Method for predicting time-varying meshing thermal stiffness of double-arc spiral bevel gear during nutation transmission

Abstract

The invention relates to a method for predicting nutation transmission time-varying meshing thermal stiffness of a double-arc spiral bevel gear, which comprises the following steps of: setting convective heat transfer coefficients of a gear meshing surface, a non-meshing surface and a gear end surface in an interaction module according to boundary conditions, and applying surface heat flow in a load module according to an obtained meshing area, so as to predict the nutation transmission time-varying meshing thermal stiffness of the double-arc spiral bevel gear. A heat transfer DC3D8R grid is selected as a grid type, and according to a boundary formula, a temperature field during meshing of the double-arc spiral bevel gear is finally calculated; in a Model of ABAQUS software structure simulation, a load module applies a predefined temperature field, a temperature field odb file is loaded into the Model, and structure simulation is carried out; according to the method, temperature field distribution and meshing characteristics can be combined, the time-varying meshing thermal stiffness of the nutation transmission double-arc spiral bevel gear can be accurately predicted, a theoretical basis can be provided for transmission performance evaluation and service life prediction of a gear pair, and important engineering value is provided for design and optimization of a high-performance gear transmission system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gear application, and particularly relates to a method for predicting time-varying meshing thermal stiffness of double circular arc spiral bevel gears in nutation transmission. BACKGROUND

[0002] As key components in mechanical transmission systems, gear pairs are widely used in the fields of aerospace, engineering machinery, energy equipment and high-end manufacturing. Especially under high-speed and heavy-load working conditions, nutation transmission double circular arc spiral bevel gears are widely used in complex transmission devices due to their high transmission efficiency, strong bearing capacity and compact structure. The double circular arc spiral bevel gear is composed of an outer bevel gear, a first inner bevel gear 2 and a second inner bevel gear 4, wherein the outer bevel gear is composed of a first outer bevel gear 1 and a second outer bevel gear 3 which are coaxial and have an integral structure, as shown in Figure 1 、 2 However, significant temperature rise and non-uniform temperature field will be generated in the actual meshing process of the gear, which will further cause thermal elastic deformation, and directly affect the meshing stiffness and transmission characteristics of the gear pair. If such time-varying characteristics cannot be accurately analyzed and predicted, it will easily lead to increased vibration and noise and early failure, thereby seriously threatening the safety and reliability of the transmission system.

[0003] Existing researches usually focus on the load distribution, contact stress and strength analysis of the gear pair, but pay little attention to the coupling law between thermal effect and time-varying meshing stiffness. Especially in the nutation transmission double circular arc spiral bevel gear, due to the existence of multi-point contact meshing area and complex tooth surface geometry, the tooth surface heat flux density distribution presents significant non-uniformity and step characteristics, which makes it difficult to directly obtain the time-varying law of thermal stiffness. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a method for predicting time-varying meshing thermal stiffness of double circular arc spiral bevel gears in nutation transmission.

[0005] The present application adopts the following scheme to realize the purpose: a method for predicting time-varying meshing thermal stiffness of double circular arc spiral bevel gears in nutation transmission, characterized by comprising the following steps: (1) based on the SolidWorks software, a three-dimensional model of the double circular arc spiral bevel gear is established to obtain a gear model; (2) according to the tooth surface contact analysis principle TCA, the contact points of the double circular arc spiral bevel gears in nutation transmission have the same position vector and normal vector, and the calculation formula is as follows: , wherein, and are the position vectors in the fixed coordinate system, and is the normal vector in the fixed coordinate system, and is the circular arc angle of the double circular arc spiral bevel gear, and is the tooth direction line included angle of the double circular arc spiral bevel gear, and is the angle of rotation of the two gears; the discretization of in equation (1.1) is carried out to obtain the remaining 5 parameters, and then the meshing point coordinates are determined; 20 meshing points are selected from the large end to the small end of the gear for the convex tooth surface and the concave tooth surface of the double circular arc spiral bevel gear, respectively; (3) the relative sliding speed , the maximum contact stress , the friction coefficient of the tooth surface are calculated, and then the average heat flux density is obtained according to the Hertz theory, and the calculation formula is as follows: , in the formula, and are the movement speeds of the external bevel gear and the internal bevel gear, respectively; and are the angular velocities of the external bevel gear and the internal bevel gear, respectively; and are the radial vectors in the coordinate system, respectively; is the normal contact force; is the contact ellipse major axis and minor axis; is the average contact stress; is the surface roughness; is the dynamic viscosity of the lubricating oil; is the sum of the sliding speeds; is the contact half-width; is the friction heat flow distribution coefficient, which is 0.5; is the heat flux density, is the average heat flux density of the external bevel gear, is the average heat flux density of the internal bevel gear; (4) the convective heat transfer coefficients of different surfaces of the gear are calculated, in the ABAQUS software, the node set command is used to name the meshing surfaces, gear end surfaces and non-meshing surfaces of the gear, and the convective heat transfer coefficients are loaded onto the selected surfaces in the software interaction module, and the calculation formula is as follows: , in the formula, is the Nusselt number; is the material thermal conductivity; is the gear rotation angular velocity; is the lubricating oil kinematic viscosity; is the half-cone angle of bevel gear; is the specific heat capacity of lubricating oil; is the density of lubricating oil; is the number of gear teeth; is the end surface heat transfer coefficient of gear; is the heat transfer coefficient of meshing surface; is the heat transfer coefficient of non-meshing surface; (5) The average heat flux density of the external bevel gear and the internal bevel gear is respectively interpolated and fitted by using the Curve Fitting Tool in Matlab software, and the function expressions of q1 and q2 are obtained, denoted as q1(x) and q2(x), wherein x is the transverse coordinate of any point on the trace line; (6) The model established in step (1) is saved as a step file, then imported into Hypermesh software for meshing, hexahedral elements with required density and mass are created and saved as an inp file, then imported into finite element software ABAQUS for finite element simulation calculation; (7) In ABAQUS software, assembly, and give the gear materials related mechanical properties and thermodynamic properties; (8) According to the boundary conditions in (4), (5) and (7), set the heat transfer coefficients of the gear meshing surface, non-meshing surface and gear end surface in the interaction module, according to the meshing area obtained in step (2), apply the surface heat flow in the load module, select the heat transfer DC3D8R grid, and finally calculate the temperature field of the double circular arc spiral bevel gear when meshing according to the boundary formula; (9) In the Model of ABAQUS software structure simulation, a pre-defined temperature field is applied in the load module, the temperature field odb file obtained in step (8) is loaded into the Model, and structure simulation is performed; (10) Set a Set set for the tooth surface to be studied, and output the CFN and U of the set in the post-processing module to obtain the normal engagement force and engagement elastic deformation, and the formula for solving the single-tooth normal engagement stiffness is: , wherein, and are the deformations of the external bevel gear and the internal bevel gear, is the normal engagement force; obtain , the normal engagement stiffness of the jth pair of teeth at a certain meshing moment can be calculated as: .

[0006] Further, in step (9), the specific steps of the structural simulation are: coupling the external bevel gear, the first internal bevel gear and the second internal bevel gear at three rp points respectively, coupling 6 all degrees of freedom, and creating three local coordinate systems with the three gear axis directions as the origins, with the x axis coinciding with the gear axis; the boundary conditions and the load conditions thereafter are all applied on the corresponding rp points of the corresponding gears; in terms of contact setting, the contact type is defined as general contact, the normal behavior adopts hard contact, the tangential behavior adopts penalty function, the friction coefficient is 0.055, and in terms of mesh setting, three-dimensional stress C3D8R mesh is selected.

[0007] Further, in terms of boundary conditions, the following processing is made for the three analysis steps set: Step 1: a small rotation angle in the opposite direction is applied to the first internal bevel gear and the second internal bevel gear with the gear axis as the rotation axis, so that the working tooth surface of the external bevel gear can realize initial contact, thereby ensuring the normal convergence of iterative calculation in the analysis process; at the same time, full constraint is applied to the external bevel gear to limit all degrees of freedom thereof.

[0008] Step 2: the degrees of freedom of the first internal bevel gear and the second internal bevel gear in the axial direction are released to play a transition buffering role, so as to reduce and smooth the displacement load applied in Step 1; at the same time, full constraint is applied to the external bevel gear to limit all degrees of freedom thereof.

[0009] Step 3: a certain rotation angle is applied to the external bevel gear to drive the first internal bevel gear and the second internal bevel gear to produce meshing motion; wherein, the first internal bevel gear and the second internal bevel gear only release the degrees of freedom thereof in the axial direction.

[0010] Compared with the prior art, the method of the present application can accurately predict the time-varying meshing thermal stiffness of the nutation transmission double-circular-arc spiral bevel gear by combining the temperature field distribution and the meshing characteristics, which not only provides a theoretical basis for the transmission performance evaluation and life prediction of the gear pair, but also provides important engineering value for the design and optimization of high-performance gear transmission systems.

[0011] In order to make the purpose, technical scheme and advantages of the present application more clear and explicit, the present application will be further described in detail below through specific examples and related drawings. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 is a structural schematic diagram of the external bevel gear of the embodiment of the present application; Figure 2 is a structural schematic diagram of the first internal bevel gear and the second internal bevel gear of the embodiment of the present application; Figure 3 is an assembly drawing of the embodiment of the present application; Figure 4 is a hexahedral mesh diagram of an embodiment of the application; Figure 5 is a temperature field simulation diagram of a second outer bevel gear of an embodiment of the application; Figure 6 is a temperature field simulation diagram of a second inner bevel gear of an embodiment of the application; Figure 7 is a meshing force diagram of a second outer bevel gear and a second inner bevel gear obtained by an embodiment of the application; Figure 8 is a deformation diagram of a second outer bevel gear obtained by an embodiment of the application; Figure 9 is a deformation diagram of a second inner bevel gear obtained by an embodiment of the application; Figure 10 is a meshing stiffness diagram of a second outer bevel gear obtained by an embodiment of the application; Figure 11 is a meshing stiffness diagram of a second inner bevel gear obtained by an embodiment of the application; Figure 12 is a single-tooth stiffness diagram obtained by an embodiment of the application; Label explanation in the figure: 1-first outer bevel gear, 2-first inner bevel gear, 3-second outer bevel gear, 4-second inner bevel gear. DETAILED DESCRIPTION

[0013] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0014] It should be noted that the terms used herein are only for the purpose of describing specific embodiments, and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and furthermore, it should be understood that when the terms "comprise" and / or "include" are used in the specification, there is a feature, step, operation, device, component and / or combination thereof.

[0015] A method for predicting the time-varying meshing thermal stiffness of a double circular arc spiral bevel gear in a walking transmission, characterized in that it comprises the following steps: (1) According to the basic parameter requirements and the tooth surface equation of the gear, the tooth profile model and the coordinates are drawn according to the Matlab software, and the three-dimensional modeling of the double circular arc spiral bevel gear is carried out based on the SolidWorks software, and the gear model is obtained; (2) According to the tooth surface contact analysis principle TCA, the contact points of the double circular arc spiral bevel gears in the walking transmission process have the same position vector and normal vector, and the calculation formula is as follows: , where, and are the position vectors in the fixed coordinate system, and are the normal vectors in the fixed coordinate system, and are the circular arc angles of the double circular arc spiral bevel gear, and are the tooth direction line included angles of the double circular arc spiral bevel gear, and are the angles of rotation of the two gears; the in equation (1.1) is discretized to obtain the remaining 5 parameters, and then the meshing point coordinates are determined; 20 meshing points are selected from the large end to the small end of the gear for the convex tooth surface and the concave tooth surface of the double circular arc spiral bevel gear, respectively; (3) the relative sliding speed , the maximum contact stress , the friction coefficient of the tooth surface are calculated, and then the average heat flux density is obtained according to the Hertz theory, and the calculation formula is as follows: , where, and are the motion speeds of the external bevel gear and the internal bevel gear, respectively; and are the angular speeds of the external bevel gear and the internal bevel gear, respectively; and are the radial vectors in the coordinate system, respectively; is the normal contact force; are the long semi-axis and the short semi-axis of the contact ellipse; is the average contact stress; is the surface roughness; is the dynamic viscosity of the lubricating oil; is the sum of the sliding speeds; is the contact half-width; is the friction heat flow distribution coefficient, which is 0.5; is the heat flux density, is the average heat flux density of the external bevel gear, is the average heat flux density of the internal bevel gear; (4) the convective heat transfer coefficients of different surfaces of the gear are calculated, in the ABAQUS software, the node set command is used to name each meshing surface, gear end surface and non-meshing surface of the gear, and the convective heat transfer coefficients are loaded onto the selected surfaces in the software interaction module, and the calculation formula is as follows: , wherein, is the Nusselt number; is the thermal conductivity of the material; is the angular velocity of the gear rotation; is the kinematic viscosity of the lubricant; is the half-cone angle of the bevel gear; is the specific heat capacity of the lubricant; is the density of the lubricant; is the number of gear teeth; is the end surface heat transfer coefficient of the gear; is the meshing surface heat transfer coefficient; is the non-meshing surface heat transfer coefficient; (5) The average heat flux densities of the external bevel gear and the internal bevel gear are respectively interpolated and fitted by using the Curve Fitting Tool in the Matlab software, and the function expressions of q1 and q2 are obtained, which are denoted as q1(x) and q2(x), wherein x is the transverse coordinate of any point on the trace line; (6) The model established in step (1) is saved as a step file after being appropriately simplified, and then is imported into the Hypermesh software for meshing, hexahedral elements with required density and mass are created and saved as an inp file, and then are imported into the finite element software ABAQUS for finite element simulation calculation; (7) In the ABAQUS software, assembly, and give the gear material related mechanical properties and thermodynamic properties; the gear material selected in the thermal-elastic coupling simulation of the embodiment is structural steel, and the material properties are as shown in Table 2-1: Table 2-1 (8) According to the boundary conditions in (4), (5) and (7), the heat transfer coefficients of the gear meshing surface, the non-meshing surface and the gear end surface are set in the interaction module, the surface heat flux is applied in the load module according to the meshing area obtained in step (2), the grid type is selected as the heat transfer DC3D8R grid, and finally the temperature field of the double circular arc spiral bevel gear during meshing is calculated according to the boundary formula (which is a function provided by the ABAQUS software); (9) The simulation of the embodiment is performed in the order coupling mode for thermal-elastic coupling, in the Model of the structure simulation of the ABAQUS software, a pre-defined temperature field is applied in the load module, the temperature field odb file obtained in step (8) is loaded into the Model, and the structure simulation is performed; (10) A set of Set is set for the tooth surface, in the post-processing module, the CFN and U of the set are output after coordinate conversion, the normal meshing force and the meshing elastic deformation are obtained, and the formula for solving the single-tooth normal meshing stiffness is: wherein, and are the deformation of the external bevel gear and the internal bevel gear respectively, is the normal meshing force; the above parameters are obtained from the results of the structural simulation in step (9); and then the normal meshing stiffness of the jth pair of teeth at a certain meshing moment can be calculated as: .

[0016] In the present embodiment, in step (9), the specific steps of the structural simulation are as follows: the external bevel gear, the first internal bevel gear 2 and the second internal bevel gear 4 are coupled at three rp points respectively, and six degrees of freedom are coupled, and three local coordinate systems are created with the three gear axis directions and with the rp points as the origins, and the x axis coincides with the gear axis; the boundary conditions and the load conditions thereafter are all applied on the corresponding rp points of the corresponding gears; in terms of contact setting, the contact type is defined as general contact, the normal behavior adopts hard contact, the tangential behavior adopts penalty function, the friction coefficient is 0.055, and in terms of mesh setting, three-dimensional stress C3D8R mesh is selected.

[0017] In order to accurately calculate the dynamic meshing stiffness, the present embodiment applies torque to the driven gear and simultaneously applies angular displacement to the driving gear.

[0018] In the present embodiment, in terms of boundary conditions, the following treatments are made for the three analysis steps set: Step 1: a micro angular displacement in the opposite direction of the rotation direction is applied to the first internal bevel gear 2 and the second internal bevel gear 4 with the gear axis as the rotation axis, so that the working tooth surface of the external bevel gear can realize initial contact, thereby ensuring the normal convergence of the iterative calculation in the analysis process; at the same time, full constraints are applied to the external bevel gear to limit all degrees of freedom thereof.

[0019] Step 2: the degrees of freedom of the first internal bevel gear and the second internal bevel gear in the axial direction are released, so as to play a transitional buffering role and thereby reduce and smooth the displacement load applied in Step 1; at the same time, full constraints are applied to the external bevel gear to limit all degrees of freedom thereof.

[0020] Step 3: a certain angular displacement, such as 1.4653 rad, is applied to the external bevel gear to drive the first internal bevel gear 2 and the second internal bevel gear 4 to generate meshing motion; wherein the first internal bevel gear 2 and the second internal bevel gear 4 only release the degrees of freedom thereof in the axial direction.

[0021] In terms of load, in Step 2, a reverse torque around the axis of the second internal bevel gear 4 is applied, and the size is 170 N•m; according to the torque balance principle, a positive torque around the axis of the first internal bevel gear 2 is applied, and the size is 168.4 N•m.

[0022] The method can combine temperature field distribution and meshing characteristics to accurately predict time-varying meshing thermal stiffness of the nutating transmission double-circular-arc spiral bevel gear, which can not only provide a theoretical basis for transmission performance evaluation and life prediction of the gear pair, but also provide important engineering value for design and optimization of a high-performance gear transmission system.

[0023] The simulation results of the application Figures 5~12 The simulation results of the application

[0024] Unless otherwise stated, if the above-mentioned any technical solution of the application discloses a numerical range, the disclosed numerical range is a preferred numerical range, and any person skilled in the art should understand that the preferred numerical range is only one of the many implementable values with more obvious technical effects or representative values. Because there are too many values, it is impossible to enumerate them all, so the application discloses part of the values to illustrate the technical solutions of the application, and the above-mentioned enumerated values should not constitute a limitation on the protection scope of the application.

[0025] If the application discloses or involves mutually fixed connecting parts or structural parts, unless otherwise stated, the fixed connection can be understood as: detachable fixed connection (for example, bolt or screw connection), and can also be understood as: non-detachable fixed connection (for example, riveting, welding), of course, the mutually fixed connection can also be replaced by an integral structure (for example, integrally formed by using casting process) (obviously, it cannot be replaced by an integral forming process).

[0026] In addition, the terms used to represent the positional relationship or shape in the above-mentioned any technical solution of the application include approximate, similar or close states or shapes, unless otherwise stated.

[0027] Any component provided by the application can be assembled from multiple individual components, or can be a single component manufactured by an integral forming process.

[0028] The above-mentioned is only a preferred embodiment of the application, and is not intended to limit the application in other forms. Any person skilled in the art can modify or change the above-mentioned disclosed technical content into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made on the basis of the technical essence of the application to the above-mentioned embodiments still belongs to the protection scope of the application.

Claims

1. A method for predicting the time-varying meshing thermal stiffness of a double-circular-arc spiral bevel gear nutation transmission, characterized in that: Includes the following steps: (1) Based on SolidWorks software, a three-dimensional model of the double circular arc spiral bevel gear was created to obtain the gear model; (2) According to the tooth surface contact analysis principle (TCA), the contact points of the double circular arc spiral bevel gears that mesh with each other during the nutation transmission process have the same position vector and normal vector. The calculation formula is as follows: ， in, and This is the position vector in a fixed coordinate system. and The normal vector in a fixed coordinate system and It refers to the arc angle of a double-circular-arc spiral bevel gear. and It is the included angle between the tooth directions of a double-circular-arc spiral bevel gear. and It is the angle through which the two gears rotate; in equation (1.1) Discretize the gear and find the remaining 5 parameters. Then determine the coordinates of the meshing points. Select 20 meshing points on the convex and concave tooth surfaces of the double circular arc spiral bevel gear from the large end to the small end of the gear. (3) Calculate the relative sliding speed Maximum contact stress tooth surface friction coefficient Next, the average heat flux density is obtained according to Hertz theory. The calculation formula is as follows: ， In the formula, and These represent the speeds of the external bevel gear and the internal bevel gear, respectively. and These are the angular velocities of the external bevel gear and the internal bevel gear, respectively. and These are the radius vectors in the coordinate system; Normal contact force; To contact the major and minor semi-axis of the ellipse; This represents the average contact stress. For surface roughness; The dynamic viscosity of the lubricating oil; It is the sum of the sliding velocities; For contact half-width; The frictional heat flow distribution coefficient is taken as 0.5; For heat flux density, The average heat flux density of the external bevel gear, The average heat flux density of the internal bevel gear; (4) Calculate the convective heat transfer coefficients of different surfaces of the gear. In the ABAQUS software, use the node set command to name each meshing surface, gear end face, and non-meshing surface of the gear. In the software interaction module, load the convective heat transfer coefficients onto the selected surfaces. The calculation formula is as follows: ， In the formula, For Nuschelt numbers; The thermal conductivity of the material; The rotational angular velocity of the gear; The kinematic viscosity of the lubricating oil; The bevel gear's half-cone angle; The specific heat capacity of lubricating oil; The density of the lubricating oil; This refers to the number of teeth on the gear. The convective heat transfer coefficient at the gear end face; The convective heat transfer coefficient of the meshing surface; The non-meshing surface convective heat transfer coefficient; (5) Using the Curve Fitting Tool in Matlab software, the average heat flux density of the external bevel gear and the internal bevel gear are interpolated and fitted to obtain the functional expressions of q1 and q2, denoted as q1(x) and q2(x), where x is the transverse coordinate of any point on the trace line; (6) Save the model established in step (1) as a step file, then import it into Hypermesh software for mesh generation, create hexahedral elements with the required density and mass and save them as inp files, then import them into the finite element software ABAQUS for finite element simulation calculation. (7) In ABAQUS software, assemble and assign relevant mechanical and thermodynamic properties to the gear material; (8) Based on the boundary conditions in (4), (5), and (7), set the convective heat transfer coefficients of the gear meshing surface, non-meshing surface, and gear end face in the interaction module. Based on the meshing area obtained in step (2), apply surface heat flow in the load module. Select the heat transfer DC3D8R mesh as the mesh type. Based on the boundary formula, finally calculate the temperature field when the double circular arc spiral bevel gear meshes. (9) In the Model of ABAQUS software structural simulation, the load module applies a predefined temperature field, and the temperature field odb file obtained in step (8) is loaded into the Model for structural simulation. (10) Set a set for each tooth surface under study. In the post-processing module, output the CFN and U of the set to obtain the normal meshing force and meshing elastic deformation. The formula for solving the normal meshing stiffness of a single tooth is: ,in, and These represent the deformation amounts of the external bevel gear and the internal bevel gear, respectively. Normal meshing force; obtain The normal meshing stiffness of the j-th pair of teeth at a certain meshing moment can then be calculated: .

2. The method for predicting the time-varying meshing thermal stiffness of a double-circular-arc spiral bevel gear nutation transmission according to claim 1, characterized in that: In step (9), the specific steps of the structural simulation are as follows: the external bevel gear, the first internal bevel gear, and the second internal bevel gear are coupled at three rp points respectively, coupling all six degrees of freedom, and three local coordinate systems are created with the three gear axis directions, the rp points as the origin, and the x-axis coinciding with the gear axis; the subsequent boundary conditions and load conditions are applied to the corresponding rp points of the corresponding gears. For contact settings, the contact type is defined as general contact, the normal behavior is hard contact, the tangential behavior is a penalty function, the friction coefficient is 0.055, and for mesh settings, a three-dimensional stress C3D8R mesh is selected.

3. The method for predicting the time-varying meshing thermal stiffness of a double-circular-arc spiral bevel gear nutation transmission according to claim 2, characterized in that: Regarding the boundary conditions, the following processing is performed for the three analysis steps: Step 1: Using the gear axis as the rotation axis, apply a small rotation angle in opposite directions to the first and second internal bevel gears so that the working tooth surfaces of the external bevel gear can achieve initial contact, thereby ensuring the normal convergence of the iterative calculation during the analysis process; at the same time, apply full constraints to the external bevel gear to restrict all its degrees of freedom.

4. Step 2: Release the axial degrees of freedom of the first and second internal bevel gears to act as a transition buffer, thereby reducing and smoothing the displacement load applied in Step 1; at the same time, apply full constraints to the external bevel gear to restrict all its degrees of freedom.

5. Step 3: Apply a certain angle to the external bevel gear to drive the first and second internal bevel gears to mesh; wherein, The first and second internal bevel gears only release their degrees of freedom in the axial direction.

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