Spindle thermal error control domain calculation method of spiral bevel gear grinding machine tool

Abstract

The invention discloses a main shaft thermal error control domain calculation method of a spiral bevel gear gear grinding machine tool. The main shaft thermal error control domain calculation method of the spiral bevel gear gear grinding machine tool comprises the steps that a first conversion matrix of a workpiece coordinate system and a tool coordinate system is calculated; calculating a first tooth surface point coordinate and a corresponding first tooth surface point normal vector based on the gear blank shaft section and the first conversion matrix; calculating a second tooth surface point coordinate based on the first main shaft thermal error boundary, the gear blank shaft section and the first conversion matrix; calculating a tooth surface deviation value based on the first tooth surface point coordinate, the first tooth surface point normal vector and the second tooth surface point coordinate; when the tooth surface deviation value is larger than the preset tooth surface deviation value and half of the first step length is smaller than the preset minimum step length, the initial main shaft thermal error boundary serves as the main shaft thermal error control boundary, and it is guaranteed that prediction under various working conditions can have enough tooth surface precision.

Description

Technical Field

[0001] The present application relates to a technical field related to calculation of a spindle thermal error control domain of a spiral bevel gear grinding machine tool, and in particular to a method for calculating a spindle thermal error control domain of a spiral bevel gear grinding machine tool. Background Art

[0002] Numerous factors influence CNC machine tool errors, including geometric errors, heat, forces, installation, and vibration. These errors severely impact the machining accuracy of spiral bevel gears, necessitating counter-tune machining to improve tooth surface accuracy. Thermal errors account for a high proportion of these error factors, and due to their time-varying nature, their impact on spiral bevel gear machining is constantly changing. Consequently, batch machining can lead to insufficient precision and instability in spiral bevel gear machining, which is difficult to resolve through counter-tune machining. Therefore, prediction and compensation of machine tool thermal errors are generally necessary.

[0003] At present, the thermal error modeling and compensation of CNC machine tools mainly focus on continuously reducing the prediction deviation through modeling algorithms and improving algorithm performance to pursue infinitely small modeling prediction errors. However, there is no clear target for the accuracy to which each thermal error needs to be predicted, making it difficult to ensure that the tooth surface accuracy requirements can be met after error compensation. Summary of the Invention

[0004] This application aims to at least address the technical problems existing in the prior art. To this end, this application proposes a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine, which can provide a clear prediction accuracy target for thermal error modeling and ensure sufficient tooth surface accuracy under various operating conditions.

[0005] In a first aspect of the present application, a method for calculating a spindle thermal error control region of a spiral bevel gear grinding machine tool is provided, comprising the following steps:

[0006] Acquire an initial spindle thermal error boundary, a gear blank shaft cross section, and a first step length, and expand the first spindle thermal error boundary according to the first step length to obtain a first spindle thermal error boundary;

[0007] Constructing a workpiece coordinate system and a tool coordinate system, and calculating a first transformation matrix of the workpiece coordinate system and the tool coordinate system;

[0008] Calculate the coordinates of a first tooth surface point and a corresponding first tooth surface point normal vector based on the gear blank axial cross section and the first transformation matrix;

[0009] Calculating the coordinates of a second tooth surface point based on the first spindle thermal error boundary, the gear blank axial cross section, and the first transformation matrix;

[0010] calculating a tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector, and the second tooth surface point coordinates;

[0011] When the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary.

[0012] The control method according to the embodiment of the present application has at least the following beneficial effects:

[0013] This method obtains the first spindle thermal error boundary by obtaining the initial spindle thermal error boundary, the gear blank shaft section and the first step length, and expanding the first spindle thermal error boundary according to the first step length; constructs a workpiece coordinate system and a tool coordinate system, and calculates the first transformation matrix of the workpiece coordinate system and the tool coordinate system; calculates the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank shaft section and the first transformation matrix; calculates the second tooth surface point coordinates based on the first spindle thermal error boundary, the gear blank shaft section and the first transformation matrix; calculates the tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector and the second tooth surface point coordinates; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by presetting the tooth surface deviation value, provides a clear prediction accuracy target for thermal error modeling, and ensures that the prediction under various working conditions can have sufficient tooth surface accuracy.

[0014] According to some embodiments of the present application, the calculating the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank axial cross section and the first transformation matrix includes:

[0015] Based on the first transformation matrix, the pinion tooth surface normal vector, relative velocity, and pinion tooth surface position vector are calculated using the following formula:

[0016] o t =[0 0 0] T

[0017] I t =[0 0 1] T

[0018] n p (θ)=[sinα·cos(θ) sinα·sin(θ) cosα] T

[0019]

[0020] r p (h,θ)=o t +h·I t +ρ(h)·n p (θ)

[0021]

[0022]

[0023]

[0024]

[0025] Among them, t is the position vector of the tool coordinate system origin in the tool coordinate system, I t is the unit vector basis of the Z axis of the tool coordinate system, n p (θ) is the unit normal vector of the rotating surface at point p, α is n p (θ) and I t The angle formed, θ is the rotation angle of a point on the cutting edge around the tool axis to the point on the rotating surface, ρ(h) is the angle between point p and point p h The distance between u is the cutter head radius, P W is the tool tip distance, α g is the contour pressure angle, h is the tool coordinate system origin and point p h The distance between h n p (θ) and I t The intersection of ± is the concave surface of the tool and - is the convex surface of the tool, r p (h,θ) is the position vector of the point on the rotating surface in the tool coordinate system, M gt is the first transformation matrix, I g (φ) is the tool axis vector in the workpiece coordinate system, o g (φ) is the position vector of the tool coordinate system origin in the workpiece coordinate system, φ is the cradle angle, n g (θ, φ) is the normal vector of the pinion tooth surface, n t (θ) is the normal vector of the rotating surface of the tool linear edge in the tool coordinate system, r g (h,θ,φ) is the position vector of the gear tooth surface, v g (h,θ,φ) is the relative velocity;

[0026] The first tooth surface point coordinates are calculated based on the pinion tooth surface normal vector, the pinion tooth surface position vector and the relative speed using the following formula:

[0027] n g (θ,φ)·v g (h,θ,φ)=0

[0028]

[0029] 0≤f≤F

[0030] -b f ≤d≤a f

[0031]

[0032]

[0033]

[0034] r g (h,θ,φ)=[x(h,θ,φ),y(h,θ,φ),z(h,θ,φ)] T

[0035]

[0036] Among them, R Q is the X coordinate of the grid point Q in the gear blank's mid-axis section in the workpiece coordinate system, L Q is the Z coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system, A0 is the outer cone distance, f is the discrete parameter of the projection surface along the tooth direction, d is the discrete parameter of the projection surface along the tooth height direction, δ2 is the pitch cone angle, F is the tooth width, a f is the tooth top corresponding to parameter f, b f is the tooth root corresponding to parameter f, m is the discrete number in the tooth direction, n is the discrete number in the tooth height direction, i is the i-th discrete point in the tooth direction, j is the j-th discrete point in the tooth height direction, h a is the tooth top height, h b is the tooth root height, δ1 is the face cone angle, δ3 is the root cone angle, x(h,θ,φ) is the X coordinate of the first tooth surface point, y(h,θ,φ) is the Y coordinate of the first tooth surface point, and z(h,θ,φ) is the Z coordinate of the first tooth surface point;

[0037] Based on the pinion tooth surface normal vector, the first tooth surface point normal vector corresponding to the first tooth surface point coordinate is calculated.

[0038] According to some embodiments of the present application, calculating the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank axial cross section, and the first transformation matrix includes:

[0039] The intersection of the grinding wheel mounting surface and the spindle axis is used as the coordinate origin to construct the spindle coordinate system;

[0040] Downsampling the first spindle thermal error boundary to obtain an offset of the origin of the spindle coordinate system along the X-axis, an offset of the origin of the spindle coordinate system along the Y-axis, an offset of the origin of the spindle coordinate system along the Z-axis, a deflection angle of the Z-axis of the spindle coordinate system around the X-axis, and a deflection angle of the Z-axis of the spindle coordinate system around the Y-axis;

[0041] The pinion tooth surface error vector is calculated based on the offset of the origin of the main axis coordinate system along the X axis, the offset of the origin of the main axis coordinate system along the Y axis, the offset of the origin of the main axis coordinate system along the Z axis, the deflection angle of the Z axis of the main axis coordinate system around the X axis, the deflection angle of the Z axis of the main axis coordinate system around the Y axis, the gear blank axial cross section and the first transformation matrix using the following formula:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] n t (θ e )=[sinα·cos(θ e ) sinα·sin(θ e ) cosα] T

[0048]

[0049] Among them, M s e is the spindle thermal error matrix, δ x is the offset of the origin of the principal axis coordinate system along the X axis, δ y is the offset of the origin of the principal axis coordinate system along the Y axis, δ z is the offset of the origin of the main axis coordinate system along the Z axis, ε x is the deflection angle of the Z axis of the principal axis coordinate system around the X axis, ε y M is the deflection angle of the Z axis around the Y axis of the main axis coordinate system, gt e is the second transformation matrix, I ge (φ e ) is the error tool axis vector in the workpiece coordinate system, o ge (φ e ) is the error position vector of the tool coordinate system origin in the workpiece coordinate system, n ge (θ e ,φ e ) is the normal vector of the pinion tooth surface error, v ge (h e ,θ e ,φ e ) is the error relative speed, φ e is the error cradle angle, θ eThe error rotation angle from a point on the cutting edge to a point on the rotating surface around the tool axis, h e is the tool coordinate system origin and point p h The error distance between ge (h e ,θ e ,φ e ) is the position vector of the pinion tooth surface error, ρ(h e ) is the error distance, n t (θ e ) is the error normal vector of the tool linear edge rotation surface in the tool coordinate system;

[0050] The coordinates of the second tooth surface point are calculated based on the pinion tooth surface error vector using the following formula:

[0051] r ge (h e ,θ e ,φ e )=[x e (h e ,θ e ,φ e ),y e (h e ,θ e ,φ e ),z e (h e ,θ e ,φ e )] T

[0052]

[0053] Among them, x e (h e ,θ e ,φ e ) is the X coordinate of the second tooth surface point, y e (h e ,θ e ,φ e ) is the Y coordinate of the second tooth surface point, z e (h e ,θ e ,φ e ) is the Z coordinate of the second tooth surface point.

[0054] According to some embodiments of the present application, the tooth surface deviation value includes an average tooth surface deviation value and a maximum tooth surface deviation value, and calculating the tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector, and the second tooth surface point coordinates includes:

[0055] Obtain the coordinates of the first center point of the first tooth surface composed of the first tooth surface point coordinates; obtain the coordinates of the second center point of the second tooth surface composed of the second tooth surface point coordinates;

[0056] Calculating a phase angle based on the Y coordinate and Z coordinate of the first center point coordinate and the Y coordinate and Z coordinate of the second center point coordinate, wherein the phase angle is used to rotate the Y coordinate and Z coordinate of the first center point coordinate around the workpiece axis by the phase angle so that the Y coordinate and Z coordinate of the first center point coordinate coincide with the Y coordinate and Z coordinate of the second center point coordinate;

[0057] Rotating the second tooth surface point coordinate around the workpiece axis by the phase angle to obtain the third tooth surface point coordinate;

[0058] The normal deviation value is calculated based on the first tooth surface point coordinates and the third tooth surface point coordinates using the following formula:

[0059] e i，j =(P 2i，j -P 1i，j )·n i,j ,(i=1,2,...,m,j=1,2,...,n);

[0060] Among them, e i,j is the normal deviation value of the jth tooth height direction in the i-th tooth direction, P 2i,j is the coordinate of the third tooth surface point in the i-th tooth direction and the j-th tooth height direction, P 1i,j is the coordinate of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction, n i,j is the normal vector of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction;

[0061] The tooth surface deviation value is calculated based on the normal deviation value using the following formula:

[0062]

[0063] f2(δ x ,δ y ,δ z ,ε x ,ε y )=max(|e i,j |);

[0064] Among them, f1(δ x ,δ y ,δ z ,ε x ,ε y ) is the tooth surface average deviation value of the tooth surface deviation value, f2(δ x ,δ y ,δ z ,ε x ,εy ) is the maximum tooth surface deviation value of the tooth surface deviation value.

[0065] According to some embodiments of the present application, the method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes:

[0066] When the tooth surface deviation value is less than the preset tooth surface deviation value, based on the first step length, the first spindle thermal error boundary is expanded to obtain a second spindle thermal error boundary;

[0067] When the second spindle thermal error boundary is greater than a preset maximum error boundary, the second spindle thermal error boundary is used as the spindle thermal error control boundary;

[0068] When the second spindle thermal error boundary is less than the preset maximum error boundary, the second tooth surface deviation value is calculated based on the second spindle thermal error boundary, and so on, until the Kth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, then the K-1th spindle thermal error boundary is used as the spindle thermal error control boundary, where K is the number of iterations.

[0069] According to some embodiments of the present application, the method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes:

[0070] When the tooth surface deviation value is greater than the preset tooth surface deviation value but half of the first step length is greater than the preset minimum step length, the first step length is halved to obtain a second step length;

[0071] Based on the first step length, the first spindle thermal error boundary is expanded to obtain a second step length spindle thermal error boundary;

[0072] When the second step-length spindle thermal error boundary is greater than the preset maximum error boundary, the second step-length spindle thermal error boundary is used as the spindle thermal error control boundary;

[0073] When the second step spindle thermal error boundary is less than the preset maximum error boundary, the corresponding tooth surface deviation value is calculated based on the second step spindle thermal error boundary, and so on, until the Qth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Qth step is less than the preset minimum step, then the Q-1th spindle thermal error boundary is used as the spindle thermal error control boundary, where Q is the number of iterations.

[0074] According to some embodiments of the present application, the calculating the first transformation matrix of the workpiece coordinate system and the tool coordinate system includes:

[0075] Construct the machine tool coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, cradle fixed coordinate system and tool rotation coordinate system;

[0076] The first transformation matrix is ​​calculated according to the workpiece coordinate system, the tool coordinate system, the machine tool coordinate system, the workpiece axis fixed coordinate system, the machine tool fixed coordinate system, the cradle fixed coordinate system and the tool rotation coordinate system using the following formula:

[0077] φ c =m*φ

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] M gt =M gd ·M dc ·M cm ·M mb ·M ba ·M at ;

[0085] Among them, M gt is the first transformation matrix, M gd M is the transformation matrix from the workpiece axis fixed coordinate system to the workpiece coordinate system, dc is the transformation matrix from the machine tool fixed coordinate system to the workpiece axis fixed coordinate system, M cm is the transformation matrix from the machine tool coordinate system to the machine tool fixed coordinate system, M mb M is the transformation matrix from the cradle fixed coordinate system to the machine tool coordinate system. ba M is the transformation matrix from the tool rotation coordinate system to the cradle fixed coordinate system. at is the transformation matrix from tool coordinate system to tool rotation coordinate system, E M is the vertical wheel position, x B For beds, x D is the horizontal wheel position, q is the angular tool position, s is the radial tool position, γ is the installation angle, I is the tool inclination angle, J is the tool rotation angle, φ c is the wheel blank rotation angle, φ is the cradle rotation angle, m is the rolling ratio, x hl is the spiral coefficient.

[0086] In a second aspect of the present application, a spindle thermal error control domain calculation system for a spiral bevel gear grinding machine tool is provided. The spindle thermal error control domain calculation system for a spiral bevel gear grinding machine tool comprises:

[0087] a data acquisition module, configured to acquire an initial spindle thermal error boundary, a gear blank shaft cross section, and a first step length, and to expand the first spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0088] a first conversion matrix calculation module, configured to construct a workpiece coordinate system and a tool coordinate system, and calculate a first conversion matrix between the workpiece coordinate system and the tool coordinate system;

[0089] A first tooth surface point coordinate calculation module, configured to calculate the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank axial cross section and the first transformation matrix;

[0090] a second tooth surface point coordinate calculation module, configured to calculate the second tooth surface point coordinates based on the first spindle thermal error boundary, the gear blank axial cross section, and the first transformation matrix;

[0091] a tooth surface deviation value calculation module, configured to calculate a tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector, and the second tooth surface point coordinates;

[0092] The spindle thermal error control boundary calculation module is used to use the initial spindle thermal error boundary as the spindle thermal error control boundary when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length.

[0093] This system obtains the first spindle thermal error boundary by obtaining the initial spindle thermal error boundary, the gear blank shaft section and the first step length, and expands the first spindle thermal error boundary according to the first step length; constructs the workpiece coordinate system and the tool coordinate system, and calculates the first transformation matrix of the workpiece coordinate system and the tool coordinate system; calculates the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank shaft section and the first transformation matrix; calculates the second tooth surface point coordinates based on the first spindle thermal error boundary, the gear blank shaft section and the first transformation matrix; calculates the tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector and the second tooth surface point coordinates; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by presetting the tooth surface deviation value, provides a clear prediction accuracy target for thermal error modeling, and ensures that the prediction under various working conditions can have sufficient tooth surface accuracy.

[0094] The third aspect of the present application provides an electronic device for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine, comprising at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor so that the at least one control processor can execute the above-mentioned method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine.

[0095] In a fourth aspect of the present application, a computer-readable storage medium is provided, which stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the above-mentioned method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine.

[0096] It should be noted that the beneficial effects between the second to fourth aspects of the present application and the prior art are the same as the beneficial effects between the spindle thermal error control domain calculation system of the above-mentioned spiral bevel gear grinding machine and the prior art, and will not be described in detail here.

[0097] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become obvious from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] 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:

[0099] Figure 1 This is a flow chart of a method for calculating a spindle thermal error control domain of a spiral bevel gear grinding machine tool according to one embodiment of the present application;

[0100] Figure 2 1. It is a schematic diagram of a spindle thermal error structure of a method for calculating a spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0101] Figure 3 2. It is a schematic diagram of the spindle thermal error coordinates of a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0102] Figure 4 Schematic diagram of a tool cutting edge in a method for calculating a spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0103] Figure 5 Schematic diagram of a spiral bevel gear pinion machining coordinate system for a method for calculating a spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0104] Figure 6Schematic diagram of a gear blank shaft cross section of a method for calculating a spindle thermal error control domain of a spiral bevel gear grinding machine according to an embodiment of the present application, wherein (a) is a schematic diagram of a gear blank shaft cross section in three dimensions, and (b) is a schematic diagram of a planar diagram of a gear blank shaft cross section;

[0105] Figure 7 Schematic diagram of tooth surface error of a method for calculating a spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0106] Figure 8 This is a concave tooth surface error topology diagram when δx is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0107] Figure 9 This is a topological diagram of the convex tooth surface error when δx is equal to 1 μm in the method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0108] Figure 10 This is a concave tooth surface error topology diagram when δy is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0109] Figure 11 This is a topological diagram of the convex tooth surface error when δy is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0110] Figure 12 This is a concave tooth surface error topology diagram when δz is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0111] Figure 13 This is a topological diagram of the convex tooth surface error when δz is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0112] Figure 14 This is a concave tooth surface error topology diagram when εx is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0113] Figure 15 This is a topological diagram of the convex tooth surface error when εx is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0114] Figure 16 This is a concave tooth surface error topology diagram when εy is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0115] Figure 17This is a topological diagram of the convex tooth surface error when εy is equal to 1 μm in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0116] Figure 18 2. It is a schematic diagram of the normal deviation change result affected by δx in the method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to one embodiment of the present application;

[0117] Figure 19 2. It is a schematic diagram of the normal deviation change result affected by δy in the method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0118] Figure 20 2. It is a schematic diagram of the normal deviation change result affected by δz in the method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0119] Figure 21 1. This is a schematic diagram of the normal deviation change results affected by εx in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to an embodiment of the present application;

[0120] Figure 22 3. This is a schematic diagram of the normal deviation change result affected by εy in the method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool according to one embodiment of the present application;

[0121] Figure 23 This is a schematic structural diagram of an embodiment of a spindle thermal error control domain calculation system for a spiral bevel gear grinding machine tool provided by the present application;

[0122] Figure 24 It is a structural diagram of an embodiment of the electronic device provided by this application. DETAILED DESCRIPTION

[0123] 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.

[0124] 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.

[0125] 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.

[0126] 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.

[0127] With the maturity of mobile Internet technology, information resources are developing more and more rapidly, and readers' needs are becoming more and more diversified.

[0128] Currently, text-based trailer generation technology uses artificial intelligence to convert text content into visual and auditory effects. However, the accuracy of the spindle thermal error control domain calculation of spiral bevel gear grinding machines is not high.

[0129] In order to solve the above technical defects, an embodiment of the present application provides a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine.

[0130] See Figure 1 , is a flow chart of a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine provided by an embodiment of the present application. The method is applied to electronic equipment, which may be a server, etc. Figure 1 As shown in FIG, the calculation method of the spindle thermal error control domain of the spiral bevel gear grinding machine tool includes:

[0131] Step S101, obtaining an initial spindle thermal error boundary, a gear blank shaft cross section, and a first step length, and expanding the first spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0132] Step S102: constructing a workpiece coordinate system and a tool coordinate system, and calculating a first transformation matrix of the workpiece coordinate system and the tool coordinate system;

[0133] Step S103, calculating the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank axial cross section and the first transformation matrix;

[0134] Step S104, calculating the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank axial cross section and the first transformation matrix;

[0135] Step S105, calculating a tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector, and the second tooth surface point coordinates;

[0136] Step S106 : When the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary.

[0137] This method obtains the first spindle thermal error boundary by obtaining the initial spindle thermal error boundary, the gear blank shaft section and the first step length, and expands the first spindle thermal error boundary according to the first step length; constructs a workpiece coordinate system and a tool coordinate system, and calculates the first transformation matrix of the workpiece coordinate system and the tool coordinate system; calculates the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank shaft section and the first transformation matrix; calculates the second tooth surface point coordinates based on the first spindle thermal error boundary, the gear blank shaft section and the first transformation matrix; calculates the tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector and the second tooth surface point coordinates; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by preset tooth surface deviation value, provides a clear prediction accuracy target for thermal error modeling, and ensures that the prediction under various working conditions can have sufficient tooth surface accuracy.

[0138] In some embodiments, reference Figures 2 to 5 In step S103, the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point are calculated based on the gear blank axial cross section and the first transformation matrix, including:

[0139] Step S201: Calculate the pinion tooth surface normal vector, relative velocity, and pinion tooth surface position vector based on the first conversion matrix using the following formula:

[0140]

[0141] n p (θ)=sinα·cos(θ) sinα·sin(θ) cosα] T

[0142]

[0143] r p (h,θ)=o t +h·I t +ρ(h)·n p (θ)

[0144]

[0145]

[0146]

[0147]

[0148] Among them, t is the position vector of the tool coordinate system origin in the tool coordinate system, I t is the unit vector basis of the Z axis of the tool coordinate system, n p (θ) is the unit normal vector of the rotating surface at point p, α is n p (θ) and I t The angle formed, θ is the rotation angle of a point on the cutting edge around the tool axis to the point on the rotating surface, ρ(h) is the angle between point p and point p h The distance between u is the cutter head radius, P W is the tool tip distance, α g is the contour pressure angle, h is the tool coordinate system origin and point p h The distance between h n p (θ) and I t The intersection of ± is the concave surface of the tool and - is the convex surface of the tool, r p (h,θ) is the position vector of the point on the rotating surface in the tool coordinate system, M gt is the first transformation matrix, I g (φ) is the tool axis vector in the workpiece coordinate system, o g (φ) is the position vector of the tool coordinate system origin in the workpiece coordinate system, φ is the cradle angle, n g (θ, φ) is the normal vector of the pinion tooth surface, n t (θ) is the normal vector of the rotating surface of the tool linear edge in the tool coordinate system, r g (h,θ,φ) is the position vector of the gear tooth surface, v g (h,θ,φ) is the relative velocity;

[0149] Step S202: Calculate the coordinates of the first tooth surface point based on the pinion tooth surface normal vector, the pinion tooth surface position vector, and the relative speed using the following formula:

[0150] n g (θ,φ)·v g (h,θ,φ)=0

[0151]

[0152]

[0153] -b f ≤d≤a f

[0154]

[0155]

[0156]

[0157] r g (h,θ,φ)=[x(h,θ,φ),y(h,θ,φ),z(h,θ,φ)] T

[0158]

[0159] Among them, R Q is the X coordinate of the grid point Q in the gear blank's mid-axis section in the workpiece coordinate system, L Q is the Z coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system, A0 is the outer cone distance, f is the discrete parameter of the projection surface along the tooth direction, d is the discrete parameter of the projection surface along the tooth height direction, δ2 is the pitch cone angle, F is the tooth width, a f is the tooth top corresponding to parameter f, b f is the tooth root corresponding to parameter f, m is the discrete number in the tooth direction, n is the discrete number in the tooth height direction, i is the i-th discrete point in the tooth direction, j is the j-th discrete point in the tooth height direction, h a is the tooth top height, h b is the tooth root height, δ1 is the face cone angle, δ3 is the root cone angle, x(h,θ,φ) is the X coordinate of the first tooth surface point, y(h,θ,φ) is the Y coordinate of the first tooth surface point, and z(h,θ,φ) is the Z coordinate of the first tooth surface point;

[0160] Step S203: Calculate the first tooth surface point normal vector corresponding to the first tooth surface point coordinate based on the pinion tooth surface normal vector.

[0161] In some embodiments, reference Figures 6 to 22 In step S104, based on the first spindle thermal error boundary, the gear blank axial cross section and the first transformation matrix, the coordinates of the second tooth surface point are calculated, including:

[0162] Step S301: construct a spindle coordinate system with the intersection of the grinding wheel mounting surface and the spindle axis as the coordinate origin;

[0163] Step S302: Downsample the thermal error boundary of the first spindle to obtain the offset of the origin of the spindle coordinate system along the X-axis, the offset of the origin of the spindle coordinate system along the Y-axis, the offset of the origin of the spindle coordinate system along the Z-axis, the deflection angle of the Z-axis of the spindle coordinate system around the X-axis, and the deflection angle of the Z-axis of the spindle coordinate system around the Y-axis;

[0164] Step S303: Calculate the pinion tooth surface error vector based on the offset of the spindle coordinate system origin along the X axis, the offset of the spindle coordinate system origin along the Y axis, the offset of the spindle coordinate system origin along the Z axis, the deflection angle of the spindle coordinate system Z axis around the X axis, the deflection angle of the spindle coordinate system Z axis around the Y axis, the gear blank axial cross section, and the first transformation matrix using the following formula:

[0165]

[0166]

[0167]

[0168]

[0169]

[0170] n t (θ e )=[sinαcos(θ e ) sinα·sin(θ e ) cosα] T

[0171]

[0172] Among them, M s e is the spindle thermal error matrix, δ x is the offset of the origin of the principal axis coordinate system along the X axis, δ y is the offset of the origin of the principal axis coordinate system along the Y axis, δ z is the offset of the origin of the main axis coordinate system along the Z axis, ε x is the deflection angle of the Z axis of the principal axis coordinate system around the X axis, ε y M is the deflection angle of the Z axis around the Y axis of the main axis coordinate system. gt e is the second transformation matrix, I ge (φ e ) is the error tool axis vector in the workpiece coordinate system, o ge (φ e ) is the error position vector of the tool coordinate system origin in the workpiece coordinate system, n ge (θ e ,φ e ) is the normal vector of the pinion tooth surface error, v ge (h e ,θ e ,φ e ) is the error relative speed, φ e is the error cradle angle, θ eThe error rotation angle from a point on the cutting edge to a point on the rotating surface around the tool axis, h e is the tool coordinate system origin and point p h The error distance between ge (h e ,θ e ,φ e ) is the position vector of the pinion tooth surface error, ρ(h e ) is the error distance, n t (θ e ) is the error normal vector of the tool linear edge rotation surface in the tool coordinate system;

[0173] Step S304: Calculate the coordinates of the second tooth surface point based on the pinion tooth surface error vector using the following formula:

[0174] r ge (h e ,θ e ,φ e )=[x e (h e ,θ e ,φ e ),y e (h e ,θ e ,φ e ),z e (h e ,θ e ,φ e )] T

[0175]

[0176] Among them, x e (h e ,θ e ,φ e ) is the X coordinate of the second tooth surface point, y e (h e ,θ e ,φ e ) is the Y coordinate of the second tooth surface point, z e (h e ,θ e ,φ e ) is the Z coordinate of the second tooth surface point.

[0177] The spindle coordinate system is established with the intersection of the grinding wheel mounting surface and the spindle axis as the coordinate origin. Therefore, the spindle thermal error can be quantitatively expressed as the deviation between the ideal position and the actual position of the spindle coordinate system after the machine tool undergoes thermal deformation, including the error components of 6 degrees of freedom. The indexing error around the Z axis has no effect on the processing and is not considered. Specifically, the offset δ of the spindle coordinate system origin along the X axis, Y axis, and Z axis isx , δ y , δ z , the deflection angle ε of the Z axis of the main axis coordinate system around the X axis and Y axis respectively x , ε y In the experiment, the five spindle thermal errors can be measured and decomposed by arranging five eddy current sensors through the "five-point method".

[0178] In some embodiments, in step S105, the tooth surface deviation value includes an average tooth surface deviation value and a maximum tooth surface deviation value, and the tooth surface deviation value is calculated based on the first tooth surface point coordinate, the first tooth surface point normal vector, and the second tooth surface point coordinate, including:

[0179] Step S401, obtaining the coordinates of the first center point of the first tooth surface composed of the first tooth surface point coordinates; obtaining the coordinates of the second center point of the second tooth surface composed of the second tooth surface point coordinates;

[0180] Step S402: Calculate a phase angle based on the Y coordinate and Z coordinate of the first center point coordinate and the Y coordinate and Z coordinate of the second center point coordinate, wherein the phase angle is used to rotate the Y coordinate and Z coordinate of the first center point coordinate around the workpiece axis by the phase angle so that they coincide with the Y coordinate and Z coordinate of the second center point coordinate;

[0181] Step S403, rotating the second tooth surface point coordinates around the workpiece axis by a phase angle to obtain the third tooth surface point coordinates;

[0182] Step S404: Calculate the normal deviation value based on the first tooth surface point coordinates and the third tooth surface point coordinates using the following formula:

[0183] e i,j =(P 2i,j -P 1i，j) ·n i,j ,(i=1,2,...,m,j=1,2,...,n);

[0184] Among them, e i,j is the normal deviation value of the jth tooth height direction in the i-th tooth direction, P 2i,j is the coordinate of the third tooth surface point in the i-th tooth direction and the j-th tooth height direction, P 1i,j is the coordinate of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction, n i,j is the normal vector of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction;

[0185] Step S405: Calculate the tooth surface deviation value based on the normal deviation value using the following formula:

[0186]

[0187] f2(δ x ,δy ,δ z ,ε x ,ε y )=max(|e i,j |);

[0188] Among them, f1(δ x ,δ y ,δ z ,ε x ,ε y ) is the average tooth surface deviation value, f2(δ x ,δ y ,δ z ,ε x ,ε y ) is the maximum tooth surface deviation value.

[0189] In some embodiments, the method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes:

[0190] Step S501: When the tooth surface deviation value is less than the preset tooth surface deviation value, based on the first step length, the first spindle thermal error boundary is expanded to obtain the second spindle thermal error boundary;

[0191] Step S502: When the second spindle thermal error boundary is greater than the preset maximum error boundary, the second spindle thermal error boundary is used as the spindle thermal error control boundary;

[0192] Step S503: When the second spindle thermal error boundary is less than the preset maximum error boundary, the second tooth surface deviation value is calculated based on the second spindle thermal error boundary, and so on, until the Kth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, then the K-1th spindle thermal error boundary is used as the spindle thermal error control boundary, where K is the number of iterations.

[0193] In some embodiments, the method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes:

[0194] Step S601: when the tooth surface deviation value is greater than the preset tooth surface deviation value but half of the first step length is greater than the preset minimum step length, the first step length is halved to obtain a second step length;

[0195] Step S602: Based on the second step length, the first spindle thermal error boundary is expanded to obtain a second step length spindle thermal error boundary;

[0196] Step S603: When the second-step spindle thermal error boundary is greater than the preset maximum error boundary, the second-step spindle thermal error boundary is used as the spindle thermal error control boundary;

[0197] Step S604: When the second-step spindle thermal error boundary is less than the preset maximum error boundary, the corresponding tooth surface deviation value is calculated based on the second-step spindle thermal error boundary, and so on, until the Q-th tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Q-th step is less than the preset minimum step, then the Q-1-th spindle thermal error boundary is used as the spindle thermal error control boundary, where Q is the number of iterations.

[0198] Taking a pair of 23 / 43 tooth spiral bevel gear pairs as an example, the influence of single spindle thermal error on spiral bevel gear error is studied. The basic parameters of the gear pair are shown in Tables 1 and 2 below. Table 1 shows the parameters of the gear pair blank, and Table 2 shows the processing parameters of the gear pair.

[0199] Table 1

[0200]

[0201]

[0202] Table 2

[0203] project Small wheel Big Wheel Radial tool position / mm 108.214 109.633 Blade inclination angle / ° 5.46 2.4 Knife angle / ° 285.5 49.55 Vertical wheel position / mm 0.837 0 Installation angle / ° 21.6 57.58 Horizontal wheel position / mm -0.7979 0 Beds / mm 14.5939 -4.093 Scroll Ratio 2.0846 1.1301 Spiral correction factor -3.452 / Angular tool position / ° 84.28 84.55 Cutter radius / mm 131.2491 133.35 Tip distance / mm 1.5928 1.373 External blade pressure angle / ° 20 20

[0204] Specifically, the normal deviation of each tooth surface point is calculated with the maximum absolute deviation and the average absolute deviation of the tooth surface as constraints. The maximum absolute deviation and the average absolute deviation of the tooth surface can be expressed as:

[0205]

[0206] f2(δ x ,δ y ,δ z ,ε x ,ε y )=max(|e i,j |)≤E2

[0207] Among them, E1 and E2 are corresponding control targets.

[0208] By optimizing the solution algorithm, the maximum allowable boundaries of various spindle thermal errors that can meet the E1 and E2 requirements are searched.

[0209]

[0210] Among them, [δ x ]、[δ y ]、[δ z ]、[ε x ]、[ε y ] is the control boundary of each thermal error.

[0211] This application provides a prediction accuracy target for spindle thermal error modeling, ensuring that when the prediction accuracy meets the requirement, the tooth surface machining accuracy after thermal error compensation can meet the given accuracy requirements. In the boundary solution algorithm, a boundary search strategy is formulated based on the influence of various spindle thermal errors on tooth surface errors. That is, the boundary search is symmetrically searched on the left and right boundaries, and the same boundary is used for each error accuracy prediction with equal difficulty. This can significantly improve the boundary solution efficiency and reduce calculation time.

[0212] In some embodiments, calculating the first transformation matrix between the workpiece coordinate system and the tool coordinate system in step S102 includes:

[0213] Step S701, constructing a machine tool coordinate system, a workpiece axis fixed coordinate system, a machine tool fixed coordinate system, a cradle fixed coordinate system and a tool rotation coordinate system;

[0214] Step S702: Calculate the first transformation matrix according to the workpiece coordinate system, tool coordinate system, machine tool coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, cradle fixed coordinate system and tool rotation coordinate system using the following formula:

[0215] φ c =m*φ

[0216]

[0217]

[0218]

[0219]

[0220]

[0221]

[0222] M gt =M gd ·M dc ·M cm ·M mb ·M ba ·M at ;

[0223] Among them, M gt is the first transformation matrix, M gd M is the transformation matrix from the workpiece axis fixed coordinate system to the workpiece coordinate system, dc is the transformation matrix from the machine tool fixed coordinate system to the workpiece axis fixed coordinate system, M cm is the transformation matrix from the machine tool coordinate system to the machine tool fixed coordinate system, M mb M is the transformation matrix from the cradle fixed coordinate system to the machine tool coordinate system. baM is the transformation matrix from the tool rotation coordinate system to the cradle fixed coordinate system. at is the transformation matrix from tool coordinate system to tool rotation coordinate system, E M is the vertical wheel position, x B For beds, x D is the horizontal wheel position, q is the angular tool position, s is the radial tool position, γ is the installation angle, I is the tool inclination angle, J is the tool rotation angle, φ c is the wheel blank rotation angle, φ is the cradle rotation angle, m is the rolling ratio, x hl is the spiral coefficient.

[0224] Specifically, to facilitate understanding by those skilled in the art, a set of best embodiments are provided below:

[0225] 1. Data Acquisition

[0226] Obtaining the initial spindle thermal error boundary, the gear blank shaft cross section, and the first step length, and expanding the first spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0227] 2. Calculation of the first conversion matrix:

[0228] Construct the workpiece coordinate system and the tool coordinate system, and calculate the first transformation matrix of the workpiece coordinate system and the tool coordinate system, specifically:

[0229] Construct the machine tool coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, cradle fixed coordinate system and tool rotation coordinate system;

[0230] The first transformation matrix is ​​calculated using the following formula based on the workpiece coordinate system, tool coordinate system, machine coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, cradle fixed coordinate system, and tool rotation coordinate system:

[0231] φ c =m*φ

[0232]

[0233]

[0234]

[0235]

[0236]

[0237]

[0238] M gt =M gd ·M dc ·M cm ·M mb ·Mba ·M at ;

[0239] Among them, M gt is the first transformation matrix, M gd M is the transformation matrix from the workpiece axis fixed coordinate system to the workpiece coordinate system, dc is the transformation matrix from the machine tool fixed coordinate system to the workpiece axis fixed coordinate system, M cm is the transformation matrix from the machine tool coordinate system to the machine tool fixed coordinate system, M mb M is the transformation matrix from the cradle fixed coordinate system to the machine tool coordinate system. ba M is the transformation matrix from the tool rotation coordinate system to the cradle fixed coordinate system. at is the transformation matrix from tool coordinate system to tool rotation coordinate system, E M is the vertical wheel position, x B For beds, x D is the horizontal wheel position, q is the angular tool position, s is the radial tool position, γ is the installation angle, I is the tool inclination angle, J is the tool rotation angle, φ c is the wheel blank rotation angle, φ is the cradle rotation angle, m is the rolling ratio, x hl is the spiral coefficient.

[0240] 3. Calculation of the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point:

[0241] The coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point are calculated based on the gear blank axial section and the first transformation matrix, specifically:

[0242] Based on the first transformation matrix, the pinion tooth surface normal vector, relative velocity, and pinion tooth surface position vector are calculated using the following formulas:

[0243] o t [0 0 0] T

[0244] I t =[0 0 1] T

[0245] n p (θ)=[sinα·cos(θ) sinα·sin(θ) cosα] T

[0246]

[0247] r p (h,θ)=o t +h·I t +ρ(h)·n p (θ)

[0248]

[0249]

[0250]

[0251]

[0252] Among them, t is the position vector of the tool coordinate system origin in the tool coordinate system, I t is the unit vector basis of the Z axis of the tool coordinate system, n p (θ) is the unit normal vector of the rotating surface at point p, α is n p (θ) and I t The angle formed, θ is the rotation angle of a point on the cutting edge around the tool axis to the point on the rotating surface, ρ(h) is the angle between point p and point p h The distance between u is the cutter head radius, P W is the tool tip distance, α g is the contour pressure angle, h is the tool coordinate system origin and point p h The distance between h n p (θ) and I t The intersection of ± is the concave surface of the tool and - is the convex surface of the tool, r p (h,θ) is the position vector of the point on the rotating surface in the tool coordinate system, M gt is the first transformation matrix, I g (φ) is the tool axis vector in the workpiece coordinate system, o g (φ) is the position vector of the tool coordinate system origin in the workpiece coordinate system, φ is the cradle angle, n g (θ, φ) is the normal vector of the pinion tooth surface, n t (θ) is the normal vector of the rotating surface of the tool linear edge in the tool coordinate system, r g (h,θ,φ) is the position vector of the gear tooth surface, v g (h,θ,φ) is the relative velocity;

[0253] The coordinates of the first tooth surface point are calculated based on the pinion tooth surface normal vector, pinion tooth surface position vector and relative speed using the following formula:

[0254] n g (θ,φ)·v g (h,θ,φ)=0

[0255]

[0256] 0≤f≤F

[0257] -b f ≤d≤af

[0258]

[0259]

[0260]

[0261] r g (h,θ,φ)=[x(h,θ,φ),y(h,θ,φ),z(h,θ,φ)] T

[0262]

[0263] Among them, R Q is the X coordinate of the grid point Q in the gear blank's mid-axis section in the workpiece coordinate system, L Q is the Z coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system, A0 is the outer cone distance, f is the discrete parameter of the projection surface along the tooth direction, d is the discrete parameter of the projection surface along the tooth height direction, δ2 is the pitch cone angle, F is the tooth width, a f is the tooth top corresponding to parameter f, b f is the tooth root corresponding to parameter f, m is the discrete number in the tooth direction, n is the discrete number in the tooth height direction, i is the i-th discrete point in the tooth direction, j is the j-th discrete point in the tooth height direction, h a is the tooth top height, h b is the tooth root height, δ1 is the face cone angle, δ3 is the root cone angle, x(h,θ,φ) is the X coordinate of the first tooth surface point, y(h,θ,φ) is the Y coordinate of the first tooth surface point, and z(h,θ,φ) is the Z coordinate of the first tooth surface point;

[0264] Based on the pinion tooth surface normal vector, a first tooth surface point normal vector corresponding to the first tooth surface point coordinate is calculated.

[0265] 4. Calculation of coordinates of the second tooth surface point:

[0266] Based on the thermal error boundary of the first spindle, the gear blank axial section and the first transformation matrix, the coordinates of the second tooth surface point are calculated as follows:

[0267] The intersection of the grinding wheel mounting surface and the spindle axis is used as the coordinate origin to construct the spindle coordinate system;

[0268] Downsample the thermal error boundary of the first spindle to obtain the offset of the origin of the spindle coordinate system along the X-axis, the offset of the origin of the spindle coordinate system along the Y-axis, the offset of the origin of the spindle coordinate system along the Z-axis, the deflection angle of the Z-axis of the spindle coordinate system around the X-axis, and the deflection angle of the Z-axis of the spindle coordinate system around the Y-axis;

[0269] Based on the offset of the origin of the spindle coordinate system along the X axis, the offset of the origin of the spindle coordinate system along the Y axis, the offset of the origin of the spindle coordinate system along the Z axis, the deflection of the Z axis of the spindle coordinate system around the X axis, the deflection of the Z axis of the spindle coordinate system around the Y axis, the gear blank axial section and the first transformation matrix, the pinion tooth surface error vector is calculated using the following formula:

[0270]

[0271]

[0272]

[0273]

[0274]

[0275] n t (θe ) =[sinα·cos(θ e ) sinα·sin(θ e ) cosα] T

[0276]

[0277] Among them, M s e is the spindle thermal error matrix, δ x is the offset of the origin of the principal axis coordinate system along the X axis, δ y is the offset of the origin of the principal axis coordinate system along the Y axis, δ z is the offset of the origin of the main axis coordinate system along the Z axis, ε x is the deflection angle of the Z axis of the principal axis coordinate system around the X axis, ε y M is the deflection angle of the Z axis around the Y axis of the main axis coordinate system. gt e is the second transformation matrix, I ge (φ e ) is the error tool axis vector in the workpiece coordinate system, o ge (φ e ) is the error position vector of the tool coordinate system origin in the workpiece coordinate system, n ge (θ e ,φ e ) is the normal vector of the pinion tooth surface error, v ge (h e ,θ e ,φ e ) is the error relative speed, φ e is the error cradle angle, θ e The error rotation angle from a point on the cutting edge to a point on the rotating surface around the tool axis, he is the tool coordinate system origin and point p h The error distance between ge (h e ,θ e ,φ e ) is the position vector of the pinion tooth surface error, ρ(h e ) is the error distance, n t (θ e ) is the error normal vector of the tool linear edge rotation surface in the tool coordinate system;

[0278] The coordinates of the second tooth surface point are calculated based on the pinion tooth surface error vector using the following formula:

[0279] r ge (h e ,θ e ,φ e )=[x e (h e ,θ e ,φ e ),y e (h e ,θ e ,φ e ),z e (h e ,θ e ,φ e )] T

[0280]

[0281] Among them, x e (h e ,θ e ,φ e ) is the X coordinate of the second tooth surface point, y e (h e ,θ e ,φ e ) is the Y coordinate of the second tooth surface point, z e (h e ,θ e ,φ e ) is the Z coordinate of the second tooth surface point.

[0282] 5. Calculation of tooth surface deviation:

[0283] The tooth surface deviation value is calculated based on the first tooth surface point coordinate, the first tooth surface point normal vector, and the second tooth surface point coordinate, wherein the tooth surface deviation value includes the tooth surface average deviation value and the tooth surface maximum deviation value, specifically:

[0284] Obtain the coordinates of the first center point of the first tooth surface composed of the first tooth surface point coordinates; obtain the coordinates of the second center point of the second tooth surface composed of the second tooth surface point coordinates;

[0285] Calculating a phase angle based on the Y coordinate and Z coordinate of the first center point coordinate and the Y coordinate and Z coordinate of the second center point coordinate, wherein the phase angle is used to rotate the Y coordinate and Z coordinate of the first center point coordinate around the workpiece axis by the phase angle so that they coincide with the Y coordinate and Z coordinate of the second center point coordinate;

[0286] Rotate the second tooth surface point coordinate around the workpiece axis by a phase angle to obtain the third tooth surface point coordinate;

[0287] The normal deviation value is calculated based on the coordinates of the first tooth surface point and the third tooth surface point using the following formula:

[0288] e i，j =(P 2i，j -P 1i，j )·n i,j ,(i=1,2,...,m,j=1,2,...,n);

[0289] Among them, e i,j is the normal deviation value of the jth tooth height direction in the i-th tooth direction, P 2i,j is the coordinate of the third tooth surface point in the i-th tooth direction and the j-th tooth height direction, P 1i,j is the coordinate of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction, n i,j is the normal vector of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction;

[0290] The tooth surface deviation is calculated based on the normal deviation using the following formula:

[0291]

[0292] f2(δ x ,δ y ,δ z ,ε x ,ε y )=max(|e i,j |);

[0293] Among them, f1(δ x ,δ y ,δ z ,ε x ,ε y ) is the average tooth surface deviation value, f2(δ x ,δ y ,δ z ,ε x ,ε y ) is the maximum tooth surface deviation value.

[0294] 6. Calculation of the control boundary of the spindle thermal error:

[0295] When the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary.

[0296] When the tooth surface deviation value is less than the preset tooth surface deviation value, based on the first step length, the thermal error boundary of the first spindle is expanded to obtain the thermal error boundary of the second spindle;

[0297] When the second spindle thermal error boundary is greater than the preset maximum error boundary, the second spindle thermal error boundary is used as the spindle thermal error control boundary;

[0298] When the second spindle thermal error boundary is less than the preset maximum error boundary, the second tooth surface deviation value is calculated based on the second spindle thermal error boundary, and so on, until the Kth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, then the K-1th spindle thermal error boundary is used as the spindle thermal error control boundary, where K is the number of iterations.

[0299] When the tooth surface deviation value is greater than the preset tooth surface deviation value but half of the first step length is greater than the preset minimum step length, the first step length is halved to obtain the second step length;

[0300] Based on the second step length, the thermal error boundary of the first spindle is expanded to obtain the thermal error boundary of the second step length spindle;

[0301] When the second-step spindle thermal error boundary is greater than the preset maximum error boundary, the second-step spindle thermal error boundary is used as the spindle thermal error control boundary;

[0302] When the second-step spindle thermal error boundary is less than the preset maximum error boundary, the corresponding tooth surface deviation value is calculated based on the second-step spindle thermal error boundary, and so on, until the Q-th tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Q-th step is less than the preset minimum step, then the Q-1-th spindle thermal error boundary is used as the spindle thermal error control boundary, where Q is the number of iterations.

[0303] This application analyzes the influence of spindle thermal error on tooth surface normal deviation; and develops a spindle thermal error control boundary solution algorithm driven by tooth surface accuracy. Taking the tooth surface processing requirements as constraints, it solves the feasible domain of various spindle thermal errors, determines the error control boundary, and provides a predicted accuracy target under given tooth surface accuracy requirements for spindle thermal error modeling and compensation, ensuring that the tooth surface accuracy can meet the requirements after the control target is achieved.

[0304] In addition, refer to Figure 23One embodiment of the present application provides a spindle thermal error control domain calculation system for a spiral bevel gear grinding machine tool, comprising a data acquisition module 1100, a first conversion matrix calculation module 1200, a first tooth surface point coordinate calculation module 1300, a second tooth surface point coordinate calculation module 1400, a tooth surface deviation value calculation module 1500, and a spindle thermal error control boundary calculation module 1600, wherein:

[0305] The data acquisition module 1100 is used to obtain the initial spindle thermal error boundary, the gear blank shaft cross section and the first step length, and expand the first spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0306] The first conversion matrix calculation module 1200 is used to construct a workpiece coordinate system and a tool coordinate system, and calculate a first conversion matrix of the workpiece coordinate system and the tool coordinate system;

[0307] The first tooth surface point coordinate calculation module 1300 calculates the first tooth surface point coordinates and the corresponding first tooth surface point normal vector using the gear blank axial cross section and the first transformation matrix;

[0308] The second tooth surface point coordinate calculation module 1400 is used to calculate the second tooth surface point coordinates based on the first spindle thermal error boundary, the gear blank axial cross section and the first transformation matrix;

[0309] The tooth surface deviation value calculation module 1500 is used to calculate the tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector and the second tooth surface point coordinates;

[0310] The spindle thermal error control boundary calculation module 1600 is used to use the initial spindle thermal error boundary as the spindle thermal error control boundary when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length.

[0311] This system obtains the first spindle thermal error boundary by obtaining the initial spindle thermal error boundary, the gear blank shaft section and the first step length, and expands the first spindle thermal error boundary according to the first step length; constructs the workpiece coordinate system and the tool coordinate system, and calculates the first transformation matrix of the workpiece coordinate system and the tool coordinate system; calculates the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank shaft section and the first transformation matrix; calculates the second tooth surface point coordinates based on the first spindle thermal error boundary, the gear blank shaft section and the first transformation matrix; calculates the tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector and the second tooth surface point coordinates; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by presetting the tooth surface deviation value, provides a clear prediction accuracy target for thermal error modeling, and ensures that the prediction under various working conditions can have sufficient tooth surface accuracy.

[0312] It should be noted that this system embodiment and the above-mentioned method embodiment are based on the same inventive concept, so the relevant content of the above-mentioned method embodiment is also applicable to this system embodiment and will not be repeated here.

[0313] Figure 24 A schematic diagram of the hardware structure for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine provided in an embodiment of the present application is shown.

[0314] The computing device in the spindle thermal error control domain of the spiral bevel gear grinding machine may include a processor 301 and a memory 302 storing computer program instructions.

[0315] 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.

[0316] 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.

[0317] 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.

[0318] The processor 301 reads and executes computer program instructions stored in the memory 302 to implement any one of the spindle thermal error control domain calculation methods for the spiral bevel gear grinding machine in the above embodiments.

[0319] In one example, the spindle thermal error control domain computing device of the spiral bevel gear grinding machine tool may further include a communication interface 303 and a bus 310. Figure 24 As shown, the processor 301 , the memory 302 , and the communication interface 303 are connected via a bus 310 and communicate with each other.

[0320] 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.

[0321] Bus 310 includes hardware, software or both, and couples the components of the spindle thermal error control domain computing device of the spiral bevel gear grinding machine to each other. For example, and not limitation, the bus may include an accelerated graphics port (AGP) or other graphics bus, an enhanced industrial standard architecture (EISA) bus, a front-side bus (FSB), a hypertransport (HT) interconnect, an industrial standard architecture (ISA) bus, an infinite bandwidth interconnect, a low pin count (LPC) bus, a memory bus, a microchannel architecture (MCA) bus, a peripheral component interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a serial advanced technology attachment (SATA) bus, a video electronics standard association local (VLB) bus or other suitable buses or a combination of two or more of these. Where appropriate, bus 310 may include one or more buses. Although the present application describes and illustrates a specific bus, the present application considers any suitable bus or interconnect.

[0322] The spindle thermal error control domain calculation device of the spiral bevel gear grinding machine tool can execute the spindle thermal error control domain calculation method of the spiral bevel gear grinding machine tool in the embodiment of the present application based on the three-dimensional design model, thereby realizing the combination Figure 1 and Figure 8 The present invention describes a method and system for calculating the thermal error control domain of the spindle of a spiral bevel gear grinding machine tool.

[0323] In addition, in conjunction with the above-described method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine, embodiments of the present application may provide a computer storage medium for implementation. The computer storage medium stores computer program instructions; when executed by a processor, the computer program instructions implement any of the above-described methods for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine.

[0324] 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.

[0325] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, they can be, for example, 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. Programs or code segments can be stored in machine-readable media, or transmitted on a transmission medium or a communication link by a data signal carried in a carrier wave. "Machine-readable media" can include any medium capable of storing or transmitting 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 segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0326] 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.

[0327] 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.

[0328] 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 calculating the spindle thermal error control region of a spiral bevel gear grinding machine tool, characterized in that: The method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool includes: Acquire an initial spindle thermal error boundary, a gear blank shaft cross section, and a first step length, and expand the first spindle thermal error boundary according to the first step length to obtain a first spindle thermal error boundary; Constructing a workpiece coordinate system and a tool coordinate system, and calculating a first transformation matrix of the workpiece coordinate system and the tool coordinate system; Calculate the coordinates of a first tooth surface point and a corresponding first tooth surface point normal vector based on the gear blank axial cross section and the first transformation matrix; Calculating the coordinates of a second tooth surface point based on the first spindle thermal error boundary, the gear blank axial cross section, and the first transformation matrix; calculating a tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector, and the second tooth surface point coordinates; When the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary.

2. The method for calculating the spindle thermal error control region of a spiral bevel gear grinding machine according to claim 1, characterized in that: The calculating of the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank axial cross section and the first transformation matrix includes: Based on the first transformation matrix, the pinion tooth surface normal vector, relative velocity, and pinion tooth surface position vector are calculated using the following formula: Among them, t is the position vector of the tool coordinate system origin in the tool coordinate system, I t is the unit vector basis of the Z axis of the tool coordinate system, n p (θ) is the unit normal vector of the rotating surface at point p, α is n p (θ) and I t The angle formed, θ is the rotation angle of a point on the cutting edge around the tool axis to the point on the rotating surface, ρ(h) is the angle between point p and point p h The distance between u is the cutter head radius, P W is the tool tip distance, α g is the contour pressure angle, h is the tool coordinate system origin and point p h The distance between h n p (θ) and I t The intersection of ± is the concave surface of the tool and - is the convex surface of the tool, r p (h,θ) is the position vector of the point on the rotating surface in the tool coordinate system, M gt is the first transformation matrix, I g (φ) is the tool axis vector in the workpiece coordinate system, o g (φ) is the position vector of the tool coordinate system origin in the workpiece coordinate system, φ is the cradle angle, n g (θ, φ) is the normal vector of the pinion tooth surface, n t (θ) is the normal vector of the rotating surface of the tool linear edge in the tool coordinate system, r g (h,θ,φ) is the position vector of the gear tooth surface, v g (h,θ,φ) is the relative velocity; The first tooth surface point coordinates are calculated based on the pinion tooth surface normal vector, the pinion tooth surface position vector and the relative speed using the following formula: Among them, R Q is the X coordinate of the grid point Q in the gear blank's mid-axis section in the workpiece coordinate system, L Q is the Z coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system, A0 is the outer cone distance, f is the discrete parameter of the projection surface along the tooth direction, d is the discrete parameter of the projection surface along the tooth height direction, δ2 is the pitch cone angle, F is the tooth width, a f is the tooth top corresponding to parameter f, b f is the tooth root corresponding to parameter f, m is the discrete number in the tooth direction, n is the discrete number in the tooth height direction, i is the i-th discrete point in the tooth direction, j is the j-th discrete point in the tooth height direction, h a is the tooth top height, h b is the tooth root height, δ1 is the face cone angle, δ3 is the root cone angle, x(h,θ,φ) is the X coordinate of the first tooth surface point, y(h,θ,φ) is the Y coordinate of the first tooth surface point, and z(h,θ,φ) is the Z coordinate of the first tooth surface point; Based on the pinion tooth surface normal vector, the first tooth surface point normal vector corresponding to the first tooth surface point coordinate is calculated.

3. The method for calculating the spindle thermal error control region of a spiral bevel gear grinding machine according to claim 2, characterized in that: The calculating the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank axial cross section and the first transformation matrix includes: The intersection of the grinding wheel mounting surface and the spindle axis is used as the coordinate origin to construct the spindle coordinate system; Downsampling the first spindle thermal error boundary to obtain an offset of the origin of the spindle coordinate system along the X-axis, an offset of the origin of the spindle coordinate system along the Y-axis, an offset of the origin of the spindle coordinate system along the Z-axis, a deflection angle of the Z-axis of the spindle coordinate system around the X-axis, and a deflection angle of the Z-axis of the spindle coordinate system around the Y-axis; The pinion tooth surface error vector is calculated based on the offset of the origin of the main axis coordinate system along the X axis, the offset of the origin of the main axis coordinate system along the Y axis, the offset of the origin of the main axis coordinate system along the Z axis, the deflection angle of the Z axis of the main axis coordinate system around the X axis, the deflection angle of the Z axis of the main axis coordinate system around the Y axis, the gear blank axial cross section and the first transformation matrix using the following formula: Among them, M s e is the spindle thermal error matrix, δ x is the offset of the origin of the principal axis coordinate system along the X axis, δ y is the offset of the origin of the principal axis coordinate system along the Y axis, δ z is the offset of the origin of the main axis coordinate system along the Z axis, ε x is the deflection angle of the Z axis of the principal axis coordinate system around the X axis, ε y M is the deflection angle of the Z axis around the Y axis of the main axis coordinate system, gt e is the second transformation matrix, I ge (φ e ) is the error tool axis vector in the workpiece coordinate system, o ge (φ e ) is the error position vector of the tool coordinate system origin in the workpiece coordinate system, n ge (θ e ,φ e ) is the normal vector of the pinion tooth surface error, v ge (h e ,θ e ,φ e ) is the error relative speed, φ e is the error cradle angle, θ e The error rotation angle from a point on the cutting edge to a point on the rotating surface around the tool axis, h e is the tool coordinate system origin and point p h The error distance between ge (h e ,θ e ,φ e ) is the position vector of the pinion tooth surface error, ρ(h e ) is the error distance, n t (θ e ) is the error normal vector of the tool linear edge rotation surface in the tool coordinate system; The coordinates of the second tooth surface point are calculated based on the pinion tooth surface error vector using the following formula: Among them, x e (h e ,θ e ,φ e ) is the X coordinate of the second tooth surface point, y e (h e ,θ e ,φ e ) is the Y coordinate of the second tooth surface point, z e (h e ,θ e ,φ e ) is the Z coordinate of the second tooth surface point.

4. The method for calculating the spindle thermal error control region of a spiral bevel gear grinding machine tool according to claim 3, characterized in that: The tooth surface deviation value includes an average tooth surface deviation value and a maximum tooth surface deviation value. The calculating of the tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector, and the second tooth surface point coordinates includes: Obtain the coordinates of the first center point of the first tooth surface composed of the first tooth surface point coordinates; obtain the coordinates of the second center point of the second tooth surface composed of the second tooth surface point coordinates; Calculating a phase angle based on the Y coordinate and Z coordinate of the first center point coordinate and the Y coordinate and Z coordinate of the second center point coordinate, wherein the phase angle is used to rotate the Y coordinate and Z coordinate of the first center point coordinate around the workpiece axis by the phase angle so that the Y coordinate and Z coordinate of the first center point coordinate coincide with the Y coordinate and Z coordinate of the second center point coordinate; Rotating the second tooth surface point coordinate around the workpiece axis by the phase angle to obtain the third tooth surface point coordinate; The normal deviation value is calculated based on the first tooth surface point coordinates and the third tooth surface point coordinates using the following formula: e i，j =(P 2i，j -P 1i，j )·n i，j ,(i=1,2,...,m,j=1,2,...,n); Among them, e i,j is the normal deviation value of the jth tooth height direction in the i-th tooth direction, P 2i,j is the coordinate of the third tooth surface point in the i-th tooth direction and the j-th tooth height direction, P 1i,j is the coordinate of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction, n i,j is the normal vector of the first tooth surface point in the i-th tooth direction and the j-th tooth height direction; The tooth surface deviation value is calculated based on the normal deviation value using the following formula: f2(d x ,d y ,d z ,he x ,he y )=max(|e i,j |); Among them, f1(δ x ,δ y ,δ z ,ε x ,ε y ) is the tooth surface average deviation value of the tooth surface deviation value, f2(δ x ,δ y ,δ z ,ε x ,ε y ) is the maximum tooth surface deviation value of the tooth surface deviation value.

5. The method for calculating the spindle thermal error control region of a spiral bevel gear grinding machine according to claim 1, characterized in that: The method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes: When the tooth surface deviation value is less than the preset tooth surface deviation value, based on the first step length, the first spindle thermal error boundary is expanded to obtain a second spindle thermal error boundary; When the second spindle thermal error boundary is greater than a preset maximum error boundary, the second spindle thermal error boundary is used as the spindle thermal error control boundary; When the second spindle thermal error boundary is less than the preset maximum error boundary, the second tooth surface deviation value is calculated based on the second spindle thermal error boundary, and so on, until the Kth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, then the K-1th spindle thermal error boundary is used as the spindle thermal error control boundary, where K is the number of iterations.

6. The method for calculating the spindle thermal error control region of a spiral bevel gear grinding machine according to claim 1, characterized in that: The method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes: When the tooth surface deviation value is greater than the preset tooth surface deviation value but half of the first step length is greater than the preset minimum step length, the first step length is halved to obtain a second step length; Based on the second step length, expanding the first spindle thermal error boundary to obtain a second step length spindle thermal error boundary; When the second step-length spindle thermal error boundary is greater than the preset maximum error boundary, the second step-length spindle thermal error boundary is used as the spindle thermal error control boundary; When the second step spindle thermal error boundary is less than the preset maximum error boundary, the corresponding tooth surface deviation value is calculated based on the second step spindle thermal error boundary, and so on, until the Qth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Qth step is less than the preset minimum step, then the Q-1th spindle thermal error boundary is used as the spindle thermal error control boundary, where Q is the number of iterations.

7. The method for calculating the spindle thermal error control region of a spiral bevel gear grinding machine according to claim 1, characterized in that: The calculating of the first transformation matrix between the workpiece coordinate system and the tool coordinate system comprises: Construct the machine tool coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, cradle fixed coordinate system and tool rotation coordinate system; The first transformation matrix is ​​calculated according to the workpiece coordinate system, the tool coordinate system, the machine tool coordinate system, the workpiece axis fixed coordinate system, the machine tool fixed coordinate system, the cradle fixed coordinate system and the tool rotation coordinate system using the following formula: Among them, M gt is the first transformation matrix, M gd M is the transformation matrix from the workpiece axis fixed coordinate system to the workpiece coordinate system, dc is the transformation matrix from the machine tool fixed coordinate system to the workpiece axis fixed coordinate system, M cm is the transformation matrix from the machine tool coordinate system to the machine tool fixed coordinate system, M mb M is the transformation matrix from the cradle fixed coordinate system to the machine tool coordinate system. ba M is the transformation matrix from the tool rotation coordinate system to the cradle fixed coordinate system. at is the transformation matrix from tool coordinate system to tool rotation coordinate system, E M is the vertical wheel position, x B For beds, x D is the horizontal wheel position, q is the angular tool position, s is the radial tool position, γ is the installation angle, I is the tool inclination angle, J is the tool rotation angle, φ c is the wheel blank rotation angle, φ is the cradle rotation angle, m is the rolling ratio, x hl is the spiral coefficient.

8. A spindle thermal error control domain calculation system for a spiral bevel gear grinding machine tool, characterized in that: The spindle thermal error control domain calculation system of the spiral bevel gear grinding machine tool includes: a data acquisition module, configured to acquire an initial spindle thermal error boundary, a gear blank shaft cross section, and a first step length, and to expand the first spindle thermal error boundary according to the first step length to obtain a first spindle thermal error boundary; a first conversion matrix calculation module, configured to construct a workpiece coordinate system and a tool coordinate system, and calculate a first conversion matrix between the workpiece coordinate system and the tool coordinate system; A first tooth surface point coordinate calculation module, configured to calculate the first tooth surface point coordinates and the corresponding first tooth surface point normal vector based on the gear blank axial cross section and the first transformation matrix; a second tooth surface point coordinate calculation module, configured to calculate the second tooth surface point coordinates based on the first spindle thermal error boundary, the gear blank axial cross section, and the first transformation matrix; a tooth surface deviation value calculation module, configured to calculate a tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vector, and the second tooth surface point coordinates; The spindle thermal error control boundary calculation module is used to use the initial spindle thermal error boundary as the spindle thermal error control boundary when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length.

9. A device for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool, characterized in that: It includes at least one control processor and a memory for communicating with the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor to execute the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool as described in any one of claims 1 to 7.

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 spindle thermal error control domain calculation method for a spiral bevel gear grinding machine according to any one of claims 1 to 7.

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