A design method of face gear pair nutation reducer

Abstract

The application provides a design method of a nutation face gear pair nutation reducer, comprising the following steps: step 1: analyzing the relationship between a gear shaping cutter and a 'face gear-face gear' meshing pair; step 2: solving a nutation face gear tooth profile; step 3: face gear tooth surface modification; step 4: deriving a nutation face gear conjugate condition; step 5: calculating a 'face gear-face gear' meshing equation; and step 6: constructing a nutation face gear reducer model. The nutation face gear designed by the technical solution has large bearing capacity, and compared with a traditional internal meshing nutation reducer, the nutation face gear is convenient to machine, has low precision requirement and low cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of gear tooth profile design and transmission technology, in particular to a design method of a face gear pair nutation reducer. BACKGROUND

[0002] As a precision transmission device, nutation reducer is widely used in industrial automation, robots, aerospace and other high-precision fields, and has the advantages of high transmission ratio and high bearing capacity. However, the traditional nutation reducer adopts internal bevel gear design, which has complex manufacturing process, high production cost, and low transmission efficiency and insufficient tooth surface contact strength in high load and high precision applications. SUMMARY

[0003] Therefore, the purpose of the present application is to provide a design method of a face gear pair nutation reducer, which significantly improves the bearing capacity and meshing efficiency of the nutation reducer, reduces the manufacturing cost, and enhances the adaptability and reliability of the system by optimizing the gear contact trajectory and tooth profile design.

[0004] To achieve the above-mentioned purpose, the present application adopts the following technical solution: a design method of a face gear pair nutation reducer, comprising the following steps:

[0005] Step 1: analyze the relationship between the gear shaping cutter and the "face gear-face gear" meshing pair;

[0006] Step 2: solve the nutation face gear tooth profile;

[0007] Step 3: face gear tooth surface modification;

[0008] Step 4: derive the nutation face gear conjugate condition;

[0009] Step 5: calculate the meshing equation of "face gear-face gear";

[0010] Step 6: build a nutation face gear reducer model.

[0011] In a preferred embodiment, the step 1 includes: in the cutting process, the gear shaping cutter is tangent to the outside of the face gear, according to the gear meshing principle, two face gears machined by the same size gear shaping cutter cannot form transmission; if face gear transmission is required, the "face-face" gear pair formed by the two face gears should be tangent to the outside of the gear shaping cutter, which is called the outside tangent face gear; at the same time, the other face gear meshing with it is tangent to the inside of the same gear shaping cutter, which is called the inside tangent face gear; the outside tangent face gear intersects with the real cutter axis, and the included angle is γ1; the inside tangent face gear intersects with the imaginary cutter axis, and the included angle is γ2; the pitch cone angle of the outside tangent face gear is β1; the pitch cone angle of the inside tangent face gear is β2; γ s is the cutter pitch cone angle.

[0012] In a preferred embodiment, in the design of the "face-to-face" gear pair, the following conditions are defined between the angles to ensure the meshing transmission between the external face gear and the internal face gear:

[0013]

[0014] Relationship between the pitch angle, the shaft angle and the number of teeth of the cutter and the nutation angle:

[0015]

[0016] wherein β m = 180° - β, β For is the nutation angle, N s , N1, N2 are the number of teeth of the gear shaper cutter, the external face gear and the internal face gear respectively.

[0017] In a preferred embodiment, the step 2 is specifically: the S 10 (O 10 -X 10 Y 10 Z 10 ) is a fixed coordinate system, Z 10 coincides with the rotation axis of the external face gear, the coordinate system S1 (O1-X1Y1Z1) is fixed to the external face gear, the coordinate system S s10 (O s10 -X s10 Y s10 Z s10 ) is a fixed coordinate system, Z s10 coincides with the rotation axis of the cutter, the coordinate system S s1 (O s1 -X s1 Y s1 Z s1 ) is fixed to the cutter; the origins of the above three coordinate systems coincide, Z 10 , Z1 coincide, X s10 , X 10 coincide, Z s1 , Z s10 coincide; the angle between Z 10 and Z s10 is π - γ1, is the instantaneous rotation angle of the cutter, is the instantaneous rotation angle of the external face gear.

[0018] In a preferred embodiment, in the internal face gear machining coordinate system S 20 (O 20 -X 20 Y 20 Z 20 ) is a fixed coordinate system, Z20 The coordinate system S2 (O2-X2Y2Z2) is fixed to the hypoid gear, and coincides with the rotation axis of the hypoid gear. s20 (O s20 -X s20 Y s20 Z s20 ) is a fixed coordinate system, and Z s20 The coordinate system S3 (O3-X3Y3Z3) coincides with the rotation axis of the cutter, and is fixed to the cutter. s2 (O s2 -X s2 Y s2 Z s2 ) is a fixed coordinate system, and Z 20 The origins of the three coordinate systems coincide, Z s20 , X 20 coincide, Z s2 , Z s20 coincide; the angle between Z 20 and Z s20 is γ2, is the instantaneous rotation angle of the cutter, is the instantaneous rotation angle of the hypoid gear.

[0019] In a preferred embodiment, the coordinate system S s10 is transformed to the fixed coordinate system S1 by a transformation matrix M 1s1 :

[0020]

[0021] The coordinate system S s20 is transformed to the fixed coordinate system S2 by a transformation matrix M 2s2 :

[0022]

[0023] The hypoid gear tooth surface equation is:

[0024]

[0025] The hypoid gear tooth surface equation is:

[0026]

[0027] where r bs is the base circle radius of the gear shaping cutter, θ s1 , θ s2 is the angle between the involute start point and any point on the involute, and θ s0 is the angle between the involute profile start point and the involute tooth groove symmetry line.

[0028] is the gear shaping cutter rotation angle coefficient, z s z1, z2 are respectively the number of teeth of the shaper cutter, the external face gear and the internal face gear,

[0029] In a preferred embodiment, the step 3 is specifically: by modifying the shaper cutter, then using the modified shaper cutter to process the face gear, the modified face gear is obtained;

[0030] The first tooth surface is modified to the second tooth surface; a parabolic modification is selected to make y = a p x 2 , the modification amount Δm is calculated, and the value of x is reduced by the modification amount Δm on the coordinates of the theoretical tooth surface to obtain a new horizontal coordinate x, and the values of y and z are kept unchanged;

[0031] Δm = a p x 2

[0032] In the formula, a p is a parabolic modification coefficient, and here a p = 0.001.

[0033] Then the second tooth surface is modified to the third tooth surface, and the equation of the gear involute in the rectangular coordinate system is with the origin of the rectangular coordinate system as the origin, assuming that the coordinate value of the O point coordinate is (x z , y z ), so:

[0034]

[0035] In the formula, r is the pitch circle radius,

[0036]

[0037] The origin of the coordinate system is translated to the O point, and rotated by β p angle to get

[0038]

[0039] In a preferred embodiment, the step 4 is specifically: the conjugate of the gear tooth surface is based on the concept of envelope; if the meshing equations of two gears with the cutter are equal, then the two gears are conjugate;

[0040] The meshing equation of the external face gear and the cutter is:

[0041]

[0042] The meshing equation of the internal face gear and the cutter is:

[0043]

[0044] According to The conjugate condition of the "face gear-face gear" engagement pair is obtained:

[0045]

[0046] In a preferred embodiment, the step 5 is specifically: the engagement form of the "face gear-face gear" engagement pair is point contact, when the engagement characteristics analysis and contact stress solution are carried out, the contact trajectory of the face gear in the engagement process needs to be determined; according to the tooth surface contact analysis principle, the coordinate system is established, and the tooth surface equations r1, r2 and normal vectors n1, n2 of the external face gear and the internal face gear are respectively converted to the coordinate system S f Down;

[0047] The transformation equation of the external face gear:

[0048]

[0049] The transformation equation of the internal face gear:

[0050]

[0051] Here, ΔE is the axis offset error, Δq is the axial offset error, and Δγ is the nutation angle deviation;

[0052]

[0053] Through the equation, a equation group with 5 independent nonlinear equations containing 6 unknowns, i.e. , is obtained, assuming that are known parameters, the equation group is solved to obtain the values of the other 5 parameters; substituted into the tooth surface equation, the contact trajectory is obtained.

[0054] In a preferred embodiment, the step 6 is specifically: using Matlab to write a simulation program for gear machining; first, according to the gear meshing theory, all instantaneous cutting point coordinates on the tooth profile from the beginning of meshing to the exit of meshing are obtained, then the node coordinates of the double-sided tooth profile of the single gear end face are obtained through the rotation projection transformation, and finally the point cloud data is processed into a ".txt" format file output; first, under the function guidance of the curve guide, the file is imported into SolidWorks using the "Scan To 3D" module function, the surface lofting function is used, the working curve and the transition curve are selected in turn, the curve is lofted into a solid surface, the rotation center is rotated through 360 / N, the boundary surface is created at the same time, and the surface stitching function is applied to obtain the complete gear slot; through the circular array command, the single gear slot is arrayed around the rotation center, and the three-dimensional entity model of the internal and external tangent gear is obtained; the internal and external tangent gears obtained finally are assembled with other parts of the nutational reducer, and the nutational face gear reducer is obtained.

[0055] Compared with the prior art, the present application has the following beneficial effects: the present application can improve the meshing efficiency and durability of the nutational reducer, to meet the demand of modern industry for high-precision and high-load transmission system, and has important theoretical and application value. BRIEF DESCRIPTION OF DRAWINGS

[0056] Fig. 1 The tool and face gear machining diagram of the preferred embodiment of the present application;

[0057] Fig. 2 The relationship diagram of the gear shaping cutter and the internal and external tangent gears of the preferred embodiment of the present application;

[0058] Fig. 3 The vertex coincidence schematic diagram of the "face gear-face gear" meshing pair of the preferred embodiment of the present application;

[0059] Fig. 4 The forming schematic diagram of the external tangent gear of the preferred embodiment of the present application;

[0060] Fig. 5 The forming schematic diagram of the internal tangent gear of the preferred embodiment of the present application;

[0061] Fig. 6 The gear shaping cutter modification schematic diagram of the two-face gear transformation of the preferred embodiment of the present application;

[0062] Fig. 7 The coordinate system relationship diagram of the two-face gear transformation of the preferred embodiment of the present application;

[0063] Fig. 8 The tooth profile of the external tangent gear of the preferred embodiment of the present application;

[0064] Fig. 9An involute face gear tooth profile for a preferred embodiment of the present application;

[0065] Fig. 10 A "face gear - face gear" pair contact path under mounting errors for a preferred embodiment of the present application;

[0066] Fig. 11 A "face gear - face gear" pair transmission error under mounting errors for a preferred embodiment of the present application;

[0067] Fig. 12 A "face gear - face gear" pair contact ellipse under mounting errors for a preferred embodiment of the present application;

[0068] Fig. 13 A "face gear - face gear" pair contact path under different modification factors for a preferred embodiment of the present application;

[0069] Fig. 14 A "face gear - face gear" pair maximum contact stress under different modification factors for a preferred embodiment of the present application.

[0070] Fig. 15 A 3D schematic view of an external face gear for a preferred embodiment of the present application.

[0071] Fig. 16 A 3D schematic view of an internal face gear for a preferred embodiment of the present application.

[0072] Fig. 17 A face gear pair nutation reducer for a preferred embodiment of the present application. DETAILED DESCRIPTION

[0073] The present application is further described by the following examples and accompanying drawings.

[0074] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the 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.

[0075] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting, as the scope of the exemplary embodiments of this application will be limited only by the appended claims. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0076] A face gear pair nutation reducer design, tooth contact analysis and performance improvement method, with reference to Figs. 1 to 17 , comprising the steps of:

[0077] The design parameters of the gear are as follows:

[0078] The design parameters of the "face gear-face gear" meshing pair

[0079]

[0080] Step one: solving the tooth profile of the "face gear-face gear" meshing pair

[0081] The construction of the accurate mathematical model needs to solve the coordinates of the points on the tooth surface by means of the Matlab software, realize the visualization of the mathematical model, and then import the three-dimensional software to generate the entity model. The tooth surface equation contains three variables, i.e. θ s and u s . Since the meshing equation is established at any point on the tooth surface, the parameter u s can be expressed by the parameters and θ s . The generation steps of the face gear working surface are as follows: (1) according to the dedendum circle of the gear shaping cutter, the tooth height parameter z of the face gear in the coordinate system S s is derived. (2) the minimum inner diameter R1 when the gear undercuts and the maximum outer diameter R2 when the gear addendum crowns are calculated, and an appropriate tooth width is selected as the known quantity y2 within the range of R1 and R2.

[0082] (3) through discretization, i discrete values of y i (y1, y2, y3…y i ) and j discrete values of z j (z1, z2, z3…z j ) are obtained, and y and z are taken as the input values, which are substituted into the tooth surface equation to obtain i x j values of S ij (S i1 , S i2 , S i3 …S ij ) and i x j values of S ij (S i1 , S i2 , S i3 …S ij ).

[0083] (4) the i x j groups of (S ij , S ij ) are substituted into the non-orthogonal and non-symmetrical face gear tooth surface equation to obtain i x j discrete coordinate points (x ij , y ij , z ij ) on the corresponding tooth surface, and the face gear working surface is generated by applying the Matlab instruction as shown in Fig. 8 and Fig. 9 .

[0084] Equation of the tooth surface of an externally tangent gear:

[0085]

[0086] Equation of the tooth surface of an internal gear:

[0087]

[0088] Step 2: Face gear shaping

[0089] By modifying the shape of the gear shaper cutter, and then using the modified cutter to machine the face gear, the modified face gear can be obtained.

[0090] like Fig. 6 The tooth surface 1 is modified into tooth surface 2. The modification parabola y = a is selected. p x 2 Calculate the modification amount Δm, and subtract the modification amount Δm from the value of x on the theoretical tooth surface coordinate to obtain a new horizontal coordinate x, while keeping the values ​​of y and z unchanged.

[0091] Δm=a p x 2

[0092] Next, the tooth surface 2 is modified to tooth surface 3. In the rectangular coordinate system, the equation of the gear involute is based on the origin of the rectangular coordinate system. Assume the coordinates of point O are (x z ,y z Therefore:

[0093]

[0094] In the formula, r is the pitch circle radius.

[0095] Therefore, according to the formula

[0096]

[0097] Translate the origin of the coordinate system to point O, and rotate it by β. p Angle

[0098]

[0099] Step 3: TCA

[0100] In order to reflect the transmission performance advantage of the nutation face gear designed in the patent, the tooth surface contact characteristics and transmission error should be calculated. In actual operation, installation error is inevitable, and among various errors, the influence of nutation angle error on the meshing performance of the nutation face gear is particularly significant. Therefore, the nutation face gear design in the patent verifies the superiority of the design by comparing the tooth surface contact imprint and the maximum contact stress difference of the unmodified tooth surface under the conditions of no error, axial offset error, axial offset error and nutation angle error through meshing trajectory design. β p = 0°, -1°, -2°, -3°.

[0101] According to the Hertz contact theory analysis, the long and short semi-axes a and b in the contact area of the elastic body when it is in contact can be expressed as:

[0102]

[0103] In the formula, E' is the elastic modulus at the elliptical contact point; R' is the equivalent curvature radius; First elliptical integral; Second elliptical integral.

[0104]

[0105] In the formula, μ A and μ B are the Poisson's ratios of the two elastic bodies; E A and E B are the elastic moduli of the two elastic bodies; R x and R y are the curvature radii in the x and y directions.

[0106]

[0107] Figs. 10-12 The contact trajectories under the four errors and their corresponding transmission errors and contact ellipses are shown. As shown in the figure, the nutation angle deviation has the greatest influence on the contact trajectory, and the axial spacing deviation and the axial displacement deviation have less influence.

[0108] Fig. 13 The contact trajectories obtained when β p is taken from 0° to -3° are shown. When β p = -1°, the contact trajectory extends from the inner diameter tooth root area of the face gear to the outer diameter tooth top area, and the contact trajectories under the four conditions are slightly inclined, but not significantly. When β p = -2°, the contact trajectories under the four conditions are significantly extended, and the inclination to the tooth top direction is significantly increased, and the contact ellipse area is also increased. Under the condition of nutation angle error, the contact trajectory is further extended. β pWhen β =-3°, the inclination of the contact path is more obvious, but part of the path is out of the tooth surface, and the influence of the axial offset error and the axial shift error on the contact path is further increased.

[0109] Fig. 14 The maximum contact stress obtained by numerical calculation is shown. As can be seen from the figure, β p When β =-2°, the maximum contact stress of the external face gear and the internal face gear reaches the minimum value, which is 1209 Mpa and 975 Mpa respectively. Compared with the maximum contact stress in the unmodified state, the external face gear is reduced by 24.2%, and the internal face gear is reduced by 22.6%. This has important engineering significance for improving the stability of the gear transmission system, reducing noise caused by vibration and meshing impact, and improving the reliability and service life of the system.

[0110] Step 3: Modeling of the “face gear-face gear” meshing pair of the nutation reducer

[0111] Firstly, all the instantaneous cutting point coordinates on the tooth profile from the beginning of engagement to the exit of engagement are obtained according to the gear engagement theory, then the node coordinates of the double-sided tooth profile of the single tooth end face are obtained through the rotation projection transformation, and finally the point cloud data is processed into a “.txt” format file output. First, under the guidance of the curve guide function, the file is imported into SolidWorks using the “ScanTo 3D” module function, the surface lofting function is used, the working curve and the transition curve are selected in turn, the curve is lofted into a solid surface, the rotation center is rotated through 360 / N, the boundary surface is created at the same time, and the surface stitching function is applied to obtain the complete tooth groove. Through the circular array command, the single tooth groove is arrayed around the rotation center, and the three-dimensional entity model of the internal face gear and the external face gear can be obtained as shown in Fig. 15 and Fig. 16 The internal and external face gears obtained finally are assembled with other parts of the nutation reducer, and the nutation face gear reducer can be obtained as shown in Fig. 17 .

[0112] The design advantages of the present application are embodied in this example.

Claims

1. A design method for a face gear pair nutation reducer, characterized in that, The method comprises the following steps: Step 1: analyzing the relationship between the gear shaping cutter and the face gear-face gear meshing pair; Step 2: solving the trochoidal face gear tooth profile; Step 3: modifying the face gear tooth surface; Step 4: deriving the trochoidal face gear conjugate condition; Step 5: calculating the face gear-face gear meshing equation; Step 6: constructing the trochoidal face gear reducer model; The step 1 includes: in the cutting process, the gear shaper cutter is tangent to the outside of the face gear, according to the gear engagement principle, two face gears processed by the same size gear shaper cutter cannot form transmission; if the face gear transmission is needed, the face-to-face gear pair composed of two face gears should be made, one face gear is tangent to the outside of the gear shaper cutter, which is called the outside tangent face gear; at the same time, the other face gear engaged with the outside tangent face gear is tangent to the inside of the same gear shaper cutter, which is called the inside tangent face gear; the outside tangent face gear intersects with the real cutter axis, and the included angle is ; the inside tangent face gear intersects with the imaginary cutter axis, and the included angle is ; the pitch cone angle of the outside tangent face gear is ; the pitch cone angle of the inside tangent face gear is ; the cutter pitch cone angle; In the design process of the face-face gear pair, in order to ensure that the external face gear and the internal face gear form meshing transmission, the following limiting conditions exist between angles: Relationship between the pitch cone angle, the shaft clamping angle, the cutter tooth number and the trochoidal angle: In the formula, , is the nutation angle, N s N1, N2 are the number of teeth of the pinion cutter, the external face gear and the internal face gear, respectively; The step 2 is specifically: S 10 (O 10 -X 10 Y 10 Z 10 ) is a fixed coordinate system, Z 10 coincides with the rotation axis of the epicyclic gear, the coordinate system S1(O1-X1Y1Z1) is fixed with the epicyclic gear, the coordinate system S s10 (O s10 -X s10 Y s10 Z s10 ) is a fixed coordinate system, Z s10 coincides with the rotation axis of the cutter, the coordinate system S s1 (O s1 -X s1 Y s1 Z s1 ) is fixed with the cutter; the origins of the above three coordinate systems coincide, Z 10 , Z1 coincide, X s10 , X 10 coincide, Z s1 , Z s10 coincide; the included angle between Z 10 and Z s10 is , is the instantaneous rotation angle of the cutter, is the instantaneous rotation angle of the epicyclic gear.

2. The method of designing a nutation reducer for a face gear pair according to claim 1, wherein Hypoid gear machining coordinate system S 20 (O 20 -X 20 Y 20 Z 20 ) is a fixed coordinate system, Z 20 coincides with the rotation axis of the hypoid gear, coordinate system S2(O2-X2Y2Z2) is fixed with the hypoid gear, coordinate system S s20 (O s20 -X s20 Y s20 Z s20 ) is a fixed coordinate system, Z s20 coincides with the rotation axis of the cutter, coordinate system S s2 (O s2 -X s2 Y s2 Z s2 ) is fixed with the cutter; the origins of the above three coordinate systems coincide, Z 20 and Z2 coincide, X s20 and X 20 coincide, Z s2 and Z s20 coincide; the angle between Z 20 and Z s20 is , is the instantaneous rotation angle of the cutter, is the instantaneous rotation angle of the hypoid gear.

3. The method of designing a nutation reducer for a face gear pair according to claim 2, wherein, Coordinate system S s10 The transformation matrix M transforming to the fixed coordinate system S1 1s1 is: Coordinate system S s20 The transformation matrix M transforming to the fixed coordinate system S2 2s2 is: External face gear tooth surface equation: Internal face gear tooth surface equation: wherein, is the base circle radius of the gear shaping cutter, , is the angle between the involute start point of the gear shaping cutter and any point on the involute, is the angle from the symmetry line of the gear shaping cutter to the start point of the involute profile. For gear shaping cutter corner coefficient, ; z s z1, z2 are the number of teeth of the gear shaper, the external gear and the internal gear respectively, , .

4. The method of designing a nutation reducer for a face gear pair according to claim 1, wherein The step 3 is specifically: the face gear can be obtained by modifying the gear shaping cutter and then using the modified gear shaping cutter to process the face gear; The first tooth surface is modified to a second tooth surface; a parabolic modification is selected , the modification amount is calculated , the value of x is reduced by the modification amount on the coordinates of the theoretical tooth surface , a new horizontal coordinate x is obtained, and the values of y and z are kept unchanged; wherein is a parabolic correction factor; Translate the coordinate system origin to the O point and rotate the angle by 。 5. The method of designing a nutation reducer for a face gear pair according to claim 1, wherein The step 4 is specifically: the conjugate of the gear tooth surface is based on the concept of envelope; if the meshing equations of two gears and the cutter are equal, the two gears are conjugate; Meshing equation of the external face gear and the cutter: Meshing equation of the internal face gear and the cutter: According to The conjugate condition of the "face gear - face gear" engagement pair is obtained: 。 6. The method of designing a nutation reducer for a face gear pair according to claim 1, wherein The step 5 is specifically: the engagement form of the "face gear-face gear" engagement pair is point contact, when the engagement characteristics analysis and the contact stress solution are carried out, the contact trajectory of the face gear in the engagement process needs to be determined; according to the tooth surface contact analysis principle, the coordinate system is established, and the tooth surface equations of the outer face gear and the inner face gear are respectively converted to the coordinate system 、 And the normal vector 、 Respectively under the coordinate system . Transformation equation of the external face gear: Transformation equation of the internal face gear: Here, is the axial offset error, is the axial offset error, is the nutation angle deviation; By the equations, a set of equations with 5 independent nonlinear equations containing 6 unknowns is obtained Assuming that are known parameters, the simultaneous equations are solved to obtain the values of the other 5 parameters; and the contact trajectory is obtained by substituting the parameters into the tooth surface equation.

7. The method of designing a nutation reducer for a face gear pair according to claim 1, wherein The step 6 is specifically: a simulation program for gear processing is written by using Matlab; firstly, all instantaneous cutting point coordinates from the start of meshing to the exit of meshing on the tooth profile are obtained according to the gear meshing theory, then the node coordinates of the double-sided tooth profile of a single gear end face are obtained through rotation projection transformation, finally, the point cloud data is processed into a ". txt" format file output; firstly, the file is imported into SolidWorks by using the "Scan To 3D" module function under the guidance of the curve wizard function, the curve lofting function is used, the working curve and the transition curve are selected in sequence, the curve is lofted into a solid surface, the boundary surface is created while rotating 360 / N around the rotation center, and the surface stitching function is applied to obtain a complete gear slot; the single gear slot is arrayed around the rotation center through the circular array command, so that the three-dimensional entity models of the internal face gear and the external face gear are obtained; the internal and external face gears obtained finally are assembled with other parts of the trochoidal reducer, so that the trochoidal face gear reducer is obtained.

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