A method for calculating tooth surface contact stress based on transient simulation results

Abstract

The present invention relates to a method for calculating tooth surface contact stress based on transient simulation results, and belongs to the technical field of gear meshing simulation. By extracting the stress-time history curve of the tooth surface unit in the transient simulation results of gear meshing and exporting the data file of the curve, the arrangement information file of all tooth surface units is further generated according to the gear unit number arrangement information; the grid length of the tooth surface unit along the tooth height direction is measured in the ANSA software, and the equivalent curvature radius at each meshing point of the driving wheel and the driven wheel is measured; the meshing load at each meshing position of the tooth surface is calculated by MATLAB programming, and the maximum contact stress and average contact stress at each meshing position of the tooth surface are further calculated based on the gear Hertz contact half-width algorithm. This meshing load algorithm breaks through the limitation of relying on empirical formulas in traditional methods, and can take into account the internal excitation response of the gear transmission system, which is conducive to obtaining a more accurate meshing load.

Description

Technical Field

[0001] The present invention relates to the technical field of gear meshing simulation, and in particular to a method for calculating tooth surface contact stress based on transient simulation results. Background Art

[0002] Tooth contact stress plays a crucial role in gear transmission systems and directly affects the Hertzian strength analysis of gears. Therefore, accurate calculation of tooth contact stress is key to ensuring the reliability of gear transmission systems.

[0003] The classical Hertz contact theory usually relies on simplified assumptions and empirical formulas when calculating tooth surface contact stress. These assumptions often assume that the tooth surface contact is idealized and fail to fully consider the influence of practical factors such as the transient characteristics of gear meshing, gear side clearance, bearing clearance, and nonlinear behavior of materials.

[0004] To this end, the inventors strive to use transient simulation methods to comprehensively consider complex actual working conditions, simulate the actual deformation of the tooth surface geometry during gear meshing, the nonlinear response of the material, and the dynamic changes under different load conditions, so as to more accurately predict the spatial distribution of tooth surface contact stress and provide more realistic and reliable tooth surface contact stress data for research work such as gear strength verification. Summary of the Invention

[0005] The present invention provides a method for calculating tooth surface contact stress based on transient simulation results, which can overcome the problem mentioned in the above background technology that "the classical Hertz contact theory method cannot fully consider the influence of actual factors such as the structural complexity of the gear transmission system, the complexity of internal excitation interaction, the dynamic characteristics of the system at high speed, the transient characteristics of gear meshing, gear side clearance, bearing clearance and nonlinear behavior of materials when calculating tooth surface contact stress by relying on empirical formulas."

[0006] The present invention is achieved through the following solutions:

[0007] A method for calculating tooth surface contact stress based on transient simulation results includes the following steps:

[0008] S1: Extract the stress-time history curve of the tooth surface unit from the gear meshing transient simulation results and export the data file of the curve;

[0009] S2: Select each row of cells in a certain order and export the cell number arrangement information file;

[0010] S3: Lock the position of the tooth surface units involved in meshing and number the nodes at the tooth surface meshing units in a specific order;

[0011] S4: Measure the mesh length of the tooth surface unit, combine the stress-time history data of the tooth surface unit and the tooth surface unit number arrangement information, and calculate the meshing load at each meshing position of the tooth surface. The meshing load calculation formula is shown in formula (1):

[0012] Where b1 is the effective contact width (unit: mm), p i is the stress of a tooth surface unit (unit: MPa), a is the grid length of the tooth surface unit along the tooth height direction (unit: mm);

[0013]

[0014] S5: Based on step 4, measure the equivalent curvature radius at each meshing point of the driving wheel and the driven wheel, and calculate the contact half-width at each meshing position of the tooth surface according to the Hertz contact width calculation formula, as shown in formula (2),

[0015] Where F is the meshing load at each meshing position on the tooth surface (unit: N), v1 and v2 are the Poisson's ratios of the driving wheel and driven wheel materials, E1 and E2 are the elastic moduli of the driving wheel and driven wheel materials, respectively (unit: MPa), L is the effective contact width (unit: mm), R1 and R2 are the equivalent curvature radii at each meshing point on the meshing interface of the driving wheel and driven wheel, respectively (unit: mm);

[0016]

[0017] or

[0018]

[0019] S6: Substitute the contact half-width at each meshing position on the tooth surface into the contact stress calculation formula shown in the formula to obtain the contact stress at each meshing position on the tooth surface.

[0020] Furthermore, in step 2, the certain order is the order from "tooth top" to "tooth root".

[0021] Furthermore, in step 3, the unit positions of the meshing tooth surfaces are locked using the gear meshing stress cloud map.

[0022] Furthermore, in step 3, the specific order is the order from "tooth root" to "tooth top".

[0023] Furthermore, in step 4, the grid length is the length of the tooth surface unit along the tooth height direction.

[0024] Furthermore, in step 6, when calculating the maximum contact stress, equation 3 is used for calculation:

[0025]

[0026] or

[0027]

[0028] Furthermore, in step 6, when calculating the average contact stress, equation 4 is used for calculation:

[0029] Where ρ1 and ρ2 are the equivalent curvature radii of the meshing points on the meshing interface of the driving wheel and the driven wheel, respectively (unit: mm);

[0030]

[0031] or

[0032]

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The present invention uses the stress-time history curves of tooth surface units from transient simulation results to determine the stress of each tooth surface unit. Furthermore, the mesh length of each tooth surface unit along the tooth height direction is measured. Finally, the sum of the products of the two is multiplied by the effective contact width at the tooth meshing location to determine the meshing load at that location. This meshing load algorithm overcomes the limitations of traditional methods that rely on empirical formulas and can consider the internal excitation response of the gear transmission system, facilitating a more accurate meshing load calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the present invention;

[0036] Figure 2 Flowchart for tooth surface stress data extraction;

[0037] Figure 3 This is a schematic diagram of the tooth surface unit to be extracted from the driving wheel;

[0038] Figure 4 Schematic diagram of the driving gear tooth surface unit array;

[0039] Figure 5 is the contact stress-time history curve of the meshing unit;

[0040] Figure 6 Schematic diagram of the meshing element contact stress-time history data file and element number arrangement information file;

[0041] Figure 7 Extract schematic diagram for tooth surface unit numbering;

[0042] Figure 8 This is a schematic diagram of the numbering array of the driving gear tooth surface units;

[0043] Figure 9Schematic diagram of the driving wheel meshing area;

[0044] Figure 10 Schematic diagram of the positions of the tooth surface units involved in meshing;

[0045] Figure 11 This is a schematic diagram of the node numbering at the tooth surface meshing unit;

[0046] Figure 12 Schematic diagram of the grid length of the tooth surface meshing unit along the tooth height direction;

[0047] Figure 13 This is a schematic diagram for meshing load calculation;

[0048] Figure 14 The stress-time history curve and stress cloud diagram of the meshing unit at a certain meshing moment of the driving wheel;

[0049] Figure 15 Schematic diagram for measuring the equivalent curvature radius at each meshing point of the driving wheel and the driven wheel;

[0050] Figure 16 Schematic diagram of the Hertzian contact half-width of gears. DETAILED DESCRIPTION

[0051] To make the objectives, technical solutions, and innovations of the embodiments of the present invention more clearly understood, the technical solutions of the embodiments of the present invention are described clearly and completely below in conjunction with the accompanying drawings of the embodiments of the present invention. It should be understood that the described embodiments are only a portion of the embodiments of the present invention, not all of them. Generally, the components of the embodiments of the present invention described and illustrated in the drawings herein may be arranged and designed in various configurations.

[0052] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0053] like Figure 1 FIG. 1 is a flow chart of the present invention. According to the steps in the flow chart, this embodiment provides a method for calculating tooth surface contact stress based on transient simulation results, which specifically includes the following steps:

[0054] Step 1:

[0055] like Figure 2 The figure shows the flow chart of tooth surface stress data extraction. Open the gear meshing transient simulation result file (intfor file) in the post-processing software Pre-post, select the mesh element of the driving wheel to be extracted tooth surface stress (see Figure 3 ), the driving wheel tooth surface unit array is shown Figure 4 ; Further, the stress-time history curves of all tooth surface units are extracted (see Figure 5 ) and export the stress-time history data file of the curve (see Figure 6 ).

[0056] Step 2:

[0057] like Figure 7 The figure shows the extraction of tooth surface unit number. Open the gear meshing transient simulation result file (intfor file) in Hyperview software. At this time, the built-in option bar of the software is defined as Element ID. Then, click on each row of units in the order of "tooth top" to "tooth root" on the tooth surface of the driving wheel to be extracted. After selection, the number arrangement information of each row of units can be output and the unit number arrangement information file (.csv file) can be exported to facilitate the subsequent program to process the simulation result data; the driving wheel tooth surface unit number array is shown. Figure 8 .

[0058] Step 3:

[0059] like Figure 9 The figure shows the meshing area of ​​the driving wheel. The meshing tooth surface of a single tooth of the driving wheel is divided into 20 nodes, that is, 19 rows of units. Further, the gear meshing stress cloud map is viewed in the Pre-post software to lock the position of the tooth surface unit involved in the meshing in the meshing area of ​​the driving wheel (see Figure 10 ), it can be seen that the part of the tooth surface involved in meshing is Figure 9 The red solid line box selects 9 rows of elements from 10 to 18, so we only need to calculate the meshing load of the meshing points corresponding to these 9 rows of elements. Furthermore, the nodes at the meshing elements of the tooth surface (i.e., meshing points) are numbered in the order from "tooth root" to "tooth top" (see Figure 11 ), which facilitates the subsequent calculation of contact stress.

[0060] Step 4:

[0061] Measuring the mesh length of the tooth surface unit along the tooth height direction in the gear meshing transient simulation model in ANSA software (see Figure 12 ), and combined with the stress-time history data of the tooth surface unit and the tooth surface unit number arrangement information, the meshing load at each meshing position of the tooth surface is calculated through MATLAB programming; the meshing load calculation formula at the meshing position of the tooth surface is shown in formula (1), where b1 is the effective contact width of the tooth surface (unit: mm), p i is the stress of a tooth surface unit (unit: MPa), and a is the grid length of the tooth surface unit along the tooth height direction (unit: mm).

[0062]

[0063] Taking the stress-time history data of a row of elements on the driving gear tooth surface as an example, the meshing load calculation process at the meshing position of tooth surface number 1 will be described in detail below.

[0064] like Figure 13 The figure shows a schematic diagram for meshing load calculation. In the figure, the contact width a of the tooth surface unit is the mesh length of the unit along the tooth height, and b1 is the effective contact width of the tooth surface (i.e., the effective tooth width). It is important to emphasize that in this example, the driving gear tooth width is 14.2mm and the driven gear tooth width is 16mm, so the effective contact width b1 of the tooth surface is 14.2mm. To calculate the meshing load at meshing point number 1 on tooth surface, the stress per unit tooth surface at meshing position number 1 is also required.

[0065] like Figure 14 The figure shows the stress-time history curve and stress nephogram of the meshing element at a certain moment of engagement of the driving gear. The gear meshing stress nephogram shows that when two gears mesh, each tooth may have 4-6 elements in contact simultaneously, sharing the gear meshing load. Therefore, when calculating the gear meshing load, it is necessary to simultaneously consider the loads of adjacent elements.

[0066] Furthermore, a row of units participating in the meshing of the driving wheel at this meshing moment is selected, and it is found that the load-bearing units at this time are 20610, 20609, 20608, and 20607; and then the stress-time history curves of the units 20610, 20609, 20608, and 20607 are extracted (see Figure 14 ), at this meshing moment, the stresses of 20610, 20609, 20608, and 20607 units are 11MPa, 122MPa, 152MPa, and 32.4MPa, respectively; therefore, Figure 12 Substituting the mesh length of the tooth surface element along the tooth height direction and the stresses of elements 20610, 20609, 20608, and 20607 into Equation (1), we obtain a meshing load of 730.147 N at the meshing position of driving wheel number 1. The meshing load calculation process for the remaining meshing positions is similar, and the results are shown in Table 1.

[0067] Table 1 Meshing load at each meshing position on the tooth surface

[0068]

[0069]

[0070] Step 5:

[0071] Based on step 4, the equivalent curvature radius at each meshing point of the driving wheel and the driven wheel is further measured in the ANSA software (see Figure 15 ), and according to the Hertz contact width calculation formula, calculate the contact half-width at each meshing position of the tooth surface. The schematic diagram of the gear Hertz contact half-width is shown in Figure 16 The calculation formula of the contact half-width is shown in formula (3), where F is the meshing load at each meshing position on the tooth surface (unit: N), v1 and v2 are the Poisson's ratios of the materials of the driving wheel and the driven wheel, respectively, E1 and E2 are the elastic moduli of the materials of the driving wheel and the driven wheel, respectively (unit: MPa), L is the effective contact width (unit: mm), R1 and R2 are the equivalent curvature radii at each meshing point on the meshing interface of the driving wheel and the driven wheel, respectively (unit: mm).

[0072]

[0073] or

[0074]

[0075] Taking the calculation of the contact half-width at the meshing position of the driving gear tooth surface number 1 as an example, the following will introduce the calculation process of the contact half-width at the meshing position of the driving gear number 1 in detail.

[0076] In this example, the meshing of the driving wheel and the driven wheel is external meshing, so formula (3.1) can be selected; in the formula, F is 730.147N, v1 and v2 are 0.3, E1 and E2 are 210000MPa, L is 14.2mm, R1 and R2 are 11.76mm and 33.29mm respectively. Further, the equivalent radius of curvature at the meshing position of tooth surface number 1 in step 4 and the meshing load at the meshing position of tooth surface number 1 in step 5 are substituted into formula (3.1), and the contact half-width at the meshing position of tooth surface number 1 is obtained to be 0.0243mm. The calculation process of the contact half-width at the other meshing positions is similar, and the results are shown in Table 2

[0077] Table 2 Equivalent curvature radius and contact half-width at each meshing point on the tooth surface

[0078]

[0079] Step 6:

[0080] Substituting the contact half-width at each meshing position on the tooth surface into the maximum contact stress calculation formula shown in formula (4), the maximum contact stress at each meshing position on the tooth surface can be obtained by simplification.

[0081]

[0082] or

[0083]

[0084] Taking the calculation of the maximum contact stress at the meshing position of the driving wheel tooth surface No. 1 as an example, the calculation process of the maximum contact stress at the meshing position of the driving wheel No. 1 will be introduced in detail below.

[0085] In this example, the meshing between the driving and driven gears is external, so Equation (4.1) is used. Based on Step 6, substituting the formula for the contact half-width into Equation (4.1), the maximum contact stress at meshing position 1 on tooth surface 1 is simplified to 1347.086 MPa. The calculation process for the maximum contact stress at the remaining meshing positions is similar, with the results shown in Table 3.

[0086] Table 3 Maximum contact stress at each meshing position on the tooth surface

[0087]

[0088] Substituting the contact half-width at each meshing position of the tooth surface into the average contact stress calculation formula shown in formula (5) can obtain the average contact stress at each meshing position of the tooth surface, where ρ1 and ρ2 are the equivalent curvature radii (unit: mm) at each meshing point on the meshing interface of the driving wheel and the driven wheel, respectively.

[0089]

[0090] or

[0091]

[0092] Taking the calculation of the average contact stress at the meshing position of the driving wheel tooth surface No. 1 as an example, the calculation process of the average contact stress at the meshing position of the driving wheel No. 1 will be introduced in detail below.

[0093] In this example, the meshing between the driving and driven gears is external, so Equation (5.1) is used. Based on Step 6, substituting the formula for the contact half-width into Equation (5.1), the simplified result is an average contact stress of 1058.0 MPa at the meshing position of tooth surface number 1. The average contact stress calculation process for the remaining meshing positions is similar, with the results shown in Table 4.

[0094] Table 4 Average contact stress at each meshing position on the tooth surface

[0095]

[0096]

[0097] By implementing the above steps, the tooth surface contact stress is calculated based on the transient simulation results. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, from all perspectives, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and range of equivalents of the claims be included in the present invention. Any reference signs in the claims should not be construed as limiting the claim to which they relate.

Claims

1. A method for calculating tooth surface contact stress based on transient simulation results, characterized by: The following steps are involved: S1: Extract the stress-time history curve of the tooth surface unit from the gear meshing transient simulation results and export the data file of the curve; S2: Select each row of cells in a certain order and export the cell number arrangement information file; S3: Lock the position of the tooth surface units involved in meshing and number the nodes at the tooth surface meshing units in a specific order; S4: Measure the mesh length of the tooth surface unit, combine the stress-time history data of the tooth surface unit and the tooth surface unit number arrangement information, and calculate the meshing load at each meshing position of the tooth surface. The meshing load calculation formula is shown in formula (1): Where b1 is the effective contact width (unit: mm), p i is the stress of a tooth surface unit (unit: MPa), a is the grid length of the tooth surface unit along the tooth height direction (unit: mm); S5: Based on step 4, measure the equivalent curvature radius at each meshing point of the driving wheel and the driven wheel, and calculate the contact half-width at each meshing position of the tooth surface according to the Hertz contact width calculation formula, as shown in formula (2), Where F is the meshing load at each meshing position on the tooth surface (unit: N), v1 and v2 are the Poisson's ratios of the driving wheel and driven wheel materials, E1 and E2 are the elastic moduli of the driving wheel and driven wheel materials, respectively (unit: MPa), L is the effective contact width (unit: mm), R1 and R2 are the equivalent curvature radii at each meshing point on the meshing interface of the driving wheel and driven wheel, respectively (unit: mm); S6: Substitute the contact half-width at each meshing position on the tooth surface into the contact stress calculation formula shown in the formula to obtain the contact stress at each meshing position on the tooth surface.

2. The method for calculating tooth surface contact stress based on transient simulation results according to claim 1, characterized in that: In step 2, the certain order is from "tooth top" to "tooth root".

3. The method for calculating tooth surface contact stress based on transient simulation results according to claim 1, characterized in that: In step 3, the gear meshing stress cloud map is used to lock the unit positions of the meshing tooth surfaces.

4. The method for calculating tooth surface contact stress based on transient simulation results according to claim 1, characterized in that: In step 3, the specific order is from "tooth root" to "tooth top".

5. The method for calculating tooth surface contact stress based on transient simulation results according to claim 1, characterized in that: In step 4, the grid length is the length of the tooth surface unit along the tooth height direction.

6. The method for calculating tooth surface contact stress based on transient simulation results according to claim 1, characterized in that: In step 6, when calculating the maximum contact stress, use formula 3 to calculate: .

7. The method for calculating tooth surface contact stress based on transient simulation results according to claim 1, characterized in that: In step 6, when calculating the average contact stress, use formula 4 to calculate: Where ρ1 and ρ2 are the equivalent curvature radii of the meshing points on the meshing interface of the driving wheel and the driven wheel, respectively (unit: mm);

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