Spline abrasion loss calculation method and system based on finite element analysis

Abstract

The invention discloses a spline abrasion loss calculation method and system based on finite element analysis, and belongs to the technical field of gearbox spline abrasion analys.The method comprises the steps that an analysis angle and an analysis increment step are set, and calculation is submitted to a spline finite element analysis model; extracting a spline node surface pressure parameter and a slip parameter of each increment step in the finite element analysis model; calculating the total slippage of each increment step; based on the spline node surface pressure and the total slip amount of each increment step, calculating the initial abrasion loss of the spline; an abrasion correction coefficient influenced by roughness is introduced, the correction coefficient is selected in a segmented mode according to a preset roughness interval, and the corrected spline abrasion loss is calculated; and calculating the final abrasion loss of the spline after temperature correction according to the actual temperature value in combination with the temperature influence correction coefficient. According to the method, through finite element analysis, the node surface pressure, the slippage, the roughness and the temperature are integrated, data are corrected, the reliability and efficiency of spline abrasion loss calculation are improved, and the method has certain adaptability.

Description

Technical Field

[0001] The present invention belongs to the technical field of gearbox spline wear analysis, and in particular relates to a method and system for calculating spline wear based on finite element analysis. Background Art

[0002] In the field of gearboxes, the involute floating spline connection structure has the advantages of strong misalignment compensation capability, strong load-bearing capacity, good self-centering performance, simple and compact structure, etc. As an important connecting component, the involute floating spline connection structure is widely used in gearboxes, such as shaft-tooth connection, gear shifting mechanism, etc.

[0003] However, factors such as tooth blank deformation and spline shaft floating often lead to fretting wear in involute floating spline connections, leading to spline failure and fracture. To prevent premature wear and failure of involute floating spline connections during service, wear characteristics are often evaluated during the design phase. However, model differences caused by roughness changes during wear are not considered, which can lead to low reliability in wear assessments of involute floating spline connections.

[0004] In the existing technology, the tooth surface contact strength calculation method in the mechanical design manual, the spline tooth surface strength calculation method in GB / T17855, and the spline tooth surface strength calculation method in AGMA945-A18 (Dudley method) are all theoretical principles. Although they all involve the tooth surface stress overload coefficient, it is relatively difficult to accurately consider the wear caused by the spline tooth surface stress overload for applications in actual working conditions.

[0005] As an improvement, Chinese patent CN114638057A describes a spline wear and fatigue life simulation method based on ABAQUS secondary development. By establishing internal and external spline models, pre-processing settings are completed in ABAQUS, and the contact pressure, stress, strain, and relative slip distance of each contact node in the current cycle are calculated. A UMESHMOTION subroutine is written in Fortran to calculate the wear depth of each node based on the Archard equation, and the mesh is updated using adaptive meshing technology. Macro commands are used to extract the stress and strain of each node, and three methods are used to calculate the fatigue life of each node in the current cycle. The cumulative damage value D of each node across all cycles is calculated, and a wear analysis image is plotted. Although the wear degree data of the spline is calculated and analyzed using the model and pressure, stress, strain, and relative slip distance, the impact of roughness changes is not considered, and no wear conversion coefficient is given at different temperatures. Therefore, in summary, in the current calculation of spline wear, parameters such as analysis force, slip, roughness change and temperature are not comprehensively considered, resulting in insufficient reliability of spline wear calculation, and the efficiency and automation of the calculation need to be further optimized. Summary of the Invention

[0006] The present invention provides a method and system for calculating spline wear based on finite element analysis, aiming to solve the problem that the current calculation of spline wear does not comprehensively consider parameters such as analysis force, slip, roughness change and temperature, resulting in insufficient reliability of spline wear calculation and the need for further optimization of the efficiency and automation of the calculation.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions: The present invention provides a method for calculating spline wear based on finite element analysis, comprising the following steps: S1. Set the analysis angle and analysis increment, and submit the calculation to the spline finite element analysis model; extract the spline node surface pressure parameters and slip parameters of each increment in the finite element analysis model through the Python program; Among them, the spline finite element analysis model is established based on the spline structural parameters and working conditions; S2. Calculate the total slip for each incremental step based on the slip parameters; Based on the spline node surface pressure and total slip for each incremental step, use the Archard wear theory formula to calculate the initial spline wear using a Matlab program, and output the maximum node and spline wear values; S3. Based on the initial wear of the spline, a wear correction coefficient for the influence of roughness is introduced, and the correction coefficient is selected in sections according to the preset roughness interval to calculate the corrected spline wear; S4. Based on the corrected spline wear amount and the temperature influence correction coefficient, calculate the final spline wear amount after temperature correction according to the actual temperature value.

[0008] In some embodiments, in S1 , the analysis increment is set based on the number of meshing rotations of the spline.

[0009] In some embodiments, in S1 , the extracted slip parameters of each incremental step in the finite element analysis model include a first slip and a second slip.

[0010] Furthermore, in S2, the total slip of each incremental step is calculated by synthesizing the slip parameters, and the calculation formula is as follows: (1); in, is the total slip, is the first slip, is the second slip amount.

[0011] In some embodiments, in S2, the Archard wear theory formula is: (2); in, is the wear amount, is the wear factor, is the Brinell hardness, is the starting time of wear, is the end time of wear occurrence, is the relative sliding speed of the spline tooth surface meshing position, is the compressive stress at the meshing position of the spline tooth surface.

[0012] In some embodiments, in S2, the initial wear amount of the spline is calculated using the following formula using a Matlab program: (3); in, is the surface pressure of the spline node at each increment.

[0013] In some embodiments, in S3 , the segmented selection rule of the roughness correction coefficient corresponds to the preset roughness interval and roughness level.

[0014] Furthermore, in S3, the initial roughness is set to a preset level, and the roughness interval is updated according to a half-adjustment rule to a specified roughness and then remains unchanged.

[0015] In some embodiments, in S4 , the value of the temperature correction coefficient corresponds to the temperature range, and the correction coefficients at other temperatures are obtained by linear difference calculation.

[0016] The present invention also provides a spline wear calculation system based on finite element analysis, which includes a parameter calculation and extraction module, a preliminary wear calculation module, a wear correction module, and a final wear calculation module, wherein: Preliminary wear calculation module: used to calculate the total slip of each incremental step based on the slip parameters; based on the spline node surface pressure and total slip of each incremental step, the Archard wear theory formula is used to calculate the preliminary spline wear through the Matlab program, and the maximum wear values ​​of the node and spline are output; Among them, the spline finite element analysis model is established based on the spline structural parameters and working conditions; Wear correction module: used to introduce the wear correction coefficient affected by roughness based on the initial wear of the spline, select the correction coefficient in sections according to the preset roughness interval, and calculate the corrected spline wear; Final wear calculation module: used to calculate the final spline wear amount after temperature correction according to the actual temperature value based on the corrected spline wear amount and the temperature influence correction coefficient.

[0017] Compared with the prior art, the present invention provides a method and system for calculating spline wear based on finite element analysis, which has the following beneficial effects: The present invention provides a method for calculating spline wear based on finite element analysis. By establishing a spline finite element analysis model and extracting node surface pressure and slip parameters, it provides accurate input data for subsequent calculations, resolving the shortcomings of traditional theoretical methods that rely on simplified assumptions and cannot reflect actual stress distribution. Based on finite element data, the present invention uses the Archard wear theory formula to calculate preliminary wear, incorporating actual operating parameters such as dynamic sliding velocity and compressive stress into the calculation, thereby enhancing the compatibility between the theoretical model and actual operating conditions. A correction coefficient for the influence of roughness is introduced to correct the wear at different roughness intervals in sections, thus compensating for the deficiency of existing technologies that ignore the influence of roughness changes on wear. In combination with the temperature correction coefficient, the final wear calculation result is further optimized.

[0018] Furthermore, the present invention uses a finite element model to accurately obtain the surface pressure and slip of spline nodes, avoiding the difficulty in accurately setting the stress eccentricity coefficient in traditional methods and improving the authenticity of the data. Dynamic corrections are performed for roughness and temperature, respectively, breaking through the limitations of existing methods that rely solely on a single theoretical model and ignore environmental and surface state changes, significantly improving the overall accuracy of wear calculations. Furthermore, the present invention uses Python and Matlab programs to automate parameter extraction, calculation, and correction, improving the method's low computational efficiency, increasing calculation accuracy, and enhancing engineering applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings in the specification are used to provide further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0020] Figure 1 A schematic flow chart of a method for calculating spline wear based on finite element analysis according to the present invention; Figure 2 This is a schematic diagram of the interface of the calculation software in the method for calculating spline wear based on finite element analysis of the present invention; Figure 3 Schematic diagram of a finite element analysis model for spline wear in a method for calculating spline wear based on finite element analysis of the present invention; Figure 4 This is a graph showing the total slip data of each incremental step calculated in an embodiment of a method for calculating spline wear based on finite element analysis of the present invention; Figure 5 Schematic diagram of the calculation interface of the spline wear finite element analysis model in the spline wear calculation method based on finite element analysis of the present invention; Figure 6This is a schematic diagram of an operating interface for roughness correction wear in a method for calculating spline wear based on finite element analysis of the present invention; Figure 7 The figure is a schematic diagram of the operation of temperature correction of wear in a method for calculating spline wear based on finite element analysis of the present invention. DETAILED DESCRIPTION

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only 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 herein can be arranged and designed in various different configurations.

[0022] 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 are intended to fall within the scope of protection of the present invention.

[0023] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not require further definition or explanation in subsequent drawings.

[0024] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0025] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0026] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0027] like Figure 1 As shown, the present invention provides a method for calculating spline wear based on finite element analysis, comprising the following steps: S1. Set the analysis angle and analysis increment, and submit the calculation to the spline finite element analysis model; extract the spline node surface pressure parameters and slip parameters of each increment in the finite element analysis model through the Python program; Among them, the spline finite element analysis model is established based on the spline structural parameters and working conditions; S2. Calculate the total slip for each incremental step based on the slip parameters; Based on the spline node surface pressure and total slip for each incremental step, use the Archard wear theory formula to calculate the initial spline wear using a Matlab program, and output the maximum node and spline wear values; S3. Based on the initial wear of the spline, a wear correction coefficient for the influence of roughness is introduced, and the correction coefficient is selected in sections according to the preset roughness interval to calculate the corrected spline wear; S4. Based on the corrected spline wear amount and the temperature influence correction coefficient, calculate the final spline wear amount after temperature correction according to the actual temperature value.

[0028] The present invention is based on a method for calculating spline wear based on finite element analysis. Research has shown that changes in roughness affect wear values. As wear time increases, the roughness of the material decreases, and the wear results also change. Temperature also has a certain impact on wear. Based on this, the present invention fully considers the wear effects caused by stress eccentricity on the spline tooth surface based on the results of finite element analysis, and proposes a wear correction coefficient for the influence of roughness, thereby improving the accuracy of wear calculation. Furthermore, the present invention also adds wear correction coefficients at different temperatures. Finally, combined with the Archard wear theory method, the wear calculation software is compiled using Matlab, further improving the automation and reliability of spline wear calculation.

[0029] In some embodiments, the analysis increment of the present invention is set based on the number of meshing rotations of the spline. By dynamically adjusting the analysis increment based on the number of meshing rotations, the present invention ensures that the step size of the finite element model corresponds to the actual spline kinematic characteristics, avoids calculation errors caused by excessively large or small step sizes, reduces redundant calculations while ensuring accuracy, and improves the applicability of the calculation.

[0030] The slip parameters of each incremental step in the finite element analysis model extracted by the present invention include the first slip and the second slip. The total slip of each incremental step is calculated by synthesizing the slip parameters, and the calculation formula is as follows: (1); in, is the total slip, is the first slip, is the second slip amount.

[0031] By separating the two slip parameters, this method accurately reflects the multidimensional relative motion during spline meshing, avoiding model simplification errors caused by single-direction slip and improving the applicability of splines under different conditions. The method also calculates the total slip using a vector synthesis formula, reflecting the geometric characteristics of the actual slip path. This avoids underestimation or overestimation of wear due to ignoring direction, ensuring the reliability of the calculation results.

[0032] In the spline wear calculation method based on finite element analysis of the present invention, the Archard wear theory formula used is: (2); in, is the wear amount, is the wear factor, is the Brinell hardness, is the starting time of wear, is the end time of wear occurrence, is the relative sliding speed of the spline tooth surface meshing position, is the compressive stress at the meshing position of the spline tooth surface.

[0033] Furthermore, the present invention uses a Matlab program to calculate preliminary wear using a step-by-step cumulative formula. This discretizes the continuous integration process into incremental cumulative calculations, adapting to the step-by-step output of finite element analysis. Segment-wise average surface pressure is used to smooth data fluctuations and reduce numerical calculation errors.

[0034] The present invention's segmented selection rules for the roughness correction coefficient correspond to preset roughness intervals and levels. This method sets correction coefficients based on roughness levels, aligning with the gradual decrease in roughness during wear. The preset intervals allow for adjustment of the segmentation rules based on actual machining accuracy or material properties, enhancing the method's engineering applicability.

[0035] Furthermore, the present invention sets the initial roughness to a preset level, then adjusts it in half to maintain the specified roughness. This method uses the binary rule to simulate the exponential decay of roughness with increasing wear, accurately reflecting the impact of surface topography on wear. By setting a lower limit for roughness, computational distortion caused by infinite corrections is avoided, ensuring model convergence.

[0036] In this method for calculating spline wear based on finite element analysis, the temperature correction coefficient corresponds to the temperature range, and the correction coefficients at other temperatures are calculated through linear interpolation. This method, by using linear interpolation to fill in the correction coefficients between discrete temperature points, can cover a wide range of temperature conditions, adapt to temperature fluctuations in actual projects, and improve the real-time and accuracy of wear prediction.

[0037] The present invention also provides a spline wear calculation system based on finite element analysis, which includes a parameter calculation and extraction module, a preliminary wear calculation module, a wear correction module, and a final wear calculation module, wherein: Preliminary wear calculation module: used to calculate the total slip of each incremental step based on the slip parameters; based on the spline node surface pressure and total slip of each incremental step, the Archard wear theory formula is used to calculate the preliminary spline wear through the Matlab program, and the maximum wear values ​​of the node and spline are output; Among them, the spline finite element analysis model is established based on the spline structural parameters and working conditions; Wear correction module: used to introduce the wear correction coefficient affected by roughness based on the initial wear of the spline, select the correction coefficient in sections according to the preset roughness interval, and calculate the corrected spline wear; Final wear calculation module: used to calculate the final spline wear amount after temperature correction according to the actual temperature value based on the corrected spline wear amount and the temperature influence correction coefficient.

[0038] Specifically, the present invention provides a method for calculating spline wear based on finite element analysis, the steps of which are as follows: According to the conditions, establish the spline finite element analysis model, set the analysis angle and analysis increment, and submit the calculation; Use Python to compile a program to extract the spline node surface pressure at each increment , slip and slip ; Calculate the total slip of each incremental step; Matlab editing program is used to calculate the initial wear of the spline and output the node and maximum wear values; Get the wear amount Finally, the wear correction factor of roughness effect is introduced , select the correction coefficient according to the segmented table 1 below. Calculate the corrected wear value (The roughness interval of 0.05 is the set value and can be adaptively changed according to actual working conditions).

[0039] Table 1 Wear depth and wear correction factor Comparison Table

[0040] Correction coefficients are given for different temperatures The coefficients are shown in Table 2 below. The temperature-affected wear is calculated based on the results. .

[0041] Table 2 Temperature effect correction coefficient

[0042]

[0043] Note: Other temperatures are calculated using linear difference.

[0044] The following is a detailed description of a method and system for calculating spline wear based on finite element analysis according to the present invention through specific embodiments.

[0045] Computing software such as Figure 2 Analysis conditions: intermediate shaft gear corresponds to midpoint A / B, input torque 2578Nm, number of spline meshing rotations 20000 times, temperature T=300K, material temperature 8620RH, 、 The initial roughness of the spline surface is Ra6.4. During the wear process, the roughness is calculated by halving every 0.05mm. After the roughness reaches Ra0.4, the roughness remains unchanged.

[0046] Requirements: Consider the wear value of T=300K under roughness correction, and consider the wear value of T=500K under roughness correction.

[0047] like Figure 3 As shown, establish the spline finite element analysis model and set the analysis angle , submit the calculation; Use Python to compile a program to extract the spline node surface pressure Cpress, slip amount CSLIP1 and slip amount CSLIP2 of each incremental step. Some results are shown in the following figure. Figure 3 As shown; like Figure 4 As shown, calculate the total slip of each incremental step: (1); Some of the results are as follows Figure 4 ; Node surface pressure , slip , slip and total slip (part).

[0048] according to (3); in, is the surface pressure of the spline node at each incremental step; like Figure 5 As shown, use Matlab to edit the program. Since the surface hardness changes slightly, set all 、 , calculate the angle , the total number of rotations M = 20000, call Cpress and CSLIP results, click calculate, get the maximum wear node Node1799522 and the maximum wear value h = 0.283mm, the results are as follows Figure 5 ; like Figure 6 As shown, open the roughness correction and set the initial roughness to Ra6.4. This calculation is set according to the roughness interval of 0.05mm (the value can be adjusted, and the correction coefficient after adjustment is unchanged), click Calculate to get the calculation result =0.270mm, because when T=300K, =1, so the final wear amount is 0.27mm. Figure 6 , the calculation process is shown in Table 3 below.

[0049] Table 3 Corrected wear calculation process

[0050] Refer to Table 2, when the temperature is T=500K, =1.0135, click on temperature correction to enable, enter the correction temperature 500 in the software, click on calculate, the result is 0.274, the calculation process is =0.27×1.0135=0.274mm.

[0051] like Figure 7The figure shows the operation of the software in the embodiment. After this operation, it can be obtained that the wear amount at T=300K with roughness correction is 0.27mm; the wear amount at T=500K with roughness correction is 0.274.

[0052] In summary, the present invention provides a method and system for calculating spline wear based on finite element analysis. Through finite element modeling, preliminary calculation based on Archard theory, roughness correction and temperature correction, the problem of inaccurate wear assessment caused by traditional methods ignoring roughness changes and temperature effects is solved. By extracting node surface pressure and slip parameters based on finite element dynamic data, combined with a multi-dimensional slip synthesis formula and step-by-step cumulative calculation, the actual working conditions are truly reflected. Through the rules of roughness grading correction and temperature linear difference calculation, the automation of parameter extraction, calculation and correction is realized based on Python and Matlab programs, thereby improving the efficiency and applicability of the calculation.

[0053] Finally, it should be noted that the above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any ordinary technician in this industry can smoothly implement the present invention as shown in the specification and described above. Any equivalent changes, modifications and evolutions made by using the technical content disclosed above are all equivalent embodiments of the present invention. At the same time, any equivalent changes, modifications and evolutions made to the above embodiments based on the essential technology of the present invention are still within the scope of protection of the technical solution of the present invention.

Claims

1. A method for calculating spline wear based on finite element analysis, characterized in that: The steps include: S1. Set the analysis angle and analysis increment, and submit the calculation to the spline finite element analysis model; extract the spline node surface pressure parameters and slip parameters of each increment in the finite element analysis model through the Python program; Among them, the spline finite element analysis model is established based on the spline structural parameters and working conditions; S2. Calculate the total slip for each incremental step based on the slip parameters; Based on the spline node surface pressure and total slip for each incremental step, use the Archard wear theory formula to calculate the initial spline wear using a Matlab program, and output the maximum node and spline wear values; S3. Based on the initial wear of the spline, a wear correction coefficient for the influence of roughness is introduced, and the correction coefficient is selected in sections according to the preset roughness interval to calculate the corrected spline wear; S4. Based on the corrected spline wear amount and the temperature influence correction coefficient, calculate the final spline wear amount after temperature correction according to the actual temperature value.

2. The method for calculating spline wear based on finite element analysis according to claim 1, wherein: In said S1, the analysis increment step is set according to the number of meshing rotations of the spline.

3. The method for calculating spline wear based on finite element analysis according to claim 1, wherein: In S1, the extracted slip parameters of each incremental step in the finite element analysis model include a first slip and a second slip.

4. The method for calculating spline wear based on finite element analysis according to claim 3, wherein: In S2, the total slip of each incremental step is calculated by synthesizing the slip parameters, and the calculation formula is as follows: （1）； in, is the total slip, is the first slip, is the second slip amount.

5. The method for calculating spline wear based on finite element analysis according to claim 1, wherein: In the S2, the Archard wear theory formula is: （2）； in, is the wear amount, is the wear factor, is the Brinell hardness, is the starting time of wear, is the end time of wear occurrence, is the relative sliding speed of the spline tooth meshing position, is the compressive stress at the meshing position of the spline tooth surface.

6. The method for calculating spline wear based on finite element analysis according to claim 1, characterized in that: In S2, the initial wear amount of the spline is calculated by the Matlab program according to the following formula: （3）； in, is the surface pressure of the spline node at each increment.

7. The method for calculating spline wear based on finite element analysis according to claim 1, characterized in that: In the step S3 , the segmented selection rule of the roughness correction coefficient corresponds to the preset roughness interval and roughness level.

8. The method for calculating spline wear based on finite element analysis according to claim 7, characterized in that: In the step S3 , the initial roughness is set to a preset level, and the roughness interval is updated according to a halving adjustment rule to a specified roughness and then remains unchanged.

9. The method for calculating spline wear based on finite element analysis according to claim 1, characterized in that: In the step S4 , the value of the temperature correction coefficient corresponds to the temperature range, and the correction coefficients at other temperatures are obtained by linear difference calculation.

10. The system on which the method for calculating spline wear based on finite element analysis according to any one of claims 1 to 9 is based, characterized in that: The system includes a parameter calculation and extraction module, a preliminary wear calculation module, a wear correction module, and a final wear calculation module, wherein: Preliminary wear calculation module: used to calculate the total slip of each incremental step based on the slip parameters; based on the spline node surface pressure and total slip of each incremental step, the Archard wear theory formula is used to calculate the preliminary spline wear through the Matlab program, and the maximum wear values ​​of the node and spline are output; Among them, the spline finite element analysis model is established based on the spline structural parameters and working conditions; Wear correction module: used to introduce the wear correction coefficient affected by roughness based on the initial wear of the spline, select the correction coefficient in sections according to the preset roughness interval, and calculate the corrected spline wear; Final wear calculation module: used to calculate the final spline wear amount after temperature correction according to the actual temperature value based on the corrected spline wear amount and the temperature influence correction coefficient.

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