Finite element simulation analysis method for meshing characteristics of spiral bevel gear containing dislocation quantity

Abstract

The invention relates to a finite element simulation analysis method for meshing characteristics of a spiral bevel gear containing dislocation quantity, and the method comprises the following steps: S1, simulation pretreatment: building a spiral bevel gear model, defining material attributes, dividing grids, and generating a spiral bevel gear discrete point set; a spiral bevel gear three-dimensional model is constructed, and then a spiral bevel gear assembly finite element analysis model containing the dislocation quantity is obtained; s2, simulation processing: establishing a gear local coordinate system, setting a reference point and a set set, establishing an analysis step, establishing a coupling constraint, setting a contact pair and applying torque and constraint to the spiral bevel gear; and S3, simulation post-processing: selecting data of contact marks, contact stress, bending stress and gear rotation angles in all step lengths on one tooth surface of the spiral bevel gear, exporting the data in the form of an EXCEL file, and processing a result. Experimental testing is replaced with a simulation means, cost is reduced for design and analysis of the gear, and time is saved. The dislocation quantity influence is considered, and the dislocation quantity is added.

Description

Technical Field

[0001] The invention belongs to the technical field of aviation gear transmission, and relates to a finite element simulation analysis method for meshing characteristics of a spiral bevel gear containing a misalignment, and in particular to a calculation method for meshing characteristics analysis of a spiral bevel gear containing a misalignment by using ABAQUS finite element numerical analysis software. Background Art

[0002] In the field of gear transmission, involute bevel gears have the advantages of high transmission efficiency, strong load-bearing capacity, and long service life. They are widely used in many fields such as robotics, aerospace, and ships. In major aircraft engine equipment, involute bevel gears are the most important basic components, and their performance directly determines the operating efficiency, service life, and safety of the engine. Aviation involute bevel gears usually work in harsh operating environments and complex and changeable working conditions, and the internal structure of the casing generally adopts a spring-supported structure. Under high-speed operation, it is very easy to produce large misalignment and it cannot be eliminated, which directly causes the position of the tooth surface contact mark to be unstable, and it is easy to produce tooth surface edge contact and low-quality meshing of the gear pair, which will lead to meshing failure in severe cases.

[0003] The meshing characteristics of the tooth surface are the evaluation index of the meshing quality of spiral bevel gears, which mainly include parameters such as tooth surface contact stress, tooth root bending stress, tooth surface contact mark, and transmission error. The above parameters have an important influence on the meshing characteristics of the tooth surface. For the study of the meshing characteristics of the tooth surface, the main means used is the finite element simulation analysis method, and a small number of studies use experimental test methods. However, due to the high cost of experimental equipment and the long processing cycle of the actual gear, the use of finite element simulation analysis methods can greatly reduce costs, and after multiple iterations of simulation analysis parameters and contact settings, the consistency between the simulation results and the experimental results can be greatly improved. Summary of the invention

[0004] In view of this, in order to solve the problems of high experimental equipment cost and long gear processing cycle in the current experimental test method for analyzing the meshing characteristics of the tooth surface of the involute bevel gear, the present invention provides a finite element simulation analysis method for the meshing characteristics of the involute bevel gear containing the misalignment, which includes ABAQUS simulation pre-processing, simulation processing and simulation post-processing.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A finite element simulation analysis method for meshing characteristics of spiral bevel gears including misalignment includes the following steps:

[0007] S1. Pre-simulation processing, including establishing a spiral bevel gear model, defining material properties and dividing the mesh, wherein establishing the spiral bevel gear model includes obtaining the processing parameters of the spiral bevel gear, generating a discrete point set of the spiral bevel gear, constructing a three-dimensional model of the spiral bevel gear, and then obtaining a finite element analysis model of the spiral bevel gear assembly including the misalignment amount;

[0008] S2, simulation processing, including establishing the local coordinate system of the gear, setting the reference point and set, establishing the analysis step, establishing the coupling constraint, setting the contact pair and applying the torque and constraint to the spiral bevel gear;

[0009] S3, post-simulation processing, select the data of contact imprint, contact stress, bending stress and gear angle in all steps on one tooth surface of the spiral bevel gear, export the data in the form of EXCEL file, and process the results.

[0010] Further, the processing parameters of the spiral bevel gear in step S1 specifically include the main cutting edge radius R BHi , Main cutting edge pressure angle a vi , tool tip radius r bi , tool tip distance W i , nominal radius of cutter head R 0 、Blade inclination angle I i 、Knife corner J i , radial tool position SR i , initial rocking angle q 1i , vertical wheel position EM i , Bed BM i , Machine tool installation angle γm i , horizontal wheel position AM i and rolling ratio i gpi , where i=p represents the small wheel related parameters, and i=w represents the large wheel related parameters.

[0011] The discrete point set of the spiral bevel gear generated in step S1 is specifically: the coordinate origin O 0 Located at the center of the tool tip distance W, coordinate system S 0 (x 0 ,y 0 ,z 0 ) is fixed on the blade, the coordinate system S e (x e ,y e ,z e ) is fixed to the center of the cutter head, S a (x a ,y a ,z a ) represents the tool tilt coordinate system, S b (x b ,y b ,z b) represents the tool rotation coordinate system, S c (x c ,y c ,z c ) represents the cradle coordinate system, S m (x m ,y m ,z m ) represents the machine tool coordinate system, S i (x i ,y i ,z i ) represents the gear coordinate system fixed to the gear blank, and the coordinate system S g (x g ,y g ,z g ), S d (x d ,y d ,z d ) and S f (x f ,y f ,z f ) is the auxiliary coordinate system, β P Represents the angle of the cutter head during rotation. Represents the rotation angle of the cradle during processing. Represents the rotation angle of the gear during the machining process; completed by the tool coordinate system S 0 (x 0 ,y 0 ,z 0 ) to the cutterhead coordinate system S e (x e ,y e ,z e ) and then to the gear blank coordinate system S i (x i ,y i ,z i )

[0012] The tool normal section expression of the small wheel is:

[0013]

[0014]

[0015] The tool normal section expression of the large wheel is:

[0016]

[0017]

[0018] In the formula, u vi With θ viRepresent the variables of the main cutting edge part and the tool tip arc part respectively, "-" represents the expression of the normal section of the inner tool of the tool, and "+" represents the expression of the normal section of the outer tool of the tool;

[0019] Convert the tool normal section expression to the cutter head coordinate system S e (x e ,y e ,z e ) is expressed as:

[0020]

[0021] Where, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel;

[0022] From the cutterhead coordinate system S e (x e ,y e ,z e ) to the gear blank coordinate system S i (x i ,y i ,z i ) is expressed as:

[0023]

[0024] Where, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel;

[0025] Gear Angle With rocking table corner Satisfies the following relationship:

[0026]

[0027] Wherein, when i=p, it represents the small wheel related parameters, when i=w, it represents the large wheel related parameters, when j=1, it represents the gear concave surface, when j=2, it represents the gear convex surface, C and D represent the second-order and third-order deformation correction coefficients when processing the small wheel, respectively. When processing the large wheel, the values ​​of C and D are zero;

[0028] The normal vector of the gear tooth surface is expressed as:

[0029]

[0030] Wherein, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel.

[0031] The meshing equation of spiral bevel gear is expressed as:

[0032]

[0033] Where i = p, it represents the small wheel related parameters, i = w, it represents the large wheel related parameters, v i Represents the relative speed between the blank and the small wheel cutting tool;

[0034] The mathematical model of the tooth surface of the spiral bevel gear can be expressed as:

[0035]

[0036] According to the principle of spatial geometric rotation projection, any point on the tooth surface satisfies the following two relationships:

[0037]

[0038] Where: x t ,y t Represents the x, y coordinates of the projection point, x p ,y p 、z p Represent the x, y, and z coordinates of discrete points respectively.

[0039] In step S1, a three-dimensional model of the spiral bevel gear is constructed, and the point set file of the spiral bevel gear is imported into the three-dimensional software Creo. After boundary blending, projection, shearing, merging, solidification and array commands, the solid models of the large wheel and small wheel of the spiral bevel gear are obtained respectively.

[0040] The finite element analysis model of the spiral bevel gear assembly containing the misalignment in step S1 includes: establishing the axis center lines of the spiral bevel gear large wheel and small wheel respectively according to the given misalignment value in the three-dimensional software Creo, and the basis for establishing the axis center line can be based on the following expression: 0 (x 0 ,y 0 ,z 0 ) is a fixed coordinate system, representing the coincidence point of the two gear pitch cones when there is no misalignment between the large wheel and the small wheel, S g (x g ,y g ,z g ) and S P (x p ,y p ,z p ) are the coordinate systems of the large wheel and the small wheel respectively, S a (x a ,y a ,z a ) and S b are the auxiliary coordinate systems of the large wheel and the small wheel respectively, S c (x c ,y c ,z c ) and S d (xd ,y d ,z d ) are the coordinate systems of the axis angle and the axis angle error respectively. There are four main types of misalignment: offset error ΔE, small wheel axial displacement error ΔX P , large wheel axial displacement error ΔX g , axis angle error ΔΣ, and are the angles of rotation of the large wheel and the small wheel during the meshing process. The mathematical model of the large wheel can be transformed into a coordinate system containing the misalignment and can be expressed as:

[0041]

[0042] The mathematical model of the small wheel can be transformed into a coordinate system containing the misalignment and can be expressed as:

[0043]

[0044] Where ΔE represents the offset error, ΔX P Represents the axial displacement error of the small wheel, ΔX g represents the axial displacement error of the large wheel, ΔΣ represents the axis angle error, and the above four errors are collectively referred to as the misalignment of the spiral bevel gear. and They represent the angles of rotation of the large wheel and the small wheel during the meshing process.

[0045] Furthermore, in step S1, defining material properties includes setting Young's modulus and Poisson's ratio, and the material is set to be isotropic, i.e., a material of uniform density.

[0046] Furthermore, in step S1, the meshing setting is that the tooth surface and the tooth blank of the large wheel and the small wheel are all divided into hexahedral units C3D8R, the contact surface is divided according to 0.2 mm / grid, the tooth top is divided according to 0.5 mm / grid, the tooth root is divided according to 0.1 mm / grid, and the tooth blank is divided according to 5 mm / grid.

[0047] Further, in step S2, a local coordinate system of the gear is established. In Module, select Assembly, then click Datum in Tools, select 3point in CSYS, click Continue, and select three points at the center of the gear circle to obtain the local coordinate system of the small gear and the local coordinate system of the large gear.

[0048] In step S2, set the reference point and set. Click reference point in Tools, select the small wheel local coordinate system and the large wheel local coordinate system respectively, obtain the small wheel reference point RP-1 and the large wheel reference point RP-2, then select Set in Tools, click Create, name them zj1 and zj2, and establish them at the reference points of the large wheel and the small wheel respectively;

[0049] In step S2, establish an analysis step, select Step in Module, click Create in Step Manager, select Static and General in Procedure type, and establish three analysis steps Step-1, Step-2, and Step-3, representing pre-contact, loading, and tooth surface meshing, respectively;

[0050] In step S2, establish coupling constraints, select Interaction in Module, select Coupling for coupling type, constrain the inner cylindrical surface and reference point of the large wheel and small wheel respectively, and select the corresponding local coordinate system respectively;

[0051] In step S2, set the contact pair. Click Create in Interaction Property Manager, select Contact in Type, click Continue, and select Tangential Behavior and Normal Behavior in Mechanical. Then click Created in Interaction Manager, select Surface-to-Surface (Standard) as the contact type, and select the working surface of the small wheel to contact the working surface of the large wheel.

[0052] In step S2, apply torque and constraints to the spiral bevel gear. Select Load in Module, click Create in BoundaryCondition Manager, and create a boundary for the small wheel and the small wheel respectively. Name the driving wheel BC-1 and the driven wheel BC-2. Select Initial as Step, select Displacement / Rotation as Types for Selected Step, click Continue, select the reference points RP-1 and RP-2 of the gear respectively, and then select the local coordinate systems of the small wheel and the large wheel respectively to constrain the degrees of freedom in six directions. For the driving wheel, modify the value of a certain degree of freedom in Step-1 in BC-1 according to the direction of rotation of the gear, so that the gear rotates a small angle, generally 0.1°, and then modify the value of the same degree of freedom in Step-3 in BC-1, which is the angle of the driving wheel at the current number of teeth. For the driven wheel, release the degree of freedom that constrains the direction of rotation of the gear in Step-2 in BC-2. Then click Create in Load Manager, select Step-2 for Step, select Moment for Types for Selected Step, select the reference point and local coordinate system of the driven wheel, and enter the rated torque. The direction of the torque is opposite to the actual driven wheel rotation direction, and the torque based on direction is 0.

[0053] Furthermore, in step S3, select Visualization in Module to see the tooth surface simulation results. Click Remove Selected and select the driven wheel. For the working surface of the driving wheel, change S to CPRESS to obtain the contact stress and contact mark position in each analysis step. Change Mises to Max.Principal in S to obtain the bending stress in each analysis step.

[0054] In step S3, in CPCRESS, the analysis step is moved to the gear tooth surface where the node coordinates are to be extracted, with the appearance of the contact mark on the tooth surface as the starting point and the disappearance of the contact mark as the ending point. The node coordinates of all the tooth surfaces in this stage of the analysis step are extracted, and the data is exported in the form of suffix .rpt. The data is then processed by MATLAB to obtain the tooth surface contact mark position, tooth surface contact mark area ratio and contact stress.

[0055] In step S3, in Max.Principal, the analysis step is moved to the gear tooth root to be extracted, with the appearance of bending stress on the extracted tooth root grid line as the starting point and the bending stress dropping to zero as the ending point. The values ​​of all node coordinates on this grid line in the analysis step of this stage are extracted, and the data is exported in the form of EXCEL, and then processed by MATLAB or Origin to obtain the tooth root stress.

[0056] In step S3, click XY Data in Tools, select ODB history output in Create, select all Rotational displacements (usually there are 6), Save as and then select Plot, select two slashes in the 6 Rotationaldisplacements to represent the rotation angle data of the small wheel and the large wheel in each analysis step, and then click Excel Utilities in Tools in Plug-ins, the data will be exported in the form of EXCEL, and then processed by MATLAB or Origin to obtain the transmission error.

[0057] The beneficial effects of the present invention are:

[0058] 1. The finite element simulation analysis method for meshing characteristics of arc bevel gears with misalignment disclosed in the present invention replaces experimental testing with simulation, and can be used as a detection method to determine the meshing condition of gear tooth surfaces before gear processing, thereby reducing costs and saving time for gear design and analysis.

[0059] 2. The present invention discloses a finite element simulation analysis method for meshing characteristics of arc bevel gears containing misalignment, which takes into account the influence of misalignment, adds misalignment on the basis of gear load-bearing contact analysis, and calculates meshing characteristic parameters including contact mark, contact stress, bending stress and transmission error.

[0060] 3. The finite element simulation analysis method for meshing characteristics of spiral bevel gears including misalignment disclosed in the present invention solidifies the entire process of the calculation method for meshing characteristics of spiral bevel gears considering misalignment, and provides a reference for the field of gear transmission meshing simulation.

[0061] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0063] Figure 1 A simulation flow chart of a finite element simulation analysis method for meshing characteristics of spiral bevel gears including misalignment according to the present invention;

[0064] Figure 2 (a) is a coordinate system model diagram of a small wheel tool in a spiral bevel gear containing a misalignment in an embodiment of a finite element simulation analysis method for meshing characteristics of a spiral bevel gear;

[0065] Figure 2 (b) is a coordinate system model diagram of the large wheel tool in the spiral bevel gear containing misalignment in the embodiment of the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear;

[0066] Figure 2 (c) is a coordinate system model diagram of the cutter head in the spiral bevel gear of the embodiment of the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment;

[0067] Figure 3 A machining coordinate system model diagram of a small wheel in a spiral bevel gear according to a finite element simulation analysis method for meshing characteristics of a spiral bevel gear including misalignment in an embodiment;

[0068] Figure 4 (a) is a schematic diagram of a discrete point set on the tooth surface of the large wheel in the spiral bevel gear in the embodiment of the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment;

[0069] Figure 4 (b) is a schematic diagram of a discrete point set on the tooth surface of the small wheel in the spiral bevel gear in the embodiment of the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment;

[0070] Figure 5 A schematic diagram of a spiral bevel gear assembly coordinate system in which the misalignment is considered in a finite element simulation analysis method for meshing characteristics of a spiral bevel gear including misalignment in an embodiment;

[0071] Figure 6 (a) is a schematic diagram of the misalignment of the spiral bevel gear when the misalignment is considered in the finite element modeling simulation analysis method of the meshing characteristics of the spiral bevel gear containing the misalignment in the embodiment;

[0072] Figure 6 (b) is a schematic diagram of a spiral bevel gear assembly in which the misalignment is considered in the finite element simulation analysis method for meshing characteristics of spiral bevel gears containing misalignment in an embodiment;

[0073] Figure 7A schematic diagram of a finite element analysis model of a spiral bevel gear with misalignment considered in a finite element simulation analysis method for meshing characteristics of a spiral bevel gear with misalignment in an embodiment;

[0074] Figure 8 (a) is a schematic diagram of the tooth surface contact mark, contact stress and area size of the spiral bevel gear under different offset errors when the misalignment is considered in the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment in the embodiment;

[0075] Figure 8 (b) is a schematic diagram of the tooth surface contact mark, contact stress and area size under different pinion axial errors of the spiral bevel gear under the condition of considering the misalignment in the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment in the embodiment;

[0076] Figure 8 (c) is a schematic diagram of the tooth surface contact mark, contact stress and area size under different large wheel axial errors of the spiral bevel gear under the condition of considering the misalignment in the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment in the embodiment;

[0077] Figure 8 (d) is a schematic diagram of the tooth surface contact mark, contact stress and area size under different axis angle errors of the spiral bevel gear under the condition of considering the misalignment in the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment in the embodiment;

[0078] Fig. 9 (a) is a schematic diagram of tooth root stress curves of spiral bevel gears with different offset errors in the embodiment of the finite element simulation analysis method of meshing characteristics of spiral bevel gears with misalignment, taking into account the misalignment;

[0079] Fig. 9 (b) is a schematic diagram of tooth root stress curves of different pinion axial errors of spiral bevel gears considering misalignment in the finite element simulation analysis method of meshing characteristics of spiral bevel gears with misalignment in the embodiment;

[0080] Fig. 9 (c) is a schematic diagram of tooth root stress curves of spiral bevel gears with different large wheel axial errors taking into account the misalignment in the finite element simulation analysis method for meshing characteristics of spiral bevel gears with misalignment in the embodiment;

[0081] Fig. 9 (d) is a schematic diagram of tooth root stress curves of different axis angle errors of spiral bevel gears considering misalignment in the finite element simulation analysis method of meshing characteristics of spiral bevel gears with misalignment in the embodiment;

[0082] Fig.10(a) is a schematic diagram of a transmission error curve of a spiral bevel gear with different offset errors when the misalignment is considered in a finite element simulation analysis method of meshing characteristics of a spiral bevel gear with misalignment in an embodiment;

[0083] Fig.10 (b) is a schematic diagram of the transmission error curve of different pinion axial errors of the spiral bevel gear considering the misalignment in the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear with misalignment in the embodiment;

[0084] Fig.10 (c) is a schematic diagram of a transmission error curve of different large wheel axial errors of a spiral bevel gear considering the misalignment in the finite element simulation analysis method of the meshing characteristics of the spiral bevel gear containing the misalignment in the embodiment;

[0085] Fig.10 (d) is a schematic diagram of the transmission error curve of different axis angle errors of the spiral bevel gears considering the misalignment in the finite element simulation analysis method of the meshing characteristics of the spiral bevel gears containing misalignment in the embodiment. DETAILED DESCRIPTION

[0086] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0087] like Figure 1-Figure 10 A finite element simulation analysis method for meshing characteristics of spiral bevel gears with misalignment based on ABAQUS is shown in FIG. The finite element simulation operation process is as follows: Figure 1 As shown, the following steps are included:

[0088] S1. Simulation pre-processing includes establishing a bevel gear model, defining material properties and dividing the mesh. Establishing the bevel gear model includes obtaining the processing parameters of the bevel gear, generating a discrete point set of the bevel gear, constructing a three-dimensional model of the bevel gear, and then obtaining a finite element analysis model of the bevel gear assembly including the misalignment.

[0089] S11, obtain the processing parameters of the spiral bevel gear, which specifically include the main cutting edge radius R BHi , Main cutting edge pressure angle a vi 、Tool tip radius r bi , tool tip distance W i , nominal radius of cutter head R 0 、Blade inclination angle I i 、Knife corner J i , radial tool position SR i, initial rocking angle q 1i , vertical wheel position EM i , Bed BM i , Machine tool installation angle γm i , horizontal wheel position AM i and rolling ratio i gpi , where i=p represents the small wheel related parameters, and i=w represents the large wheel related parameters.

[0090] S12, generate a discrete point set of spiral bevel gear, specifically: coordinate origin O 0 Located at the center of the tool tip distance W, coordinate system S 0 (x 0 ,y 0 ,z 0 ) is fixed on the blade, the coordinate system S e (x e ,y e ,z e ) is fixed to the center of the cutter head, S a (x a ,y a ,z a ) represents the tool tilt coordinate system, S b (x b ,y b ,z b ) represents the tool rotation coordinate system, S c (x c ,y c ,z c ) represents the cradle coordinate system, S m (x m ,y m ,z m ) represents the machine tool coordinate system, S i (x i ,y i ,z i ) represents the gear coordinate system fixed to the gear blank, and the coordinate system S g (x g ,y g ,z g ), S d (x d ,y d ,z d ) and S f (x f ,y f ,z f ) is the auxiliary coordinate system, β P Represents the angle of the cutter head during rotation. Represents the rotation angle of the cradle during processing. Represents the rotation angle of the gear during the machining process; completed by the tool coordinate system S0 (x 0 ,y 0 ,z 0 ) to the cutterhead coordinate system S e (x e ,y e ,z e ) and then to the gear blank coordinate system S i (x i ,y i ,z i )

[0091] The tool normal section expression of the small wheel is:

[0092]

[0093] The tool normal section expression of the large wheel is:

[0094]

[0095] In the formula, u vi With θ vi Represent the variables of the main cutting edge part and the tool tip arc part respectively, "-" represents the expression of the normal section of the inner tool of the tool, and "+" represents the expression of the normal section of the outer tool of the tool;

[0096] Convert the tool normal section expression to the cutter head coordinate system S e (x e ,y e ,z e ) is expressed as:

[0097]

[0098] Wherein, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel.

[0099] From the cutterhead coordinate system S e (x e ,y e ,z e ) to the gear blank coordinate system S i (x i ,y i ,z i ) is expressed as:

[0100]

[0101] Wherein, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel.

[0102] Gear Angle With rocking table corner Satisfies the following relationship:

[0103]

[0104] Wherein, when i=p, it represents the relevant parameters of the small wheel, when i=w, it represents the relevant parameters of the large wheel, when j=1, it represents the concave surface of the gear, when j=2, it represents the convex surface of the gear, C and D represent the second-order and third-order deformation correction coefficients during small wheel processing, respectively. When processing the large wheel, the values ​​of C and D are zero.

[0105] The normal vector of the gear tooth surface can be expressed as:

[0106]

[0107] Wherein, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel.

[0108] The meshing equation of spiral bevel gear can be expressed as:

[0109]

[0110] Where i = p, it represents the small wheel related parameters, i = w, it represents the large wheel related parameters, v i Represents the relative speed between the blank and the small wheel cutting tool.

[0111] The mathematical model of the tooth surface of the spiral bevel gear can be expressed as:

[0112]

[0113] According to the principle of spatial geometric rotation projection, any point on the tooth surface satisfies the following two relationships:

[0114]

[0115] Where: x t ,y t Represents the x, y coordinates of the projection point, x p ,y p 、z p Represent the x, y, and z coordinates of discrete points respectively.

[0116] S13. Construct a three-dimensional model of the bevel gear, import the point set file of the bevel gear into the three-dimensional software Creo, and obtain the solid models of the large wheel and small wheel of the bevel gear respectively after boundary blending, projection, cutting, merging, solidification and array commands.

[0117] S14. Establishment of a finite element analysis model of a spiral bevel gear assembly including misalignment, including: establishing the axis center lines of the large and small wheels of the spiral bevel gear in the three-dimensional software Creo according to the given misalignment value. The basis for establishing the axis center lines can be based on the following expression: S 0 (x 0 ,y 0 ,z 0 ) is a fixed coordinate system, representing the coincidence point of the two gear pitch cones when there is no misalignment between the large wheel and the small wheel, S g (x g ,y g ,z g ) and S P (x p ,y p ,z p ) are the coordinate systems of the large wheel and the small wheel respectively, S a (x a ,y a ,z a ) and S b are the auxiliary coordinate systems of the large wheel and the small wheel respectively, S c (x c ,y c ,z c ) and S d (x d ,y d ,z d ) are the coordinate systems of the axis angle and the axis angle error respectively. There are four main types of misalignment: offset error ΔE, small wheel axial displacement error ΔX P , large wheel axial displacement error ΔX g , axis angle error ΔΣ, and are the angles of rotation of the large wheel and the small wheel during the meshing process. The mathematical model of the large wheel can be transformed into a coordinate system containing the misalignment and can be expressed as:

[0118]

[0119] The mathematical model of the small wheel can be transformed into a coordinate system containing the misalignment and can be expressed as:

[0120]

[0121] Where ΔE represents the offset error, ΔX P Represents the axial displacement error of the small wheel, ΔX g represents the axial displacement error of the large wheel, ΔΣ represents the axis angle error, and the above four errors are collectively referred to as the misalignment of the spiral bevel gear. and They represent the angles that the large wheel and the small wheel rotate during the meshing process.

[0122] S15. Define material properties, set Young's modulus and Poisson's ratio, and set the material to be isotropic, a material of uniform density.

[0123] S16. Grid division settings: the tooth surface and tooth blank of the large and small wheels all use hexahedral elements C3D8R. The contact surface is divided according to 0.2mm / grid, the tooth top is divided according to 0.5mm / grid, the tooth root is divided according to 0.1mm / grid, and the tooth blank is divided according to 5mm / grid.

[0124] S2. Simulation processing includes establishing the local coordinate system of the gear, setting reference points and sets, establishing analysis steps, establishing coupling constraints, setting contact pairs, and applying torque and constraints to the spiral bevel gear.

[0125] S21. Establish the local coordinate system of the gear. Select Assembly in Module, click Datum in Tools, select 3point in CSYS, click Continue, and select three points at the center of the gear to obtain the local coordinate system of the small wheel and the local coordinate system of the large wheel.

[0126] S22. Set the reference point and set. Click reference point in Tools, select the small wheel local coordinate system and the large wheel local coordinate system respectively, obtain the small wheel reference point RP-1 and the large wheel reference point RP-2, then select Set in Tools, click Create, name them zj1 and zj2, and establish them at the reference points of the large wheel and the small wheel respectively.

[0127] S23. Establish analysis steps, select Step in Module, click Create in Step Manager, select Static and General in Procedure type, and establish three analysis steps Step-1, Step-2, and Step-3, representing pre-contact, loading, and tooth surface meshing, respectively.

[0128] S24. Establish coupling constraints. Select Interaction in Module and Coupling as the coupling type. Constrain the inner cylindrical surfaces and reference points of the large and small wheels respectively, and select the corresponding local coordinate systems respectively.

[0129] S25. Set up the contact pair. Click Create in the Interaction Property Manager. Select Contact in Type. Click Continue. Select Tangential Behavior and Normal Behavior in Mechanical. Then click Created in the Interaction Manager. Select Surface-to-Surface (Standard) as the contact type. Select the working surface of the small wheel to make contact with the working surface of the large wheel.

[0130] S26. Apply torque and constraints to the spiral bevel gear. Select Load in Module, click Create in BoundaryCondition Manager, and create a boundary for the small wheel and the small wheel respectively. Name the driving wheel BC-1 and the driven wheel BC-2. Select Initial for Step, select Displacement / Rotation for Types for Selected Step, click Continue, select the reference points RP-1 and RP-2 of the gear respectively, and then select the local coordinate systems of the small wheel and the large wheel respectively to constrain the degrees of freedom in six directions. For the driving wheel, modify the value of a certain degree of freedom in Step-1 in BC-1 based on the direction of rotation of the gear, so that the gear rotates a small angle, generally 0.1°, and then modify the value of the same degree of freedom in Step-3 in BC-1, the value is the angle of the driving wheel at the current number of teeth. For the driven wheel, release the degree of freedom that constrains the direction of rotation of the gear in Step-2 in BC-2. Then click Create in Load Manager, select Step-2 for Step, select Moment for Types for Selected Step, select the reference point and local coordinate system of the driven wheel, and enter the rated torque. The direction of the torque is opposite to the actual driven wheel rotation direction, and the torque based on direction is 0.

[0131] S3, post-simulation processing, select the data of contact imprint, contact stress, bending stress and gear angle in all steps on one tooth surface of the spiral bevel gear, export the data in the form of EXCEL file, and process the results.

[0132] S31. Select Visualization in Module to see the tooth surface simulation results. Click RemoveSelected and select the driven wheel. For the working surface of the driving wheel, change S to CPRESS to get the contact stress and contact mark position in each analysis step. Change Mises to Max.Principal in S to get the bending stress in each analysis step.

[0133] S32. In CPRESS, move the analysis step to the gear tooth surface where the node coordinates are to be extracted, with the appearance of the contact mark on the tooth surface as the starting point and the disappearance of the contact mark as the ending point. Extract the node coordinates of all the tooth surfaces in this stage of the analysis step, export the data in the form of suffix .rpt, and then process the data through MATLAB to obtain the tooth surface contact mark position, tooth surface contact mark area ratio and contact stress.

[0134] S33. In Max.Principal, move the analysis step to the gear tooth root to be extracted, with the appearance of bending stress on the extracted tooth root grid line as the starting point and the bending stress dropping to zero as the ending point. Extract the values ​​of all node coordinates on this grid line in this stage of the analysis step, export the data in the form of EXCEL, and then process the data through MATLAB or Origin to obtain the tooth root stress.

[0135] S34. Click XY Data in Tools, select ODB history output in Create, select all Rotational displacements (usually there are 6), Save as and then select Plot, select two slashes in the 6 Rotationaldisplacements to represent the rotation angle data of the small wheel and the large wheel in each analysis step, and then click Excel Utilities in Tools in Plug-ins. The data will be exported in the form of EXCEL, and then processed by MATLAB or Origin to obtain the transmission error.

[0136] Example

[0137] Taking a pair of aviation spiral bevel gears as an example, the small wheel is the driving wheel, the large wheel is the driven wheel, the small wheel concave surface and the large wheel convex surface are the working surfaces, and the above-mentioned calculation method is used to calculate the meshing characteristic parameter results of the spiral bevel gears under the condition of considering the misalignment, such as: tooth surface contact mark area, tooth surface contact stress position, tooth surface contact stress, tooth root bending stress and transmission error.

[0138] Table 1 shows the basic geometric parameters of spiral bevel gears, and Table 2 shows the processing parameters of spiral bevel gears.

[0139] Table 1

[0140]

[0141] Table 2

[0142]

[0143] Figure 2 (a) is the coordinate system model diagram of the small wheel tool in the spiral bevel gear; Figure 2 (b) is the coordinate system model diagram of the large wheel tool in the spiral bevel gear; Figure 2 (c) is the coordinate system model diagram of the cutter head in the spiral bevel gear; Figure 3 This is the machining coordinate system model diagram of the small wheel in the spiral bevel gear; Figure 4 (a) is a schematic diagram of the discrete point set on the tooth surface of the large wheel in the spiral bevel gear; Figure 4 (b) is a schematic diagram of the discrete point set on the tooth surface of the small wheel in the spiral bevel gear;

[0144] Figure 5 The schematic diagram of the coordinate system for the spiral bevel gear assembly considering the misalignment; Figure 6 (a) is a schematic diagram of the misalignment of the spiral bevel gear when the misalignment is considered; Figure 6 (b) is a schematic diagram of the spiral bevel gear assembly considering the misalignment; Figure 7 This is a schematic diagram of the finite element analysis model of spiral bevel gears considering the misalignment;

[0145] Table 3 shows the values ​​of various misalignment amounts.

[0146] Table 3

[0147]

[0148] Figure 8 (a) is a schematic diagram of the tooth surface contact imprint, contact stress and area size of the spiral bevel gear under different offset errors considering the misalignment. The offset error of the upper left spiral bevel gear is -0.1mm, the maximum tooth surface contact stress is 991.1Mpa, and the tooth surface area accounts for 19.21%. The offset error of the upper right spiral bevel gear is -0.05mm, the maximum tooth surface contact stress is 1002.5Mpa, and the tooth surface area accounts for 20.05%. The offset error of the lower left spiral bevel gear is 0.05mm, the maximum tooth surface contact stress is 1060.1Mpa, and the tooth surface area accounts for 21.88%. The offset error of the lower right spiral bevel gear is 0.1mm, the maximum tooth surface contact stress is 1131.3Mpa, and the tooth surface area accounts for 24.10%; Figure 8(b) is a schematic diagram of the tooth surface contact mark, contact stress and area size under different axial errors of the spiral bevel gear under the condition of misalignment. The axial displacement error of the upper left spiral bevel gear is -0.1mm, the maximum stress of the tooth surface contact is 1081.5Mpa, and the tooth surface area accounts for 22.77%; the axial displacement error of the upper right spiral bevel gear is -0.05mm, the maximum stress of the tooth surface contact is 1062.4Mpa, and the tooth surface area accounts for 21.98%; the axial displacement error of the lower left spiral bevel gear is 0.05mm, the maximum stress of the tooth surface contact is 988.4Mpa, and the tooth surface area accounts for 19.26%; the axial displacement error of the lower right spiral bevel gear is 0.1mm, the maximum stress of the tooth surface contact is 1004.4Mpa, and the tooth surface area accounts for 18.67%; Figure 8 (c) is a schematic diagram of the tooth surface contact mark, contact stress and area size of the arc bevel gear under different large wheel axial errors considering the misalignment. The axial displacement error of the large wheel of the upper left arc bevel gear is -0.1mm, the maximum stress of the tooth surface contact is 1001.6Mpa, and the tooth surface area accounts for 20.84%. The axial displacement error of the large wheel of the upper right arc bevel gear is -0.05mm, the maximum stress of the tooth surface contact is 1011.2Mpa, and the tooth surface area accounts for 20.59%. The axial displacement error of the large wheel of the lower left arc bevel gear is 0.05mm, the maximum stress of the tooth surface contact is 997.3Mpa, and the tooth surface area accounts for 20.79%. The axial displacement error of the large wheel of the lower right arc bevel gear is 0.1mm, the maximum stress of the tooth surface contact is 1034.5Mpa, and the tooth surface area accounts for 21.83%; Figure 8 (d) is a schematic diagram of the tooth surface contact mark, contact stress and area size of the arc bevel gear under different shaft angle errors considering the misalignment. The shaft angle error of the upper left arc bevel gear is -0.1°, the maximum stress of the tooth surface contact is 1014.1Mpa, and the tooth surface area accounts for 21.23%. The shaft angle error of the upper right arc bevel gear is -0.05°, the maximum stress of the tooth surface contact is 1009.1Mpa, and the tooth surface area accounts for 21.53%. The shaft angle error of the lower left arc bevel gear is 0.05°, the maximum stress of the tooth surface contact is 1028.3Mpa, and the tooth surface area accounts for 20.84%. The shaft angle error of the lower right arc bevel gear is 0.1°, the maximum stress of the tooth surface contact is 1000.8Mpa, and the tooth surface area accounts for 20.79%; Fig. 9(a) is a schematic diagram of the tooth root stress curve of the spiral bevel gear with different offset errors considering the misalignment. The upper left shows that the offset error of the spiral bevel gear is -0.1mm, and the maximum root bending stress is 8.1Mpa when the root tooth width is 169.152mm. The upper right shows that the offset error of the spiral bevel gear is -0.05mm, and the maximum root bending stress is 7.35Mpa when the root tooth width is 164.281mm. The lower left shows that the offset error of the spiral bevel gear is 0.05, and the maximum root bending stress is 5.7Mpa when the root tooth width is 204.24mm. The lower right shows that the offset error of the spiral bevel gear is 0.1mm, and the maximum root bending stress is 4.65Mpa when the root tooth width is 179.852mm. Fig. 9 (b) is a schematic diagram of the tooth root stress curve of different small wheel axial errors of the spiral bevel gear considering the amount of misalignment. The upper left shows that the axial displacement error of the small wheel of the spiral bevel gear is -0.1mm, and the maximum root bending stress is 5.7Mpa when the root tooth width is 166.772mm. The upper right shows that the axial displacement error of the small wheel of the spiral bevel gear is -0.05mm, and the maximum root bending stress is 6.6Mpa when the root tooth width is 193.817mm. The lower left shows that the axial displacement error of the small wheel of the spiral bevel gear is 0.05, and the maximum root bending stress is 8.25Mpa when the root tooth width is 166.721mm. The lower right shows that the axial displacement error of the small wheel of the spiral bevel gear is 0.1mm, and the maximum root bending stress is 8.7Mpa when the root tooth width is 234.145mm. Fig. 9 (c) is a schematic diagram of the tooth root stress curve of the spiral bevel gear with different large wheel axial errors considering the misalignment. The upper left shows that the axial displacement error of the large wheel of the spiral bevel gear is -0.1mm, and the maximum root bending stress is 7.5Mpa when the root tooth width is 182.149mm. The upper right shows that the axial displacement error of the large wheel of the spiral bevel gear is -0.05mm, and the maximum root bending stress is 7.05Mpa when the root tooth width is 172.57mm. The lower left shows that the axial displacement error of the large wheel of the spiral bevel gear is 0.05, and the maximum root bending stress is 8.25Mpa when the root tooth width is 196.988mm. The lower right shows that the axial displacement error of the large wheel of the spiral bevel gear is 0.1mm, and the maximum root bending stress is 7.35Mpa when the root tooth width is 171.517mm. Fig. 9(d) is a schematic diagram of the tooth root stress curve of the spiral bevel gear with different shaft angle errors considering the misalignment. The upper left shows that the shaft angle error of the spiral bevel gear is -0.1°, and the maximum root bending stress is 7.8 MPa when the tooth root width is 154.112 mm. The upper right shows that the shaft angle error of the spiral bevel gear is -0.05°, and the maximum root bending stress is 8.55 MPa when the tooth root width is 221.07 mm. The lower left shows that the shaft angle error of the spiral bevel gear is 0.05°, and the maximum root bending stress is 8.4 MPa when the tooth root width is 183.481 mm. The lower right shows that the shaft angle error of the spiral bevel gear is 0.1°, and the maximum root bending stress is 6 MPa when the tooth root width is 226.703 mm. Fig.10 (a) is a schematic diagram of the transmission error curve of the spiral bevel gear with different offset errors considering the misalignment; Fig.10 (b) is a schematic diagram of the transmission error curve of different pinion axial errors of the spiral bevel gear considering the misalignment; Fig.10 (c) is a schematic diagram of the transmission error curve of the spiral bevel gear with different large wheel axial errors considering the misalignment; Fig.10 (d) is a schematic diagram of the transmission error curve of different axis angle errors of spiral bevel gears considering the misalignment.

[0149] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A finite element simulation analysis method for meshing characteristics of spiral bevel gears with misalignment, characterized in that: The following steps are involved: S1. Pre-simulation processing, including establishing a spiral bevel gear model, defining material properties and dividing the mesh, wherein establishing the spiral bevel gear model includes obtaining the processing parameters of the spiral bevel gear, generating a discrete point set of the spiral bevel gear, constructing a three-dimensional model of the spiral bevel gear, and then obtaining a finite element analysis model of the spiral bevel gear assembly including the misalignment amount; S2, simulation processing, including establishing the local coordinate system of the gear, setting the reference point and set, establishing the analysis step, establishing the coupling constraint, setting the contact pair and applying the torque and constraint to the spiral bevel gear; S3, post-simulation processing, select the data of contact imprint, contact stress, bending stress and gear angle in all steps on one tooth surface of the spiral bevel gear, export the data in the form of EXCEL file, and process the results.

2. The finite element modeling and simulation method for meshing characteristics of spiral bevel gears with misalignment as claimed in claim 1, characterized in that: The processing parameters of the spiral bevel gear in step S1 specifically include the main cutting edge radius R BHi , Main cutting edge pressure angle a vi , tool tip radius r bi , tool tip distance W i , nominal radius of cutter head R0, inclination angle of cutter I i 、Knife corner J i , radial tool position SR i , initial rocking angle q 1i , vertical wheel position EM i , Bed BM i , Machine tool installation angle γm i , horizontal wheel position AM i and rolling ratio i gpi , where i=p represents the small wheel related parameters, and i=w represents the large wheel related parameters; The discrete point set of the spiral bevel gear generated in step S1 is specifically as follows: the coordinate origin O0 is located at the center of the tool tip distance W, the coordinate system S0 (x0, y0, z0) is fixed on the blade, and the coordinate system S e (x e ,y e ,z e ) is fixed to the center of the cutter head, S a (x a ,y a ,z a ) represents the tool tilt coordinate system, S b (x b ,y b ,z b ) represents the tool rotation coordinate system, S c (x c ,y c ,z c ) represents the cradle coordinate system, S m (x m ,y m ,z m ) represents the machine tool coordinate system, S i (x i ,y i ,z i ) represents the gear coordinate system fixed to the gear blank, and the coordinate system S g (x g ,y g ,z g ), S d (x d ,y d ,z d ) and S f (x f ,y f ,z f ) is the auxiliary coordinate system, β P Represents the angle of the cutter head during rotation. Represents the rotation angle of the cradle during processing. Represents the rotation angle of the gear during the machining process; completes the conversion from the tool coordinate system S0 (x0, y0, z0) to the cutter disc coordinate system S e (x e ,y e ,z e ) and then to the gear blank coordinate system S i (x i ,y i ,z i ) The tool normal section expression of the small wheel is: The tool normal section expression of the large wheel is: In the formula, u vi With θ vi Represent the variables of the main cutting edge part and the tool tip arc part respectively, "-" represents the expression of the normal section of the inner tool, and "+" represents the expression of the normal section of the outer tool; Convert the tool normal section expression to the cutter head coordinate system S e (x e ,y e ,z e ) is expressed as: Where, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel; From the cutterhead coordinate system S e (x e ,y e ,z e ) to the gear blank coordinate system S i (x i ,y i ,z i ) is expressed as: Where, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel; Gear Angle With rocking table corner Satisfies the following relationship: Wherein, when i=p, it represents the small wheel related parameters, when i=w, it represents the large wheel related parameters, when j=1, it represents the gear concave surface, when j=2, it represents the gear convex surface, C and D represent the second-order and third-order deformation correction coefficients when processing the small wheel, respectively. When processing the large wheel, the values ​​of C and D are zero; The normal vector of the gear tooth surface is expressed as: Where, when i=p, it represents the parameters related to the small wheel, and when i=w, it represents the parameters related to the large wheel; The meshing equation of spiral bevel gear is expressed as: Where i = p, it represents the small wheel related parameters, i = w, it represents the large wheel related parameters, v i Represents the relative speed between the blank and the small wheel cutting tool; The mathematical model of the tooth surface of the spiral bevel gear is expressed as: According to the principle of spatial geometric rotation projection, any point on the tooth surface satisfies the following two relationships: Where: x t ,y t Represents the x, y coordinates of the projection point, x p ,y p 、z p Represent the x, y, and z coordinates of discrete points respectively; In step S1, a three-dimensional model of a spiral bevel gear is constructed, and a point set file of the spiral bevel gear is imported into the three-dimensional software Creo. After boundary blending, projection, shearing, merging, solidification and array commands, solid models of the large wheel and small wheel of the spiral bevel gear are obtained respectively; The finite element analysis model of the spiral bevel gear assembly containing the misalignment in step S1 includes: establishing the axis center lines of the large wheel and the small wheel of the spiral bevel gear respectively according to the given misalignment value in the three-dimensional software Creo, and the basis for establishing the axis center line is referenced to the following expression: S0 (x0, y0, z0) is a fixed coordinate system, representing the coincidence point of the two gear pitch cones of the large wheel and the small wheel when there is no misalignment, S g (x g ,y g ,z g ) and S P (x p ,y p ,z p ) are the coordinate systems of the large wheel and the small wheel respectively, S a (x a ,y a ,z a ) and S b are the auxiliary coordinate systems of the large wheel and the small wheel respectively, S c (x c ,y c ,z c ) and S d (x d ,y d ,z d ) are the coordinate systems of the axis angle and the axis angle error respectively; there are four types of misalignment: offset error ΔE, small wheel axial displacement error ΔX P , large wheel axial displacement error ΔX g , axis angle error ΔΣ, and are the rotation angles of the large wheel and the small wheel during the meshing process; the mathematical model of the large wheel is transformed into a coordinate system containing the misalignment and is expressed as: The mathematical model of the small wheel is transformed into a coordinate system containing the misalignment and expressed as: Where ΔE represents the offset error, ΔX P Represents the axial displacement error of the small wheel, ΔX g represents the axial displacement error of the large wheel, ΔΣ represents the axis angle error, and the above four errors are collectively referred to as the misalignment of the spiral bevel gear. and They represent the angles of rotation of the large wheel and the small wheel during the meshing process.

3. The finite element simulation analysis method for meshing characteristics of spiral bevel gears with misalignment as claimed in claim 2, characterized in that: Defining material properties in step S1 includes setting Young's modulus and Poisson's ratio, and the material is set to be isotropic, i.e., a material of uniform density.

4. The finite element simulation analysis method for meshing characteristics of spiral bevel gears with misalignment as claimed in claim 3, characterized in that: In the step S1, the meshing setting is that the tooth surface and the tooth blank of the large wheel and the small wheel are all divided into hexahedral units C3D8R, the contact surface is divided according to 0.2mm / grid, the tooth top is divided according to 0.5mm / grid, the tooth root is divided according to 0.1mm / grid, and the tooth blank is divided according to 5mm / grid.

5. The finite element simulation analysis method for meshing characteristics of spiral bevel gears with misalignment as claimed in claim 1, characterized in that: In step S2, a local coordinate system of the gear is established. In Module, Assembly is selected, Datum is clicked in Tools, 3point is selected in CSYS, and Continue is clicked. Three points at the center of the gear are selected to obtain the local coordinate system of the small gear and the local coordinate system of the large gear. In step S2, set the reference point and set. Click reference point in Tools, select the small wheel local coordinate system and the large wheel local coordinate system respectively, obtain the small wheel reference point RP-1 and the large wheel reference point RP-2, then select Set in Tools, click Create, name them zj1 and zj2, and establish them at the reference points of the large wheel and the small wheel respectively; In step S2, establish an analysis step, select Step in Module, click Create in Step Manager, select Static and General in Procedure type, and establish three analysis steps Step-1, Step-2, and Step-3, representing pre-contact, loading, and tooth surface meshing, respectively; In step S2, establish coupling constraints, select Interaction in Module, select Coupling for coupling type, constrain the inner cylindrical surface and reference point of the large wheel and small wheel respectively, and select the corresponding local coordinate system respectively; In step S2, set the contact pair. Click Create in the Interaction Property Manager, select Contact in Type, click Continue, and select Tangential Behavior and Normal Behavior in Mechanical. Then click Created in the Interaction Manager, select Surface-to-Surface as the contact type, and select the working surface of the small wheel to contact the working surface of the large wheel. In step S2, apply torque and constraints to the spiral bevel gear. Select Load in Module, click Create in Boundary Condition Manager, and create a boundary for the small wheel and the small wheel respectively. Name the driving wheel BC-1 and the driven wheel BC-2. Select Initial in Step and Displacement / Rotation in Types for Selected Step, click Continue, select the reference points RP-1 and RP-2 of the gear respectively, and then select the local coordinate systems of the small wheel and the large wheel respectively to constrain the degrees of freedom in six directions; for the driving wheel, modify the value of a certain degree of freedom in Step-1 in BC-1 according to the rotation direction of the gear, so that the gear rotates a small angle, and then modify the value of the same degree of freedom in Step-3 in BC-1, and the value is the angle of the driving wheel under the current number of teeth; for the driven wheel, release the degree of freedom that constrains the rotation direction of the gear in Step-2 in BC-2; then click Create in Load Manager, select Step-2, Types for Selected Step, and click Create in Load Manager. Select Moment for Step, select the reference point and local coordinate system of the driven wheel, and enter the rated torque. The direction of the torque is opposite to the actual rotation direction of the driven wheel, and the torque based on the direction is 0.

6. The finite element simulation analysis method for meshing characteristics of spiral bevel gears with misalignment as claimed in claim 1, characterized in that: In step S3, select Visualization in Module to see the tooth surface simulation results, click RemoveSelected, select the driven wheel, and for the working surface of the driving wheel, change S to CPRESS to obtain the contact stress and contact mark position in each analysis step, and change Mises to Max.Principal in S to obtain the bending stress in each analysis step; In step S3, in CPRESS, the analysis step is moved to the gear tooth surface where the node coordinates are to be extracted, with the appearance of the contact mark on the tooth surface as the starting point and the disappearance of the contact mark as the ending point. The node coordinates of all the tooth surfaces in this stage of the analysis step are extracted, and the data is exported in the form of suffix .rpt. The data is then processed by MATLAB to obtain the tooth surface contact mark position, tooth surface contact mark area ratio and contact stress; In step S3, in Max.Principal, the analysis step is moved to the gear tooth root to be extracted, the bending stress appears on the extracted tooth root grid line as the starting point, and the bending stress drops to zero as the ending point, the values ​​of all node coordinates on this root grid line in this stage of the analysis step are extracted, the data is exported in the form of EXCEL, and then the data is processed by MATLAB or Origin to obtain the tooth root stress; In step S3, click XY Data in Tools, select ODB history output in Create, select all Rotational displacements, Save as and then select Plot, select two slashes in Rotational displacements to represent the rotation angle data of the small wheel and the large wheel in each analysis step, and then click Excel Utilities in Tools in Plug-ins. The data will be exported in the form of EXCEL, and then processed by MATLAB or Origin to obtain the transmission error.

Images