Tooth surface contact stress calculation method based on transient simulation result

Abstract

The invention relates to a tooth surface contact stress calculation method based on a transient simulation result, and belongs to the technical field of gear meshing simulation. A tooth surface unit stress-time history curve in a gear meshing transient simulation result is extracted, a data file of the curve is exported, and an arrangement information file of all tooth surface units is further generated according to gear unit number arrangement information; measuring the grid length of the tooth surface unit along the tooth height direction in ANSA software, and measuring the equivalent curvature radius of each meshing point of the driving wheel and the driven wheel; the meshing load at each meshing position of the tooth surface is calculated by utilizing MATLAB programming, and the maximum contact stress and the average contact stress at each meshing position of the tooth surface are further calculated based on a gear Hertz contact half-width algorithm. According to the meshing load algorithm, the limitation of dependence on an empirical formula in a traditional method is broken through, the internal excitation response of the gear transmission system can be considered, and a more accurate meshing load can be obtained.

Description

Technical Field

[0001] The 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 vital role in the gear transmission system, which directly affects the verification analysis of the gear Hertz strength. Therefore, accurate calculation of tooth contact stress is the key to ensure the reliability of the gear transmission system.

[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 practical 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 comprises the following steps:

[0008] S1: Extract the stress-time history curve of the tooth surface unit in the gear meshing transient simulation result, 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 certain 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 radius of curvature 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), v 1 and v 2 are the Poisson's ratio of the driving wheel and the driven wheel materials, E 1 and E 2 are the elastic modulus of the driving wheel and the driven wheel materials (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 (unit: mm);

[0016]

[0017] or

[0018]

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

[0020] Further, 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 diagram.

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

[0023] Further, 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 ρ 1 , 2 are the equivalent radius of curvature at each meshing point on the meshing interface of the driving wheel and the driven wheel (unit: mm);

[0030]

[0031] or

[0032]

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

[0034] The present invention obtains the stress of each unit of the tooth surface based on the stress-time history curve of the tooth surface unit in the transient simulation result; further obtains the grid length of each unit of the tooth surface along the tooth height direction by measurement; finally, the sum of the products of the two is multiplied by the effective contact width at the tooth surface meshing position to obtain the meshing load at the tooth surface meshing position. This meshing load algorithm breaks through the limitation of relying on empirical formulas in traditional methods, and can consider the internal excitation response of the gear transmission system, which is conducive to obtaining a more accurate meshing load. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0036] Figure 2 Flow chart for extracting tooth surface stress data;

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

[0038] Figure 4 It is a schematic diagram of the driving wheel tooth surface unit array;

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

[0040] Figure 6 It is a schematic diagram of the meshing unit contact stress-time history data file and the unit number arrangement information file;

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

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

[0043] Fig. 9 It is a schematic diagram of the driving wheel meshing area;

[0044] Fig.10 It is a schematic diagram of the positions of the tooth surface units involved in meshing;

[0045] Fig.11 It is a schematic diagram of node numbering at the tooth surface meshing unit;

[0046] Fig.12 A schematic diagram of the grid length of the tooth surface meshing unit along the tooth height direction;

[0047] Fig.13 This is a schematic diagram of meshing load calculation;

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

[0049] Fig.15 A schematic diagram of measuring the equivalent radius of curvature at each meshing point of the driving wheel and the driven wheel;

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

[0051] In order to make the purpose, technical solution and innovation of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention is clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different 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 claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are 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, the present embodiment provides a method for calculating the contact stress of the tooth surface based on the transient simulation results, which specifically includes the following steps:

[0054] Step 1:

[0055] like Figure 2The 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 unit of the driving wheel to extract the 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 units on the tooth surface 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 schematic diagram of tooth surface unit number extraction. 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 each row of units in the order from "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 array diagram of the driving wheel tooth surface unit number is shown in the figure. Figure 8 .

[0058] Step 3:

[0059] like Fig. 9 The figure shows a schematic diagram of the meshing area of ​​the driving wheel. In the figure, the meshing tooth surface of a single gear 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 Fig.10 ), it can be seen that the part of the tooth surface involved in meshing is Fig. 9 There are 9 rows of units in total, so we only need to calculate the meshing loads of the meshing points corresponding to the 9 rows of units. Furthermore, the nodes (i.e. meshing points) at the meshing units of the tooth surface are numbered in the order from "tooth root" to "tooth top" (see Fig.11 ), which facilitates the subsequent calculation of contact stress.

[0060] Step 4:

[0061] Measuring the mesh length of the gear surface unit along the tooth height direction in the gear meshing transient simulation model in ANSA software (see Fig.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 certain 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 units 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 introduced in detail below.

[0064] like Fig.13 The figure shows the meshing load calculation diagram. In the figure, the contact width a of the tooth surface unit is the grid length of the unit along the tooth height direction, and b 1 is the effective contact width of the tooth surface (i.e., the effective tooth width); it should be emphasized that in this example, the driving gear tooth width is 14.2 mm, and the driven gear tooth width is 16 mm, so the effective contact width of the tooth surface b 1 In order to calculate the meshing load at the meshing point of tooth surface No. 1, it is also necessary to obtain the stress per unit of tooth surface at the meshing position No. 1.

[0065] like Fig.14 The figure shows the stress-time history curve and stress cloud diagram of the meshing unit at a certain meshing moment of the driving wheel. From the gear meshing stress cloud diagram, it can be found that when two gears are meshing, each gear tooth may have 4-6 units in contact at the same time, sharing the gear meshing load together. Therefore, when calculating the gear meshing load, it is necessary to consider the load of the adjacent units at the same time.

[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 Fig.14 ), at this meshing moment, the stresses of 20610, 20609, 20608, and 20607 units are 11MPa, 122MPa, 152MPa, and 32.4MPa, respectively; therefore, Fig.12 Substituting the mesh length of the tooth surface unit along the tooth height direction and the stress of the 20610, 20609, 20608, and 20607 units into equation (1), the meshing load at the meshing position of the driving wheel No. 1 is 730.147 N. The meshing load calculation process at the other 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 radius of curvature at each meshing point of the driving wheel and the driven wheel is further measured in the ANSA software (see Fig.15 ), and according to the Hertz contact width calculation formula, the contact half-width at each meshing position of the tooth surface is calculated. The schematic diagram of the gear Hertz contact half-width is shown in Fig.16 The calculation formula of contact half width is shown in formula (3), where F is the meshing load at each meshing position of the tooth surface (unit: N), v 1 and v 2 are the Poisson's ratio of the driving wheel and the driven wheel materials, E 1 and E 2 are the elastic modulus of the driving wheel and the driven wheel materials (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 (unit: mm).

[0072]

[0073] or

[0074]

[0075] Taking the calculation of the contact half-width at the meshing position of the driving wheel tooth surface No. 1 as an example, the calculation process of the contact half-width at the meshing position of the driving wheel No. 1 will be introduced in detail below.

[0076] In this example, the meshing between the driving wheel and the driven wheel is external meshing, so formula (3.1) can be selected; in the formula, F is 730.147N, v 1 and v 2 is 0.3, E 1 and E 2 is 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 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 radius of curvature 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 of the tooth surface into the maximum contact stress calculation formula shown in formula (4), the maximum contact stress at each meshing position of the tooth surface can be obtained by simplifying it.

[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 wheel and the driven wheel is external meshing, so formula (4.1) is selected. Based on step 6, the formula of contact half-width is substituted into formula (4.1), and the maximum contact stress at the meshing position of tooth surface number 1 is simplified to 1347.086MPa. The calculation process of the maximum contact stress at the other meshing positions is similar, and the results are 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 ρ 1 , 2 They are the equivalent radius of curvature at each meshing point on the meshing interface of the driving wheel and the driven wheel (unit: mm).

[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 wheel and the driven wheel is external meshing, so formula (5.1) is selected. Based on step 6, the formula of contact half-width is substituted into formula (5.1), and the average contact stress at the meshing position of tooth surface number 1 is simplified to 1058.0MPa. The calculation process of the average contact stress at the other meshing positions is similar, and the results are 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. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims. Any figure mark in the claims should not be regarded as limiting the claims involved.

Claims

1. A method for calculating tooth surface contact stress based on transient simulation results, characterized in that: The following steps are involved: S1: Extract the stress-time history curve of the tooth surface unit in the gear meshing transient simulation result, 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 certain 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 radius of curvature 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 of 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); S6: Substitute the contact half-width at each meshing position of the tooth surface into the contact stress calculation formula shown in the formula to obtain the contact stress at each meshing position of 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 unit positions of the meshing tooth surfaces are locked using the gear meshing stress cloud map.

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 at each meshing point on the meshing interface of the driving wheel and the driven wheel, respectively (unit: mm);

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