Machine tool key geometric error tracing method, device, equipment and medium

Abstract

The invention discloses a machine tool key geometric error tracing method, device and equipment and a storage medium. The method comprises the steps that a kinematic chain of a spiral bevel gear machine tool is acquired; according to the kinematic chain, a coordinate transformation matrix from a grinding wheel coordinate system to a spiral bevel gear coordinate system is obtained; establishing a tooth surface model of the spiral bevel gear according to the profile and the coordinate transformation matrix of the grinding wheel of the spiral bevel gear machine tool; discretizing the tooth surface model, and solving coordinates of tooth surface points; acquiring multiple groups of geometric error parameters of the spiral bevel gear machine tool; executing a tooth surface error calculation strategy on each group of geometric error parameters to obtain a group of tooth surface error form parameters corresponding to each group of geometric error parameters; and based on a Sobol sensitivity analysis method, performing sensitivity analysis by utilizing the multiple groups of geometric error parameters and the corresponding multiple groups of tooth surface error form parameters, and determining key geometric error terms. According to the method, the key geometric error of the spiral bevel gear machine tool can be efficiently traced.

Description

Technical Field

[0001] The present application relates to the field of mechanical manufacturing technology, and in particular to a method, device, equipment and medium for tracing key geometric errors of machine tools. Background Art

[0002] Spiral bevel gears are widely used in modern industry due to their high strength and smooth transmission. Small-module bevel gears, in particular, have enormous potential and promising prospects in the field of electric gear drives. However, their complex tooth surface shapes make high-precision manufacturing difficult. The quality and precision of spiral bevel gears depend on the machine tools used to manufacture them. Spiral bevel gear grinding machines, also known as spiral bevel gear machines, are key equipment for machining spiral bevel gears. Therefore, to improve the machining accuracy of spiral bevel gears, it is essential to analyze and control the error sources of spiral bevel gear machines. Error sources include geometric error, thermal error, force-induced deformation error, vibration error, dynamic and servo error, and others. Of these various error factors, geometric error accounts for approximately 40%, and this percentage is even higher for precision and ultra-precision machine tools, thus giving it a high control priority.

[0003] There are numerous geometric error terms, and considering and compensating for all of them would severely impact compensation efficiency. Therefore, it is necessary to identify key error terms, which are not only related to the machine tool's structure but also to the machining process. Therefore, based on the establishment of a geometric error influence model, it is of great significance to clarify the error propagation mechanism based on this model, quantitatively evaluate the impact of various geometric errors of gear machine tools on machining errors, and trace back to the sensitive terms, namely key geometric errors.

[0004] At present, the existing technology is still relatively lacking in research on spiral bevel gear machine tools. The geometric error structure of spiral bevel gear machine tools is complex and the number of items is large. The tooth surface shape of spiral bevel gears is complex. The key error item analysis method of previous general machine tools is not fully applicable to spiral bevel gear machine tools, and there are problems of calculation difficulty and low efficiency. Summary of the Invention

[0005] The present application aims to propose a method, device, equipment and medium for tracing the key geometric errors of machine tools, which can achieve efficient tracing of the key geometric errors of spiral bevel gear machine tools.

[0006] A method for tracing the source of key geometric errors of machine tools according to an embodiment of the first aspect of the present application includes:

[0007] Obtaining a kinematic chain of the spiral bevel gear machine tool;

[0008] According to the kinematic chain, a coordinate transformation matrix from the grinding wheel coordinate system to the spiral bevel gear coordinate system is obtained;

[0009] Establishing a tooth surface model of the spiral bevel gear according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix;

[0010] Discretizing the tooth surface model and solving the tooth surface point coordinates, wherein one tooth surface point coordinate is the coordinate of a tooth surface point in the spiral bevel gear coordinate system;

[0011] Acquire multiple sets of geometric error parameters of the spiral bevel gear machine tool, each set of the geometric error parameters including K geometric error terms, the specific values ​​of the K geometric error terms in each set of the geometric error parameters being different, wherein the number K of the geometric error terms is determined according to the structure of the spiral bevel gear machine tool;

[0012] Executing a tooth surface error calculation strategy on each set of the geometric error parameters to obtain a set of tooth surface error formal parameters corresponding to each set of the geometric error parameters;

[0013] Based on the Sobol sensitivity analysis method, a sensitivity analysis is performed using multiple groups of the geometric error parameters and corresponding multiple groups of the tooth surface error formal parameters to determine key geometric error terms, wherein the key geometric error terms are one or more of the K geometric error terms;

[0014] The execution of the tooth surface error calculation strategy includes:

[0015] Obtaining an error tooth surface model of the spiral bevel gear according to a set of the geometric error parameters, the coordinate transformation matrix and the tooth surface model;

[0016] Discretizing the error tooth surface model and solving the tooth surface error point coordinates, wherein one tooth surface error point coordinate is the coordinate of a tooth surface error point corresponding to one tooth surface point in the spiral bevel gear coordinate system;

[0017] Obtaining the tooth surface error of each tooth surface point according to the tooth surface point coordinates and the tooth surface error point coordinates corresponding to each tooth surface point;

[0018] A set of tooth surface error formal parameters is obtained according to the tooth surface point coordinates and the tooth surface errors corresponding to each tooth surface point.

[0019] According to some embodiments of the present application, establishing a tooth surface model of the spiral bevel gear according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix includes:

[0020] Establishing a grinding wheel model according to the axial cross-sectional profile of the grinding wheel of the spiral bevel gear machine tool;

[0021] Obtaining a motion grinding wheel model according to the grinding wheel model and the coordinate transformation matrix;

[0022] The tooth surface model is established based on the motion grinding wheel model and the grinding contact conditions, wherein the grinding contact conditions are used to characterize the geometric and kinematic characteristics of the contact area between the grinding wheel and the spiral bevel gear during the grinding process of the spiral bevel gear machine tool.

[0023] According to some embodiments of the present application, obtaining the error tooth surface model of the spiral bevel gear according to a set of the geometric error parameters, the coordinate transformation matrix, and the tooth surface model includes:

[0024] Obtaining an error coordinate transformation matrix according to a set of the geometric error parameters and the coordinate transformation matrix;

[0025] Obtaining an error motion grinding wheel model according to the grinding wheel model and the error coordinate transformation matrix;

[0026] The error tooth surface model is established according to the error motion grinding wheel model and the grinding contact condition.

[0027] According to some embodiments of the present application, discretizing the tooth surface model and solving the tooth surface point coordinates includes:

[0028] Obtaining tooth surface design parameters of the spiral bevel gear;

[0029] A point on the tooth surface of the spiral bevel gear is rotated about the axis and then projected onto a projection plane passing through the rotation axis, to obtain a quadrilateral projection area on the projection plane;

[0030] Discretize the quadrilateral projection area, and evenly select N×M sample points in the quadrilateral projection area;

[0031] Establishing a projection plane coordinate system on the projection plane, and determining the tooth surface point projection coordinates of the tooth surface points corresponding to the four vertices of the quadrilateral projection area according to the tooth surface design parameters, wherein the tooth surface point projection coordinates are the coordinates of the tooth surface points in the projection plane coordinate system;

[0032] Determine the tooth surface point projection coordinates of the tooth surface points corresponding to N×M sample points according to the tooth surface point projection coordinates of the four vertices;

[0033] The tooth surface point coordinates of the tooth surface points corresponding to the N×M sample points are determined according to the tooth surface model, the tooth surface point projection coordinates of the tooth surface points corresponding to the N×M sample points, and a group of association relationship equations; wherein the group of association relationship equations includes a relationship equation for associating the tooth surface point coordinates with the tooth surface point projection coordinates determined based on geometric characteristics.

[0034] According to some embodiments of the present application, obtaining a set of tooth surface error formal parameters according to the tooth surface point coordinates corresponding to each tooth surface point and the tooth surface error includes:

[0035] Based on the general second-order surface equation, the intermediate tooth surface error model is established;

[0036] The coordinate values ​​of the tooth surface point coordinates of the tooth surface points corresponding to the N×M sample points and the tooth surface errors are input into the intermediate tooth surface error formal model to obtain a set of tooth surface error formal parameters.

[0037] According to some embodiments of the present application, the intermediate tooth surface error model is constrained by the following mathematical expression:

[0038]

[0039] Among them, x1, x2, …, x M with y1,y2,…,y N The coordinate values ​​of the tooth surface point coordinates corresponding to the N×M sample points, Z1, Z2, ..., Z N×M represents the tooth surface error corresponding to the N×M sample points, and c1, c2, c3, c4, and c5 are a set of formal parameters of the tooth surface error.

[0040] According to some embodiments of the present application, each group of the tooth surface error formal parameters includes a first tooth surface error formal parameter, a second tooth surface error formal parameter, a third tooth surface error formal parameter, a fourth tooth surface error formal parameter, and a fifth tooth surface error formal parameter;

[0041] The Sobol sensitivity analysis method is based on performing sensitivity analysis using multiple groups of geometric error parameters and corresponding multiple groups of tooth surface error formal parameters to determine key geometric error terms, including:

[0042] Based on the Sobol sensitivity analysis method, sensitivity analysis is performed respectively using multiple groups of the geometric error parameters and multiple first tooth surface error formal parameters, multiple second tooth surface error formal parameters, multiple third tooth surface error formal parameters, multiple fourth tooth surface error formal parameters and multiple fifth tooth surface error formal parameters in the corresponding multiple groups of the tooth surface error formal parameters to determine the key geometric error items corresponding to the first tooth surface error formal parameters, the second tooth surface error formal parameters, the third tooth surface error formal parameters, the fourth tooth surface error formal parameters and the fifth tooth surface error formal parameters, respectively.

[0043] According to the second embodiment of the present application, a device for tracing the source of key geometric errors of machine tools includes:

[0044] A first acquisition module is used to acquire the kinematic chain of the spiral bevel gear machine tool;

[0045] An obtaining module is used to obtain a coordinate transformation matrix from a grinding wheel coordinate system to a spiral bevel gear coordinate system according to the kinematic chain;

[0046] a tooth surface model building module, configured to build a tooth surface model of the spiral bevel gear according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix;

[0047] A tooth surface point coordinate solving module, used for discretizing the tooth surface model and solving the tooth surface point coordinates, wherein one tooth surface point coordinate is the coordinate of a tooth surface point in the spiral bevel gear coordinate system;

[0048] a second acquisition module, configured to acquire multiple sets of geometric error parameters of the spiral bevel gear machine tool, each set of the geometric error parameters including K geometric error terms, the specific values ​​of the K geometric error terms in each set of the geometric error parameters being different, wherein the number K of the geometric error terms is determined according to the structure of the spiral bevel gear machine tool;

[0049] a tooth surface error calculation module, configured to execute a tooth surface error calculation strategy on each set of the geometric error parameters to obtain a set of tooth surface error formal parameters corresponding to each set of the geometric error parameters;

[0050] a key geometric error term determination module, configured to perform sensitivity analysis based on a Sobol sensitivity analysis method using multiple groups of geometric error parameters and corresponding multiple groups of tooth surface error formal parameters to determine key geometric error terms, wherein the key geometric error term is one or more of the K geometric error terms;

[0051] The execution of the tooth surface error calculation strategy includes:

[0052] Obtaining an error tooth surface model of the spiral bevel gear according to a set of the geometric error parameters, the coordinate transformation matrix and the tooth surface model;

[0053] Discretizing the error tooth surface model and solving the tooth surface error point coordinates, wherein one tooth surface error point coordinate is the coordinate of a tooth surface error point corresponding to one tooth surface point in the spiral bevel gear coordinate system;

[0054] Obtaining the tooth surface error of each tooth surface point according to the tooth surface point coordinates and the tooth surface error point coordinates corresponding to each tooth surface point;

[0055] A set of tooth surface error formal parameters is obtained according to the tooth surface point coordinates and the tooth surface errors corresponding to each tooth surface point.

[0056] According to an embodiment of the third aspect of the present application, an electronic device includes a processor and a memory, wherein the memory stores programs or instructions that can be run on the processor, and when the program or instructions are executed by the processor, the steps of the machine tool key geometric error tracing method as described in any one of the embodiments of the second aspect are implemented.

[0057] According to the computer-readable storage medium of the fourth embodiment of the present application, computer-executable instructions are stored, and the computer-executable instructions are used to execute the method for tracing the key geometric errors of machine tools as described in the first embodiment above.

[0058] In the embodiment of the present application, by inputting the geometric error, the corresponding tooth surface error is obtained, and then by calculating the tooth surface error formal parameters, the quantitative representation of the tooth surface error of the spiral bevel gear machine tool is realized. Finally, the sensitivity analysis of the geometric error and the tooth surface error formal parameters is performed. The influence of the geometric error on the processing of spiral bevel gears can be fully simulated, the sensitive items can be accurately traced, the key geometric error items can be determined, and the traceability accuracy can be improved. At the same time, based on the sensitivity analysis of the tooth surface error formal parameters of the spiral bevel gear machine tool, the key geometric errors of the spiral bevel gear machine tool can be efficiently traced and the key geometric error items can be quickly determined.

[0059] Other features and advantages of the present application will be set forth in the following description, and in part will be apparent from the description, or may be learned by practicing the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0061] Figure 1 1 is a flow chart of an embodiment of a method for tracing the source of key geometric errors of machine tools of the present application;

[0062] Figure 2 Schematic diagram of the spiral bevel gear machine tool structure according to an embodiment of the present application;

[0063] Figure 3 Schematic diagram of the kinematic chain of a spiral bevel gear machine tool according to an embodiment of the present application;

[0064] Figure 4 Schematic diagram of position-related geometric errors of the linear axis of the spiral bevel gear machine tool according to an embodiment of the present application;

[0065] Figure 5 Schematic diagram of position-independent geometric error of the linear axis of the spiral bevel gear machine tool according to an embodiment of the present application;

[0066] Figure 6 Schematic diagram of position-related geometric errors of the rotating axis of the spiral bevel gear machine tool according to an embodiment of the present application;

[0067] Figure 7 Schematic diagram of position-independent geometric error of the rotating axis of the spiral bevel gear machine tool according to an embodiment of the present application;

[0068] Figure 8 Schematic diagram of a grinding wheel of a spiral bevel gear machine tool according to an embodiment of the present application;

[0069] Figure 9 2. It is a schematic diagram of the cross-sectional profile of the grinding wheel shaft according to an embodiment of the present application;

[0070] Figure 10 2. It is a schematic diagram of the machine tool adjustment parameter coordinate system according to an embodiment of the present application;

[0071] Figure 11 This is a schematic diagram of the tooth surface axial cross-section projection process of an embodiment of the present application;

[0072] Figure 12 is a schematic diagram of the projection area and discrete tooth surface points within the projection area according to an embodiment of the present application;

[0073] Figure 13 Schematic diagram of five tooth surface error forms in the embodiment of the present application;

[0074] Figure 14 Schematic diagram of the position of the tooth surface error sampling points of the spiral bevel gear in the embodiment of the present application;

[0075] Figure 15 is a schematic diagram of a reference tooth surface based on a tooth surface error analysis coordinate system according to an embodiment of the present application;

[0076] Figure 16 is a schematic diagram of an error tooth surface based on a tooth surface error analysis coordinate system according to an embodiment of the present application;

[0077] Figure 17 It is a schematic diagram of the spiral bevel gear tooth surface obtained by fitting the tooth surface point coordinates in an embodiment of the present application.

[0078] Figure 18 Schematic diagram of the tooth surface error of the spiral bevel gear according to the embodiment of the present application;

[0079] Figure 19 is a histogram of sensitivity coefficients corresponding to the tooth surface error form (a) of the embodiment of the present application;

[0080] Figure 20 is a histogram of sensitivity coefficients corresponding to the tooth surface error form (b) of the embodiment of the present application;

[0081] Figure 21 is a histogram of sensitivity coefficients corresponding to the tooth surface error form (c) of the embodiment of the present application;

[0082] Figure 22 is a histogram of sensitivity coefficients corresponding to the tooth surface error form (d) of the embodiment of the present application;

[0083] Figure 23 is a histogram of sensitivity coefficients corresponding to the tooth surface error form (e) of the embodiment of the present application;

[0084] Figure 24 Schematic diagram of the structure of an embodiment of a key geometric error tracing device for a machine tool according to the present application;

[0085] Figure 25 It is a hardware structure diagram of an embodiment of the electronic device of the present application. DETAILED DESCRIPTION

[0086] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application and are not to be construed as limiting the present application.

[0087] In the description of this application, if there is a description of first, second, etc., it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0088] In the description of this application, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application.

[0089] In the description of this application, it should be noted that, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technical personnel in the relevant technical field can reasonably determine the specific meaning of the above terms in this application based on the specific content of the technical solution.

[0090] The technical solution of the present application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described below are only part of the embodiments of the present application, not all of the embodiments.

[0091] Figure 1 This is a flow chart of an embodiment of the method for tracing the source of key geometric errors of machine tools provided in this application. Figure 1 , further elaborating on the embodiments of this application.

[0092] like Figure 1As shown, the embodiment of the present application proposes a method for tracing the key geometric errors of machine tools, which can be applied to spiral bevel gear machine tools. The method for tracing the key geometric errors of machine tools includes:

[0093] Step 101: Obtain the kinematic chain of the spiral bevel gear machine tool;

[0094] Step 102: Obtain a coordinate transformation matrix from the grinding wheel coordinate system to the spiral bevel gear coordinate system according to the kinematic chain;

[0095] Step 103: Establish a tooth surface model of the spiral bevel gear according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix;

[0096] Step 104: discretize the tooth surface model and solve the tooth surface point coordinates, where a tooth surface point coordinate is the coordinate of a tooth surface point in the spiral bevel gear coordinate system;

[0097] Step 105: Acquire multiple sets of geometric error parameters of the spiral bevel gear machine tool, each set of geometric error parameters including K geometric error terms, and the specific values ​​of the K geometric error terms in each set of geometric error parameters are different, wherein the number K of geometric error terms is determined according to the structure of the spiral bevel gear machine tool;

[0098] Step 106: Execute the tooth surface error calculation strategy for each set of geometric error parameters to obtain a set of tooth surface error formal parameters corresponding to each set of geometric error parameters;

[0099] Step 107: Based on the Sobol sensitivity analysis method, a sensitivity analysis is performed using multiple sets of geometric error parameters and corresponding multiple sets of tooth surface error formal parameters to determine key geometric error terms, where the key geometric error terms are one or more of the K geometric error terms.

[0100] Among them, the tooth surface error calculation strategy is implemented, including:

[0101] According to a set of geometric error parameters, coordinate transformation matrix and tooth surface model, the error tooth surface model of the spiral bevel gear is obtained;

[0102] Discretize the error tooth surface model and solve the tooth surface error point coordinates, where a tooth surface error point coordinate is the coordinate of a tooth surface error point corresponding to a tooth surface point in the spiral bevel gear coordinate system;

[0103] According to the tooth surface point coordinates and tooth surface error point coordinates corresponding to each tooth surface point, the tooth surface error of each tooth surface point is obtained;

[0104] According to the tooth surface point coordinates and tooth surface errors corresponding to each tooth surface point, a set of tooth surface error formal parameters are obtained.

[0105] In the embodiment of the present application, by inputting the geometric error, the corresponding tooth surface error is obtained, and then by calculating the tooth surface error formal parameters, the quantitative representation of the tooth surface error of the spiral bevel gear machine tool is realized. Finally, the sensitivity analysis of the geometric error and the tooth surface error formal parameters is performed. The influence of the geometric error on the processing of spiral bevel gears can be fully simulated, the sensitive items can be accurately traced, the key geometric error items can be determined, and the traceability accuracy can be improved. At the same time, based on the sensitivity analysis of the tooth surface error formal parameters of the spiral bevel gear machine tool, the key geometric errors of the spiral bevel gear machine tool can be efficiently traced and the key geometric error items can be quickly determined.

[0106] The spiral bevel gear may be a spiral bevel gear or a hypoid gear.

[0107] The above is applied to spiral bevel gear machine tools, which can be six-axis five-link spiral bevel gear machine tools, such as Figure 2 As shown in the figure, it consists of three linear axes X-axis, Y-axis, and Z-axis and three rotation axes A-axis, B-axis, and C-axis. The C-axis is a high-precision spindle and its geometric error can be ignored.

[0108] The kinematic chain of the machine tool mentioned above refers to the motion transmission path formed by the mechanical connection and transmission relationship between the various moving parts of the machine tool, which reflects the relative motion relationship and motion transmission method between the various moving parts of the machine tool. Figure 2 The kinematic chain of the six-axis five-link spiral bevel gear machine tool is shown as Figure 3 shown.

[0109] The coordinate transformation matrix described above is determined based on the kinematic chain and can represent the posture transformation relationship between different coordinate systems. The coordinate transformation matrix can be derived from multiple adjacent coordinate transformation matrices through matrix multiplication. It should be noted that the coordinate transformation matrix represents an idealized state and does not take into account the effects of geometric errors.

[0110] For example, Figure 2 The six-axis five-link spiral bevel gear machine shown is based on Figure 3 The kinematic chain shown can be used to obtain the coordinate transformation matrix from the grinding wheel coordinate system to the spiral bevel gear coordinate system when the gear grinding machine tool works without error, as shown in the following formula:

[0111]

[0112] Among them, the adjacent coordinate transformation matrix M ij (u) can represent the posture transformation relationship between the coordinate systems of adjacent coordinate axes, where the subscripts i and j represent the ending coordinate system and the starting coordinate system, respectively, and u represents the motion of each axis. For details, see Table 1 below. In Table 1, X, Y, Z, a, and b are the motions of each axis.

[0113]

[0114] Table 1

[0115] In spiral bevel gear machines, each axis exhibits geometric errors due to installation deviations and manufacturing defects. Geometric errors include position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs). PDGEs vary with position, while PIGEs do not.

[0116] Generally speaking, for linear axes, refer to Figure 4 and Figure 5 Each linear axis has 6 PDGEs, including 3 translation errors (TE) and 3 rotation errors (RE) for each motion axis. In addition, there is 1 PIGE between every two linear axes. For the rotation axis, refer to Figure 6 and Figure 7 As shown in Figure 3, each rotation axis has 6 PDGEs, including 3 translation errors (TE) and 3 rotation errors (RE). In addition, each rotation axis has 4 PIGEs.

[0117] Specifically, a six-axis, five-axis spiral bevel gear machine tool has three linear axes (X, Y, and Z) and two rotary axes (A and B). The three linear axes (X, Y, and Z) have a total of 18 PDGEs and 3 PIGEs, for a total of 21 geometric error terms. The two rotary axes (A and B) have a total of 12 PDGEs and 8 PIGEs, for a total of 20 geometric error terms. In summary, the six-axis, five-axis spiral bevel gear machine tool has a total of 41 geometric error terms, as defined in Tables 1 through 3. Table 1 lists the PDGEs and their numbers for the machine tool, while Tables 2 and 3 list the PIGEs and their numbers for the machine tool.

[0118] For details, see Table 2 below. Figure 4 As shown, there are 6 PDGEs for the linear axis Y axis, and 3 TEs including the positioning error δ y (y), straightness error δ x (y) and δ z (y), the three REs include the pitch angle error ε x (y), roll angle error ε y (y) and the yaw angle error ε z (y), the same is true for the PDGEs of other linear axes, i.e., the X-axis and the Z-axis; Figure 6As shown, there are 6 PDGEs of the rotation axis A, and 3 TEs including axial deviation δ z (a) Radial deviation δ x (a) and δ y (a), the three REs include the positioning error ε z (a) Angular deviation ε x (a) and ε y (a), The same is true for the PDGEs of the other rotation axis, i.e., the B axis.

[0119]

[0120] Table 2

[0121] For details, see Table 3 and Table 4 below. Figure 5 As shown, there is one PIGEs between every two linear axes. For the three linear axes X, Y, and Z, there are three PIGEs, including the perpendicularity S between the X and Y axes. xy , the verticality S between the Y axis and the Z axis yz And the perpendicularity S between X-axis and Z-axis xz ;like Figure 7 As shown, there are four PIGEs of the rotation axis A, including the positioning error δ Ay and δ Az , azimuth error γ AY and β AZ The same applies to the PIGEs of other rotation axes, namely the B-axis.

[0122]

[0123]

[0124] Table 3

[0125] PIGEs serial number <![CDATA[S xy 、S yz 、S xz ]]> 31～33 <![CDATA[δ Ay 、d Az 、c AY 、b AZ ]]> 34～37 <![CDATA[δ Bx 、d Bz 、c BX ,a BZ ]]> 38～41

[0126] Table 4

[0127] It should be noted that if Figure 2 The six-axis five-link spiral bevel gear grinding machine shown has three linear axes X, Y, and Z and three rotation axes A, B, and C. However, the C-axis is a high-precision spindle and its geometric error can be ignored. Therefore, its geometric error is still the same as the 41 geometric error items in Tables 2 to 4 above.

[0128] Each of the above-mentioned sets of geometric error parameters includes K geometric error terms, and the number K of geometric error terms is determined according to the structure of the spiral bevel gear machine tool. Specifically, when the machine tool is a six-axis five-linkage spiral bevel gear machine tool, the number K can be 41, that is, each set of geometric error parameters includes 41 geometric error terms.

[0129] In some embodiments, a tooth surface model of a spiral bevel gear is established based on the profile of a grinding wheel of a spiral bevel gear machine tool and a coordinate transformation matrix, including:

[0130] According to the axial cross-section profile of the grinding wheel of the spiral bevel gear machine tool, a grinding wheel model is established;

[0131] According to the grinding wheel model and coordinate transformation matrix, the motion grinding wheel model is obtained;

[0132] The tooth surface model is established based on the motion grinding wheel model and the grinding contact conditions. The grinding contact conditions are used to characterize the geometric and kinematic characteristics of the contact area between the grinding wheel and the spiral bevel gear during the grinding process of the spiral bevel gear machine tool.

[0133] In this embodiment, based on the principle that the envelope surface of the surface family generated by the grinding wheel motion is the tooth surface, the axial cross-sectional profile of the grinding wheel of the spiral bevel gear machine tool, the coordinate transformation matrix and the grinding contact conditions are comprehensively considered, and the geometric shape conditions of the grinding wheel, the grinding wheel motion conditions and the conditions that need to be met during the grinding contact between the grinding wheel and the spiral bevel gear are constructed to construct the envelope surface of the surface family generated by the grinding wheel motion and establish the tooth surface model of the spiral bevel gear.

[0134] The grinding wheel model is established according to the axial cross-sectional profile of the grinding wheel of the spiral bevel gear machine tool.

[0135] Specifically, the grinding wheel of the spiral bevel gear machine tool is as follows Figure 8 As shown, the axial cross-section profile of the spiral bevel gear grinding wheel is as follows Figure 9 As shown, it consists of 3 straight lines (AB, CD, EF) and 2 arcs (BC, DE). Figure 9 Where θ is the phase angle of the point on the grinding wheel, n o is the normal vector of the concave surface of the grinding wheel, n i is the normal vector of the convex surface of the grinding wheel, h is the projection height of the point on the grinding wheel on the grinding wheel axis, ρ(h) is the position vector length of the point on the grinding wheel, R u is the nominal radius of the grinding wheel, P w is the point width of the grinding wheel, r f is the transition fillet radius of the grinding wheel, and α is the pressure angle of the grinding wheel.

[0136] The intersection of the end face of the grinding wheel and the rotation axis is taken as the origin, and the direction of the rotation axis is the z-axis to establish a rectangular coordinate system S t ,like Figure 8 and Figure 9 As shown in the figure, the sand profile is mainly composed of straight line AB, arc BC, straight line CD, arc DE, and straight line EF. The AB and BC segments are used to process the convex surface of the bevel gear, and the DE and EF segments are used to process the concave surface of the bevel gear. t The grinding wheel model is established in the coordinate system and is constrained by the following expressions:

[0137] r t (h,θ)=h·l+ρ(h)·n;(2)

[0138] Among them, r t (h,θ) is the position vector of the grinding wheel profile, h is the projection height of the point on the grinding wheel axis, ρ(h) is the position vector length of the point on the grinding wheel, n is the normal vector, and l is S t Unit vector along the positive direction of the z-axis in the coordinate system: l = (0 0 1) T .

[0139] The straight line segment EF used to machine the concave surface of the bevel gear is constrained by the following expression:

[0140]

[0141] The straight line segment AB used to machine the convex surface of the bevel gear is constrained by the following expression:

[0142]

[0143]

[0144] Among them, R u is the nominal radius of the grinding wheel, P w is the point width of the grinding wheel, r f is the transition fillet radius of the grinding wheel, and α is the pressure angle of the grinding wheel.

[0145] During the processing of spiral bevel gears, the machine tool adjusts the parameter coordinate system as follows Figure 10 As shown. Among them, the coordinate system S t is the grinding wheel coordinate system, which is fixed to the grinding wheel. The coordinate system S w is the spiral bevel gear coordinate system, which is fixed to the processed gear, S R is the radial tool position, q is the angular tool position, E m For vertical wheel position, X B For beds, X D is the horizontal wheel position, γ m For the installation angle, is the wheel blank angle, is the cradle angle. When processing spiral bevel gears on a machine tool, the wheel blank angle and the cradle angle are limited by the following expression:

[0146]

[0147] Where r is the roll ratio, C is the second-order roll ratio correction coefficient, and D is the third-order roll ratio correction coefficient.

[0148] Then, in the machine tool adjustment parameter coordinate system, from the grinding wheel coordinate system S tTo the spiral bevel gear coordinate system S w The coordinate transformation matrix can be expressed as:

[0149]

[0150] in:

[0151]

[0152] Based on the grinding wheel model and coordinate transformation matrix, the motion grinding wheel model is obtained. The motion grinding wheel model is restricted by the following expression:

[0153]

[0154] in, is the coordinate transformation matrix, r t (h,θ) is the position vector of the sand contour, is the origin of the grinding wheel coordinate system in motion, is the unit vector of the grinding wheel coordinate system along the positive direction of the z-axis, h is the projection height of the point on the grinding wheel on the grinding wheel axis, ρ(h) is the position vector length of the point on the grinding wheel..., is the normal vector of a point on the moving grinding wheel.

[0155] The grinding contact condition can be that during the grinding process, the normal vector of the point on the grinding wheel contact line is perpendicular to the velocity vector. This relationship ensures that the grinding wheel can properly contact the workpiece during the machining process, thereby achieving the desired machining effect. Specifically, the grinding contact condition is limited by the following expression:

[0156]

[0157] The tooth surface model is established based on the moving grinding wheel model and grinding contact conditions.

[0158] Specifically, according to formula (9), the speed of each point on the grinding wheel can be expressed as:

[0159]

[0160] Substituting formula (11) into formula (10), we have:

[0161]

[0162] because represents the normal vector of a point, Indicates the instantaneous change of the normal vector, and its direction must be perpendicular to Therefore is 0, so:

[0163]

[0164] The point at height h on the grinding wheel axis can be represented as:

[0165]

[0166] According to formula (14), the velocity of the point at height h on the grinding wheel axis can be expressed as:

[0167]

[0168] Considering formula (15) and formula (13) comprehensively, we have:

[0169]

[0170] Substituting equation (16) into equation (9), we can obtain the tooth surface equation:

[0171]

[0172] Among them, o and l are in the grinding wheel coordinate system S t The following is expressed as:

[0173] o t =[0 0 0 1] T ,l t =[0 0 1 0] T ; (18)

[0174] Considering the homogeneous coordinate transformation, o and l are in the spiral bevel gear coordinate system S w The following is expressed as:

[0175] o w (φ)=M tw (φ)·o t =[M 14 M 24 M 34 ] T ; (19)

[0176] l w (φ)=M tw (φ)·l t =[M 13 M 23 M 33 ] T ; (20)

[0177] So we have:

[0178]

[0179] in:

[0180]

[0181] The above tooth surface model is constrained by the tooth surface equation (17). By solving equation (17), the tooth surface points on the tooth surface can be obtained.

[0182] It should be noted that in the above steps, from the grinding wheel coordinate system S t To the spiral bevel gear coordinate system S w The coordinate transformation matrix adopts the representation shown in the above formula (8) in the machine tool adjustment parameter coordinate system. In fact, this is equivalent to the coordinate transformation matrix shown in formula (1), but there is a difference in the representation. The representation of the coordinate transformation matrix shown in formula (1) is convenient for embedding geometric error parameters, while the representation shown in formula (8) is convenient for calculation. The two forms can be converted into each other.

[0183] In some embodiments, an error tooth surface model of a spiral bevel gear is obtained according to a set of geometric error parameters, a coordinate transformation matrix, and a tooth surface model, including:

[0184] According to a set of geometric error parameters and a coordinate transformation matrix, an error coordinate transformation matrix is ​​obtained;

[0185] According to the grinding wheel model and the error coordinate transformation matrix, the error motion grinding wheel model is obtained;

[0186] According to the error motion grinding wheel model and grinding contact conditions, the error tooth surface model is established.

[0187] In this embodiment, a corresponding error coordinate transformation matrix can be obtained based on a set of geometric error parameters and a coordinate transformation matrix. The error coordinate transformation matrix is ​​used to replace the coordinate transformation matrix for modeling to obtain an error tooth surface model.

[0188] According to a set of geometric error parameters and a coordinate transformation matrix, an error coordinate transformation matrix is ​​obtained.

[0189] Specifically, based on Figure 3 The kinematic chain shown in Tables 1 to 3 and the 41 geometric error items shown in Tables 1 to 3 can be used to obtain the adjacent coordinate transformation matrix M ij (N) corresponds to the position-independent error matrix and position-dependent error matrix It reflects the error impact of PIGE and PDGE in the geometric error on the motion process of the machine tool, as shown in Table 5 below.

[0190]

[0191]

[0192] Table 5

[0193] Therefore, according to formula (1), Table 1 and Table 5, after considering the geometric error, the grinding wheel coordinate system S t To the spiral bevel gear coordinate system S w The error coordinate transformation matrix can be expressed as:

[0194]

[0195] Among them, x, y, z, a, b are the displacements of each axis, and the vector E=[e1,e2,…,e 41 ] T Indicates 41 geometric errors.

[0196] It should be noted that in the above steps, from the grinding wheel coordinate system S t To the spiral bevel gear coordinate system S w The coordinate transformation matrix adopts the representation shown in the above formula (8) in the machine tool adjustment parameter coordinate system. In fact, this is equivalent to the coordinate transformation matrix shown in formula (1), but there is a difference in the representation. The representation of the coordinate transformation matrix shown in formula (1) is convenient for embedding geometric error parameters, while the representation shown in formula (8) is convenient for calculation.

[0197] Therefore, in the actual implementation process, the coordinate transformation matrix of the form shown in formula (8) is often calculated based on the design parameters. Then perform the form conversion and re-express it in the form shown in formula (1) to obtain On this basis, the geometric error parameters are embedded to obtain the error coordinate transformation matrix Then convert it into the error coordinate transformation matrix represented as shown in formula (8): Finally, substitute it into the calculation. Where, the superscript i represents the ideal coordinate transformation matrix without considering the geometric error, and the superscript a represents the actual coordinate transformation matrix, that is, the coordinate transformation matrix with considering the geometric error.

[0198] The above process of establishing the error tooth surface model is different from the process of establishing the tooth surface model in the previous article. The only difference is that the coordinate transformation matrix is ​​replaced by the error coordinate transformation matrix. The other steps are the same.

[0199] Specifically, the error motion grinding wheel model is obtained based on the grinding wheel model and the error coordinate transformation matrix. Referring to formula (9), the error motion grinding wheel model is restricted by the following expression:

[0200]

[0201] Referring to formula (16), we can obtain the following equation when the geometric error is taken into account:

[0202]

[0203] The error tooth surface model can be obtained, which is restricted by the following expression:

[0204]

[0205] Therefore, the process of establishing the error tooth surface model is completed.

[0206] In some embodiments, as Figure 11 and Figure 12 As shown, the tooth surface model is discretized and the tooth surface point coordinates are solved, including:

[0207] Obtain the tooth surface design parameters of the spiral bevel gear;

[0208] The points on the tooth surface of the spiral bevel gear are rotated around the axis and projected onto a projection plane passing through the axis of rotation, and a quadrilateral projection area is obtained on the projection plane;

[0209] Discretize the quadrilateral projection area and evenly select N×M sample points in the quadrilateral projection area;

[0210] Establish a projection plane coordinate system on the projection plane, and determine the tooth surface point projection coordinates of the tooth surface points corresponding to the four vertices of the quadrilateral projection area according to the tooth surface design parameters, wherein the tooth surface point projection coordinates are the coordinates of the tooth surface points in the projection plane coordinate system;

[0211] According to the tooth surface point projection coordinates of the four vertices corresponding to the tooth surface points, determine the tooth surface point projection coordinates of the N×M sample points corresponding to the tooth surface points;

[0212] The tooth surface point coordinates of the tooth surface points corresponding to the N×M sample points are determined according to the tooth surface model, the tooth surface point projection coordinates of the tooth surface points corresponding to the N×M sample points, and a group of association relationship equations; wherein the group of association relationship equations includes a relationship equation for associating the tooth surface point coordinates determined based on geometric characteristics with the tooth surface point projection coordinates.

[0213] In this embodiment, the tooth surface of the spiral bevel gear represented by the tooth surface equation (17) is relatively complex and has no explicit solution. In order to conveniently obtain the tooth surface, it is necessary to discretize the tooth surface to obtain discrete tooth surface points. The tooth surface points can then be solved to obtain the tooth surface point coordinates of each tooth surface point, thereby reducing the difficulty of solving the problem.

[0214] The tooth surface design parameters of the spiral bevel gear may include the root cone angle, pitch cone angle, face cone angle, pitch circle radius and face width of the spiral bevel gear.

[0215] The above points on the spiral bevel gear tooth surface are rotated around the axis and projected onto the projection plane passing through the rotation axis, and a quadrilateral projection area is obtained on the projection plane. Figure 11 Project as shown, and get Figure 12As shown in the schematic diagram of the projection area, the above-mentioned quadrilateral projection area is the quadrilateral area composed of points A, B, C, and D.

[0216] The above discretization of the quadrilateral projection area, uniformly taking N × M sample points in the quadrilateral projection area, can be, uniformly taking N × M sample points in the polygon composed of points A, B, C, and D, R ij and Z ij Represents the coordinates of each sample point, i and j represent the index numbers of the sample point in the tooth height and tooth width directions respectively, where i = 1, 2, ..., N; j = 1, 2, ...M.

[0217] The above-mentioned projection plane coordinate system is established on the projection plane, such as Figure 12 As shown, the projection plane coordinate system takes the axis of the spiral bevel gear as the longitudinal axis Z-axis, the origin of the spiral bevel gear design coordinate system as the origin, and the straight line passing through the origin and perpendicular to the Z-axis as the horizontal axis R-axis.

[0218] According to the tooth surface design parameters, the tooth surface point projection coordinates of the four vertices of the quadrilateral projection area corresponding to the tooth surface points are determined. Specifically, for points A, B, C, and D, their coordinates are as follows:

[0219]

[0220] Among them, δ f is the root cone angle, δ0 is the pitch cone angle, δ a is the cone angle, R a is the pitch circle radius, b is the face width. When the tooth surface design parameter δ of the spiral bevel gear f ,δ0,δ a 、R a After a and b are determined, the points on the gear tooth surface are rotated around the axis and projected onto the plane passing through the axis of rotation. The range of the tooth surface point projection is limited to the polygonal area formed by points A, B, C, and D.

[0221] The tooth surface point projection coordinates of the tooth surface points corresponding to the four vertices are determined based on the tooth surface point projection coordinates of the N×M sample points, which are restricted by the following expression:

[0222]

[0223] Among them, R ij and Z ij Represents the coordinates of each sample point, i and j represent the index numbers of the sample point in the tooth height and tooth width directions, respectively, where i = 1, 2, ..., N; j = 1, 2, ...M. Therefore, the coordinates of any discrete point on the tooth surface axial section can be expressed based on the coordinates of points A, B, C, and D.

[0224] According to the relationship between the spiral bevel gear coordinate system and the projection plane coordinate system, the three-dimensional coordinates (x ij ,y ij ,z ij ) and the two-dimensional coordinates of the tooth surface point in the projection plane coordinate system (R ij ,Z ij ) satisfy a certain relationship, namely the above-mentioned association relationship group, which can be expressed as follows:

[0225]

[0226] Then, the tooth surface model can be solved by combining equations (17) and (30) to obtain the tooth surface point coordinate r based on the spiral bevel gear coordinate system:

[0227]

[0228] in,

[0229] For the error tooth surface model with the geometric error substituted, the error tooth surface model can be solved by the simultaneous equation (31) to obtain the tooth surface error point coordinates based on the spiral bevel gear coordinate system:

[0230]

[0231] in,

[0232] In some embodiments, the tooth surface error of each tooth surface point is obtained based on the tooth surface point coordinates and the tooth surface error point coordinates corresponding to each tooth surface point, which is limited by the following expression:

[0233] Z=(r a -r)·n; (35)

[0234] Among them, Z is the tooth surface error of each point. By comparing the theoretical tooth surface point without considering the geometric error with the tooth surface error point considering the geometric error, the tooth surface error of each point can be obtained.

[0235] In some embodiments, a set of tooth surface error formal parameters is obtained based on the tooth surface point coordinates and tooth surface errors corresponding to each tooth surface point, including:

[0236] Based on the general second-order surface equation, the intermediate tooth surface error model is established;

[0237] The coordinate values ​​of the tooth surface point coordinates corresponding to the tooth surface points of N×M sample points and the tooth surface errors are input into the intermediate tooth surface error formal model to obtain a set of tooth surface error formal parameters.

[0238] In this embodiment, in order to further analyze the influence of geometric errors on the tooth surface, it is also necessary to fit the tooth surface errors. By establishing an intermediate tooth surface error form model, a set of tooth surface error form parameters are obtained according to the tooth surface errors of N×M tooth surface points. Since the tooth surface error form of N×M tooth surface points is relatively complicated, this step can convert the complicated tooth surface errors into a set of simple tooth surface error form parameters, which is convenient for subsequent sensitivity analysis and calculation, improves calculation efficiency, and realizes efficient tracing of key geometric errors of spiral bevel gear machine tools.

[0239] The general second-order surface equation above is:

[0240] Z=c1X+c2Y+c3X 2 +c4Y 2 +c5XY; (36)

[0241] Among them, the first-order coefficients c1 and c2 are the characterizations of the slopes of the difference surface along the X-axis and the Y-axis respectively, c1 is the inclination along the tooth length direction, and c2 is the inclination along the tooth height direction; the second-order coefficients c3, c4, and c5 are the expressions of the curvature of the error surface, c3 is the tooth profile change in the tooth length direction, c4 is the tooth profile crown change, and c5 is the tooth surface distortion influence coefficient. The above set of tooth surface error form parameters includes five parameters, namely c1, c2, c3, c4, and c5. Each parameter corresponds to a tooth surface error form. There are five tooth surface error forms in total, such as Figure 13 As shown, the tooth surface error form (a) is tilted along the tooth length direction, represented by c1, the tooth surface error form (b) is tilted along the tooth height direction, represented by c2, the tooth surface error form (c) is the change of tooth shape along the tooth length direction, represented by c3, the tooth surface error form (d) is the change of tooth profile drum shape, represented by c4, and the tooth surface error form (e) is the distortion of the tooth surface, represented by c5.

[0242] It should be noted that the five tooth surface error forms are all the tooth surface error forms of spiral bevel gear tooth surfaces. Spur gears and the like do not have these five tooth surface error forms. Therefore, the error conditions of the helical gear tooth surfaces can be accurately characterized by corresponding five tooth surface error form parameters. At the same time, compared with the tooth surface error data of N×M tooth surface points, a set of five tooth surface error form parameters greatly simplifies the representation of the error conditions, which is convenient for improving subsequent calculation efficiency.

[0243] In some embodiments, the intermediate tooth surface error form model is constrained by the following mathematical expression:

[0244]

[0245] Among them, x1, x2, …, x M with y1,y2,…,y nIndicates the coordinate values ​​of the tooth surface points corresponding to the N×M sample points, Z1, Z2,…, Z N×M It represents the tooth surface error corresponding to N×M sample points, and c1, c2, c3, c4, and c5 are a set of tooth surface error formal parameters.

[0246] In this embodiment, based on the intermediate tooth surface error formal model, the coordinate values ​​of the tooth surface point coordinates and the tooth surface errors of the N×M sample points corresponding to the tooth surface points can be substituted to obtain a set of tooth surface error formal parameters, which characterize the error conditions of the N×M tooth surface points.

[0247] Formula (37) can be simplified as:

[0248] {Z}=[S]·{c};(38)

[0249] Formula (38) is a statically indeterminate linear equation system, and its least squares solution can be calculated, that is,

[0250] {c}=([S] T [S]) -1 [S] T {Z}; (39)

[0251] The tooth surface error formal parameters can be solved.

[0252] In some embodiments, N×M points are selected as 9×5 points during the discretization of the tooth surface model, that is, 45 points are selected on the tooth surface to calculate the tooth surface error, such as Figure 14 As shown in the figure, each point on the grid is the point for calculating the tooth surface error, with a total of 5 rows and 9 columns.

[0253] In order to further analyze the influence of geometric error on tooth surface, it is also necessary to fit the tooth surface error. Therefore, for the 5×9 grid difference surface, the center point M of the tooth surface is selected as the reference point, the tooth length direction is taken as the X axis, the tooth height direction is taken as the Y axis, and the tooth surface error Z is the tooth surface error analysis coordinate system of the Z axis, as shown in the following figure: Figure 15 and Figure 16 As shown, Figure 15 Where is the reference tooth surface without tooth surface error solved in the case of no geometric error, Figure 16 It includes the error tooth surface containing tooth surface error and the reference tooth surface solved after considering the geometric error.

[0254] In this embodiment, the intermediate tooth surface error model is constrained by the following mathematical expression:

[0255]

[0256] Among them, [X1, X2, X3, X4, X5, X6, X7, X8, 9×5 It represents the tooth surface error corresponding to 9×5 sample points, and c1, c2, c3, c4, and c5 are a set of tooth surface error formal parameters.

[0257] It should be noted that, since the discrete sample points are already equally spaced on the tooth surface when they are selected, substituting the x and y coordinate values ​​of the tooth surface point coordinates of the sample points corresponding to the tooth surface points into the intermediate tooth surface error formal model, or directly assigning the values ​​into the intermediate tooth surface error formal model, actually has little effect on the tracing results of the key geometric errors. Therefore, the values ​​can be directly assigned into the intermediate tooth surface error formal model to simplify the calculation.

[0258] In some embodiments, each set of tooth surface error formal parameters includes a first tooth surface error formal parameter, a second tooth surface error formal parameter, a third tooth surface error formal parameter, a fourth tooth surface error formal parameter, and a fifth tooth surface error formal parameter;

[0259] Based on the Sobol sensitivity analysis method, multiple sets of geometric error parameters and corresponding multiple sets of tooth surface error formal parameters are used to perform sensitivity analysis to determine the key geometric error terms, including:

[0260] Based on the Sobol sensitivity analysis method, sensitivity analysis is performed using multiple groups of geometric error parameters and multiple first tooth surface error formal parameters, multiple second tooth surface error formal parameters, multiple third tooth surface error formal parameters, multiple fourth tooth surface error formal parameters and multiple fifth tooth surface error formal parameters in the corresponding multiple groups of tooth surface error formal parameters to determine the key geometric error terms corresponding to the first tooth surface error formal parameters, the second tooth surface error formal parameters, the third tooth surface error formal parameters, the fourth tooth surface error formal parameters and the fifth tooth surface error formal parameters, respectively.

[0261] In this embodiment, the Sobol sensitivity analysis method can be used to analyze the key geometric error terms corresponding to the first tooth surface error formal parameter, the second tooth surface error formal parameter, the third tooth surface error formal parameter, the fourth tooth surface error formal parameter and the fifth tooth surface error formal parameter. If the tooth surface error form corresponding to a certain tooth surface error formal parameter is more prominent, the key geometric error term corresponding to this tooth surface error formal parameter can be separately focused on and controlled, so as to facilitate the precise compensation and reduction of the geometric error terms in the actual processing process.

[0262] Each group of tooth surface error formal parameters c includes a first tooth surface error formal parameter c1, a second tooth surface error formal parameter c2, a third tooth surface error formal parameter c3, a fourth tooth surface error formal parameter c4 and a fifth tooth surface error formal parameter c5, and each parameter corresponds to a tooth surface error form.

[0263] Combine Figure 13 There are five tooth surface error forms in the tooth surface error form. The tooth surface error form (a) is tilted along the tooth length direction, which is characterized by the first tooth surface error form parameter c1. The tooth surface error form (b) is tilted along the tooth height direction, which is characterized by the second tooth surface error form parameter c2. The tooth surface error form (c) is the change of tooth profile along the tooth length direction, which is characterized by the third tooth surface error form parameter c3. The tooth surface error form (d) is the change of tooth profile crown, which is characterized by the fourth tooth surface error form parameter c4. The tooth surface error form (e) is the tooth surface distortion, which is characterized by the fifth tooth surface error form parameter c5.

[0264] Sensitivity analysis is a method used to identify and quantify the relationship between input and output uncertainties. The Sobol sensitivity analysis method is a typical variance-based global sensitivity analysis method that decomposes the variance fluctuation of the system output into the contribution ratios of each input term. This method can analyze complex problems such as nonlinearity and can determine the coupling effects of different parameters across the entire domain.

[0265] Assume that the relationship between the geometric error E and the tooth surface error c can be expressed as:

[0266] c=f(E); (41)

[0267] Where, c=[c1,c2,c3,c4,c6], E=[e1,e2,...,e 41 ],e1,e2,...,e 41 There are 41 geometric errors.

[0268] According to the Sobol method, the function f(E) is decomposed into formula (41):

[0269]

[0270] Where: f0 is a constant, f i is the tooth surface error value calculated by the i-th geometric error term, f ij is the coupling effect of the i-th geometric error term and the j-th geometric error term. By analogy, the function value under the combined effect of all geometric error terms will be obtained. The integral of each sub-term with respect to any variable it contains is equal to 0, then:

[0271]

[0272] Among them, s is the number of variables contained in a sub-item.

[0273] Combining equations (42) and (43), we can see that each decomposition sub-item is unique and each sub-item is orthogonal to each other, so we can get:

[0274]

[0275] Among them, e ～i is all error terms except the i-th geometric error term, e ～ij are all error terms except the i-th and j-th geometric error terms. Square and integrate the left and right sides of equation (44) in the entire spatial domain to obtain:

[0276]

[0277] Then the total variance of the function c=f(E) is:

[0278]

[0279] The remaining partial variances are:

[0280]

[0281] The total variance can be expressed as:

[0282] D=D i +∑ j＞i D ij +…+D 1,2,…,n ; (48)

[0283] From equations (46) and (48), we can see that the ratio of the partial variance to the total variance of the function c = f(E) is the sensitivity of each input geometric error, so the global sensitivity is It can be expressed as:

[0284]

[0285] At the same time, according to formula (49), the sum of the sensitivities of all input geometric errors is equal to 1:

[0286]

[0287] Combining equations (47) to (50), we can see that the input geometric error sensitivity coefficient can be expressed as:

[0288]

[0289] Where: S i It represents the first-order sensitivity of the i-th input geometric error, and its value represents the influence weight on the objective function; S ijIt represents the influence of the i-th and j-th input geometric errors on the objective function under the coupling effect. By analogy, the high-order sensitivity coefficient can be obtained. Ti Represents x i The first-order sensitivity coefficient S i With all x i The sum of coupled high-order sensitivity coefficients.

[0290] Based on the above analysis, in practice, the Monte Carlo estimation method can be used to conveniently calculate various sensitivity indices.

[0291] The first step is to determine the number of geometric error terms and the value range corresponding to each geometric error term.

[0292] In the second step, according to the number of geometric error terms and the value range of each geometric error term, two N S ×n S The sample matrices are sample matrix P and sample matrix H, N S is the total number of samples, which is usually greater than 1000. S is the number of input parameters, n S Take the number of geometric error terms, here we take 41, as shown below:

[0293]

[0294] Among them, the first row (e p1,1 ,e p1,2 ,...,e p1,41 ) is a set of geometric error parameters, including 41 geometric error items, and each geometric error item is randomly selected within a certain corresponding value range. Similarly, the sample matrix P has a total of N S Lines, including N S A set of geometric error parameters, each set of geometric error parameters includes 41 geometric error items, and each geometric error item is randomly selected within a determined corresponding value range;

[0295]

[0296] Among them, the first row (e h1,1 ,e h1,2 ,...,e h1,41 ) is a set of geometric error parameters, including 41 geometric error items, and each geometric error item is randomly selected within a certain corresponding value range. Similarly, the sample matrix H has a total of N S Lines, including N S A set of geometric error parameters is provided, each set of geometric error parameters includes 41 geometric error items, and each geometric error item is randomly selected within a determined corresponding value range.

[0297] It should be noted that the above steps of randomly generating two sample matrices are the above-mentioned process of obtaining multiple sets of geometric error parameters of the spiral bevel gear machine tool.

[0298] The third step is to construct according to the sample matrix P and sample matrix H The construction principle of the matrix is ​​to replace the i-th column element in the H matrix with the i-th column element in the P matrix. Only the i-th input parameter is different from P, as shown below:

[0299]

[0300] The fourth step is to calculate the total number of samples N. S , P matrix, H matrix and Matrix, substitute it into the Monte Carlo estimation formula to calculate the sensitivity. Specifically, the Monte Carlo estimation formula is:

[0301]

[0302] Where f(P) n represents the tooth surface error formal parameter calculated based on a set of geometric error parameters in the nth row of the P matrix, f(H) n represents the tooth surface error formal parameters calculated based on a set of geometric error parameters in the nth row of the H matrix, Indicates based on The tooth surface error formal parameters are calculated from a set of geometric error parameters in the nth row of the matrix.

[0303] It should be noted that the above f(P) n 、f(H) n 、 The specific values ​​of are obtained according to the above steps of executing the tooth surface error calculation strategy for each set of geometric error parameters to obtain a set of tooth surface error formal parameters corresponding to each set of geometric error parameters.

[0304] From formula (51), we know that the sensitivity coefficient estimation formula is:

[0305]

[0306] in, is the Monte Carlo estimate of the first-order sensitivity coefficient, Estimate the population sensitivity coefficient for Monte Carlo.

[0307] It should be noted that, since the tooth surface error formal parameter c includes the first tooth surface error formal parameter c1, the second tooth surface error formal parameter c2, the third tooth surface error formal parameter c3, the fourth tooth surface error formal parameter c4 and the fifth tooth surface error formal parameter c5, sensitivity analysis can be performed on a certain tooth surface error formal parameter separately.

[0308] For example, the first tooth surface error parameter c1 represents the inclination of the tooth surface along the tooth length direction. When it is necessary to analyze the key sensitive item of the geometric error of the tooth surface error form (a) along the tooth length direction, it is necessary to perform a sensitivity analysis on the first tooth surface error parameter c1 separately. Specifically, in formula (53), f(P) n Substitute the first tooth surface error formal parameter c1 calculated based on a set of geometric error parameters in the nth row of the P matrix, f(H) n Substitute the first tooth surface error formal parameter c1 calculated based on a set of geometric error parameters in the nth row of the H matrix, Use according to The first tooth surface error formal parameter c1 calculated from a set of geometric error parameters in the nth row of the matrix is ​​substituted into the matrix, and the sensitivity coefficient finally calculated is the first tooth surface error formal parameter c1, that is, the sensitivity coefficient corresponding to the tooth surface error form (a).

[0309] In some implementations, a method for tracing the source of a critical geometric error of a machine tool includes the following steps.

[0310] Step 1: Set the machine adjustment parameters and grinding wheel parameters of the spiral bevel gear machine tool, and calculate the tooth surface point coordinates according to the method described above. The tooth surface point coordinates are coordinates without geometric error. The spiral bevel gear tooth surface schematic diagram obtained by fitting the calculated tooth surface point coordinates is as follows: Figure 17 The machine tool adjustment parameters are shown in Table 6 below, and the grinding wheel parameters are shown in Table 7 below.

[0311] Grinding wheel parameters value Grinding wheel diameter 152.4mm Outer end pressure angle 18.48° Inner end pressure angle 20.5251° Point width 2.3mm

[0312] Table 6

[0313] Machine tool adjustment parameters value Radial tool position 76.4988mm Angular tool position 59.4458° Horizontal wheel position 0.3428 bed -0.8047 Vertical wheel position -0.1843 Installation angle 52.2058 Rolling ratio 1.2086

[0314] Table 7

[0315] Step 2: Set the value range of each geometric error item in the 41 geometric error items, and randomly generate multiple groups of geometric error parameters. Each group of geometric error parameters includes 41 geometric error items, and each geometric error item is randomly selected within the corresponding value range. Then, according to the previous method, calculate the corresponding tooth surface error for each group of geometric error parameters and obtain the tooth surface error formal parameters. The schematic diagram of the spiral bevel gear tooth surface error is shown as follows: Figure 18 As shown in Table 8, the value ranges of various geometric error items are shown in Table 8.

[0316]

[0317]

[0318] Table 8

[0319] Step 3: Decompose the tooth surface error into five tooth surface error forms according to the method described above. Randomly generate multiple groups of geometric error parameters and tooth surface error form parameters corresponding to each group of geometric error parameters, specifically including five types. Use the sensitivity analysis method to calculate and statistically analyze the sensitivity indicators.

[0320] The sensitivity coefficient histogram of each geometric error term corresponding to the five tooth surface error forms is as follows: Figures 19 to 23 As shown in the figure, the horizontal axis is the geometric error item number, and the vertical axis is the sensitivity coefficient value. The geometric error item with a higher sensitivity coefficient value is the sensitive error item, that is, the key geometric error item. Therefore, according to Figure 19 The sensitive error term corresponding to the tooth surface error form (a) can be obtained according to Figure 20 The sensitive error term corresponding to the tooth surface error form (b) can be obtained according to Figure 21 The sensitive error term corresponding to the tooth surface error form (c) can be obtained according to Figure 22 The sensitive error term corresponding to the tooth surface error form (d) can be obtained according to Figure 23 The sensitive error term corresponding to the tooth surface error form (e) can be obtained. The sensitivity coefficient includes the Monte Carlo estimation of the first-order sensitivity coefficient and Monte Carlo estimation of the overall sensitivity coefficient The left column in the figure represents the first-order sensitivity coefficient The left column represents the overall sensitivity coefficient

[0321] according to Figures 19 to 23 The sensitivity analysis results can be obtained, as shown in Table 9 below.

[0322]

[0323]

[0324] Table 9

[0325] According to Table 9, 10 key errors were selected from the 41 geometric errors, including δ x (x), δ x (y), δ y (y), ε x (y), ε y (y), δ x (z), ε y (z), Syz 、S xz , γ BX Therefore, in the subsequent precise compensation of key errors, these 10 errors should be the focus of compensation and reduction. In the actual processing process, if the measurement results of the tooth surface error show that a certain tooth surface error form is more prominent, the corresponding sensitive error item needs to be controlled.

[0326] The key geometric error tracing method for machine tools provided in the embodiments of the present application can be performed by the key geometric error tracing device 200. In the embodiments of the present application, the key geometric error tracing device 200 executing the key geometric error tracing method for machine tools is used as an example to illustrate the key geometric error tracing device 200 provided in the embodiments of the present application.

[0327] See Figure 24 , is a structural diagram of a machine tool key geometric error tracing device 200 provided in an embodiment of the present application. Figure 24 As shown, the machine tool key geometric error tracing device 200 includes:

[0328] A first acquisition module 201 is used to acquire a kinematic chain of a spiral bevel gear machine tool;

[0329] Obtaining module 202, for obtaining a coordinate transformation matrix from the grinding wheel coordinate system to the spiral bevel gear coordinate system according to the kinematic chain;

[0330] The tooth surface model building module 203 is used to build a tooth surface model of the spiral bevel gear according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix;

[0331] The tooth surface point coordinate solving module 204 is used to discretize the tooth surface model and solve the tooth surface point coordinates, wherein a tooth surface point coordinate is the coordinate of a tooth surface point in the spiral bevel gear coordinate system;

[0332] A second acquisition module 205 is configured to acquire multiple sets of geometric error parameters of the spiral bevel gear machine tool, each set of geometric error parameters including K geometric error terms, wherein the specific values ​​of the K geometric error terms in each set of geometric error parameters are different, and wherein the number K of geometric error terms is determined according to the structure of the spiral bevel gear machine tool;

[0333] a tooth surface error calculation module 206 for executing a tooth surface error calculation strategy on each set of geometric error parameters to obtain a set of tooth surface error formal parameters corresponding to each set of geometric error parameters;

[0334] a key geometric error term determination module 207 for performing sensitivity analysis based on a Sobol sensitivity analysis method using multiple sets of geometric error parameters and corresponding multiple sets of tooth surface error formal parameters to determine key geometric error terms, wherein the key geometric error terms are one or more of the K geometric error terms;

[0335] Among them, the tooth surface error calculation strategy is implemented, including:

[0336] According to a set of geometric error parameters, coordinate transformation matrix and tooth surface model, the error tooth surface model of the spiral bevel gear is obtained;

[0337] Discretize the error tooth surface model and solve the tooth surface error point coordinates, where a tooth surface error point coordinate is the coordinate of a tooth surface error point corresponding to a tooth surface point in the spiral bevel gear coordinate system;

[0338] According to the tooth surface point coordinates and tooth surface error point coordinates corresponding to each tooth surface point, the tooth surface error of each tooth surface point is obtained;

[0339] According to the tooth surface point coordinates and tooth surface errors corresponding to each tooth surface point, a set of tooth surface error formal parameters are obtained.

[0340] In some embodiments, the tooth surface model building module 203 may be used to:

[0341] According to the axial cross-section profile of the grinding wheel of the spiral bevel gear machine tool, a grinding wheel model is established;

[0342] According to the grinding wheel model and coordinate transformation matrix, the motion grinding wheel model is obtained;

[0343] The tooth surface model is established based on the motion grinding wheel model and the grinding contact conditions. The grinding contact conditions are used to characterize the geometric and kinematic characteristics of the contact area between the grinding wheel and the spiral bevel gear during the grinding process of the spiral bevel gear machine tool.

[0344] In some embodiments, the tooth surface error calculation module 206 may be configured to:

[0345] According to a set of geometric error parameters and a coordinate transformation matrix, an error coordinate transformation matrix is ​​obtained;

[0346] According to the grinding wheel model and the error coordinate transformation matrix, the error motion grinding wheel model is obtained;

[0347] According to the error motion grinding wheel model and grinding contact conditions, the error tooth surface model is established.

[0348] In some embodiments, the tooth surface point coordinate solving module 204 may be used to:

[0349] Obtain the tooth surface design parameters of the spiral bevel gear;

[0350] The points on the tooth surface of the spiral bevel gear are rotated around the axis and projected onto a projection plane passing through the axis of rotation, and a quadrilateral projection area is obtained on the projection plane;

[0351] Discretize the quadrilateral projection area and evenly select N×M sample points in the quadrilateral projection area;

[0352] Establish a projection plane coordinate system on the projection plane, and determine the tooth surface point projection coordinates of the tooth surface points corresponding to the four vertices of the quadrilateral projection area according to the tooth surface design parameters, wherein the tooth surface point projection coordinates are the coordinates of the tooth surface points in the projection plane coordinate system;

[0353] According to the tooth surface point projection coordinates of the four vertices corresponding to the tooth surface points, determine the tooth surface point projection coordinates of the N×M sample points corresponding to the tooth surface points;

[0354] The tooth surface point coordinates of the tooth surface points corresponding to the N×M sample points are determined according to the tooth surface model, the tooth surface point projection coordinates of the tooth surface points corresponding to the N×M sample points, and a group of association relationship equations; wherein the group of association relationship equations includes a relationship equation for associating the tooth surface point coordinates determined based on geometric characteristics with the tooth surface point projection coordinates.

[0355] In some embodiments, the tooth surface error calculation module 206 may be configured to:

[0356] Based on the general second-order surface equation, the intermediate tooth surface error model is established;

[0357] The coordinate values ​​of the tooth surface point coordinates corresponding to the tooth surface points of N×M sample points and the tooth surface errors are input into the intermediate tooth surface error formal model to obtain a set of tooth surface error formal parameters.

[0358] In some embodiments, the intermediate tooth surface error form model is constrained by the following mathematical expression:

[0359]

[0360] Among them, x1, x2, …, x M with y1,y2,…,y N Indicates the coordinate values ​​of the tooth surface points corresponding to the N×M sample points, Z1, Z2,…, Z N×M It represents the tooth surface error corresponding to N×M sample points, and c1, c2, c3, c4, and c5 are a set of tooth surface error formal parameters.

[0361] In some embodiments, each set of tooth surface error formal parameters includes a first tooth surface error formal parameter, a second tooth surface error formal parameter, a third tooth surface error formal parameter, a fourth tooth surface error formal parameter, and a fifth tooth surface error formal parameter;

[0362] The key geometric error term determination module 207 can be used to:

[0363] Based on the Sobol sensitivity analysis method, sensitivity analysis is performed using multiple groups of geometric error parameters and multiple first tooth surface error formal parameters, multiple second tooth surface error formal parameters, multiple third tooth surface error formal parameters, multiple fourth tooth surface error formal parameters and multiple fifth tooth surface error formal parameters in the corresponding multiple groups of tooth surface error formal parameters to determine the key geometric error terms corresponding to the first tooth surface error formal parameters, the second tooth surface error formal parameters, the third tooth surface error formal parameters, the fourth tooth surface error formal parameters and the fifth tooth surface error formal parameters, respectively.

[0364] Since the machine tool key geometric error tracing device 200 adopts all the technical solutions of the machine tool key geometric error tracing method of the above embodiment, it has at least all the beneficial effects brought by the technical solutions of the above embodiment, which will not be described in detail here.

[0365] Figure 25 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present application.

[0366] The electronic device may include a processor 301 and a memory 302 storing computer program instructions.

[0367] Specifically, the processor 301 may include a central processing unit (CPU), or an application-specific integrated circuit (ASIC), or may be configured to implement one or more integrated circuits of the embodiments of the present application.

[0368] The memory 302 may include a large capacity memory for data or instructions. By way of example and not limitation, the memory 302 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a universal serial bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory 302 may include removable or non-removable (or fixed) media. Where appropriate, the memory 302 may be inside or outside the integrated gateway disaster recovery device. In a specific embodiment, the memory 302 is a non-volatile solid-state memory.

[0369] In some embodiments, the memory 302 may include read-only memory (ROM), random access memory (RAM), magnetic disk storage media devices, optical storage media devices, flash memory devices, electrical, optical, or other physical / tangible memory storage devices. Thus, generally, the memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to an aspect of the present disclosure.

[0370] The processor 301 reads and executes computer program instructions stored in the memory 302 to implement any one of the machine tool key geometric error tracing methods in the above embodiments.

[0371] In one example, the electronic device may further include a communication interface 303 and a bus 310. Figure 25 As shown, the processor 301 , the memory 302 , and the communication interface 303 are connected via a bus 310 and communicate with each other.

[0372] The communication interface 303 is mainly used to implement communication between various modules, devices, units and / or equipment in the embodiments of the present application.

[0373] Bus 310 includes hardware, software or both, and the components of online data flow metering equipment are coupled to each other. For example, but not limitation, bus can include accelerated graphics port (AGP) or other graphics bus, enhanced industry standard architecture (EISA) bus, front side bus (FSB), hypertransport (HT) interconnection, industry standard architecture (ISA) bus, infinite bandwidth interconnection, low pin count (LPC) bus, memory bus, micro channel architecture (MCA) bus, peripheral component interconnection (PCI) bus, PCI-Express (PCI-X) bus, serial advanced technology attachment (SATA) bus, video electronics standard association local (VLB) bus or other suitable bus or two or more of these combinations. In appropriate cases, bus 310 can include one or more buses. Although the present application embodiment describes and shows specific bus, the application considers any suitable bus or interconnection.

[0374] The electronic device can execute the key geometric error tracing method of the machine tool in the embodiment of the present application, thereby realizing the combination Figure 1 and Figure 24 The invention describes a method and device for tracing the source of key geometric errors of machine tools.

[0375] In addition, in conjunction with the method for tracing the source of a critical geometric error of a machine tool in the above-mentioned embodiment, the present application can provide a computer storage medium for implementation. The computer storage medium stores computer program instructions; when the computer program instructions are executed by a processor, any of the methods for tracing the source of a critical geometric error of a machine tool in the above-mentioned embodiment is implemented.

[0376] It should be understood that the present application is not limited to the specific configurations and processes described above and illustrated in the figures. For the sake of brevity, a detailed description of known methods is omitted here. In the above embodiments, several specific steps are described and illustrated as examples. However, the method process of the present application is not limited to the specific steps described and illustrated. Those skilled in the art can make various changes, modifications, and additions, or change the order of the steps after understanding the spirit of the present application.

[0377] The functional blocks shown in the above-described block diagram can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, they can be electronic circuits, application specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of the present application are programs or code segments that are used to perform the required tasks. The program or code segment can be stored in a machine-readable medium, or transmitted on a transmission medium or communication link by a data signal carried in a carrier wave. "Machine-readable medium" can include any medium that can store or transmit information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROMs, flash memories, erasable ROMs (EROMs), floppy disks, CD-ROMs, optical disks, hard disks, optical fiber media, radio frequency (RF) links, etc. The code segment can be downloaded via a computer network such as the Internet, an intranet, etc.

[0378] It should also be noted that the exemplary embodiments mentioned in this application describe some methods or systems based on a series of steps or devices. However, this application is not limited to the order of the above steps. In other words, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0379] Aspects of the present disclosure have been described above with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer or other programmable data processing device to produce a machine so that these instructions executed by the processor of the computer or other programmable data processing device enable the implementation of the function / action specified in one or more boxes of the flowchart and / or block diagram. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor or a field programmable logic circuit. It is also understood that each box in the block diagram and / or flowchart and the combination of the boxes in the block diagram and / or flowchart can also be implemented by dedicated hardware that performs the specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0380] The above description is only a specific embodiment of the present application. Those skilled in the art will clearly understand that for the convenience and brevity of description, the specific working processes of the systems, modules and units described above can refer to the corresponding processes in the aforementioned method embodiments, and will not be repeated here. It should be understood that the scope of protection of the present application is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present application, and these modifications or replacements should be included in the scope of protection of the present application.

Claims

1. A method for tracing the source of key geometric errors of machine tools, applied to spiral bevel gear machine tools, characterized in that: include: Obtaining a kinematic chain of the spiral bevel gear machine tool; According to the kinematic chain, a coordinate transformation matrix from the grinding wheel coordinate system to the spiral bevel gear coordinate system is obtained; Establishing a tooth surface model of the spiral bevel gear according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix; Discretizing the tooth surface model and solving the tooth surface point coordinates, wherein one tooth surface point coordinate is the coordinate of a tooth surface point in the spiral bevel gear coordinate system; Acquire multiple sets of geometric error parameters of the spiral bevel gear machine tool, each set of the geometric error parameters including K geometric error terms, the specific values ​​of the K geometric error terms in each set of the geometric error parameters being different, wherein the number K of the geometric error terms is determined according to the structure of the spiral bevel gear machine tool; Executing a tooth surface error calculation strategy on each set of the geometric error parameters to obtain a set of tooth surface error formal parameters corresponding to each set of the geometric error parameters; Based on the Sobol sensitivity analysis method, a sensitivity analysis is performed using multiple groups of the geometric error parameters and corresponding multiple groups of the tooth surface error formal parameters to determine key geometric error terms, wherein the key geometric error terms are one or more of the K geometric error terms; The execution of the tooth surface error calculation strategy includes: Obtaining an error tooth surface model of the spiral bevel gear according to a set of the geometric error parameters, the coordinate transformation matrix and the tooth surface model; Discretizing the error tooth surface model and solving the tooth surface error point coordinates, wherein one tooth surface error point coordinate is the coordinate of a tooth surface error point corresponding to one tooth surface point in the spiral bevel gear coordinate system; Obtaining the tooth surface error of each tooth surface point according to the tooth surface point coordinates and the tooth surface error point coordinates corresponding to each tooth surface point; A set of tooth surface error formal parameters is obtained according to the tooth surface point coordinates and the tooth surface errors corresponding to each tooth surface point.

2. The method for tracing the source of key geometric errors of machine tools according to claim 1, characterized in that: The tooth surface model of the spiral bevel gear is established according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix, including: Establishing a grinding wheel model according to the axial cross-sectional profile of the grinding wheel of the spiral bevel gear machine tool; Obtaining a motion grinding wheel model according to the grinding wheel model and the coordinate transformation matrix; The tooth surface model is established based on the motion grinding wheel model and the grinding contact conditions, wherein the grinding contact conditions are used to characterize the geometric and kinematic characteristics of the contact area between the grinding wheel and the spiral bevel gear during the grinding process of the spiral bevel gear machine tool.

3. The method for tracing the source of key geometric errors of machine tools according to claim 2, characterized in that: Obtaining the error tooth surface model of the spiral bevel gear according to a set of the geometric error parameters, the coordinate transformation matrix and the tooth surface model includes: Obtaining an error coordinate transformation matrix according to a set of the geometric error parameters and the coordinate transformation matrix; Obtaining an error motion grinding wheel model according to the grinding wheel model and the error coordinate transformation matrix; The error tooth surface model is established according to the error motion grinding wheel model and the grinding contact condition.

4. The method for tracing the source of key geometric errors of machine tools according to claim 1, characterized in that: Discretizing the tooth surface model and solving the tooth surface point coordinates includes: Obtaining tooth surface design parameters of the spiral bevel gear; A point on the tooth surface of the spiral bevel gear is rotated about the axis and then projected onto a projection plane passing through the rotation axis, to obtain a quadrilateral projection area on the projection plane; Discretize the quadrilateral projection area, and evenly select N×M sample points in the quadrilateral projection area; Establishing a projection plane coordinate system on the projection plane, and determining the tooth surface point projection coordinates of the tooth surface points corresponding to the four vertices of the quadrilateral projection area according to the tooth surface design parameters, wherein the tooth surface point projection coordinates are the coordinates of the tooth surface points in the projection plane coordinate system; Determine the tooth surface point projection coordinates of the tooth surface points corresponding to N×M sample points according to the tooth surface point projection coordinates of the four vertices; The tooth surface point coordinates of the tooth surface points corresponding to the N×M sample points are determined according to the tooth surface model, the tooth surface point projection coordinates of the tooth surface points corresponding to the N×M sample points, and a group of association relationship equations; wherein the group of association relationship equations includes a relationship equation for associating the tooth surface point coordinates with the tooth surface point projection coordinates determined based on geometric characteristics.

5. The method for tracing the source of key geometric errors of machine tools according to claim 4, characterized in that: The step of obtaining a set of tooth surface error formal parameters according to the tooth surface point coordinates and the tooth surface errors corresponding to the tooth surface points includes: Based on the general second-order surface equation, the intermediate tooth surface error model is established; The coordinate values ​​of the tooth surface point coordinates of the tooth surface points corresponding to the N×M sample points and the tooth surface errors are input into the intermediate tooth surface error formal model to obtain a set of tooth surface error formal parameters.

6. The method for tracing the source of key geometric errors of machine tools according to claim 5, characterized in that: The intermediate tooth surface error model is constrained by the following mathematical expression: Among them, x1, x2, …, x M with y1,y2,…,y N The coordinate values ​​of the tooth surface point coordinates corresponding to the N×M sample points, Z1, Z2, ..., Z N×M represents the tooth surface error corresponding to the N×M sample points, and c1, c2, c3, c4, and c5 are a set of formal parameters of the tooth surface error.

7. The method for tracing the source of key geometric errors of machine tools according to claim 1 or 6, characterized in that: Each group of tooth surface error formal parameters includes a first tooth surface error formal parameter, a second tooth surface error formal parameter, a third tooth surface error formal parameter, a fourth tooth surface error formal parameter and a fifth tooth surface error formal parameter; The Sobol sensitivity analysis method is based on performing sensitivity analysis using multiple groups of geometric error parameters and corresponding multiple groups of tooth surface error formal parameters to determine key geometric error terms, including: Based on the Sobol sensitivity analysis method, sensitivity analysis is performed respectively using multiple groups of the geometric error parameters and multiple first tooth surface error formal parameters, multiple second tooth surface error formal parameters, multiple third tooth surface error formal parameters, multiple fourth tooth surface error formal parameters and multiple fifth tooth surface error formal parameters in the corresponding multiple groups of the tooth surface error formal parameters to determine the key geometric error items corresponding to the first tooth surface error formal parameters, the second tooth surface error formal parameters, the third tooth surface error formal parameters, the fourth tooth surface error formal parameters and the fifth tooth surface error formal parameters, respectively.

8. A device for tracing the source of key geometric errors of machine tools, characterized in that: include: A first acquisition module is used to acquire the kinematic chain of the spiral bevel gear machine tool; An obtaining module is used to obtain a coordinate transformation matrix from a grinding wheel coordinate system to a spiral bevel gear coordinate system according to the kinematic chain; a tooth surface model building module, configured to build a tooth surface model of the spiral bevel gear according to the profile of the grinding wheel of the spiral bevel gear machine tool and the coordinate transformation matrix; A tooth surface point coordinate solving module, used for discretizing the tooth surface model and solving the tooth surface point coordinates, wherein one tooth surface point coordinate is the coordinate of a tooth surface point in the spiral bevel gear coordinate system; a second acquisition module, configured to acquire multiple sets of geometric error parameters of the spiral bevel gear machine tool, each set of the geometric error parameters including K geometric error terms, the specific values ​​of the K geometric error terms in each set of the geometric error parameters being different, wherein the number K of the geometric error terms is determined according to the structure of the spiral bevel gear machine tool; a tooth surface error calculation module, configured to execute a tooth surface error calculation strategy on each set of the geometric error parameters to obtain a set of tooth surface error formal parameters corresponding to each set of the geometric error parameters; a key geometric error term determination module, configured to perform sensitivity analysis based on a Sobol sensitivity analysis method using multiple groups of geometric error parameters and corresponding multiple groups of tooth surface error formal parameters to determine key geometric error terms, wherein the key geometric error term is one or more of the K geometric error terms; The execution of the tooth surface error calculation strategy includes: Obtaining an error tooth surface model of the spiral bevel gear according to a set of the geometric error parameters, the coordinate transformation matrix and the tooth surface model; Discretizing the error tooth surface model and solving the tooth surface error point coordinates, wherein one tooth surface error point coordinate is the coordinate of a tooth surface error point corresponding to one tooth surface point in the spiral bevel gear coordinate system; Obtaining the tooth surface error of each tooth surface point according to the tooth surface point coordinates and the tooth surface error point coordinates corresponding to each tooth surface point; A set of tooth surface error formal parameters is obtained according to the tooth surface point coordinates and the tooth surface errors corresponding to each tooth surface point.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores programs or instructions that can be run on the processor, and when the programs or instructions are executed by the processor, the steps of the method for tracing the key geometric errors of machine tools as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the method for tracing the key geometric errors of a machine tool according to any one of claims 1 to 7.

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