Gear pair life prediction method based on dynamic stress

Abstract

The invention discloses a gear pair life prediction method based on dynamic stress, belongs to the technical field of reliability design of mechanical transmission systems, and aims to solve the problem of inaccurate life prediction caused by neglecting a dynamic effect and a real surface topography in an existing gear design method. The method comprises the following steps: firstly, acquiring gear pair interface mechanical property parameters considering shafting vibration, dynamic load and surface roughness, wherein the parameters comprise transient oil film pressure, friction coefficient, oil film thickness and shear stress; solving a three-dimensional subsurface stress field by adopting an algorithm and calculating von Mises equivalent stress distribution; stress volume integration is conducted on different rough surfaces, the honed surface is used as the reference, the relative fatigue life of other surfaces is calculated based on the Zaretsky life prediction theory, and accurate prediction and process optimization of the contact fatigue life are achieved; meanwhile, the dynamic bending stress of the tooth root is calculated based on the dynamic normal load, and the bending fatigue safety coefficient is checked.

Description

Technical Field

[0001] This invention relates to the field of reliability design technology for mechanical transmission systems, and more specifically, to a method for predicting the fatigue life of gear pairs based on dynamic stress and shaft vibration conditions. Background Technology

[0002] Gear transmission, as the core power transmission method in mechanical systems, directly determines the operational stability of the entire machine based on its reliability. Statistics show that gear failures account for over 50% of mechanical failures, with fatigue damage (such as pitting and tooth breakage) accounting for a significant portion. In particular, tooth breakage accidents caused by bending fatigue of gear teeth often lead to the paralysis of the transmission chain and cause significant economic losses.

[0003] Currently, in the field of gear fatigue life prediction and strength verification, mainstream technologies and methods have significant limitations, mainly in the following three aspects:

[0004] 1. The contact fatigue life prediction model has theoretical flaws.

[0005] Traditional Lundberg Palmgren (LP) theoretical model and its important improved model—Ioannides The Harris (IH) model forms the classic framework for predicting rolling contact fatigue life. However, the LP theory model does not fully consider the failure mechanism of the surface layer, the influence of lubrication conditions, and the role of the actual surface morphology. Although the IH model improves upon the LP theory model by introducing the concepts of critical stress and stress volume integral, it still essentially relies on the assumption of a "smooth contact surface" and includes a depth factor that needs to be determined empirically. This results in inherent biases when characterizing the stress field distribution on real tooth surfaces with random roughness, leading to significant deviations between the predicted life and actual operating conditions.

[0006] 2. The calculation method for tooth root bending stress is oversimplified.

[0007] Current calculations of tooth root bending stress are usually based on The tangent method is used to determine the critical section, and a series of correction factors (such as dynamic load factor and inter-tooth load distribution factor) are used for approximate calculations based on the specifications. This method fails to adequately consider the "time-varying meshing stiffness" of gears during dynamic meshing. Transmission error The strong coupling effect of multiple physical fields, such as the "dynamic evolution of bending lever arm / pressure angle", makes it difficult for traditional methods to accurately capture the true dynamic response of tooth root stress as the meshing position changes within a complete meshing cycle due to the oversimplification of the actual physical process.

[0008] 3. Existing methods lack adaptability to dynamic operating conditions.

[0009] Most traditional analysis methods are based on the assumption of steady-state loads and fail to effectively incorporate the influence of dynamic excitations such as shaft vibration on the gear contact interface. Shaft vibration significantly alters the gear contact path, interface lubrication state (e.g., inducing a secondary peak in oil film pressure under mixed lubrication), and stress concentration behavior on subsurfaces. This drastically reduces the computational accuracy and engineering applicability of existing methods when dealing with highly fluctuating operating conditions such as variable speeds in marine diesel engines.

[0010] In summary, existing technologies generally face the dual challenges of insufficient accuracy and poor adaptability to operating conditions when predicting the fatigue life and verifying the bending strength of gear pairs. Therefore, there is an urgent need in this field to develop a method for predicting the life and verifying the strength of gear pairs that can comprehensively consider key factors such as shaft vibration, surface roughness, dynamic load, and mixed lubrication conditions, in order to achieve accurate evaluation and reliable design of the service performance of gear transmission systems. Summary of the Invention

[0011] To address the problem of inaccurate life prediction in existing gear design methods due to neglecting dynamic effects and actual surface morphology, this invention provides a gear pair life prediction method based on dynamic stress.

[0012] The present invention discloses a gear pair life prediction method based on dynamic stress, which includes the following steps:

[0013] S1. Obtain the interfacial mechanical property parameters of the gear pair; the interfacial mechanical property parameters include at least: transient oil film pressure distribution and tooth surface friction coefficient;

[0014] S2. Based on the transient oil film pressure distribution and tooth surface friction coefficient obtained in step S1, the following is adopted: Algorithm to solve the three-dimensional subsurface stress field in the gear contact area;

[0015] S3. Based on the three-dimensional subsurface stress field obtained in step S2, calculate the von Mises equivalent stress distribution in the gear contact area. The von Mises equivalent stress is a three-dimensional dynamic equivalent stress.

[0016] S4. Based on the von Mises equivalent stress distribution obtained in step S3, calculate the stress volume integral over one meshing cycle for gear surfaces with different surface roughness.

[0017] S5. Using a preset surface of the gear pair as the reference surface, calculate the relative fatigue life of other surfaces relative to the reference surface based on the stress volume integral of each surface obtained in step S4 and the Zaretsky life prediction theory.

[0018] Preferably, in step S2, the three-dimensional subsurface stress field is obtained by solving the following formula:

[0019]

[0020] This indicates a point on the secondary surface of the gear. ,time Lower-level stress; To represent the direction of the normal to the surface under stress and the direction of the stress components, respectively, , Represents the coordinates of points on the subsurface. Indicates the coordinates of the point where the oil film pressure applies on the contact surface;

[0021] The equivalent stress at any point in a three-dimensional equivalent stress field consists of six stress components:

[0022] : normal direction is Axial, stress direction is The normal stress components of the shaft;

[0023] : normal direction is Axial, stress direction is The shear stress components of the shaft;

[0024] : normal direction is Axial, stress direction is The normal stress components of the shaft;

[0025] : normal direction is The axis, the stress direction is The shear stress components of the shaft;

[0026] : normal direction is Axial, stress direction is The normal stress components of the shaft;

[0027] : normal direction is Axial, stress direction is The shear stress components of the shaft;

[0028] Indicates the gear oil film pressure distribution;

[0029] Indicates the coefficient of friction of the tooth surface;

[0030] Indicates the wheel contact area;

[0031] Indicates the point of contact. When a unit normal force is applied, the location point The magnitude of the generated stress components;

[0032] Indicates the contact point When a unit tangential frictional force is applied, the location point The magnitude of the generated stress components.

[0033] Preferably, in step S3, the von Mises equivalent stress Calculate using the following formula:

[0034]

[0035] The von Mises equivalent stress distribution in the gear contact area is composed of the equivalent stress values ​​at all points in the entire gear contact area.

[0036] Preferably, in step S4, the gear surfaces with different surface roughness include honed rough surfaces, shaved rough surfaces, and ground rough surfaces, and the calculation process for the stress volume integral of each surface is as follows:

[0037] First, calculate the von Mises equivalent stress on each surface according to step S3: von Mises equivalent stress on the honed rough surface. von Mises equivalent stress when shaving rough surfaces von Mises equivalent stress for grinding rough surfaces ;

[0038] Then, through screening and optimization, the equivalent stress of honed rough surfaces for fatigue assessment was obtained. Equivalent stress of shaving rough surfaces for fatigue assessment Equivalent stress for fatigue assessment of ground rough surfaces ; Indicates the stress index, Indicates the Weibull slope;

[0039] Finally, the stress volume integral for each surface is calculated using the following formula:

[0040]

[0041]

[0042]

[0043] in, This represents the stress volume integral of a honed rough surface. This represents the volume integral of stress when shaving a rough surface. This represents the volume integral of stress during grinding of a rough surface; This indicates the effective stress volume region.

[0044] Preferably, in step S5, using the honed rough surface as the reference surface, the relative fatigue life of the shaved rough surface and the ground rough surface relative to the reference surface is calculated using the following formula:

[0045]

[0046]

[0047] This indicates the relative fatigue life of the shaved rough surface compared to a reference surface. It represents the relative fatigue life of the ground rough surface relative to the reference surface.

[0048] Preferably, using the honed roughened surface as the reference surface, the relative risk ratio of the shaving roughened surface and the grinding roughened surface relative to the reference surface is calculated using the following formula:

[0049]

[0050]

[0051] This indicates the relative risk ratio of shaving a rough surface to a reference surface. This indicates the relative risk ratio of grinding a rough surface to a reference surface.

[0052] Preferably, the method further includes a tooth root bending strength verification step:

[0053] S6. Calculate dynamic loads :

[0054]

[0055] In the formula, Represents circumferential force. Indicates the load sharing factor. This is the meshing pressure angle;

[0056] S7. Based on dynamic load, the most dangerous peak dynamic bending stress at the tooth root during a complete meshing cycle is captured through dynamic contact analysis or precise finite element method. ;

[0057] S8. Calculate the safety factor for gear bending fatigue. :

[0058]

[0059] In the formula, This indicates the ultimate bending stress related to the gear material. Indicates the lifespan factor;

[0060] S9. Calculate the gear bending fatigue safety factor. The bending strength of the gear pair is checked by comparing it with a preset safety factor reference value.

[0061] Preferably, the lifespan factor Take 0.9.

[0062] Preferably, the preset safety factor reference value =2, satisfying When the bending strength of the gear pair is deemed acceptable, it is determined that the gear pair is within acceptable limits.

[0063] The beneficial effects of this invention: The gear pair life prediction and strength verification method provided by this invention, by deeply integrating key physical factors such as dynamic load, shaft vibration, and actual surface morphology, fundamentally overcomes the limitations of traditional models that rely on steady-state assumptions and empirical coefficients. This method significantly improves the accuracy of fatigue life prediction and tooth root bending stress calculation, making the theoretical results highly consistent with the actual service behavior of gears under fluctuating conditions, and is particularly suitable for harsh operating environments such as marine diesel engines. Furthermore, this method not only clarifies the advantages of honing processes in extending tooth surface contact fatigue life, providing direct technical basis for gear manufacturing, but also provides a solid guarantee for the design of high-reliability gear transmission systems through quantitative safety factor verification, achieving a leap from approximate estimation to precise design. Specifically, it includes the following aspects:

[0064] 1. Significantly improved prediction accuracy: By introducing key factors such as surface roughness, shaft vibration and dynamic load, and using an accurate stress field solution model, the errors caused by traditional empirical assumptions are effectively eliminated, reducing the relative fatigue life prediction error by more than 30% and improving the calculation accuracy of tooth root bending stress by more than 25%.

[0065] 2. Enhanced adaptability to dynamic working conditions: This method breaks through the limitations of the traditional steady-state load assumption and can accurately capture the dynamic evolution of stress with the meshing cycle under fluctuating working conditions such as variable speed of marine diesel engines, which significantly improves the applicability and reliability of the method in actual engineering.

[0066] 3. Clear engineering guidance value: By comparing the fatigue performance of tooth surfaces processed by different methods, it is clear that honed surfaces have the longest relative fatigue life and the smallest stress volume integral, providing direct data support for the optimization of gear manufacturing processes; at the same time, the quantified safety factor verification standard provides a clear basis for the design of high-reliability gears.

[0067] 4. Significantly improved computational efficiency: using DC The FFT algorithm efficiently solves the contact stress field and simplifies the life prediction process by combining stress volume integral. While ensuring accuracy, the overall computational efficiency is improved by more than 40% compared with the traditional finite element analysis method. Attached Figure Description

[0068] Figure 1 This is a flowchart of a gear pair life prediction method based on dynamic stress as described in this invention;

[0069] Figure 2 This is a schematic diagram of a gear pair under dynamic load;

[0070] Figure 3 It is a subsurface stress diagram of the biting point on a smooth surface;

[0071] Figure 4 It is a diagram of the secondary surface stress at the meshing point on the honed rough surface;

[0072] Figure 5 This is a graph showing the oil film pressure and oil film thickness at the biting point on a smooth surface.

[0073] Figure 6 This is a schematic diagram of the oil film pressure, thickness and subsurface stress distribution at the XOZ section of the meshing point under shaft fluctuation conditions (grinding rough surface).

[0074] Figure 7 This is a schematic diagram of the oil film pressure, thickness, and subsurface stress distribution at the XOZ section of the meshing point under shaft fluctuation conditions (honed rough surface).

[0075] Figure 8 This is a schematic diagram of the oil film pressure, thickness and subsurface stress distribution at the XOZ section of the meshing point under shaft fluctuation conditions (shaving rough surface).

[0076] Figure 9 This is a comparison chart of the volumetric stress volume integral ratio of different surfaces of gear pairs under shaft fluctuation conditions;

[0077] Figure 10 This is a comparison chart of the relative risk ratios of different surfaces of a gear pair under shaft fluctuation conditions;

[0078] Figure 11 This is a diagram showing the bending stress distribution at the root of the pinion gear on the camshaft. Detailed Implementation

[0079] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0080] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0081] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0082] Specific Implementation Method 1: The following is combined with... Figures 1 to 11 This embodiment describes the gear pair life prediction method based on dynamic stress.

[0083] The following is an example of the intermediate gear and camshaft pinion pair in the transmission system of a marine diesel engine (material: Taking high-strength medium-alloy carburized steel as an example, this invention will be described in detail. This example demonstrates the complete process of predicting the contact fatigue life and verifying the tooth root bending strength of this gear pair under the condition of shaft vibration fluctuation.

[0084] I. Parameters required for implementation

[0085] The specific parameters required to implement this invention are shown in the table below:

[0086]

[0087] II. Implementation steps for relative fatigue life prediction:

[0088] S1. Obtain the interfacial mechanical property parameters of the gear pair; the interfacial mechanical property parameters include at least: transient oil film pressure distribution and tooth surface friction coefficient;

[0089] By integrating the dynamic model of shaft vibration conditions with elastohydrodynamic lubrication analysis, the interfacial mechanical property parameters of the gear pair are calculated. Specifically, the following methods are employed: A rheological model was used to perform mixed lubrication analysis to obtain transient distribution parameters within a complete meshing cycle (0.007s in this example): gear oil film pressure. tooth surface friction coefficient In this example, the average friction coefficient is calculated comprehensively. .

[0090] S2. Based on the transient oil film pressure distribution and tooth surface friction coefficient obtained in step S1, the following is adopted: Discrete Convolution The Fast Fourier Transform (FFT) algorithm is used to solve the three-dimensional subsurface stress field in the gear contact area.

[0091]

[0092] This indicates a point on the secondary surface of the gear. ,time Lower-level stress; To represent the direction of the normal to the surface under stress and the direction of the stress components, respectively, , Represents the coordinates of points on the subsurface. Indicates the coordinates of the point where the oil film pressure applies on the contact surface;

[0093] The equivalent stress at any point in a three-dimensional equivalent stress field consists of six stress components:

[0094] : normal direction is Axial, stress direction is The normal stress components of the shaft;

[0095] : normal direction is Axial, stress direction is The shear stress components of the shaft;

[0096] : normal direction is Axial, stress direction is The normal stress components of the shaft;

[0097] : normal direction is The axis, the stress direction is The shear stress components of the shaft;

[0098] : normal direction is Axial, stress direction is The normal stress components of the shaft;

[0099] : normal direction is Axial, stress direction is The shear stress components of the shaft;

[0100] Indicates the gear oil film pressure distribution;

[0101] Indicates the coefficient of friction of the tooth surface;

[0102] Indicates the wheel contact area;

[0103] Indicates the contact point When a unit normal force is applied, the location point The magnitude of the generated stress components;

[0104] Indicates the contact point When a unit tangential frictional force is applied, the location point The magnitude of the generated stress components.

[0105] S3. Based on the three-dimensional subsurface stress field obtained in step S2, calculate the von Mises equivalent stress distribution in the gear contact area;

[0106]

[0107] The von Mises equivalent stress distribution in the gear contact area is composed of the equivalent stress values ​​at all points in the entire gear contact area.

[0108] Calculate the von Mises equivalent stress for each surface: von Mises equivalent stress for honed rough surfaces von Mises equivalent stress when shaving rough surfaces von Mises equivalent stress for grinding rough surfaces .

[0109] S4. Based on the von Mises equivalent stress distribution obtained in step S3, calculate the stress volume integral over one meshing cycle for gear surfaces with different surface roughness.

[0110] Define equivalent stress for fatigue assessment It is the von Mises equivalent stress on each surface. The set of all stress points exceeding the material's fatigue limit yields the equivalent stress for fatigue assessment of the honed rough surface. Equivalent stress of shaving rough surfaces for fatigue assessment Equivalent stress for fatigue assessment of ground rough surfaces ; Indicates the stress index, Indicates the Weibull slope;

[0111] Then, for the three types of surfaces—honed rough surface, shaved rough surface, and ground rough surface—the stress volume integral at each instant within one meshing cycle is calculated:

[0112]

[0113]

[0114]

[0115] in, This represents the stress volume integral of a honed rough surface. This represents the volume integral of stress when shaving a rough surface. This represents the volume integral of stress during grinding of a rough surface; This indicates the effective stress volume region.

[0116] The calculated stress volume integral values ​​for the three surfaces at a typical meshing instant are: Honed rough surface =25 shaving rough surfaces =58 Grinding rough surfaces =42 .

[0117] S5. Using a preset surface of the gear pair as the reference surface, calculate the relative fatigue life of other surfaces relative to the reference surface based on the stress volume integral of each surface obtained in step S4 and the Zaretsky life prediction theory.

[0118] Using the honed rough surface as the reference surface, the relative fatigue life of the shaved rough surface and the ground rough surface relative to the reference surface is calculated using the following formula:

[0119]

[0120]

[0121] This indicates the relative fatigue life of the shaved rough surface compared to a reference surface. ;

[0122] This indicates the relative fatigue life of the ground rough surface relative to a reference surface. .

[0123] The Zaretsky life prediction model also outputs the relative risk ratio parameter.

[0124] The relative risk ratio of shaving rough surfaces and grinding rough surfaces relative to the reference surface:

[0125]

[0126]

[0127] This indicates the relative risk ratio of shaving a rough surface to a reference surface.

[0128] This indicates the relative risk ratio of grinding a rough surface to a reference surface.

[0129] The results show that under this fluctuating operating condition, the honing surface has the longest life, which is 2.15 times that of the grinding surface and 3.53 times that of the shaving surface.

[0130] In the field of contact fatigue life prediction, while the LP theory model has laid an important theoretical foundation, it has three main limitations: it does not consider the surface layer failure mechanism, ignores the influence of lubrication conditions, and does not account for the effect of surface morphology. Engineering practice shows that surface roughness significantly alters the Hertzian distribution characteristics of the subsurface stress field, thus affecting the accuracy of life prediction. The IH modified model improves the LP theory model by introducing volume discretization and the concept of critical stress, but its smooth surface assumption and empirical depth factor still have theoretical defects. This invention employs a deterministic analysis method to establish a stress field calculation model that considers the effect of surface roughness by eliminating the limit stress assumption and the dependence of the depth factor. Based on the von Mises stress distribution and combined with Zaretsky's life prediction theory, the fatigue life of the gear tooth surface is predicted. This method improves the accuracy of the prediction.

[0131] The above method effectively eliminates the dependence of traditional methods on stress depth parameters when calculating relative fatigue life, while fully preserving the theoretical consistency of the influence mechanism of operating conditions on fatigue life. This method simplifies the calculation process and ensures the accurate characterization of operating conditions on the life prediction results.

[0132] III. Steps for verifying the bending strength of the tooth root

[0133] The core principle of traditional tooth root bending stress calculation methods is to use [method / approach] under steady-state load conditions. The tangent method is used to determine the critical evaluation section. During dynamic operation, the load distribution characteristics of a gear system are significantly affected by key parameters such as time-varying meshing stiffness and transmission error. Even under constant external loads, the tooth surface contact stress exhibits obvious time-varying characteristics due to these factors. Notably, with the continuous migration of the meshing position, both the bending arm and pressure angle from the critical section to the meshing point exhibit dynamic evolution, significantly increasing the difficulty of stress field analysis. While current methods for assessing tooth root bending stress can approximate stress change trends by introducing correction parameters such as dynamic load coefficients and tooth form factors, they fail to fully consider the dynamic stress evolution mechanism during meshing, making it difficult to accurately characterize the true stress variation during meshing. Furthermore, using inter-tooth load distribution coefficients to consider the impact of load distribution on stress can also affect the accuracy of bending stress prediction results due to oversimplification of the actual physical process.

[0134] To more accurately capture the dynamic changes in gear root bending stress during transmission, this invention proposes a method for calculating gear bending stress under dynamic load. This method abandons the simplification of approximating a constant load in traditional algorithms, and instead introduces a dynamic load model to more realistically simulate the dynamic effects during gear transmission. The specific steps are as follows:

[0135] S6. Calculate dynamic loads :

[0136]

[0137] In the formula, Represents circumferential force. Indicates the load sharing factor. This is the meshing pressure angle;

[0138] Given circumferential force =12000N, meshing pressure angle Load sharing factor The dynamic load coefficient obtained by solving the dynamic model (the instantaneous peak value is taken as 1.4 in this example) is substituted into the peak value of the dynamic normal load to obtain the dynamic load. .

[0139] S7. Based on dynamic load, the most dangerous peak dynamic bending stress at the tooth root during a complete meshing cycle is captured through dynamic contact analysis or precise finite element method. ;

[0140] Peak dynamic bending stress at tooth root .

[0141] S8. Calculate the safety factor for gear bending fatigue. :

[0142]

[0143] In the formula, This indicates the ultimate bending stress related to the gear material. Indicates the lifespan factor;

[0144] According to gear material ultimate bending stress and lifespan factor Calculate the tooth root bending fatigue safety factor .

[0145] S9. Calculate the gear bending fatigue safety factor. The bending strength of the gear pair is checked by comparing it with a preset safety factor reference value.

[0146] Preset safety factor reference value =2, Therefore, it is determined that the bending strength of the camshaft pinion pair under the fluctuating operating conditions meets the high reliability design requirements, and the risk of tooth root bending fatigue fracture is extremely low.

[0147] IV. Analysis of Gear Surface Stress and Relative Fatigue Life under Fluctuating Operating Conditions

[0148] First, the von Mises stresses of smooth surfaces and honed rough surfaces under fluctuating conditions were calculated respectively. (The text then abruptly shifts to a seemingly unrelated topic: "Attached...") Figure 3 A more in-depth analysis of the smooth surface conditions revealed that the maximum von Mises stress occurs below the gear surface. This phenomenon is partly attributed to the presence of a secondary peak in oil film pressure during elastohydrodynamic lubrication, as shown in the attached diagram. Figure 5 The secondary peak of oil film pressure leads to a small amount of stress concentration near the surface, which in turn affects the distribution of the entire subsurface stress field. To compare the effect of a rough surface on subsurface stress, [the following is a separate, unrelated sentence:] ...by attaching... Figure 4 It is evident that the subsurface stress distribution on a honed rough surface exhibits distinctly different characteristics within the contact region compared to a smooth surface. On a rough surface, the maximum von Mises stress occurs at the surface location, and its value is significantly greater than that on a smooth surface, approximately 1.8 times higher. Therefore, the rough surface significantly enhances stress concentration within the contact region. This result clearly demonstrates the impact of rough surfaces on stress concentration on gear tooth surfaces. Consequently, rough surfaces may exacerbate damage phenomena such as micropitting, making it essential to analyze the influence of different surface roughness on gear tooth surface stress.

[0149] The following analysis focuses on the stress distribution and fatigue life characteristics of different surfaces under shaft vibration conditions. (Appendix) Figures 6 to 8 A comparison of lubrication parameters and stress distribution at the XOZ cross-section of the meshing point region is shown. Due to the influence of surface roughness, the oil film thickness and oil film pressure distribution in the gear pair contact area differ significantly from those on smoother surfaces. Contact between micro-protrusions at the gear interface causes a sharp increase in oil film pressure at the corresponding location on this cross-section, and a corresponding decrease in oil film thickness within the contact area. Furthermore, micro-protrusion contact not only causes a sudden increase in local pressure and a sharp decrease in film thickness but also leads to a redistribution of the stress field. At the meshing point, the shaving surface has three stress peak points, with the maximum von Mises stress in the contact area reaching 1205 MPa; the grinding surface has five stress peak points, with the maximum von Mises stress in its contact area reaching 1045 MPa; and the honing surface has two stress peak points, with the maximum von Mises stress in its contact area reaching 874 MPa, the lowest maximum stress value.

[0150] Finally, to compare the working life of various rough surfaces of the gear pair under shaft vibration conditions, a honed surface was used as a benchmark to compare and analyze the differences in fatigue performance of gear pairs with different machined surfaces. (See attached...) Figure 9 and Figure 10As shown, the stress volume integral parameter is significantly correlated with the machining process. A comparative analysis using honed rough surfaces as a benchmark reveals that shaving rough surfaces have the highest stress volume integral value, followed by grinding rough surfaces, while honed rough surfaces have the lowest value. Particularly noteworthy is that shaving rough surfaces exhibit the largest contact area stress volume integral in all meshing transients. This phenomenon indicates that the equivalent stress level on the gear subsurface is most significant under this process condition, making it more prone to interfacial fatigue wear. (Appendix) Figure 10 The study revealed the relative fatigue life distribution of various rough surfaces under shaft vibration conditions. Within one meshing cycle, the honed rough surface exhibited the longest overall fatigue life. Compared to the honed rough surface, the fatigue life of the shaving rough surface significantly decreased at most meshing instants, although at some instants its fatigue life was greater than that of the honed rough surface. This was due to the change in surface roughness distribution caused by fluctuating rotational speed, leading to lower surface stress. The relative fatigue life value of the grinding rough surface fell between that of the honed and shaving rough surfaces at most instants within the meshing cycle. Honing can be used to treat the tooth surfaces to extend the fatigue life of gear pairs and prevent pitting wear.

[0151] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A dynamic stress-based gear pair life prediction method, characterized in that, The method comprises the following steps: S1, obtaining interface mechanical property parameters of the gear pair; the interface mechanical property parameters at least include transient oil film pressure distribution and gear face friction coefficient; S2, based on the transient oil film pressure distribution and the friction coefficient of the tooth surface obtained in step S1, a three-dimensional subsurface stress field of the gear contact area is solved by using an algorithm. algorithm, a three-dimensional subsurface stress field of the gear contact area is solved. S3, calculating von Mises equivalent stress distribution of the gear contact area according to the three-dimensional subsurface stress field obtained in step S2; S4, based on the von Mises equivalent stress distribution obtained in step S3, calculating stress volume integrals of gear surfaces with different surface roughnesses in one meshing period respectively; S5, taking a preset gear surface as a reference surface, calculating relative fatigue life of other surfaces relative to the reference surface based on Zaretsky life prediction theory according to the stress volume integrals of each surface obtained in step S4.

2. The dynamic stress-based gear pair lifetime prediction method of claim 1, wherein, In step S2, the three-dimensional subsurface stress field is solved according to the following formula: denotes a point on the gear secondary surface , time equivalent stress; denotes the normal direction of the stress plane and the direction of the stress component, respectively, , denotes the coordinates of the secondary surface point, denotes the coordinates of the oil film pressure action point on the contact surface; Equivalent stress of any position point in the three-dimensional equivalent stress field includes six stress components: : normal to : axis, stress direction is : normal stress component of the axis; : the normal is : the axis, stress direction is : the shear stress component of the axis : normal to : axis, stress direction is : normal stress component of the axis; : normal to axis, stress direction is : shear stress component of the axis : normal to the plane of the sheet : stress direction : normal stress component of the stress : the normal is : the axis, stress direction is : the shear stress component of the axis; represents the gear oil film pressure distribution; denotes the tooth flank friction coefficient; denotes the wheel contact patch; represents the contact surface point position point when the normal force of the acting unit the size of the stress component generated; represents the contact surface point position point when the tangential friction force of the action unit is applied the magnitude of the stress component generated 3. The dynamic stress-based gear pair lifetime prediction method of claim 2, wherein, In step S3, the von Mises equivalent stress is calculated as follows: The von Mises equivalent stress distribution of the gear contact area is composed of equivalent stress values of all points in the entire gear contact area.

4. The dynamic stress-based gear pair lifetime prediction method of claim 3, wherein, In step S4, the gear surfaces with different surface roughnesses include honing rough surface, shaving rough surface and grinding rough surface, and the calculation process of the stress volume integrals of each surface is as follows: First, the von Mises equivalent stresses of the surfaces are calculated according to step S3: von Mises equivalent stress of the honed rough surface von Mises equivalent stress of the shaved rough surface and von Mises equivalent stress of the ground rough surface ; Then, the screening optimization is performed to obtain equivalent stresses for fatigue assessment of honed rough surface , shaved rough surface , and ground rough surface , respectively; denotes the stress exponent, denotes the Weibull slope; Finally, the stress volume integrals of each surface are calculated according to the following formula: wherein represents the stress volume integral of honing a rough surface, represents the stress volume integral of shaving a rough surface, represents the stress volume integral of grinding a rough surface; represents the effective stress volume area.

5. The dynamic stress-based gear pair lifetime prediction method of claim 4, wherein, In step S5, taking the honing rough surface as the reference surface, the relative fatigue life of the shaving rough surface and the grinding rough surface relative to the reference surface is calculated according to the following formula: represents the relative fatigue life of a shaved rough surface with respect to a reference surface, represents the relative fatigue life of a ground rough surface with respect to a reference surface.

6. The dynamic stress-based gear pair lifetime prediction method of claim 5, wherein, Taking the honing rough surface as the reference surface, the relative risk ratio of the shaving rough surface and the grinding rough surface relative to the reference surface is calculated according to the following formula: represents the relative risk ratio of a shaved rough surface relative to a reference surface, represents the relative risk ratio of a ground rough surface relative to a reference surface.

7. The dynamic stress-based gear pair lifetime prediction method of claim 1, wherein It also includes a tooth root bending strength checking step: S6, calculating dynamic load : wherein represents the circumferential force, represents the load sharing coefficient, is the mesh pressure angle; S7, based on dynamic load, capture the most dangerous tooth root dynamic bending stress peak value in a complete meshing cycle through dynamic contact analysis or precise finite element method ; S8, calculating the gear bending fatigue safety factor : wherein represents the limit bending stress related to the gear material, represents the life factor; S9. Calculate the gear bending fatigue safety factor. The bending strength of the gear pair is checked by comparing it with a preset safety factor reference value.

8. The dynamic stress-based gear pair lifetime prediction method of claim 7, wherein, Life factor Take 0.

9.

9. The dynamic stress-based gear pair lifetime prediction method of claim 7, wherein, Pre-set safety factor reference value = 2, satisfies When, it is determined that the bending strength of the gear pair is qualified.

Images