Gear tooth root peak stress fast prediction method based on tooth root dangerous path correction
By defining the dangerous path at the tooth root and combining the nominal bending moment of the cantilever plate with the finite element correction coefficient, the problem of rapid prediction of gear tooth root stress calculation methods in the prior art under non-standard tooth root transition curves and different meshing side conditions is solved, realizing efficient gear strength analysis and structural optimization.
Patent Information
- Application Number
- CN202610727870.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-25
- Publication Date
- 2026-08-25
AI Technical Summary
Existing methods for calculating gear root stress are difficult to predict peak stress quickly and accurately under non-standard root transition curves and different meshing side conditions. Traditional methods rely on a single critical section, resulting in large errors. Finite element analysis is computationally expensive and not suitable for screening a large number of schemes.
By defining the dangerous path at the tooth root, extracting equivalent geometric and load features, and combining the nominal bending moment model of the cantilever plate with the finite element fitting correction coefficient, a correction coefficient prediction model is constructed to quickly predict the peak stress at the gear tooth root.
It enables rapid prediction of peak stress in complex tooth root conditions under non-single dangerous section conditions, improves the efficiency of gear strength analysis and structural optimization, and reduces the number of finite element calculations.
Smart Images
Figure CN122634859A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of gear tooth root analysis, and specifically to a method for rapid prediction of peak stress at gear tooth roots based on tooth root dangerous path correction. Background Technology
[0002] During gear meshing, the tooth root region is subjected to cyclic bending loads. When the tensile stress at the tooth root is too high or when it is under high-stress cycling for a long period of time, tooth root cracks are prone to occur, which can further develop into tooth breakage. Therefore, accurately predicting the peak stress at the tooth root is an important foundation for gear strength design, life assessment, and tooth root structure optimization.
[0003] Existing methods for calculating tooth root stress mainly employ standard formula methods and finite element analysis (FEM). Standard formula methods are typically based on gear strength calculation standards such as ISO 6336-3, AGMA 2101, DIN 3990, and GB / T 3480, estimating tooth root bending stress through tooth form factor, stress correction factor, and load factor. While these methods are relatively fast, they often rely on standard tooth root shapes and specific critical section assumptions, frequently using the vicinity of the 30° critical section as the primary evaluation location. For non-standard tooth root transition curves, tool-modified tooth roots, different meshing sides of planetary gears, and load positions varying over time, the location of maximum tooth root stress may migrate along the tooth root edge, making it difficult for traditional single-section methods to accurately reflect the true peak stress at the tooth root. While FEM can accurately obtain the stress distribution in the tooth root region, it typically requires remodeling, meshing, applying loads, and solving for each set of changes in tooth root geometry, tool parameters, or load conditions, resulting in high computational costs and making it unsuitable for extensive screening of numerous candidate solutions.
[0004] Therefore, in order to solve the problem that existing tooth root stress analysis methods rely on a single critical section and that it is difficult to quickly predict peak stress under non-standard tooth root geometry, a rapid prediction method for gear tooth root peak stress based on tooth root critical path correction is needed. This method can quickly predict peak stress in complex tooth root conditions under non-single critical section conditions, thereby improving the efficiency of strength analysis and structural optimization. Summary of the Invention
[0005] In view of this, the purpose of this invention is to overcome the defects in the prior art and provide a method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction. This method can achieve rapid prediction of peak stress in complex tooth root conditions under non-single dangerous section conditions, thereby improving the efficiency of strength analysis and structural optimization.
[0006] The present invention provides a method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction, comprising:
[0007] Obtain basic gear parameters and tooth root geometry information;
[0008] A gear tooth profile geometric model is established based on the basic parameters of the gear and the geometric information of the tooth root, and the tooth root transition zone is determined.
[0009] Determine the dangerous path of the tooth root within the tooth root transition zone, and extract the features of the dangerous path of the tooth root along the dangerous path of the tooth root.
[0010] Determine the nominal bending moment of the tooth root dangerous path based on the characteristics of the tooth root dangerous path;
[0011] Determine the nominal bending stress of the dangerous path of the tooth root based on the nominal bending moment of the dangerous path of the tooth root.
[0012] A modified coefficient prediction model is constructed based on the nominal bending stress of the dangerous path at the tooth root, and the peak stress at the tooth root of the gear is predicted using the modified coefficient prediction model.
[0013] Furthermore, the basic parameters of the gear include the number of teeth, module, pressure angle, displacement coefficient, and tooth width; the tooth root geometry information includes the standard tooth root curve, the tooth root curve given by the tooth profile point cloud or CAD curve, and the tooth root curve generated by the hob head profile through the generating machining principle.
[0014] Furthermore, the tooth root transition zone is the area where the working tooth surface transitions to the bottom of the tooth groove.
[0015] Furthermore, the dangerous path at the tooth root is a curved path distributed along the boundary of the tooth root transition zone or its adjacent area and used to characterize the location where high stress occurs at the tooth root.
[0016] Furthermore, the tooth root dangerous path features include equivalent geometric features, path shape features, and load-related features;
[0017] The equivalent geometric features include equivalent tooth thickness, equivalent force arm, and dangerous path length. The tooth width and the effective load-bearing width are at least one of the following: the path shape features include at least one of curvature, root mean square curvature, maximum curvature, tooth root fillet and non-standard tooth root transition curve; the load-related features include at least one of peak normal load, peak tangential load, load application location, peak load time and load change rate.
[0018] Furthermore, the nominal bending moment along the dangerous path at the tooth root is determined according to the following formula:
[0019] ;
[0020] in, The nominal bending moment of the dangerous path at the tooth root; Equivalent load; As an equivalent force arm; The bending moment influence coefficient of the cantilever slab. For the relative position of the load, This is the equivalent width.
[0021] Furthermore, the nominal bending stress along the dangerous path at the tooth root is determined according to the following formula:
[0022] ;
[0023] in, The nominal bending stress is the stress along the dangerous path of the tooth root. The coordinates of the arc length on the dangerous path of the tooth root; Effective load-bearing width; This is the equivalent tooth thickness.
[0024] Furthermore, a prediction model for the correction coefficient is constructed, specifically including:
[0025] Finite element analysis was performed on several gear samples to extract the critical path at the tooth root for each sample. Dangerous path points Finite element stress at the point and with point Nominal bending stress at the point Correspondingly, construct the path point correction coefficient:
[0026] ;
[0027] in, Dangerous path points Stress correction factor at the location;
[0028] Dangerous waypoints The path characteristics, load-related characteristics, analysis object category characteristics, and meshing side category characteristics are used as inputs, with path point correction coefficients. As output, we obtain the corrected coefficient prediction model:
[0029] ;
[0030] in, Dangerous path points Stress correction factor at the location; Dangerous path points Path characteristics at the location; For load-related characteristics; To analyze the category characteristics of objects; Features for the meshing side category; This is the fitting function.
[0031] Furthermore, the peak stress at the tooth root of the gear is predicted using a prediction model with correction coefficients, specifically including:
[0032] The prediction model using the correction coefficients is used to obtain the dangerous path points. Prediction correction coefficient at the location And calculate the corrected rapid prediction stress. :
[0033] ;
[0034] in, Dangerous path points The nominal bending stress at the point;
[0035] Dangerous pathways for tooth root extraction The maximum value on the [value] is used as a rapid prediction of the peak stress at the tooth root of the gear. :
[0036] .
[0037] The beneficial effects of this invention are as follows: This invention discloses a rapid prediction method for peak stress at the gear tooth root based on the correction of the dangerous path at the tooth root. By defining the high-stress region at the tooth root as the dangerous path, features such as equivalent tooth thickness, curvature, dangerous path length, and equivalent force arm are extracted along this path. Combined with the nominal bending moment model and finite element fitting correction coefficients, rapid and stable prediction of peak stress at the tooth root is achieved. This invention is not dependent on a single dangerous section and is applicable to non-standard tooth root transition curves and different meshing side conditions. It can reduce the number of complete finite element calculations and improve the efficiency of tooth root strength analysis and structural optimization. Attached Figure Description
[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments:
[0039] Figure 1 This is a schematic diagram of the rapid prediction method for tooth root peak stress of the present invention;
[0040] Figure 2 This is a schematic diagram of the dangerous path and dangerous path point extraction of the tooth root according to the present invention;
[0041] Figure 3 This is a schematic diagram of the equivalent geometric parameters of the dangerous path of the tooth root in this invention;
[0042] Figure 4 This is a schematic diagram of the nominal bending moment calculation model for the dangerous path of the tooth root according to the present invention;
[0043] Figure 5 This is a schematic diagram illustrating the construction and rapid prediction of the finite element calibration correction coefficients of the present invention. Detailed Implementation
[0044] The present invention will be further described below with reference to the accompanying drawings, as shown in the figures:
[0045] This embodiment discloses a rapid prediction method for peak stress at the gear tooth root based on tooth root dangerous path correction, including the following steps:
[0046] S1. Obtain the basic parameters of the gear and the geometric information of the tooth root;
[0047] S2. Establish a gear tooth profile geometric model based on the basic parameters of the gear and the tooth root geometric information, and determine the tooth root transition zone;
[0048] S3. Determine the dangerous path of the tooth root within the tooth root transition zone, and extract the features of the dangerous path of the tooth root along the dangerous path;
[0049] S4. Determine the nominal bending moment of the tooth root dangerous path based on the characteristics of the tooth root dangerous path;
[0050] S5. Determine the nominal bending stress of the dangerous path at the tooth root based on the nominal bending moment of the dangerous path at the tooth root;
[0051] S6. Construct a prediction model with correction coefficients based on the nominal bending stress of the dangerous path at the tooth root, and use the prediction model with correction coefficients to predict the peak stress at the tooth root of the gear.
[0052] This invention provides a method for rapid prediction of peak stress at the tooth root of gears by extracting equivalent geometric features along the dangerous path of the tooth root and combining them with finite element sample fitting correction.
[0053] In this embodiment, in step S1, the basic gear parameters include the number of teeth, module, pressure angle, displacement coefficient, and tooth width, and may further include the addendum coefficient, dedendum coefficient, and root fillet parameter; the root geometry information includes the standard root curve, the root curve given by the tooth profile point cloud or CAD curve, and the root curve generated by the hob head profile through the generating machining principle.
[0054] It can also acquire meshing load data and analysis object information; the meshing load data includes equivalent meshing directional load or torque and tangential force information used to calculate the equivalent meshing directional load, and may further include load application location, load time history and peak load; the analysis object information includes sun gear, planet gear or internal gear ring, and corresponding meshing side information.
[0055] In this embodiment, in step S2, for the standard tooth root curve, the gear tooth profile geometric model is directly generated based on the basic gear parameters; for the tooth root curve given by the tooth profile point cloud or CAD curve, the curve is reconstructed to form the gear tooth profile geometric model; for the tooth root curve generated by the hob head contour, the tooth root transition curve is obtained according to the generating machining principle and the gear tooth profile geometric model is formed, which will not be elaborated here. The tooth root transition area is the area where the working tooth surface transitions to the bottom of the tooth groove.
[0056] In this embodiment, in step S3, as follows: Figure 2 As shown, a dangerous path for the tooth root is determined within the tooth root transition zone, and this path can be discretized into several dangerous path points. The dangerous path is a curved path distributed along the boundary of the tooth root transition zone or its adjacent area, used to characterize the location of high stress at the tooth root. Specifically, this path can be determined based on the area of the tooth surface load, the normal direction within the tooth surface, and the location of the dangerous point, which will not be elaborated further here.
[0057] The tooth root dangerous path features include equivalent geometric features, path shape features, and load-related features; the equivalent geometric features include equivalent tooth thickness, equivalent force arm, and dangerous path length. The tooth width and the effective load-bearing width are at least one of the following: the path shape features include at least one of curvature, root mean square curvature, maximum curvature, tooth root fillet and non-standard tooth root transition curve; the load-related features include at least one of peak normal load, peak tangential load, load application location, peak load time and load change rate.
[0058] A schematic diagram of the equivalent geometric parameters of the dangerous path at the tooth root, as shown below. Figure 3 As shown, This represents the arc length coordinates along the path of the dangerous tooth root edge. Tooth width. The actual structural width of the gear along the axial direction, and the effective load-bearing width. This represents the equivalent width of the current meshing load in the tooth width direction. When the load in the tooth width direction is approximately uniform or a two-dimensional plane stress model is used, we take... = When there is uneven loading, edge contact, or uneven tooth load, Determined based on the load distribution along the tooth width or the tooth load distribution coefficient. The analysis object category is used to distinguish between the sun gear, planet gears, or internal gear ring.
[0059] In this embodiment, in step S4, as follows: Figure 4 As shown, the tooth root region is equivalent to a cantilever plate with a fixed edge under load. The nominal bending moment of the tooth root critical path is calculated based on the equivalent load, the equivalent arm, and the bending moment influence coefficient of the cantilever plate.
[0060] ;
[0061] in, The nominal bending moment of the dangerous path at the tooth root; Equivalent load; As an equivalent force arm; The bending moment influence coefficient of the cantilever slab. For the relative position of the load, This is the equivalent width.
[0062] equivalent load Determined by the load time history on the target meshing side, the peak load or the equivalent load within the peak window can be taken; equivalent force arm The distance from the load application point to the critical path point and its projection in the bending direction are determined, and will not be elaborated further here.
[0063] Furthermore, equivalent tooth thickness The length of the dangerous path is determined by the effective thickness of the tooth body passing through the local normal or the direction of the pre-set dangerous section at the dangerous path point; Determined by summing the distances between adjacent discrete hazardous path points; effective load-bearing width The tooth width, actual contact width, or equivalent width after load distribution correction can be used; curvature The load variation rate is obtained by calculating the first and second derivatives or discrete differences of the tooth root path; the load variation rate is obtained by differentiating the load time history with respect to time within the peak window, which will not be elaborated here.
[0064] In this embodiment, in step S5, the nominal bending moment of the tooth root critical path and the equivalent tooth thickness are used to calculate the nominal bending stress of the tooth root critical path:
[0065] ;
[0066] in, The nominal bending stress is the stress along the dangerous path of the tooth root. The coordinates of the arc length on the dangerous path of the tooth root; Effective load-bearing width; This is the equivalent tooth thickness.
[0067] Furthermore, the maximum value along the path is taken as the nominal peak stress of the dangerous path at the tooth root:
[0068] .
[0069] In this embodiment, in step S6, as follows: Figure 5 As shown, a correction coefficient prediction model is constructed, specifically including:
[0070] Finite element analysis was performed on several gear samples to extract the critical path at the tooth root for each sample. Dangerous path points Finite element stress at the point and with point Nominal bending stress at the point Correspondingly, construct the path point correction coefficient:
[0071] ;
[0072] in, Dangerous path points The stress correction factor at the specified location is used to absorb the combined effects of factors not explicitly expressed in the nominal cantilever plate model, such as tooth root fillet, local curvature, non-standard tooth root transition curve, critical path length, boundary conditions, dynamic load peak, and the combined forces of different analysis objects and different meshing sides. Furthermore, a peak value correction factor can be constructed based on the ratio of the finite element path peak stress to the nominal path peak stress. ;
[0073] in, The peak stress in the dangerous path of the tooth root is represented by the finite element results. This represents the peak stress of the nominal model on the critical path at the tooth root. Path point correction factors are used to correct the path stress distribution, and peak value correction factors are used for rapid peak value estimation.
[0074] Dangerous waypoints The path characteristics, load-related characteristics, analysis object information, and meshing side information are used as inputs, with path point correction coefficients as the input. As output, establish a prediction model for object-meshing side-load related correction coefficients: ;in, Dangerous path points The corresponding feature vector includes one or more of the following: path features, load-related features, analysis object category features, and meshing side category features. The path features include equivalent geometric features and path shape features; these features characterize the influence of the geometry of the critical path at the tooth root on stress concentration. The load-related features characterize the influence of the target load time history on the peak stress; the analysis object category features and meshing side category features characterize the differences in load direction, working tooth surface, and tension root region between the sun gear and planetary gears.
[0075] That is: ultimately, the dangerous path point The path characteristics, load-related characteristics, analysis object category characteristics, and meshing side category characteristics are used as inputs, with path point correction coefficients. As output, we obtain the corrected coefficient prediction model:
[0076] ;
[0077] in, Dangerous path points Stress correction factor at the location; Dangerous path points Path characteristics at the location; For load-related characteristics; To analyze the category characteristics of objects; Features for the meshing side category; This is the fitting function.
[0078] For correction coefficient prediction models, different data fitting or machine learning methods can be used to establish the mapping relationship between input features and correction coefficients, thereby obtaining the fitting function. For example, to ensure that the correction coefficient is positive, the following logarithmic form can be used: ;
[0079] Using a logarithmic form is not the only constraint on the prediction model, but rather a preferred approach. On the one hand, the correction coefficient is the ratio of the finite element stress to the nominal stress, which should physically be positive. On the other hand, the effects of tooth thickness, lever arm, curvature, load amplitude, and differences on the meshing side on tooth root stress have a certain multiplicative correction characteristic. Taking the logarithm of the correction coefficient helps to transform the multiplicative relationship into an additive expression, thereby improving the model's stability and interpretability.
[0080] The prediction model using correction coefficients is used to predict the peak stress at the tooth root of gears, specifically including:
[0081] For the gear to be analyzed, the prediction model with correction coefficients is used to obtain each dangerous path point. Prediction correction coefficient at the location And calculate the corrected rapid prediction stress. :
[0082] ;
[0083] in, Dangerous path points The nominal bending stress at the point;
[0084] Dangerous pathways for tooth root extraction The maximum value is used as a rapid prediction of the peak stress at the tooth root of the gear to be analyzed. :
[0085] .
[0086] The prediction results may also include the critical tooth root path location corresponding to the peak stress, the corresponding load time, the analysis object category, and the meshing side category, so as to determine the critical tooth root area under the sun gear or planet gear.
[0087] Additionally, a peak value correction factor can be used when only a rapid estimation of the peak value is required, without predicting the path stress distribution. Directly correct the nominal peak stress of the dangerous path at the tooth root:
[0088] .
[0089] This invention is not limited to the traditional 30° critical section, but defines the high-stress region at the tooth root as the critical path at the tooth root, which can describe the migration of the maximum stress location along the edge of the tooth root transition zone. The geometry of the critical path at the tooth root is described by path shape features such as equivalent tooth thickness, equivalent force arm, critical path length, effective load width, and curvature. Furthermore, dynamic load features such as peak load and load change rate are introduced, making it more suitable for predicting tooth root stress where the load location changes over time compared to single-point or single-section methods.
[0090] This invention employs a cantilever plate nominal bending moment model to establish a physical calculation framework for the load-to-tooth root bending moment. Then, it compensates for local geometric and operational condition influences through finite element fitting correction coefficients, achieving both computational efficiency and physical interpretability. A prediction model of the object, meshing side, and load-related path correction coefficients can be established using a small number of finite element samples. This allows for rapid prediction of stress distribution and peak stress on the critical path of the tooth root under new tooth root geometry, load conditions, or planetary gear meshing conditions, reducing the number of full finite element calculations. Furthermore, it can be used for rapid stress comparison and candidate scheme screening under different meshing side conditions, based on tooth root structural parameters, tool parameters, or other parameters.
[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A method for rapid prediction of peak stress at the tooth root of gears based on tooth root dangerous path correction, characterized in that: include: Obtain basic gear parameters and tooth root geometry information; A gear tooth profile geometric model is established based on the basic parameters of the gear and the geometric information of the tooth root, and the tooth root transition zone is determined. Determine the dangerous path of the tooth root within the tooth root transition zone, and extract the features of the dangerous path of the tooth root along the dangerous path of the tooth root. Determine the nominal bending moment of the tooth root dangerous path based on the characteristics of the tooth root dangerous path; Determine the nominal bending stress of the dangerous path of the tooth root based on the nominal bending moment of the dangerous path of the tooth root. A modified coefficient prediction model is constructed based on the nominal bending stress of the dangerous path at the tooth root, and the peak stress at the tooth root of the gear is predicted using the modified coefficient prediction model.
2. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 1, characterized in that: The basic parameters of the gear include the number of teeth, module, pressure angle, displacement coefficient, and tooth width; the tooth root geometry information includes the standard tooth root curve, the tooth root curve given by the tooth profile point cloud or CAD curve, and the tooth root curve generated by the hob head profile through the generating machining principle.
3. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 1, characterized in that: The tooth root transition zone is the area where the working tooth surface transitions to the bottom of the tooth groove.
4. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 3, characterized in that: The dangerous path at the tooth root is a curved path distributed along the boundary of the tooth root transition zone or its adjacent area and used to characterize the location where high stress occurs at the tooth root.
5. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 1, characterized in that: The tooth root dangerous path characteristics include equivalent geometric features, path shape features, and load-related features; The equivalent geometric features include equivalent tooth thickness, equivalent force arm, and dangerous path length. The tooth width and the effective load-bearing width are at least one of the following: the path shape features include at least one of curvature, root mean square curvature, maximum curvature, tooth root fillet and non-standard tooth root transition curve; the load-related features include at least one of peak normal load, peak tangential load, load application location, peak load time and load change rate.
6. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 1, characterized in that: The nominal bending moment of the dangerous path at the tooth root is determined according to the following formula: ； in, The nominal bending moment of the dangerous path at the tooth root; Equivalent load; As an equivalent force arm; The bending moment influence coefficient of the cantilever slab. For the relative position of the load, This is the equivalent width.
7. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 6, characterized in that: The nominal bending stress along the dangerous path at the tooth root is determined using the following formula: ； in, The nominal bending stress is the stress along the dangerous path of the tooth root. The coordinates of the arc length on the dangerous path of the tooth root; Effective load-bearing width; This is the equivalent tooth thickness.
8. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 7, characterized in that: Constructing a prediction model with corrected coefficients specifically includes: Finite element analysis was performed on several gear samples to extract the critical path at the tooth root for each sample. Dangerous path points Finite element stress at the point and with point Nominal bending stress at the point Correspondingly, construct the path point correction coefficient: ； in, Dangerous path points Stress correction factor at the location; Dangerous waypoints The path characteristics, load-related characteristics, analysis object category characteristics, and meshing side category characteristics are used as inputs, with path point correction coefficients. As output, we obtain the corrected coefficient prediction model: ； in, Dangerous path points Stress correction factor at the location; Dangerous path points Path characteristics at the location; For load-related characteristics; To analyze the category characteristics of objects; Features for the meshing side category; This is the fitting function.
9. The method for rapid prediction of peak stress at the gear tooth root based on tooth root dangerous path correction according to claim 8, characterized in that: The prediction model using correction coefficients is used to predict the peak stress at the tooth root of gears, specifically including: The prediction model using the correction coefficients is used to obtain the dangerous path points. Prediction correction coefficient at the location And calculate the corrected rapid prediction stress. : ； in, Dangerous path points The nominal bending stress at the point; Dangerous pathways for tooth root extraction The maximum value on the [value] is used as a rapid prediction of the peak stress at the tooth root of the gear. : 。