A method and related device for calculating gear contact stress and predicting fatigue life under fluctuating working conditions

Abstract

The application discloses a gear contact stress calculation and fatigue life prediction method and related device under fluctuating working conditions, relates to the technical field of gear design and analysis, and comprises the following steps: collecting dynamic data of a gear transmission system under fluctuating working conditions, respectively establishing a transmission efficiency calculation model and a contact fatigue life analysis model, then performing numerical calculation under fluctuating working conditions, and obtaining gear contact stress and gear contact fatigue life under fluctuating working conditions. The application comprehensively considers dynamic load and instantaneous rotating speed and other fluctuating working condition conditions caused by shaft vibration characteristics, so that the calculation and prediction results are more accurate and comprehensive. Through establishment of a multi-factor coupling transmission efficiency calculation model and a contact fatigue life analysis model based on a three-dimensional dynamic stress field and a Zaretsky life prediction model, gear contact stress can be more accurately calculated and fatigue life can be more accurately predicted, so that reliable basis is provided for optimization design and processing technology selection of gears.

Description

Technical Field

[0001] This application relates to the field of gear design and analysis technology, and in particular to a method and related apparatus for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions. Background Technology

[0002] During gear transmission, due to the existence of vibration characteristics, the variability of the sliding and rolling motion of the tooth surface, and the complexity of the interaction between the micro-roughness of the tooth surface and the lubrication environment, these factors work together to significantly increase the local contact pressure on the tooth surface. This not only exacerbates power loss, but also causes complex changes in the contact fatigue performance of the gear under multiaxial stress.

[0003] Currently, traditional gear design methods are based on Hertzian contact theory, and evaluation relies heavily on experimental statistics. However, these methods struggle to reveal the stress distribution and contact fatigue life characteristics of gears under complex operating conditions, failing to meet the demands of high-precision gear design and performance evaluation. Therefore, there is an urgent need for a method that can comprehensively consider multiple factors, accurately calculate gear contact stress under fluctuating operating conditions, and effectively predict its fatigue life performance. Summary of the Invention

[0004] The purpose of this application is to provide a method and related device for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions, which can accurately calculate gear contact stress and effectively predict fatigue life under fluctuating operating conditions.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] Firstly, this application provides a method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions, including:

[0007] Collect dynamic data of the gear transmission system under fluctuating operating conditions; dynamic data includes dynamic load, speed, lubrication conditions, surface roughness and material parameters.

[0008] Taking into account the coupling of multiple loss factors, a gear transmission efficiency calculation model is established; the multiple loss factors include sliding friction power loss, rolling friction power loss, oil churning power loss, wind resistance power loss, and bearing loss.

[0009] A gear contact fatigue life analysis model is established based on the three-dimensional dynamic stress field and the Zaretsky life prediction model; the three-dimensional dynamic stress field includes subsurface stress and von Mises stress.

[0010] The dynamic data were substituted into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model respectively to perform numerical calculations under fluctuating conditions, so as to obtain the gear contact stress and gear contact fatigue life under fluctuating conditions.

[0011] Optionally, the sliding friction power loss is determined according to the following formula:

[0012] P S =fv H ×10 -3 .

[0013] Among them, P S For the power loss due to gear sliding friction, v H The entrainment speed U e The instantaneous sliding velocity component in the equation is f, which is the instantaneous frictional force obtained from the lubrication model.

[0014] The average value of instantaneous sliding friction power loss is taken to make the calculation results closer to the actual situation;

[0015]

[0016] Among them, P SA is the average value of sliding friction power loss, and L is the actual meshing line length.

[0017] Rolling friction power loss is determined by the following formula:

[0018]

[0019] Among them, P R For the power loss due to gear rolling friction, v TM U is the entrainment velocity in the formula. e The instantaneous rolling velocity component, h is the oil film thickness, B0 is the tooth width, β b The base circle helix angle.

[0020] Optionally, the oil stirring power loss is determined according to the following formula:

[0021] P C =P C1 +P C2 +P C3 .

[0022] Among them, P C For the total churning power loss, P C1 P is the churning power loss related to the outer diameter of the optical axis. C2 For the oil churning power loss related to the smooth surface of the disc, P C3 This refers to the power loss due to churning related to the tooth surface.

[0023] The churning loss power related to the outer diameter of the optical axis, the churning loss power related to the smooth surface of the disk, and the churning loss power related to the tooth surface are determined by the following formulas:

[0024]

[0025] Among them, f g Let η be the gear immersion factor obtained from the relationship between lubricating oil depth and tooth height, and n be the viscosity of the lubricating oil in the gear. i Let L be the rotational speed of the i-th element, D0 be the outer diameter of the element, and L be the rotational speed of the i-th element. 03 For the component length, A g As a configuration constant, it is set to 0.2, B0 is the tooth width, and R... f β is the roughness coefficient, and β0 is the pitch circle helix angle.

[0026] Wind resistance power loss is determined by the following formula:

[0027]

[0028] Among them, P W ρ3 represents wind resistance power loss, η3 represents the density of the oil-gas mixture, n represents the oil-gas mixture viscosity, R represents the rotational speed, and R represents the gear radius.

[0029] Bearing losses are determined based on empirical values; the bearing loss range for sliding bearings is 98% to 99.5%; and the bearing loss range for rolling bearings is 97% to 99%.

[0030] Alternatively, the subsurface stress is calculated according to the following formula:

[0031]

[0032] Where, τ ij Let i = x, y, z; j = x, y, z, where xyz represents the coordinates of the primary surface of the gear, x'y'z' represents the coordinates of the secondary surface of the gear, t is time, and p(x', y', t) is the instantaneous oil film pressure distribution. and These represent the influence coefficients of unit normal pressure-stress and unit tangential force-stress, respectively, and μ is the viscosity of the lubricating oil.

[0033] von Mises stress is calculated according to the following formula:

[0034]

[0035] Where, τ νM This refers to von Mises stress, which is the gear contact stress.

[0036] Alternatively, the Zaretsky lifetime prediction model is shown in the following equation:

[0037]

[0038] Among them, S vM N represents the survival probability. vM To reach fatigue life, V vMFor the stress volume, τ vM For von Mises stress, e vM Let c be the Weibull slope. vM This is the stress index.

[0039] The gear contact fatigue life is determined according to the following formula:

[0040]

[0041] Among them, L R This refers to the fatigue life of gear contact. The equivalent stress at surface 0 is the control surface. The equivalent stress under surface 1 is N. vM0 With N vM1 , where represents the number of stress cycles on the two surfaces, and V represents the stress volume.

[0042] Optionally, the dynamic data is substituted into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model respectively to perform numerical calculations under fluctuating conditions, thereby obtaining the gear contact stress and gear contact fatigue life under fluctuating conditions. This specifically includes the following steps:

[0043] Based on dynamic data and a gear transmission efficiency calculation model, the friction dynamics model is iteratively solved to obtain the convergent oil film stiffness and friction excitation.

[0044] Based on the convergent oil film stiffness and friction excitation, DC-FFT is used to accelerate the calculation of the three-dimensional dynamic stress field, and the distribution of oil film pressure and gear contact stress at each meshing instant is solved.

[0045] By integrating the volumetric stress field of the gear contact and substituting it into the Zaretsky life prediction model, the number of stress cycles, i.e., the gear contact fatigue life, is obtained.

[0046] Secondly, this application provides a system for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions, including:

[0047] The dynamic data acquisition module under fluctuating operating conditions is used to collect dynamic data of the gear transmission system under fluctuating operating conditions; the dynamic data includes dynamic load, speed, lubrication conditions, surface roughness and material parameters.

[0048] The gear transmission efficiency calculation model construction module is used to comprehensively consider the coupling of multiple loss factors and establish a gear transmission efficiency calculation model. The multiple loss factors include sliding friction power loss, rolling friction power loss, oil churning power loss, wind resistance power loss and bearing loss.

[0049] The contact fatigue life analysis model building module is used to establish a gear contact fatigue life analysis model based on the three-dimensional dynamic stress field and the Zaretsky life prediction model; the three-dimensional dynamic stress field includes subsurface stress and von Mises stress.

[0050] The gear contact stress and fatigue life prediction module is used to substitute dynamic data into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model to perform numerical calculations under fluctuating working conditions, and obtain the gear contact stress and gear contact fatigue life under fluctuating working conditions.

[0051] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for calculating gear contact stress and predicting fatigue life under fluctuating working conditions described above.

[0052] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions described above.

[0053] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions described above.

[0054] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0055] This application provides a method and related apparatus for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions. The method first collects dynamic data of the gear transmission system under fluctuating operating conditions, then establishes a transmission efficiency calculation model and a contact fatigue life analysis model, followed by numerical calculations under fluctuating operating conditions to obtain the gear contact stress and contact fatigue life. In the calculation and prediction process, this application comprehensively considers various factors such as the dynamic load and instantaneous speed caused by shaft vibration characteristics, fluctuating operating conditions, surface conditions, transmission efficiency, lubrication conditions, and material parameters, making the calculation and prediction results more accurate and comprehensive. Furthermore, by establishing a multi-factor coupled transmission efficiency calculation model and a deterministic contact fatigue life analysis model based on a three-dimensional dynamic stress field and the Zaretsky life prediction model, it can more accurately calculate gear contact stress and predict fatigue life, providing a reliable basis for gear optimization design and processing technology selection. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a flowchart illustrating a method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions, provided in an embodiment of this application.

[0058] Figure 2 This is a schematic diagram of the friction loss curves for different surface types analyzed in another embodiment of this application.

[0059] Figure 3 This is a bar chart showing the statistical data of friction loss analyzed in another embodiment of this application.

[0060] Figure 4(a) is a schematic diagram of stress distribution on a smooth surface without friction in another embodiment of this application.

[0061] Figure 4(b) is a schematic diagram of the stress distribution on a smooth surface affected by friction in another embodiment of this application.

[0062] Figure 5(a) is a schematic diagram of the stress distribution on the hobbing-grinding surface without friction in another embodiment of this application.

[0063] Figure 5(b) is a schematic diagram of the stress distribution on the hobbing-grinding surface affected by friction in another embodiment of this application.

[0064] Figure 6(a) is a schematic diagram of von Mises stress distribution under the hobbing-shaving process in another embodiment of this application.

[0065] Figure 6(b) is a schematic diagram of von Mises stress distribution under the hobbing-shaving-quenching-honing process in another embodiment of this application.

[0066] Figure 6(c) is a schematic diagram of von Mises stress distribution under the gear hobbing-quenching-grinding process in another embodiment of this application.

[0067] Figure 6(d) is a schematic diagram of von Mises stress distribution under the hobbing-grinding process in another embodiment of this application.

[0068] Figure 7(a) is a schematic diagram of the special meshing points distributed during the meshing cycle in another embodiment of this application.

[0069] Figure 7(b) is a schematic diagram of the proportion of surface stress volume integral ratio under four different processes in another embodiment of this application.

[0070] Figure 7(c) is a schematic diagram of the relative fatigue life of each special meshing point under four different processes in another embodiment of this application.

[0071] Figure 7(d) is a schematic diagram of the overall transmission efficiency under four different processes in another embodiment of this application.

[0072] Figure 8 This is a schematic diagram of the functional modules of a gear contact stress calculation and fatigue life prediction system under fluctuating working conditions, provided in an embodiment of this application.

[0073] Figure 9 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0074] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0075] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0076] This application provides a method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions. In one exemplary embodiment, such as... Figure 1 As shown, it includes the following steps:

[0077] Step 1: Collect dynamic data of the gear transmission system under fluctuating operating conditions. Dynamic data includes dynamic load, speed, lubrication conditions (oil film thickness, viscosity), surface roughness (such as the surface morphology of gear hobbing-grinding, gear hobbing-shaving, etc.) and material parameters (elastic modulus, Poisson's ratio, etc.).

[0078] Step 2: Taking into account the coupling of multiple loss factors, establish a gear transmission efficiency calculation model; the multiple loss factors include sliding friction power loss, rolling friction power loss, oil churning power loss, wind resistance power loss and bearing loss.

[0079] In extreme operating environments, such as bearing enormous torque, achieving high-speed rotation, and coping with frequent fluctuations in operating conditions, the importance of transmission efficiency in gear transmission systems becomes increasingly significant, serving as a key link between environmental and economic benefits. Gear power loss is affected by various factors, such as the properties of elastic materials, fluctuations in operating conditions, and the actual rough peak contact environment. In particular, the deterioration of the working environment further amplifies the power loss characteristics, thereby threatening the lifespan and reliability of the gears.

[0080] Improving gear transmission efficiency not only saves energy but also reduces operating costs. Power loss, as an inverse indicator of efficiency, mainly originates from gear meshing, air resistance, and lubricating oil turbulence, with the majority of the lost energy being converted into heat. Excessive power loss can cause operating temperatures to exceed permissible ranges, leading to transmission failure. Based on a coupled tribodynamic model of gear transmission systems, a numerical method for calculating power loss on realistically rough three-dimensional surfaces is developed to support improvements in the efficiency and reliability of gear transmission systems.

[0081] Gear meshing power loss is a key component of gear transmission power loss, and its generation mechanism is complex and diverse. Specifically, the power loss during gear meshing mainly includes two parts: sliding friction power loss and rolling friction power loss. Among them, sliding friction power loss is related to the contact position of gear meshing.

[0082] In this embodiment, the sliding friction power loss is determined according to the following formula:

[0083] P S =fv H ×10 -3 .

[0084] Among them, P S For the power loss due to gear sliding friction, v H The entrainment speed U e The instantaneous sliding velocity component in the equation is f, which is the instantaneous frictional force obtained from the lubrication model.

[0085] The average value of instantaneous sliding friction power loss is taken to make the calculation results closer to the actual situation;

[0086]

[0087] Among them, P SA is the average value of sliding friction power loss, and L is the actual meshing line length.

[0088] The rolling friction power loss of gears mainly occurs during meshing. Friction occurs when the surface of one gear rolls against the surface of another, resulting in rolling friction power loss. Under elastohydrodynamic lubrication conditions, the uneven distribution of the kinetic oil film between the gear surfaces leads to significant power loss. This loss is influenced by both the instantaneous rolling speed and the real-time state of the lubricating oil film thickness. In this embodiment, the rolling friction power loss is determined according to the following formula:

[0089]

[0090] Among them, P R For the power loss due to gear rolling friction, vTM U is the entrainment velocity in the formula. e The instantaneous rolling velocity component, h is the oil film thickness, B0 is the tooth width, β b The base circle helix angle.

[0091] The power loss in oil churning is mainly attributed to frictional losses between the lubricating oil and internal components. Rotating parts that are in direct contact with the lubricating oil, such as shafts and gears, are the primary influencing factors. Key factors affecting oil churning loss include the viscosity of the lubricating oil, the input speed, the operating temperature, the gear helix angle, and the oil immersion depth of the gears.

[0092] Since Seetharaman and Kahraman proposed that gears, when rotating, cause the lubricating oil adhering to them to move along with them, this process includes frictional losses between the gear's outer and side surfaces and the lubricating oil, as well as energy losses due to the vortex effect of the lubricating oil between the two tooth surfaces. During gear meshing, due to the periodic variation in the clearance between the two tooth surfaces, lubricating oil is periodically drawn in and expelled, leading to additional power losses. These two main components constitute the primary source of churning losses. Furthermore, churning losses at high speeds encompass three parts: first, churning losses related to the outer diameter of the gear shaft; second, churning losses related to the gear's outer surface (such as the two side surfaces); and third, churning losses related to the tooth surfaces (such as the outer surfaces of the large and small gears). The churning power loss is determined by the following formula:

[0093] P C =P C1 +P C2 +P C3 .

[0094] Among them, P C For the total churning power loss, P C1 P is the churning power loss related to the outer diameter of the optical axis. C2 For the oil churning power loss related to the smooth surface of the disc, P C3 This refers to the power loss due to churning related to the tooth surface.

[0095] The churning loss power related to the outer diameter of the optical axis, the churning loss power related to the smooth surface of the disk, and the churning loss power related to the tooth surface are determined by the following formulas:

[0096]

[0097] Among them, f g Let η be the gear immersion factor obtained from the relationship between lubricating oil depth and tooth height, and n be the viscosity of the lubricating oil in the gear. i Let L be the rotational speed of the i-th element, D0 be the outer diameter of the element, and L be the rotational speed of the i-th element. 03 For the component length, A gAs a configuration constant, it is set to 0.2, B0 is the tooth width, and R... f β is the roughness coefficient, and β0 is the pitch circle helix angle.

[0098] Wind resistance power loss is mainly caused by the rotational motion of the pinion and gear within the oil-gas space of the gearbox. This loss is influenced by several key factors, including the gear rotational speed, the concentration distribution of the oil-gas mixture within the gearbox, and the gear's own geometric dimensions. To scientifically assess this loss, the following formula is typically used to quantify the gear's wind resistance power loss:

[0099]

[0100] Among them, P W ρ3 represents wind resistance power loss, η3 represents the density of the oil-gas mixture, n represents the oil-gas mixture viscosity, R represents the rotational speed, and R represents the gear radius.

[0101] Bearing power loss is influenced by various factors, such as geometric parameters, lubrication methods, pressure loads, and inner ring speed. Given the complexity of actual working environments, these influencing factors are often difficult to calculate accurately, leading to significant deviations in the calculated power loss values. To address this issue, in practical design applications, a series of empirical values ​​or experimental data are typically referenced to determine the bearing's power loss. These reference values ​​are usually derived from extensive experimental and practical application data and have undergone certain corrections and calibrations to improve their accuracy and reliability. By referring to these reference values, the bearing's power loss can be estimated more accurately during the design process, thereby optimizing bearing performance and extending its service life. Simultaneously, this provides important reference for bearing selection and configuration.

[0102] Table 1 Reference values ​​for bearing efficiency

[0103] type Efficiency range (%) sliding bearings 98.0-99.5 rolling bearings 97.0-99.0

[0104] Table 2 Measured values ​​of bearing efficiency

[0105] Rotational speed range (r / min) Torque range (Nm) Bearing efficiency range (%) 959-961 1889-1966 99.44-99.47

[0106] Based on the bearing efficiency reference values ​​shown in Table 1 and the measured bearing efficiency results in Table 2, it can be seen that the bearing efficiency values ​​change little during the calculation and testing process. In the following analysis, the bearing efficiency is uniformly selected as 99.5%.

[0107] In practical applications, bearing losses are determined based on empirical values; the bearing loss range for sliding bearings is 98% to 99.5%; and the bearing loss range for rolling bearings is 97% to 99%.

[0108] Step 3: Based on the three-dimensional dynamic stress field and Zaretsky life prediction model, establish a gear contact fatigue life analysis model; the three-dimensional dynamic stress field includes subsurface stress and von Mises stress.

[0109] High-power-density, high-torque gears operate in a complex environment where lubrication and roughness peak contact coexist, facing extremely complex lubrication conditions. In this environment, the presence of localized roughness peak contact makes stress concentration and micropitting on the tooth surface unavoidable, posing a potential threat to stable operation and potentially significantly reducing the gear's contact fatigue life. To accurately predict the three-dimensional dynamic stress evolution and relative fatigue life of gears during operation, a three-dimensional dynamic stress and relative fatigue life calculation model for gears was constructed based on the characteristic parameters and shear stress parameters obtained from the established tribodynamic coupling model under fluctuating conditions, taking into full account the effects of actual machined surface roughness and transient operating conditions.

[0110] Taking into account the oil film pressure distribution and inter-tooth friction coefficient under the actual machined surface, the secondary surface stress in the gear contact region under the actual machined surface is solved. Specifically, in this embodiment, the secondary surface stress is calculated according to the following formula:

[0111]

[0112] Where, τ ij Let i = x, y, z; j = x, y, z, where xyz represents the coordinates of the primary surface of the gear, x'y'z' represents the coordinates of the secondary surface of the gear, t is time, and p(x', y', t) is the instantaneous oil film pressure distribution. and These represent the influence coefficients of unit normal pressure-stress and unit tangential force-stress, respectively, and μ is the viscosity of the lubricating oil.

[0113] After detailed calculation of the three-dimensional subsurface stress within the gear contact region, the von Mises stress τ can be further solved. νM von Mises stress, calculated based on the fourth strength theory, is an important tool for describing the deformation behavior of materials under complex stress states. By applying this theory, the degree of interface material failure during gear meshing can be effectively assessed, providing an important theoretical basis for gear design optimization and failure analysis. Von Mises stress is calculated according to the following formula:

[0114]

[0115] Where, τ νM This refers to the von Mises stress, which is the gear contact stress.

[0116] Zaretsky's lifetime prediction model is shown in the following equation:

[0117]

[0118] Among them, S vM N represents the survival probability. vM To reach fatigue life, V vM For the stress volume, τ vM For von Mises stress, e vM Let c be the Weibull slope. vM This is the stress index.

[0119] Using the equivalent stress at 0 on the control surface Equivalent stress under surface 1 The number of stress cycles N on both surfaces can be calculated separately. vM0 With N vM1 The ratio of the two is taken as the relative fatigue life L of the two surfaces. R This method can be used to evaluate fatigue life levels under different roughness types, materials, and operating conditions. For clarity, the hobbing-grinding surface without texture is uniformly used as the control surface 0. In this embodiment, the gear contact fatigue life is determined according to the following formula:

[0120]

[0121] Among them, L R This refers to the fatigue life of gear contact. The equivalent stress at surface 0 is the control surface. The equivalent stress under surface 1 is N. vM0 With N vM1 , where represents the number of stress cycles on the two surfaces, and V represents the stress volume.

[0122] Further, the relative fatigue life of the gear and the stress volume integral Vol(τ) can be obtained. vM It is inversely proportional, as shown in the following formula:

[0123]

[0124] In the formula, M R This represents the stress volume integral ratio.

[0125] Step 4: Substitute the dynamic data into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model respectively to perform numerical calculations under fluctuating conditions, obtaining the gear contact stress and gear contact fatigue life under fluctuating conditions. In this embodiment, Step 4 specifically includes the following steps:

[0126] Step 41: Based on dynamic data and the gear transmission efficiency calculation model, iteratively solve the friction dynamics model to obtain the convergent oil film stiffness and friction excitation.

[0127] Step 42: Based on the convergent oil film stiffness and friction excitation, DC-FFT is used to accelerate the calculation of the three-dimensional dynamic stress field and solve the distribution of oil film pressure and gear contact stress at each meshing instant.

[0128] Step 43: Perform volume integration on the gear contact stress field and substitute it into the Zaretsky life prediction model to obtain the number of stress cycles, i.e., the gear contact fatigue life.

[0129] In another exemplary embodiment of this application, in order to study in depth the variation law of gear transmission efficiency under different real machined surface morphologies, a systematic analysis was performed on the friction loss power that varies along the meshing line. Figure 2 The curves showing the variation of frictional loss power under different surface conditions are presented to reflect the dynamic characteristics of frictional loss power in gear transmission under various actual machined surface conditions. As can be seen from the figures, the actual surface roughness has a significant impact on frictional loss power, which differs significantly from the results under ideal smooth surface conditions. Furthermore, to further quantify this impact, [the following text is incomplete and requires further context]. Figure 3 This paper systematically presents the average value and standard deviation of typical surface friction loss power for driving and driven gears under four different progressive machining strategies, as detailed in the paper, to measure the distribution trend and dispersion of friction loss power. Comparative analysis shows that the presence of actual machined surface roughness not only increases the average value of friction loss power but also makes the data distribution more discrete, with a significantly increased standard deviation. Therefore, in the in-depth study of friction power loss performance, it is necessary to consider the influence of actual machined surface roughness. Considering this factor is of great significance for accurately evaluating the efficiency of gear transmissions and optimizing the design of transmission systems.

[0130] Table 3 Other power losses besides friction loss

[0131] Oil churning loss (%) Wind resistance loss (%) Bearing loss (%) 0.0041 0.026 0.5

[0132] From Table 3 and Figure 2It is known that during gear meshing, friction loss accounts for the largest proportion compared to oil churning, air resistance, and bearing power loss. Furthermore, except for theoretically perfectly smooth, ideal surfaces, hobbing-grinding surfaces exhibit the lowest friction loss characteristics, contributing to improved gear transmission efficiency and extended gear life. In contrast, hobbing-shaving surfaces have the highest maximum friction loss, reaching 5.40%, which is 1.59 times that of hobbing-grinding surfaces. This significant difference indicates that hobbing-shaving surfaces generate substantial energy loss during gear meshing, which is detrimental to gear transmission performance and stability. Moreover, hobbing-quenching-grinding surfaces and hobbing-shaving-quenching-honing surfaces exhibit similar characteristics in terms of friction loss power. Figure 3 Statistical data shows that hobbing-grinding surfaces not only have the lowest average friction loss but also the lowest standard deviation. This means that the friction loss values ​​of hobbing-grinding surfaces are generally low, and the fluctuations in their distribution trend are also small, exhibiting high stability. This stability is crucial for ensuring the reliability and consistency of gear transmissions.

[0133] In another exemplary embodiment of this application, as can be seen from the subsurface stress calculation formula, the formation of gear subsurface stress is not solely determined by the surface normal pressure, but is influenced by multiple factors including shear stress and normal pressure. Therefore, to more intuitively demonstrate the influence of frictional characteristics on gear surface stress distribution, Figures 4 and 5 show the specific effects of the presence or absence of frictional characteristics on the von Mises stress distribution at the meshing point of smooth surfaces and hobbing-grinding surfaces.

[0134] A further analysis of the smooth surfaces shown in Figures 4(a) and 4(b) reveals that the maximum von Mises stress occurs below the surface. This phenomenon is partly attributed to the presence of a secondary peak in the oil film pressure during elastohydrodynamic lubrication. This secondary peak leads to a small amount of stress concentration near the surface, thus affecting the overall distribution of the subsurface stress field. Furthermore, the distribution of subsurface stress changes significantly with altered friction conditions. The influence of friction makes the stress distribution more asymmetrical, and the average value increases from 605.56 MPa to 735.94 MPa, showing a clear increasing trend.

[0135] To gain a more comprehensive understanding of the influence of surface roughness on subsurface stress, further studies of Figures 5(a) and 5(b) reveal that the subsurface stress distribution on the hobbing-grinding surface exhibits characteristics distinctly different from that on a smooth surface. In this case, the maximum von Mises stress is significantly higher than that on a smooth surface, approximately 1.3 times greater. This finding indicates that increasing surface roughness significantly enhances stress concentration. More importantly, the maximum von Mises stress further increases when friction is considered. This result clearly reveals the aggravating effect of frictional characteristics on gear stress concentration. Therefore, it can be inferred that existing frictional conditions will adversely affect the stress distribution of gears and may exacerbate damage phenomena such as micropitting.

[0136] This paper delves into the detailed characteristics of von Mises stress distribution and the potential laws governing relative fatigue life of gear pairs with four different machined surfaces during a single tooth meshing cycle under the same working conditions. To more comprehensively and objectively demonstrate and compare the influence of different machining methods on stress distribution, Figures 6(a) to (d) present the stress distribution of the subsurface of the cross-section within the contact region at the end point of a single tooth meshing on different machined surfaces. As shown in the figures, due to the differences in surface roughness characteristics produced by each machining method, the contact between roughness peaks has a significant impact on the stress distribution at local meshing positions during gear pair meshing. The stress concentration phenomenon at these local positions is particularly prominent, and the maximum von Mises stress distribution does not strictly follow the traditional linear distribution pattern.

[0137] The comparative analysis of stress distribution on the tooth surface under different machining processes in Figure 6 shows that a significant high stress concentration area was observed on the hobbing-shaving surface in Figure 6(a). This area exhibits the highest stress level among the four surfaces, with the maximum von Mises stress reaching 1900 MPa. In contrast, the stress concentration phenomenon on the hobbing-shaving-quenching-honing surface in Figure 6(b) is relatively mild, but six distinct areas appear. The stress distribution pattern on the hobbing-grinding surface in Figure 6(d) is very clear, with the lowest stress level, and the maximum stress value is approximately 57.89% of that on the hobbing-shaving surface.

[0138] To systematically evaluate the contact failure probability, relative fatigue life, and overall transmission efficiency of gears on various surfaces, Figures 7(b)-(c) detail the key meshing locations of gears under different surface conditions. Figure 7(a) shows the proportion of contact domain stress volume integral ratio and the trend of relative fatigue life across the four surfaces. Figure 7(d) further presents the distribution of overall transmission efficiency, including gear meshing friction loss, wind resistance, lubricating oil turbulence, and bearing losses.

[0139] like Figures 7(b) to 7(c)As shown, by comparing and analyzing the stress distribution characteristics of different machined surfaces, it was found that the overall stress volume integral ratio of the hobbing-shaving surface is the largest among the four surfaces compared to the hobbing-grinding surface, while the stress volume integral of the hobbing-shaving-quenching-honing and gear shaping-quenching-grinding surfaces falls between the two. Furthermore, the stress volume integral of the contact domain on the hobbing-shaving surface reaches its peak value at each meshing instant, directly indicating that the overall equivalent stress on the gear surface is particularly prominent under this machining process, thus easily leading to fatigue failure at the gear interface. Further quantitative analysis shows that, under the same working conditions, the interface fatigue life of the hobbing-grinding surface is significantly better than other machined surfaces, with its relative fatigue life during meshing being approximately 8.17 times that of the gear shaping-quenching-grinding surface. In addition, the hobbing-shaving surface also exhibits the lowest overall transmission efficiency, further exacerbating its limitations in practical applications. Based on the above analysis, in order to extend the service life of gears, reduce the risk of fatigue failure at the gear interface, and reduce power loss, the hobbing-shaving process should be avoided as much as possible, and the hobbing-grinding process should be the preferred technical solution.

[0140] Compared with the prior art, this application has the following beneficial effects:

[0141] Multiple factors were taken into account: In the calculation and prediction process, this application comprehensively considered many factors such as the dynamic load and instantaneous speed fluctuation conditions caused by the vibration characteristics of the shaft system, macroscopic geometric dimensions, microscopic tooth surface morphology, transmission efficiency, lubrication performance and material mechanical properties, so as to make the calculation and prediction results more accurate and comprehensive.

[0142] Improved calculation accuracy: By establishing a multi-factor coupled transmission efficiency calculation model and a deterministic contact fatigue life analysis model based on a three-dimensional dynamic stress field and Zaretsky life prediction model, and by adopting advanced calculation methods such as DC-FFT, the accuracy of gear contact stress and fatigue life calculation has been improved.

[0143] Providing a basis for gear design and process selection: By analyzing the transmission efficiency and fatigue life of different machined surfaces, a reliable theoretical basis can be provided for gear design optimization and processing technology selection, which helps to improve gear service life and transmission efficiency, and reduce costs.

[0144] Based on the same inventive concept, this application also provides a system for implementing the above-described method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions. The solution provided by this system is similar to the solution described in the above method. In an exemplary embodiment, such as... Figure 8 As shown, a system for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions is provided, including the following functional modules:

[0145] The dynamic data acquisition module under fluctuating operating conditions is used to collect dynamic data of the gear transmission system under fluctuating operating conditions; the dynamic data includes dynamic load, speed, lubrication conditions, surface roughness and material parameters.

[0146] The gear transmission efficiency calculation model construction module is used to comprehensively consider the coupling of multiple loss factors and establish a gear transmission efficiency calculation model. The multiple loss factors include sliding friction power loss, rolling friction power loss, oil churning power loss, wind resistance power loss and bearing loss.

[0147] The contact fatigue life analysis model building module is used to establish a gear contact fatigue life analysis model based on the three-dimensional dynamic stress field and the Zaretsky life prediction model; the three-dimensional dynamic stress field includes subsurface stress and von Mises stress.

[0148] The gear contact stress and fatigue life prediction module is used to substitute dynamic data into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model to perform numerical calculations under fluctuating working conditions, and obtain the gear contact stress and gear contact fatigue life under fluctuating working conditions.

[0149] certainly, Figure 8 The architecture shown is merely exemplary; it can be omitted as needed when implementing different functionalities. Figure 8 One or at least two components of the system shown.

[0150] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 9 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it can implement the gear contact stress calculation and fatigue life prediction method under fluctuating operating conditions provided in the previous embodiment.

[0151] Those skilled in the art will understand that Figure 9The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0152] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0153] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0154] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0155] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0156] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0157] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0158] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0159] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions, characterized in that, include: Collect dynamic data of the gear transmission system under fluctuating operating conditions; The dynamic data includes dynamic load, rotational speed, lubrication conditions, surface roughness, and material parameters; Taking into account the coupling of multiple loss factors, a gear transmission efficiency calculation model is established; the multiple loss factors include sliding friction power loss, rolling friction power loss, oil churning power loss, wind resistance power loss, and bearing loss; A gear contact fatigue life analysis model is established based on a three-dimensional dynamic stress field and the Zaretsky life prediction model; the three-dimensional dynamic stress field includes subsurface stress and von Mises stress. The dynamic data are substituted into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model respectively to perform numerical calculations under fluctuating conditions, so as to obtain the gear contact stress and gear contact fatigue life under fluctuating conditions. The sliding friction power loss is determined according to the following formula: ； in, This is the power loss due to gear sliding friction. For entrainment speed The instantaneous sliding velocity component in f The instantaneous frictional force is obtained from the lubrication model; The average value of instantaneous sliding friction power loss is taken to make the calculation results closer to the actual situation; ； in, This represents the average value of the sliding friction power loss. This is the actual length of the line of engagement; The rolling friction power loss is determined according to the following formula: ； in, Power loss due to gear rolling friction The entrainment speed in the formula The instantaneous rolling speed component in For oil film thickness, For tooth width, The base circle helix angle; The oil stirring power loss is determined according to the following formula: ； in, For the total power loss from oil stirring, The churning power loss is related to the outer diameter of the optical axis. The power loss due to oil stirring is related to the smooth surface of the disc. Power loss due to churning related to tooth surface; The churning loss power related to the outer diameter of the optical axis, the churning loss power related to the smooth surface of the disk, and the churning loss power related to the tooth surface are determined by the following formulas: ； ； ； in, The gear immersion factor is obtained from the relationship between lubricating oil depth and tooth height. The viscosity of the lubricating oil in the middle, Let i be the rotational speed of the i-th element. The outer diameter of the component. For the length of the component, As a configuration constant, it is set to 0.

2. For tooth width, Roughness coefficient β 0 The pitch circle helix angle; Wind resistance power loss is determined by the following formula: ； in, Due to wind resistance power loss, The density of the oil-gas mixture, The viscosity of the oil-gas mixture. n For rotational speed, R Where is the gear radius; The bearing loss is determined based on empirical values; the bearing loss range for sliding bearings is 98% to 99.5%; the bearing loss range for rolling bearings is 97% to 99%. The subsurface stress is calculated according to the following formula: ； in, For the secondary surface stress of the gear, , xyz This indicates the coordinates corresponding to the main surface of the gear. x'y' z’ This indicates the coordinates corresponding to the secondary surface of the gear. t For time, Instantaneous oil film pressure distribution, and These represent the influence coefficients of unit normal pressure-stress and unit tangential force-stress, respectively. μ This refers to the viscosity of the lubricating oil. The von Mises stress is calculated according to the following formula: ； in, This refers to von Mises stress, i.e., gear contact stress; Zaretsky's lifetime prediction model is shown in the following equation: ； in, For the probability of survival, To reach fatigue life, For stress volume, For von Mises stress, Let Weibull slope be the slope. Stress index; The gear contact fatigue life is determined according to the following formula: ； in, L R For gear contact fatigue life, The equivalent stress at surface 0 is the control surface. The equivalent stress under surface 1, and These represent the number of stress cycles on the two surfaces, respectively. V For stress volume.

2. The method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions according to claim 1, characterized in that, The dynamic data are substituted into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model respectively to perform numerical calculations under fluctuating conditions, obtaining the gear contact stress and gear contact fatigue life under fluctuating conditions, specifically including: Based on the dynamic data and the gear transmission efficiency calculation model, the friction dynamics model is iteratively solved to obtain the convergent oil film stiffness and friction excitation. Based on the convergent oil film stiffness and friction excitation, DC-FFT is used to accelerate the calculation of the three-dimensional dynamic stress field and solve the distribution of oil film pressure and gear contact stress at each meshing instant. By integrating the volumetric stress field of the gear contact and substituting it into the Zaretsky life prediction model, the number of stress cycles, i.e., the gear contact fatigue life, is obtained.

3. A system for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions, characterized in that, For implementing the method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions as described in any one of claims 1-2, the system for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions includes: The dynamic data acquisition module under fluctuating operating conditions is used to collect dynamic data of the gear transmission system under fluctuating operating conditions; the dynamic data includes dynamic load, rotational speed, lubrication conditions, surface roughness, and material parameters; The gear transmission efficiency calculation model construction module is used to comprehensively consider the coupling of multiple loss factors and establish a gear transmission efficiency calculation model; the multiple loss factors include sliding friction power loss, rolling friction power loss, oil churning power loss, wind resistance power loss and bearing loss; The contact fatigue life analysis model construction module is used to establish a gear contact fatigue life analysis model based on a three-dimensional dynamic stress field and the Zaretsky life prediction model; the three-dimensional dynamic stress field includes subsurface stress and von Mises stress. The gear contact stress and fatigue life prediction module is used to substitute the dynamic data into the gear transmission efficiency calculation model and the gear contact fatigue life analysis model respectively to perform numerical calculations under fluctuating conditions, so as to obtain the gear contact stress and gear contact fatigue life under fluctuating conditions.

4. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the method for calculating gear contact stress and predicting fatigue life under fluctuating operating conditions as described in any one of claims 1-2.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the method for calculating gear contact stress and predicting fatigue life under fluctuating working conditions as described in any one of claims 1-2.

6. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the method for calculating gear contact stress and predicting fatigue life under fluctuating working conditions as described in any one of claims 1-2.

Images