A tooth profile modification method based on UMESHMOTION

Abstract

The invention provides a tooth profile modification method based on UMESHMOTION. This method is used to solve the problem of complicated pre-processing operations in finite element gear analysis. The present invention describes the finite element simulation process of gear transmission in detail, selects the gear contact area as the adaptive mesh update area, and then derives the theoretical tooth profile modification formula. Finally, the UMESHMOTION subroutine written in Fortran is used to realize the mesh node movement in the adaptive area, thereby completing the tooth profile modification. The present invention streamlines the tooth profile modification process in the finite element software, greatly improving the simulation efficiency and calculation time. Finally, the tooth profile modification under different parameters can be achieved by modifying the parameter variables of the subroutine, and the optimal modification scheme can be selected by viewing the comparison diagram of the maximum Mises stress and contact pressure before and after the modification.

Description

Technical Field

[0001] The present invention relates to the technical field of gear simulation, and in particular to a tooth profile modification method based on UMESHMOTION. Background Art

[0002] Involute gears are susceptible to machining and installation errors, as well as load-induced deformation of the gear teeth during transmission. This can lead to edge contact and stress concentration on the gear tooth surfaces, resulting in tooth surface failure. During gear meshing, machining and installation errors, as well as thermal deformation, can cause the base pitches of the driving and driven gears on the meshing line to become unequal. Interference occurs at alternating critical points, known as engagement and disengagement interference, leading to vibration and noise during gear transmission.

[0003] Tooth profile modification involves slightly modifying the tooth profile by removing material from the tooth surface along the tooth width. This reduces the impact of engagement and engagement, as well as geometric interference, during gear meshing, resulting in a smoother meshing process. Tooth profile modification can effectively reduce gear vibration and noise, improve load-bearing capacity, and extend the gear's service life.

[0004] However, in the existing technology, the pre-processing link of the gear pair model in the finite element simulation is complicated. Updating a set of shaping parameters requires reassembling the gear pair and repeating its pre-processing process, which is not only time-consuming but also difficult to streamline.

[0005] Therefore, there is an urgent need to find a simulation method that can quickly and effectively analyze the meshing performance of gears before and after modification. Summary of the Invention

[0006] The purpose of the present invention is to provide a tooth profile modification method based on UMESHMOTION to solve the problems existing in the prior art.

[0007] The technical solution adopted to achieve the purpose of the present invention is as follows: a tooth profile modification method based on UMESHMOTION, comprising the following steps:

[0008] 1) Build a gear pair model and import it into ABAQUS. The gear pair includes a sun gear and planet gears that mesh with each other.

[0009] 2) Perform pre-processing of the gear pair model. The pre-processing specifically includes the following sub-steps.

[0010] 2-1) Define the material property parameters of the gear pair model.

[0011] 2-2) Based on the kinematic characteristics of the gear pair model, establish the assembly and contact relationships. The sun gear and planet gears are tangent to each other at their pitch circles. In the gear pair contact area, set the sun gear contact surface as the active surface, and the planet gear contact surface as the driven surface.

[0012] 2-3) Create the analysis steps and required output variables.

[0013] 2-4) Select the gear modification area as the adaptive mesh area. Select the gear pair contact area as the adaptive mesh node movement area.

[0014] 2-5) Set the load and constraint relationship according to the actual working conditions of the gear pair.

[0015] 2-6) Mesh the gear pair model.

[0016] 3) Theoretical derivation of tooth profile modification is performed to obtain a tooth profile modification calculation formula, wherein the tooth profile modification calculation formula can solve the angle between the unmodified involute and the modified involute and the modification amount for any radius in the modified area.

[0017] 4) Use the modification amount, modification length and modification curve as program variables, and write the tooth profile modification calculation formula derived in step 3) in the ABAQUS subroutine UMESHMOTION.

[0018] 5) Realize the movement of mesh nodes in the adaptive area to complete the tooth profile modification.

[0019] 6) Compare the meshing performance of gears before and after modification under different modification parameters and select the optimal modification parameters.

[0020] 7) Substitute the optimal modification parameters into the modified profile equation. Use machining methods to modify the tooth profile of a standard involute gear. The tooth flank and tooth top of the involute gear transition with the resulting modified curve.

[0021] Furthermore, in step 1), a three-dimensional model of the gear pair is drawn using drawing software.

[0022] Furthermore, in step 2-1), the material properties include Young's modulus and Poisson's ratio.

[0023] Furthermore, in steps 2-3), four analysis steps are created and the output variables are selected as contact pressure, stress, strain, and displacement.

[0024] Furthermore, the analysis step time is set to 1s. The specific settings of the 4 analysis steps are:

[0025] Step 1) Use UMESHMOTION to modify the gear tooth profile. Set the increment step to 1, with a minimum increment of 1e-5.

[0026] Step 2) Make the gear pair reach interference contact. Set the incremental step to 1, with a minimum increment of 1e-15.

[0027] Step 3) Ensure the gear pair transmits torque smoothly. Set the incremental step to 1, with a minimum increment of 1e-15.

[0028] Step 4) Make the gear pair rotate continuously. The increment step is set to 0.04, and the minimum increment is 1e-5.

[0029] Furthermore, in step 4), the tooth profile modification calculation formula is written in Fortran language.

[0030] Furthermore, in step 5), if the gear node number is less than the total number of nodes, the gear in the global coordinate is modified.

[0031] Furthermore, in step 6), the optimal shaping parameters are selected by viewing the comparison diagram of the maximum Mises stress and contact pressure before and after shaping.

[0032] The present invention also discloses an involute gear, which is processed by a standard involute gear using any one of the above-mentioned tooth profile modification methods based on UMESHMOTION.

[0033] The present invention also discloses a planetary reduction mechanism, comprising an involute gear planetary gear train, wherein the involute gears in the involute gear planetary gear train are processed from standard involute gears using any of the above-mentioned UMESHMOTION-based tooth profile modification methods.

[0034] The technical effects of the present invention are unquestionable:

[0035] A. Provides a simulation method that can quickly and effectively analyze the meshing performance of gears before and after modification. The subroutine UMESHMOTION is used to move mesh nodes to achieve tooth profile modification, providing a new approach to involute gear tooth profile modification.

[0036] B. The three shaping parameters can be modified in the subroutine to achieve tooth profile shaping with different shaping amounts, shaping lengths and shaping curves;

[0037] C. The tooth profile modification can be processed in a targeted and accurate manner, avoiding repeated finite element pre-processing steps and greatly improving the efficiency of finite element simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a flow chart of the tooth profile modification method;

[0039] Figure 2 Schematic diagram of the tooth profile modification end face;

[0040] Figure 3Schematic diagram of tooth profile meshing line;

[0041] Figure 4 Select regions for adaptive meshing;

[0042] Figure 5 Schematic diagram of tooth profile modification in ABAQUS;

[0043] Figure 6 This is the maximum Mises stress output result diagram of the gear pair;

[0044] Figure 7 This is the output result diagram of the maximum contact pressure of the gear pair;

[0045] Figure 8 Schematic diagram of the planetary reduction mechanism and gears before and after modification. DETAILED DESCRIPTION

[0046] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all should be included in the scope of protection of the present invention.

[0047] Example 1:

[0048] This embodiment provides a tooth profile modification method based on UMESHMOTION, comprising the following steps:

[0049] 1) Build a gear pair model and import it into ABAQUS. The gear pair includes a sun gear and planet gears that mesh with each other.

[0050] 2) Perform pre-processing of the gear pair model. The pre-processing specifically includes the following sub-steps.

[0051] 2-1) Define the material property parameters of the gear pair model.

[0052] 2-2) Based on the kinematic characteristics of the gear pair model, establish the assembly and contact relationships. The sun gear and planet gears are tangent to each other at their pitch circles. In the gear pair contact area, set the sun gear contact surface as the active surface, and the planet gear contact surface as the driven surface.

[0053] 2-3) Create the analysis steps and required output variables.

[0054] 2-4) Select the gear modification area as the adaptive mesh area. Select the gear pair contact area as the adaptive mesh node movement area.

[0055] 2-5) Set the load and constraint relationship according to the actual working conditions of the gear pair.

[0056] 2-6) Mesh the gear pair model.

[0057] It is worth noting that the sub-steps are generally performed in the time sequence of 2-1) to 2-6). In actual production, the order of the sub-steps can be changed, but they cannot be performed simultaneously.

[0058] 3) Theoretical derivation of tooth profile modification is performed to obtain a tooth profile modification calculation formula, wherein the tooth profile modification calculation formula can solve the angle between the unmodified involute and the modified involute and the modification amount for any radius in the modified area.

[0059] 4) Use the modification amount, modification length and modification curve as program variables, and write the tooth profile modification calculation formula derived in step 3) in the ABAQUS subroutine UMESHMOTION.

[0060] 5) Realize the movement of mesh nodes in the adaptive area to complete the tooth profile modification.

[0061] 6) Compare the meshing performance of the gears before and after modification under different modification parameters and select the optimal modification parameters. Select the optimal modification parameters by comparing the maximum Mises stress and contact pressure before and after modification.

[0062] 7) Substitute the optimal modification parameters into the modified profile equation. Use machining methods to modify the tooth profile of a standard involute gear. The tooth flank and tooth top of the involute gear transition with the resulting modified curve.

[0063] In actual production, the tooth profile modification function of UMESHMOTION is programmed into a streamlined process within the finite element method, greatly simplifying the finite element pre-processing analysis. The method described in this example can be extended to other mechanical structure simulation methods and can also be used for finite element analysis using other simulation software.

[0064] Example 2:

[0065] This embodiment provides a basic tooth profile modification method based on UMESHMOTION, including the following steps:

[0066] 1) Use drawing software to draw a 3D model of the gear pair and import it into ABAQUS. The gear pair includes a sun gear and planet gears that mesh with each other.

[0067] 2) Perform pre-processing of the gear pair model. The pre-processing specifically includes the following sub-steps.

[0068] 2-1) Define the material property parameters of the gear pair model. Material properties include Young's modulus and Poisson's ratio.

[0069] 2-2) Based on the kinematic characteristics of the gear pair model, establish the assembly and contact relationships. The sun gear and planet gears are tangent to each other at their pitch circles. In the gear pair contact area, set the sun gear contact surface as the active surface, and the planet gear contact surface as the driven surface.

[0070] 2-3) Create the analysis steps and the required output variables. Create four analysis steps and select the output variables as contact pressure, stress, strain, and displacement. Set the analysis step time to 1 second. The specific settings for the four analysis steps are:

[0071] Step 1) Use UMESHMOTION to modify the gear tooth profile. Set the increment step to 1, with a minimum increment of 1e-5.

[0072] Step 2) Make the gear pair reach interference contact. Set the incremental step to 1, with a minimum increment of 1e-15.

[0073] Step 3) Ensure the gear pair transmits torque smoothly. Set the incremental step to 1, with a minimum increment of 1e-15.

[0074] Step 4) Make the gear pair rotate continuously. The increment step is set to 0.04, and the minimum increment is 1e-5.

[0075] 2-4) Select the gear modification area as the adaptive mesh area. Select the gear pair contact area as the adaptive mesh node movement area.

[0076] 2-5) Set the load and constraint relationship according to the actual working conditions of the gear pair.

[0077] 2-6) Mesh the gear pair model.

[0078] 3) Theoretical derivation of tooth profile modification is performed to obtain a tooth profile modification calculation formula, wherein the tooth profile modification calculation formula can solve the angle between the unmodified involute and the modified involute and the modification amount for any radius in the modified area.

[0079] 4) Using the modification amount, modification length and modification curve as program variables, the tooth profile modification calculation formula derived in step 3) was written in Fortran language in the ABAQUS subroutine UMESHMOTION.

[0080] 5) Move the mesh nodes in the adaptive area to complete the tooth profile modification. If the gear node number is less than the total number of nodes, the gear in the global coordinate system is modified.

[0081] 6) Compare the meshing performance of gears before and after modification under different modification parameters and select the optimal modification parameters.

[0082] 7) Substitute the optimal modification parameters into the modified profile equation. Use machining methods to modify the tooth profile of a standard involute gear. The tooth flank and tooth top of the involute gear transition with the resulting modified curve.

[0083] Example 3:

[0084] The main steps of this embodiment are the same as those of Example 2, except that a 3D model of the gear pair is drawn using drawing software. In actual production, the gear pair can be accurately modeled based on the gear design or processing parameters using 3D modeling software such as KISSsoft, Romax, MASTA, or Solidworks. This 3D model can be obtained. For subsequent import into finite element software, the file can be saved in formats such as .x_t, .igs, or .stp.

[0085] Example 4:

[0086] The main steps of this embodiment are the same as those of embodiment 2, wherein in step 2-1), the material properties include Young's modulus and Poisson's ratio. The units are mm-N-MPa, and the gear pair materials are the same.

[0087] Example 5:

[0088] The main steps of this embodiment are the same as those of Example 2. In steps 2-3), four analysis steps are created, and the output variables are selected as contact pressure, stress, strain, and displacement. The analysis step time is set to 1 second. The specific settings of the four analysis steps are:

[0089] Step 1) Use UMESHMOTION to modify the gear tooth profile. Set the increment step to 1, with a minimum increment of 1e-5.

[0090] Step 2) Make the gear pair reach interference contact. Set the incremental step to 1, with a minimum increment of 1e-15.

[0091] Step 3) Ensure the gear pair transmits torque smoothly. Set the incremental step to 1, with a minimum increment of 1e-15.

[0092] Step 4) Make the gear pair rotate continuously. The increment step is set to 0.04, and the minimum increment is 1e-5.

[0093] Example 6:

[0094] The main steps of this embodiment are the same as those of embodiment 2, wherein, in step 4), the tooth profile modification calculation formula is written in Fortran language.

[0095] Example 7:

[0096] The main steps of this embodiment are the same as those of Example 2. In step 5), if the gear node number is less than the total number of nodes, the gear in the global coordinate system is modified. Otherwise, the gear in the local coordinate system is modified. Depending on the actual requirements, one or two gears can be modified. Modifying two gears requires a judgment, while modifying one gear does not.

[0097] Example 8:

[0098] The main steps of this embodiment are the same as those of embodiment 2, wherein, in step 6), the optimal shaping parameters are selected by viewing the comparison diagram of the maximum Mises stress and contact pressure before and after shaping.

[0099] Example 9:

[0100] The main steps of this embodiment are the same as those of embodiment 1, wherein this embodiment follows Figure 1 The simulation process steps shown include the following steps:

[0101] 1) Create a 3D model of the gear pair. This can be done using 3D modeling software such as KISSsoft, Romax, MASTA, or Solidworks. Accurately model the gear pair based on the gear design or processing parameters to obtain a 3D model. For subsequent import into finite element analysis software, save the file in formats such as .x_t, .igs, or .stp.

[0102] 2) Complete the pre-processing settings of the gear pair model using ABAQUS simulation software:

[0103] 2-1) Define the material properties of the gear pair model using ABAQUS simulation software. The material properties include Young's modulus and Poisson's ratio, with units of mm-N-MPa. Set the gear pair materials to be the same.

[0104] 2-2) Establish assembly and contact relationships through the motion characteristics of the gear pair model. The assembly drawing is completed based on the tangency of the sun gear and planetary gears at the pitch circle. The sun gear contact surface is set as the active surface, the planetary gear contact surface as the driven surface, and the contact mode and static friction coefficient are set.

[0105] 2-3) Create analysis steps and required output variables using ABAQUS simulation software; create four analysis steps, all with large deformation enabled, and set the analysis step time and increment.

[0106] 2-4) Update the mesh using adaptive mesh technology; wherein, the contact area of the gear pair is separated and selected as the adaptive mesh area (i.e., the gear modification area), and the gear pair contact surface is the adaptive mesh node movement area.

[0107] 2-5) Set loads and constraints according to the actual working conditions of the gear pair.

[0108] Among them, the load application principle is:

[0109] a) Establish a coupling point on the inner surface of the driving wheel and apply a torque load to the node to simulate actual load transfer.

[0110] b) Establish a coupling point on the inner ring surface of the driven wheel and impose a displacement constraint on the node to ensure the normal rotation of the subsequent gears

[0111] Principles for imposing constraints:

[0112] a) The coupling point on the inner ring surface of the driving wheel restricts all degrees of freedom except the axial direction, that is, it can only rotate around the axis.

[0113] b) The coupling point on the inner annular surface of the driven wheel restricts all degrees of freedom except the axial direction, that is, it can only rotate around the axis.

[0114] 2-6) The gear pair model was meshed using ABAQUS simulation software. The contact area of the gear pair was finely meshed. To ensure the continuity of the contact pressure image, the mesh size ratio of the tooth diameter to the tooth width was set to approximately 1:6. The remaining areas were coarsely meshed.

[0115] 3) To carry out theoretical derivation of tooth profile modification, it is necessary to calculate the angle between the unmodified involute and the modified involute for any radius in the modified area, which can be completed in the following two steps.

[0116] a) The first step is to find the amount of trimming at any angle corresponding to any radius within the trimming area.

[0117] Figure 2 The schematic diagram of the tooth profile modification end face is given below: arc length BD is the original involute, B′D is the modified curve, and B′C is the maximum modification amount Δ max , we need to find the central angle ∠B′OB and the radius r at this time a The relationship between , and then replace it with any angle θ i and any radius r i The relationship between , the derivation process is as follows.

[0118] According to the geometric relationship, ΔBAO and ΔB′A′O are congruent triangles, and we can get:

[0119]

[0120] Since ∠AOB′ is the common angle of ΔBAO and ΔB′A′O, we can get:

[0121] ∠A′OA=∠B′OB,A′B′=AB (3)

[0122] Because B′C=Δ max , we can get the following equation:

[0123] A′C=A′B′+B′C=AB+Δ max (4)

[0124] Among them, A′C and AB are generating lines, which can be obtained by the involute function:

[0125]

[0126] Among them, α and α′ are the central angles of AB and A′C respectively, r b is the base circle radius.

[0127] According to formula (4), we can get ∠A′OA=∠A′OK-∠AOK=(A′C-AB) / r b , combined with formula (3), we can get the central angle ∠B′OB and radius r a The relationship between them is as follows.

[0128]

[0129] Δ max Replace it with the modification amount Δ to get any radius r i The corresponding angle θ i The amount of modification Δ i for:

[0130]

[0131] The shaping curve is:

[0132]

[0133] b) In the second step, combining equations (6) and (7), we need to derive the arbitrary radius r i Corresponding trimming length x i .

[0134] Figure 3 is a schematic diagram of the tooth profile meshing line. In formula (7), x and L represent the relative modification amount and modification length of the meshing line length. n is a different modification curve, and the default value is 1. Therefore, the extended tooth top circle and the modification starting point arc intersect the meshing line NN′ at points B″ and D1, respectively. Then, an arc of arbitrary radius r is made to intersect the involute and the meshing line at points E and E1, respectively. The modification length L is:

[0135] L = k × m n (9)

[0136] Among them, k is the modification length coefficient, mn is the normal modulus.

[0137] Because sin(∠ND1O)=r b / r1, we can get:

[0138] ∠B″D1O=180°-∠ND1O (10)

[0139] Then, in the triangle ΔD1OE1, according to the cosine theorem, the relationship between the relative shaping amount x=D1E1 and the shaping radius r=OE1 can be obtained as follows:

[0140]

[0141] Among them, r1≤r≤r a , r1 is the radius corresponding to the starting point D of the modification.

[0142] Furthermore, L can be expressed as:

[0143]

[0144] Combining equations (8) and (11), the expression of the radius r1 of the starting point of the modification can be obtained as follows:

[0145]

[0146] Finally, combining equations (6), (7) and (10), we can get the value of any radius r in the modified area: i The angle θ between the unmodified involute and the modified involute i and the modification amount x i .

[0147] 4) In the subroutine UMESHMOTION, use the Fortran language to write the tooth profile modification formula derived in the above step 3); in the formula written in Fortran, use the modification amount, modification length and modification curve as program variables to facilitate subsequent changes to the three modification parameters.

[0148] 5) Submit the job to move the mesh nodes in the adaptive area and complete the tooth profile modification. Due to the presence of multiple gears, the total number of nodes is calculated by adding the number of reference points plus 1 to the number of nodes in the global coordinate system. This is used as the basis for determining whether the gear needs to be modified. If the gear node number is less than the total number of nodes, the gear in the global coordinate system is modified, otherwise the other gears are modified. In UMESHMOTION, the coordinate conversion formula is used to convert the current node coordinates to the modified node coordinates. The formula is as follows:

[0149]

[0150] Where: Cx,y,z is the three-dimensional coordinate value of the current node, θ is the angle derived in step 3), N x,y,z The three-dimensional coordinate value of the node after modification.

[0151] 6) Compare the meshing performance of the gears before and after modification under different modification parameters and select the optimal modification parameters. This includes the following two aspects:

[0152] 6-1) Extract the maximum Mises stress of the intermediate gear pair at each moment and plot it;

[0153] 6-2) Extract the maximum contact pressure of the intermediate gear pair at each moment and draw a graph.

[0154] 7) Substitute the optimal modification parameters into the modified profile equation. Use machining methods to modify the tooth profile of a standard involute gear. The tooth flank and tooth top of the involute gear transition with the resulting modified curve.

[0155] Example 10:

[0156] In this embodiment, a finite element simulation is performed on a modified helical gear pair. The specific parameters of the gear pair are shown in Table 1.

[0157] Table 1

[0158]

[0159]

[0160] The main steps of this embodiment are the same as those of embodiment 9, wherein this embodiment specifically includes the following steps:

[0161] 1) Establish a three-dimensional model of the gear pair. Enter the basic parameters in Table 1 in KISSsoft to generate a three-dimensional model of the gear pair. Save the file in .x_t format and import it into ABAQUS.

[0162] 2) Complete the pre-processing settings of the gear pair model using ABAQUS simulation software;

[0163] 2-1) Define the material properties of the gear pair model using ABAQUS simulation software; the Young's modulus is set to 216000 MPa and the Poisson's ratio is set to 0.3.

[0164] 2-2) Establish assembly and contact relationships through the motion characteristics of the gear pair model. The assembly drawing is completed based on the tangency of the sun gear and planetary gears at the pitch circle. The contact surface of the sun gear is set as the active surface, the contact surface of the planetary gear is set as the driven surface, and the friction coefficient is set to 0.05.

[0165] 2-3) Create four analysis steps and the required output variables, turning on large deformation for all of them; set the analysis step time to 1s, specifically:

[0166] Step-1: The incremental step is set to 1, and the minimum increment is 1e-5. The purpose is to first use UMESHMOTION to modify the gear tooth profile;

[0167] Step-2: The incremental step is set to 1, and the minimum increment is 1e-15, in order to make the gear pair have interference contact;

[0168] Step-3: The incremental step is set to 1, and the minimum increment is 1e-15, in order to ensure that the gear pair transmits torque smoothly;

[0169] Step-4: The incremental step is set to 0.04 and the minimum increment is 1e-5. The purpose is to make the gear pair rotate continuously.

[0170] 2-4) Update the mesh using adaptive mesh technology: The contact area of the gear pair is separated and selected as the adaptive mesh area (i.e., the gear modification area). The contact surface of the gear pair is the adaptive mesh node movement area. The adaptive mesh is only applied to the first analysis step and is not used in the remaining analysis steps. Figure 4 shown.

[0171] 2-5) Set loads and constraints based on the actual working conditions of the gear pair: Create a coupling point on the inner annular surface of the sun gear and apply a moment load of 1.1361E+07 N·mm to this node in the second analysis step.

[0172] Principles for imposing constraints:

[0173] a) For the sun gear, all degrees of freedom are constrained in the initial analysis step and passed to the first analysis step. In the second analysis step, a rotational displacement constraint of 0.003 rad is applied around the axial direction. The rotational displacement degrees of freedom around the axial direction are released in subsequent analysis steps.

[0174] b) For the planetary gear, constrain all degrees of freedom in the initial analysis step, transfer to the third analysis step, and apply a displacement constraint of 1 rad around the axial direction in the fourth analysis step;

[0175] Through the above settings, it is ensured that the intermediate gear pair undergoes a complete meshing process during the simulated transmission process.

[0176] 2-6) The gear pair model is meshed using ABAQUS simulation software: the contact area of the gear pair is finely meshed. To ensure the continuity of the contact pressure image, the mesh sizes in the tooth diameter and tooth width directions are set to 0.5:3, respectively. The remaining areas are coarsely meshed, and the mesh size is set to 15.

[0177] 3) Conduct theoretical deduction of tooth profile modification.

[0178] 4) In the subroutine UMESHMOTION, use the Fortran language to write the tooth profile modification formula derived in the above step 3); in the formula written in Fortran, use the modification amount, modification length and modification curve as program variables to facilitate subsequent changes to the three modification parameters.

[0179] 5) Submit the job and implement the tooth profile modification in the subroutine UMESHMOTION. The tooth profile modification diagram is as follows: Figure 5 In this example, the planetary gear is a gear in global coordinates, with a node number of 338572. Add 2 reference points and 1, and the total node number is 338575. If the node number is less than the total node number, the planetary gear is modified; otherwise, the sun gear is modified.

[0180] 6) Compare the meshing performance of gears before and after modification under different modification parameters and select the optimal modification parameters.

[0181] 6-1) Extract the maximum Mises stress of the intermediate gear pair at each moment and draw a graph: Set the fourth analysis step time to 1s, the incremental step to 0.04, and a total of 25 time points. Only the maximum Mises stress value of the intermediate gear pair at each moment is extracted.

[0182] 6-2) Extract the maximum contact stress of the intermediate gear pair at each moment and draw a graph; set the fourth analysis step time to 1s, the incremental step to 0.04, and a total of 25 time points, and only extract the maximum contact pressure value of the intermediate gear pair at each moment.

[0183] According to the stress and contact pressure images, it is judged whether the expected shaping standard is met. If not, the shaping parameter variables (shaping amount, shaping length and shaping curve) are modified until the expected expectation is met.

[0184] In addition, changing the value of n in formula (8) can achieve different curve modifications. For example, take four modification curves of n = 1, n = 1.2, n = 1.5 and n = 2 to compare Mises stress and contact pressure, and select the optimal modification curve, such as Figure 6 and Figure 7 As shown, Figure a represents the sun gear and Figure b represents the planetary gear. It is found that when n=2, the shaping effect is best.

[0185] 7) Substitute the optimal modification parameters into the modified profile equation. Use machining methods to modify the tooth profile of a standard involute gear. The tooth flank and tooth top of the involute gear transition with the resulting modified curve.

[0186] Example 11:

[0187] This embodiment provides an involute gear, which is processed from a standard involute gear using a tooth profile modification method based on UMESHMOTION as described in any one of Embodiments 1 to 10.

[0188] Example 12:

[0189] See also Figure 8 This embodiment provides a planetary reduction mechanism, including an involute gear planetary gear train, wherein the involute gears in the involute gear planetary gear train are made of standard involute gears processed using any one of the UMESHMOTION-based tooth profile modification methods in Examples 1 to 10. Figure 8 a is the planetary reduction mechanism gear simulation model, Figure 8 b is the tooth profile before modification, Figure 8 c is the tooth profile after modification. The simulation scaling factor is magnified 70 times in this figure.

Claims

1. A tooth profile modification method based on UMESHMOTION, characterized in that: The following steps are involved: 1) Establish a gear pair model and import it into ABAQUS; wherein the gear pair includes a sun gear and planet gears that mesh with each other; 2) Performing pre-processing settings for the gear pair model; the pre-processing settings specifically include the following sub-steps; 2-1) Define the material property parameters of the gear pair model; 2-2) Based on the kinematic characteristics of the gear pair model, establish assembly and contact relationships; where the sun gear and planet gears are tangent to each other at the pitch circle; set the sun gear contact surface as the active surface and the planet gear contact surface as the driven surface in the gear pair contact area; 2-3) Create the analysis steps and required output variables; 2-4) Select the gear modification area as the adaptive mesh area; select the gear pair contact area as the adaptive mesh node movement area; 2-5) Set the load and constraint relationship according to the actual working conditions of the gear pair; 2-6) Mesh the gear pair model; 3) Theoretical derivation of tooth profile modification is performed to obtain a tooth profile modification calculation formula; wherein, the tooth profile modification calculation formula can solve any radius r in the modification area i The angle θ between the unmodified involute and the modified involute i and the modification amount x i ; 4) Use the modification amount, modification length, and modification curve as program variables and write the tooth profile modification calculation formula derived in step 3) in the ABAQUS subroutine UMESHMOTION; 5) Realize the movement of grid nodes in the adaptive area to complete the tooth profile modification; 6) Compare the meshing performance of gears before and after modification under different modification parameters and select the optimal modification parameters; 7) Substituting the obtained optimal modification parameters into the modification profile equation; modifying the tooth profile of the standard involute gear by a machining method; and transitioning the tooth surface and tooth top of the involute gear with the formed modification curve.

2. The tooth profile modification method based on UMESHMOTION according to claim 1, characterized in that: In step 1), a three-dimensional model of the gear pair is drawn using drawing software.

3. The tooth profile modification method based on UMESHMOTION according to claim 1, characterized in that: In step 2-1), the material properties include Young's modulus and Poisson's ratio.

4. The tooth profile modification method based on UMESHMOTION according to claim 1, characterized in that: In steps 2-3), create 4 analysis steps and select the output variable as a tooth profile modification method based on UMESHMOTION-1- Contact pressure, stress, strain, and displacement.

5. The tooth profile modification method based on UMESHMOTION according to claim 4, characterized in that: The analysis step time is set to 1s; the specific settings of the 4 analysis steps are: Step-1) Use UMESHMOTION to modify the gear tooth profile; the incremental step is set to 1, and the minimum increment is 1e-5; Step-2) Make the gear pair in interference contact; the incremental step is set to 1, and the minimum increment is 1e-15; Step-3) Make the gear pair transmit torque smoothly; The increment step is set to 1, and the minimum increment is 1e-15; Step-4) Make the gear pair rotate continuously; the incremental step is set to 0.04, and the minimum increment is 1e-5.

6. The tooth profile modification method based on UMESHMOTION according to claim 1, characterized in that: In step 4), the tooth profile modification calculation formula is written in Fortran language.

7. The tooth profile modification method based on UMESHMOTION according to claim 1, characterized in that: In step 5), if the gear node number is less than the total number of nodes, the gear in the global coordinate is modified.

8. The tooth profile modification method based on UMESHMOTION according to claim 1, characterized in that: In step 6), the optimal shaping parameters are selected by viewing the comparison diagram of the maximum Mises stress and contact pressure before and after shaping.

9. An involute gear, characterized in that: The standard involute gear is processed by using any one of the tooth profile modification methods based on UMESHMOTION as claimed in claims 1 to 8.

10. A planetary reduction mechanism comprising an involute gear planetary gear train, characterized in that: The involute gears in the involute gear planetary gear train are made of standard involute gears processed by using any one of the UMESHMOTION-based tooth profile modification methods as claimed in claims 1 to 8.

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