-direction.

5. The method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors as described in claim 1 or 2, characterized in that: The specific steps for establishing a machine tool geometric error—contact line spatial pose error model are as follows: The kinematic chain of the grinding system of a CNC forming gear grinding machine includes two linear axes, X and Z, and two rotary axes, A and C. The position-related error caused by manufacturing defects in the moving parts of the machine tool is defined. Define position-independent error caused by inaccurate relative positional relationships between motion axes during machine tool assembly; The machine tool kinematic chain is divided into two parts: the tool chain and the workpiece chain. The coordinate transformation between two adjacent coordinate systems is obtained by multiplying three matrices: a position-independent error transformation matrix, a motion transformation matrix, and a position-dependent error transformation matrix. Let X, Y, Z, A, and C represent the motion quantities along the X, Y, Z, A, and C axes, respectively, and let M... ij This represents the coordinate transformation from coordinate system i to coordinate system j; Comprehensive motion transformation matrix of the workpiece chain M RX M is the comprehensive motion transformation matrix from the X-axis coordinate system to the workpiece coordinate system. XZ M is the comprehensive motion transformation matrix from the Z-axis coordinate system to the X-axis coordinate system. ZA M is the comprehensive motion transformation matrix from the A-axis coordinate system to the Z-axis coordinate system. AW The comprehensive motion transformation matrix from the grinding wheel coordinate system to the A-axis coordinate system, and the comprehensive motion transformation matrix of the tool chain. M RC M is the comprehensive motion transformation matrix from the C-axis coordinate system to the machine tool coordinate system. CG This represents the comprehensive motion transformation matrix from the gear coordinate system to the C-axis coordinate system, and the transformation matrix from the grinding wheel coordinate system to the gear coordinate system affected by geometric errors. as follows; ； M RW M is the comprehensive motion transformation matrix of the workpiece chain. RG This is the comprehensive motion transformation matrix of the toolchain; During profile grinding, the X-axis motion X and the A-axis motion A remain constant and are related to the grinding wheel parameters and the parameters of the gear to be machined. X=D x A = γ, Z = -p·C, where p is the gear helical parameter, and the transformation matrix from the grinding wheel coordinate system to the gear coordinate system under the influence of geometric errors. To simplify, There is only one variable, C, in the model of the rotating surface of the grinding wheel r. s and surface unit normal model n s The process of transforming to the gear coordinate system is as follows; （7）； The point on the tooth surface where the dot product of the relative velocity and the unit normal is 0 is the point of contact, and the following equation is established accordingly; （8）； Equation (8) is a transcendental equation. For each involute parameter u and C-axis motion C input, combined with formula (7), the point on the contact line is obtained. x cl Let x and y be the x-coordinates of points on the contact line in the gear coordinate system. cl Let be the y-coordinate of a point on the contact line in the gear coordinate system, and z be the z-coordinate of the point on the contact line. cl Let z be the z-coordinate of a point on the contact line in the gear coordinate system, and the actual machined tooth surface is obtained by the envelope of a series of contact lines.

6. The method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors as described in claim 5, characterized in that: The specific steps for establishing a machine tool geometric error model—tooth profile / helix curve error model—are as follows: The point on the contact line passing through the end section satisfies z=z es , z es The z-coordinate represents the end section. To establish a quantitative mapping model for gear evaluation deviation, the contact conditions are modified, resulting in contact condition one, as follows. （9）； Solve the system of equations (9) and substitute r q The tooth profile curve model with respect to the involute parameter u is obtained. x tpl (u) represents the x-coordinate of a point on the tooth profile at the lower end of the gear coordinate system, and y-coordinate of... tpl (u) is the y-coordinate of a point on the tooth profile at the lower end of the gear coordinate system, z tpl (u) is the z-coordinate of the point on the tooth profile at the lower end of the gear coordinate system, and the machine tool geometric error-tooth profile curve error model is established accordingly. Take the contact line to meet the requirements The points are used to construct the helical curve, where r is the pitch circle radius of the gear. The contact conditions are modified to obtain contact condition two, as follows. （10）； Solve the system of equations (10) and substitute r q The spiral curve model is obtained from it. ; x hl (u) represents the x-coordinate of a point on the pitch circle helix in the gear coordinate system, and y-coordinate of the point on the pitch circle helix. hl (u) is the y-coordinate of a point on the pitch circle helix in the gear coordinate system, z hl (u) is the z-coordinate of a point on the pitch circle helix in the gear coordinate system, and the machine tool geometric error-helix curve error model is established accordingly.

7. The method for identifying sensitive geometric errors in forming grinding machine tools for evaluating gear errors as described in claim 1 or 2, characterized in that: Identify the sensitive geometric errors that affect the evaluation deviation of tooth profile / helix, specifically: Based on the machine tool geometric error-tooth profile / helix error model, the sensitivity index is used to represent the degree of influence of a single error term change on gear error, and the coupling index is used to represent the degree of correlation between a single error term and other errors; Based on the multi-contact line correlation characteristics of the evaluation of tooth surface deviation in forming grinding, the improved Morris method is used to calculate the sensitivity index and coupling index of each geometric error; Obtain the form grinding machine tool sensitive geometric error terms that affect the deviation of gear tooth profile / helix.

8. The method for identifying sensitive geometric errors in forming grinding machine tools for gear evaluation errors as described in claim 7, characterized in that: The specific steps for using a coupling index to represent the degree of correlation between a single error term and other errors are as follows: The machine tool geometric error-tooth profile deviation model is simplified as follows: （20）； Construct a randomized matrix F with respect to the variables. * as follows; （21）； Construct the randomized sampling matrix S * as follows; （22）； Set the lower limit of all input parameters to E. min =[ , , , ..., ], the upper limit is E max =[ , , , ..., ], Input parameter value range matrix = repmat (E max -E min If m+1,1), then the random error matrix ER is obtained from the randomized sampling matrix S*: （23）； S * If only one variable changes between two adjacent rows, with a difference of ∆, then the basic effect EE caused by the change in only the element in the i-th column between two adjacent rows is as follows: i for, （24）； S * Using adjacent rows of elements as model input variables, we obtain the basic effects of m variables. We repeat this process SN times to obtain the SN basic effects of a single variable. Calculate the mean μ of the basic effect for each error term. i and standard deviation σ i As a sensitivity index and coupling index （25）； Where D* is a diagonal matrix constructed based on the number of variables, with diagonal elements randomly generated with equal probability, and S 34×33 To generate a strictly lower triangular matrix where all elements are 1, F is a 34×33 dimensional identity matrix; The sensitivity index and coupling index of each geometric error are calculated using the improved Morris method, including the following steps: A novel method for constructing the random error matrix ER is presented. First, the range of input parameter values ​​R is modified. E For R E *, vector R E The structure is as follows: （26）； X max Y max Z max A max C max Represent the maximum travel distance of each motion axis and construct a random matrix. The matrix elements are 1 or -1 with equal probability distribution. The random error ER in equation (23) is reconstructed as follows: （27）； The basic effects of the variables are calculated using the reconstructed random error matrix ER, and the sensitivity index and coupling index of each error term are calculated according to Equation (25). Obtaining the form grinding machine tool sensitive geometric error terms that affect gear tooth profile / helix deviation includes the following steps. A sensitivity index greater than the average value is considered a sensitive geometric error, while a coupling index greater than the average value is considered a strong coupling error.

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