Arc-tooth bevel gear elastic-plastic fluid dynamic lubrication contact analysis and calculation method, device, equipment and medium

Abstract

The invention discloses a spiral bevel gear elastic-plastic fluid dynamic lubrication contact analysis and calculation method, device and equipment and a medium, and relates to the technical field of gear detection. Calculating the elastic deformation of the tooth surface in the gear meshing process based on the elastohydrodynamic parameters; calculating the tooth surface roughness distribution of the gear; constructing a mixed time-varying thermal elastohydrodynamic lubrication model of the spiral bevel gear according to the elastic deformation and the tooth surface roughness distribution; on the basis of a mixed time-varying thermal elastohydrodynamic lubrication model of the spiral bevel gear, subsurface stress field analysis and tooth surface morphology updating are introduced, bidirectional coupling iterative calculation of plastic deformation and lubrication behaviors is carried out, and a coupling solving result of a pressure field, oil film thickness distribution and a temperature field in a tooth surface contact area is obtained. According to the method, the influence of elastohydrodynamic lubrication on the contact stress is considered, and the accuracy of spiral bevel gear elastoplastic hydrodynamic lubrication contact analysis is improved.

Description

Technical Field

[0001] This application relates to the field of gear testing technology, and in particular to a method, apparatus, equipment and medium for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears. Background Art

[0002] As a key component of helicopter intermediate gearboxes, spiral bevel gears may enter a dry-running state under lubrication loss conditions. This can lead to lubricant film rupture and roughness peaks in the tooth contact area, resulting in plastic deformation, seizing, or galling failure. Studies have shown that when the roughness peak contact stress exceeds the material's yield strength, irreversible plastic deformation and residual stress occur on the tooth surface, significantly altering the oil film distribution and stress state in the contact area. Traditional elastohydrodynamic lubrication (EHL) models do not adequately consider the impact of material plastic deformation on tooth surface contact characteristics, leading to biases in the assessment of elastic deformation in the contact area. Summary of the Invention

[0003] The purpose of this application is to provide a method, apparatus, equipment, and medium for calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears, which takes into account the influence of elasto-hydrodynamic lubrication on contact stress and improves the accuracy of the elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, this application provides a method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears, the method comprising:

[0006] Calculate the elastohydrodynamic parameters during gear meshing; the gear is an arc bevel gear;

[0007] The elastic deformation of the gear tooth surface during gear meshing is calculated based on the aforementioned elastohydrodynamic parameters;

[0008] Calculate the surface roughness distribution of the gear teeth;

[0009] A hybrid time-varying thermo-elasto-hydrodynamic lubrication model for spiral bevel gears is constructed based on the elastic deformation and the tooth surface roughness distribution.

[0010] Based on the hybrid time-varying thermo-elastohydrodynamic lubrication model of spiral bevel gears, subsurface stress field analysis and tooth surface morphology update are introduced to perform bidirectional coupled iterative calculation of plastic deformation and lubrication behavior, and obtain coupled solution results of pressure field, oil film thickness distribution and temperature field in tooth surface contact area.

[0011] Optionally, based on the hybrid time-varying thermo-elasto-hydrodynamic lubrication model of spiral bevel gears, subsurface stress field analysis and tooth surface morphology updating are introduced to perform bidirectional coupled iterative calculations of plastic deformation and lubrication behavior. This yields coupled solution results for the pressure field, oil film thickness distribution, and temperature field within the tooth surface contact area, specifically including:

[0012] Based on the zero plastic deformation, the current elastic deformation is substituted into the hybrid time-varying thermo-elasto-hydrodynamic lubrication model of the spiral bevel gear to calculate the current tooth surface contact pressure and tooth surface contact shear stress.

[0013] Based on the current tooth surface contact pressure and tooth surface contact shear stress, calculate the stress components on the corresponding subsurface of the tooth surface.

[0014] The equivalent stress of the paradigm is calculated based on the stress components on the subsurface.

[0015] Based on the stress components and equivalent stress of each subsurface, the radial return algorithm is used to calculate the equivalent plastic strain components.

[0016] Calculate the residual stress on the subsurface based on the equivalent plastic strain components;

[0017] The stress components on the subsurface are superimposed with the stress components on the subsurface obtained by the action of residual stress to obtain superimposed stress components. The plastic deformation of the subsurface is calculated based on the superimposed stress components.

[0018] The calculated plastic deformation is substituted into the film thickness equation of the hybrid time-varying thermo-elastohydrodynamic lubrication model of the spiral bevel gear to obtain new tooth surface contact pressure and tooth surface contact shear stress. The new tooth surface contact pressure and tooth surface contact shear stress are used as the current tooth surface contact pressure and tooth surface contact shear stress. The process returns to the step of "calculate the stress components on the corresponding subsurface of the tooth surface based on the current tooth surface contact pressure and tooth surface contact shear stress" until the plastic deformation, pressure field, oil film thickness distribution and temperature field in the tooth surface contact area all reach the convergence condition. Finally, the plastic deformation, pressure field, oil film thickness distribution and temperature field in the tooth surface contact area are output.

[0019] Optionally, the elastohydrodynamic parameters during gear meshing are calculated, specifically including:

[0020] Based on the contact analysis of spiral bevel gear tooth surfaces and Hertz contact theory for point contact, the elastohydrodynamic parameters during gear meshing are calculated.

[0021] The elastodynamic parameters include the combined radius of curvature of the tooth surface in the x-direction, the combined radius of curvature in the y-direction, the entrainment speed, the major axis of the contact ellipse, and the minor axis of the contact ellipse during gear meshing; the elastodynamic parameters change with time during the meshing process from gear engagement to disengagement.

[0022] Optionally, the expression for calculating the elastic deformation of the tooth surface during gear meshing is:

[0023]

[0024] Where v(x,y) is the elastic deformation at the target point (x,y), E' is the combined elastic modulus of the upper and lower contact surfaces during gear meshing, p(x',y') is the pressure at the load application point (x',y'), Ω is the elliptical contact area, x' and y' are the x-axis coordinates and y-axis coordinates of the load application point (x',y') respectively, and x and y are the x-axis coordinates and y-axis coordinates of the target point (x,y) respectively.

[0025] Optionally, calculating the surface roughness distribution of the gear teeth specifically includes:

[0026] Generate a two-dimensional random sequence of Gaussian-distributed white noise;

[0027] The surface roughness distribution of the gear tooth is obtained by passing a two-dimensional random sequence of Gaussian distributed white noise through a two-dimensional filter.

[0028] Optionally, the film thickness equation of the hybrid time-varying thermo-elastohydrodynamic lubrication model of the spiral bevel gear is expressed as:

[0029]

[0030] Where h is the oil film thickness, h0 is the film thickness at the rigid body center, and R x and R y Let be the combined radii of curvature in the x and y directions, respectively; v(x,y) be the elastic deformation at point (x,y); z(x,y) be the tooth surface roughness at point (x,y); and u be the tooth surface roughness. z (x,y) represents the plastic deformation at point (x,y).

[0031] Optionally, based on the stress components and normative equivalent stress on the subsurface, the equivalent plastic strain components are calculated using a radial return algorithm, specifically including:

[0032] Each stress component and the equivalent stress of the paradigm on the subsurface are taken as the initial values ​​of each stress component and the equivalent stress, respectively.

[0033] At the nth iteration step of the radial return algorithm:

[0034] The difference between the paradigm equivalent stress and the material yield strength is used as the yield function; the paradigm equivalent stress is determined based on the initial value of the equivalent stress at the nth iteration step.

[0035] Determine whether the yield function is lower than the set value at the nth iteration step. If so, output the current equivalent plastic strain component; otherwise, calculate the equivalent plastic strain increment based on the yield function.

[0036] The sum of equivalent plastic strain increments, the total equivalent plastic strain, and the plastic strain components are calculated based on the equivalent plastic strain increments at the (n+1)th iteration step. The sum of equivalent plastic strain increments is used to calculate the paradigm equivalent stress and perform the (n+1)th iteration.

[0037] Secondly, this application provides a calculation device for elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears. The calculation device applies the aforementioned method for elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears. The calculation device includes:

[0038] The elastohydrodynamic parameter calculation module is used to calculate the elastohydrodynamic parameters during gear meshing.

[0039] The elastic deformation calculation module is used to calculate the elastic deformation of the tooth surface during gear meshing based on the elastohydrodynamic parameters.

[0040] A tooth surface roughness distribution calculation module is used to calculate the tooth surface roughness distribution of the gear.

[0041] A hybrid time-varying thermo-elastohydrodynamic lubrication model construction module for spiral bevel gears is used to construct a hybrid time-varying thermo-elastohydrodynamic lubrication model for spiral bevel gears based on the elastic deformation and the tooth surface roughness distribution.

[0042] The elasto-plastic hydrodynamic lubrication calculation module for spiral bevel gears is used to perform bidirectional coupled iterative calculations of plastic deformation and lubrication behavior based on a hybrid time-varying thermo-elasto-hydrodynamic lubrication model of spiral bevel gears. It introduces subsurface stress field analysis and tooth surface morphology update to obtain coupled solution results of pressure field, oil film thickness distribution and temperature field in the tooth surface contact area.

[0043] 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 analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of the spiral bevel gear as described above.

[0044] 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 above-described method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of bevel gears.

[0045] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears.

[0046] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0047] This application provides a method, apparatus, equipment, and medium for elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears. Based on a hybrid time-varying thermo-elasto-hydrodynamic lubrication model of spiral bevel gears, it introduces subsurface stress field analysis and tooth surface morphology updates to perform bidirectional coupled iterative calculations of plastic deformation and lubrication behavior. The coupled solution results of pressure field, oil film thickness distribution, and temperature field in the tooth surface contact area are obtained. The influence of elasto-hydrodynamic lubrication on contact stress is considered, and the influence of residual stress after material yielding on oil film distribution can be accurately captured. This enables multi-scale analysis of gear pairs from microscopic rough peak contact to macroscopic plastic deformation, improving the accuracy of elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears. Attached Figure Description

[0048] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0049] Figure 1 This is a flowchart illustrating a method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears, as provided in an embodiment of this application.

[0050] Figure 2 A detailed flowchart illustrating a calculation method for elasto-plastic hydrodynamic lubrication contact analysis of an embodiment of this application.

[0051] Figure 3 This is a schematic diagram illustrating the change of the tooth surface curvature radius over time according to an embodiment of this application.

[0052] Figure 4 This is a schematic diagram illustrating the change of the magnitude and direction of the suction speed over time, as provided in an embodiment of this application.

[0053] Figure 5 This is a schematic diagram illustrating the change of the major and minor axes of the contact ellipse over time, according to an embodiment of this application.

[0054] Figure 6 This is a schematic diagram of elastic deformation provided in an embodiment of this application.

[0055] Figure 7 This is a schematic diagram of tooth surface contact pressure and tooth surface contact shear stress provided in an embodiment of this application.

[0056] Figure 8 This is a schematic diagram of the stress components of the subsurface at section x, provided in an embodiment of this application.

[0057] Figure 9 A schematic diagram of the initial paradigm (Von Mises) equivalent stress provided for an embodiment of this application.

[0058] Figure 10 A schematic diagram of the plastic deformation region and the solution space rectangular mesh provided in an embodiment of this application.

[0059] Figure 11 This is a schematic diagram of plastic deformation distribution provided in an embodiment of this application.

[0060] Figure 12 This is a schematic diagram of residual stress distribution provided in an embodiment of this application.

[0061] Figure 13 The pressure, thickness, and temperature distribution of the elasto-plastic hydrodynamic lubricating oil film for an embodiment of this application.

[0062] Figure 14 This is a schematic diagram of the functional modules of a spiral bevel gear elasto-plastic hydrodynamic lubrication contact analysis and calculation device provided in an embodiment of this application.

[0063] Figure 15 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0064] 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.

[0065] 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.

[0066] In one exemplary embodiment, this application provides a method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears, such as... Figure 1 and Figure 2 As shown, the method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears includes steps 101-105.

[0067] Step 101: Calculate the elastohydrodynamic parameters during gear meshing; the gear is an arc bevel gear.

[0068] Step 102: Calculate the elastic deformation of the tooth surface during gear meshing based on the elastohydrodynamic parameters.

[0069] Step 103: Calculate the surface roughness distribution of the gear.

[0070] Step 104: Construct a hybrid time-varying thermo-elastohydrodynamic lubrication model for spiral bevel gears based on the elastic deformation and the tooth surface roughness distribution.

[0071] Step 105: Based on the hybrid time-varying thermo-elastohydrodynamic lubrication model of spiral bevel gears, subsurface stress field analysis and tooth surface morphology update are introduced to perform bidirectional coupled iterative calculation of plastic deformation and lubrication behavior, and obtain the coupled solution results of pressure field, oil film thickness distribution and temperature field in the tooth surface contact area.

[0072] This application establishes a hybrid time-varying thermo-elastohydrodynamic lubrication model for spiral bevel gears, performs elasto-plastic hydrodynamic lubrication (PEHL) contact analysis of gear pairs, and obtains the elasto-plastic lubrication characteristic parameters of the target spiral bevel gear. The elastohydrodynamic lubrication characteristic parameters include: oil film pressure, oil film thickness, temperature field, and plastic deformation in the tooth surface contact area. This improves the ability of the hybrid time-varying thermo-elastohydrodynamic lubrication model to characterize the actual micro-morphological features of the tooth surface, and provides a more accurate theoretical analysis tool for predicting the dynamic service behavior of modern high-performance gear systems. It has important theoretical guiding significance for optimizing the design parameters of gear transmission systems and improving their service reliability.

[0073] In an exemplary embodiment, step 101 specifically includes: calculating the elastohydrodynamic parameters during gear meshing based on the contact analysis of the spiral bevel gear tooth surface and the Hertz contact theory of point contact.

[0074] The elastodynamic parameters include the combined radius of curvature of the tooth surface in the x-direction, the combined radius of curvature of the gear meshing in the y-direction, the entrainment speed, the major axis of the contact ellipse, and the minor axis of the contact ellipse during gear meshing. The entrainment speed includes the magnitude and direction of the entrainment speed. The elastodynamic parameters change with time during the meshing process from engagement to disengagement.

[0075] Step 101 specifically includes: calculating the combined radius of curvature R in the x and y directions of the spiral bevel gear meshing based on the Hertzian contact theory of point contact. x With R y , entrainment speed u h The magnitude and direction (substituted into subsequent governing equations for solution), and the variation of the major axis a and minor axis b of the contact ellipse with time t during the engagement to disengagement process, such as... Figures 3-5 As shown.

[0076] In an exemplary embodiment, the expression for calculating the elastic deformation of the tooth surface during gear meshing in step 102 is as follows:

[0077]

[0078] Among them, such as Figure 6 As shown, v(x,y) represents the elastic deformation at the target point (x,y), E' is the combined elastic modulus of the upper and lower contact surfaces during gear meshing, p(x',y') is the pressure at the load application point (x',y'), Ω is the elliptical contact region, x' and y' are the x-axis and y-axis coordinates of the load application point (x',y') respectively, and x and y are the x-axis and y-axis coordinates of the target point (x,y) respectively. E' is determined by the elastic modulus E of the gear material itself. 1,2 And Poisson ratio υ 1,2 The calculations show that (x', y') represents the specific coordinates of the load applied to the contact surface, and (x, y) represents the point where elastic deformation needs to be calculated.

[0079] The elliptical contact region is composed of regions with major and minor semi-axes of the contact ellipse, namely a and b.

[0080] In an exemplary embodiment, step 103 calculates the surface roughness distribution of the gear, specifically including:

[0081] A two-dimensional random sequence η(x,y) of Gaussian white noise is generated by computer, with the dimension set to (m+M)×(n+N).

[0082] The surface roughness distribution of a gear is obtained by passing a two-dimensional random sequence of Gaussian distributed white noise through a two-dimensional filter. Specifically, this involves passing η(x,y) through a two-dimensional filter to obtain the surface roughness distribution function z(x,y), the expression of which is as follows:

[0083]

[0084] Where M and N are the size parameters of the two-dimensional filter, corresponding to the length of the filter in the x and y directions respectively, and are both positive integers; τ x =1, ...,N;τ y =1,...,N; n=N / 2, m=M / 2, h(τ x ,τ y ) is the impulse response function of the filter.

[0085] In an exemplary embodiment, the establishment of the elastoplastic fluid lubrication numerical model in step 104 needs to take into account the influence of plastic behavior, and at the same time, it needs to deal with the rough peak dry contact situation in the mixed elastoplastic lubrication. Therefore, roughness term and plastic deformation term are added to the film thickness equation.

[0086] The film thickness equation for the hybrid time-varying thermo-elastohydrodynamic lubrication model of the spiral bevel gear is expressed as:

[0087]

[0088] Where h is the oil film thickness, h0 is the film thickness at the rigid body center, and R xand R y Let be the combined radii of curvature in the x and y directions, respectively; v(x,y) be the elastic deformation at point (x,y); z(x,y) be the tooth surface roughness at point (x,y); and u be the tooth surface roughness. z (x,y) represents the plastic deformation at point (x,y). The rigid body is the gear.

[0089] In actual gear transmissions, gear surfaces are subjected to loads, typically undergoing a certain degree of elastic or even plastic deformation. However, when establishing an elasto-plastic hydrodynamic lubrication model, to simplify the analysis process, an ideal scenario is first considered: the gear is treated as a rigid body, meaning no elastic or plastic deformation occurs on the surface. The resulting central film thickness is the rigid body central film thickness h0. Subsequently, factors such as elastic and plastic deformation are introduced to modify and refine the model, thereby more accurately describing the actual lubrication state of the gear.

[0090] In an exemplary embodiment, based on the hybrid time-varying thermo-elastohydrodynamic lubrication model of spiral bevel gears, subsurface stress field analysis and tooth surface morphology update are introduced to perform bidirectional coupled iterative calculation of plastic deformation and lubrication behavior, and obtain coupled solution results of pressure field, oil film thickness distribution and temperature field in the tooth surface contact area, specifically including steps 201-207.

[0091] Step 201: Based on the fact that the plastic deformation is zero, substitute the current elastic deformation into the hybrid time-varying thermo-elastohydrodynamic lubrication model of the spiral bevel gear to calculate the current tooth surface contact pressure and tooth surface contact shear stress.

[0092] Step 201 specifically includes: using the Reynolds equation as the core, coupling governing equations such as oil film thickness, viscosity-pressure-temperature, density-pressure-temperature, load balance, oil film energy, solid energy, interface continuity, oil film velocity, and shear force to obtain the pressure P and shear stress τ at each node of the mixed lubrication tooth surface contact (grid points formed after discretizing the tooth surface contact area). The tooth surface contact pressure and tooth surface contact shear stress are as follows: Figure 7 As shown in parts (a) and (b).

[0093] In solving the hybrid time-varying thermo-elastohydrodynamic lubrication model, the solutions for the pressure field (the pressure field constituted by the oil film pressure), oil film thickness, and temperature field (the temperature field constituted by the oil film temperature) are strongly coupled: the Reynolds equation takes the oil film thickness h and the lubricating oil properties η and ρ as inputs and outputs the oil film pressure p. The oil film pressure p corrects for the oil film thickness h through the elastic deformation v(x,y) equation. The pressure p and thickness h together determine the velocity field (oil film velocity equation), viscosity field, and density field (viscosity-pressure-temperature equation and density-pressure-temperature equation), thereby controlling the dissipation and storage of oil film energy (oil film energy equation). The temperature change caused by energy dissipation alters the viscosity η and density ρ, which in turn affects the calculation of the Reynolds equation and elastic deformation.

[0094] The formulas for each equation are as follows.

[0095] 1) The Reynolds equation is as follows:

[0096]

[0097] In the formula, the positive x-axis and y-axis are the minor and major axes that form acute angles with the entrainment velocity at the meshing point, respectively; ρ is the density of the lubricating oil; h is the film thickness; p is the pressure; η is the viscosity of the lubricating oil; u and v represent the entrainment velocities of the lubricating oil along the major and minor axes of the contact ellipse, respectively; and t represents the single-tooth meshing time of the spiral bevel gear.

[0098] 2) The viscosity-pressure-temperature equation is as follows:

[0099] η=η0exp{(lnη0+9.67)

[0100]

[0101] In the formula, η0 is the viscosity of lubricating oil under normal pressure, T0 is the initial temperature, T is the oil film temperature, and Z and S are both calculated exponents.

[0102] 3) The density-pressure-temperature equation is as follows:

[0103]

[0104] In the formula, ρ0 is the initial density, and D = 0.0007K. -1 .

[0105] 4) The load balance equations are as follows:

[0106]

[0107] In the formula, Q is the applied external load, that is, the load at the gear meshing point.

[0108] 5) The oil film velocity equation is as follows.

[0109] The entrainment speed of the lubricating oil along its major and minor axes is as follows:

[0110]

[0111] In the formula, u1 and u2 are the velocities of the solid along the x-direction, and v1 is the velocity of the solid along the y-direction.

[0112] The velocity gradient of the lubricating oil along its major and minor axes is as follows.

[0113]

[0114] 6) The oil film energy equation is as follows.

[0115]

[0116] In the formula, c p is the thermal conductivity coefficient, k is the specific heat coefficient, and T is the oil film temperature.

[0117] When the effect of plastic deformation is taken into account in the film thickness equation, the oil film pressure, film thickness and temperature obtained by solving the above equation are the convergent solutions of the elastoplastic lubrication of spiral bevel gears.

[0118] Step 202: Calculate the stress components on the corresponding subsurface of the tooth surface based on the current tooth surface contact pressure and tooth surface contact shear stress.

[0119] Specifically, step 202 includes: calculating the stress components σ at any point on the subsurface based on the tooth surface contact pressure and tooth surface contact shear stress. xx (Normal stress acting in a plane perpendicular to the x-axis and along the x-direction), σ yy (Normal stress acting on a plane perpendicular to the y-axis and along the y-direction), σ zz (Normal stress acting in a plane perpendicular to the z-axis and along the z-direction), σ xy (Shear stress acting in a plane perpendicular to the x-axis and along the y-direction), σ xz (Shear stress acting in a plane perpendicular to the x-axis and along the z-direction), σ yz (Shear stress acting on a plane perpendicular to the y-axis and along the z-direction). Where σ on the x-section... xx σ xy and σ xz Distribution as Figure 8 As shown in (a), σ on the x-section yy σ zz and σ yz Distribution as Figure 8 As shown in (b).

[0120] The stress components of the subsurface are calculated as follows: σ qr=∑∑[p·D Nqr +τ·D Sqr ];

[0121] Where, σ qr Represents the stress components of the subsurface (without considering residual stress), where q and r can be x, y, or z, and D Nqr and D Sqr Let p and τ represent the tooth surface contact pressure and shear stress τ, respectively, and σ represent the subsurface stress components. qr The influence coefficient.

[0122] Step 203: Calculate the equivalent stress of the paradigm based on the stress components on the subsurface.

[0123] The formula for calculating the equivalent stress of the paradigm is:

[0124]

[0125] Where, σ mises The initial paradigm equivalent stress is as follows: Figure 9 As shown.

[0126] Step 204: Based on the stress components and paradigm equivalent stress on the subsurface, calculate the equivalent plastic strain components using the radial return algorithm.

[0127] Step 205: Calculate the residual stress on the subsurface based on the equivalent plastic strain components.

[0128] Step 206: Superimpose the stress components on the subsurface with the stress components on the subsurface obtained by the residual stress to obtain the superimposed stress components, and calculate the plastic deformation of the subsurface based on the superimposed stress components.

[0129] Step 207: Substitute the currently calculated plastic deformation into the film thickness equation of the hybrid time-varying thermo-elastohydrodynamic lubrication model of the spiral bevel gear to obtain the new tooth surface contact pressure and tooth surface contact shear stress; use the new tooth surface contact pressure and tooth surface contact shear stress as the current tooth surface contact pressure and tooth surface contact shear stress, and return to the step of "calculate the stress components on the corresponding subsurface of the tooth surface based on the current tooth surface contact pressure and tooth surface contact shear stress" until the plastic deformation, pressure field, oil film thickness distribution and temperature field in the tooth surface contact area all reach the convergence condition, and output the final obtained plastic deformation, pressure field, oil film thickness distribution and temperature field in the tooth surface contact area.

[0130] In one exemplary embodiment, during the plasticity analysis process, it is necessary to continuously update the equivalent plastic strain. Step 205 specifically includes:

[0131] Step (1), given the treatment.

[0132] The stress components and equivalent stress on the subsurface are taken as the initial values ​​of the stress components and equivalent stress, respectively.

[0133] Initial value of equivalent plastic strain increment Δλ (0) =0, the initial value of the equivalent plastic strain λ = λ N-1 The number of iterations in the radial return algorithm is represented by the superscript (n). When n = 0, it represents the initial state at the start of the plastic analysis. The subscript N represents the number of cycles between the tooth surface lubrication contact analysis and the subsurface stress-strain analysis in the subsequent elastoplastic lubrication analysis.

[0134] Step (2), yield function.

[0135] The yield function is the difference between the normal equivalent stress and the yield strength of the tooth surface material, and its expression is as follows:

[0136] Among them, f (n) Let σ be the yield function when the number of iterations is n. Y For a linear isotropic reinforcement model, λ (n) The equivalent plastic strain when the number of iterations is n. This represents the normal equivalent stress when the number of iterations is n.

[0137] The calculation expression is:

[0138] Where G is the shear modulus of the material, calculated as G = E / 2(1+υ), E is the elastic modulus of the material, υ is the Poisson's ratio of the material, and Δλ (n) This is the sum of the accumulated equivalent plastic strain increments when the number of iterations is n. When f (n) If the value is below 100 Pa, the iterative calculation is terminated; otherwise, the subsequent calculations continue.

[0139] Step (3), calculate the equivalent plastic strain increment, the expression is:

[0140] Where, δλ (n) E represents the equivalent plastic strain increment when the number of iterations is n. T This represents the tangential modulus of the material.

[0141] Step (4), update the variables.

[0142] From step (3) δλ (n) Other relevant variables can be calculated when the number of iteration steps is n+1.

[0143] The sum of the equivalent plastic strain increments is: Δλ (n+1) =Δλ(n) +δλ (n) ;

[0144] The equivalent total plastic strain is:

[0145] The stress components of each subsurface are:

[0146] The plastic strain components are:

[0147] Where, φ qr To calculate the intermediate variable, its calculation expression is:

[0148]

[0149] In the formula, S qr Represents the subsurface deviatoric stress components, including S xx S yy S zz S xy S yz and S xz .

[0150] S qr =σ qr -σ hydro ·δ qr ;

[0151] In the formula, σ hydro For hydrostatic stress,

[0152] After updating the variables, return to step (2) to continue iterative calculation until the yield function is lower than the set value, and output the plastic strain component ε. Pqr The value is set to 100Pa.

[0153] In an exemplary embodiment, at the nth iteration step of the radial return algorithm:

[0154] The difference between the paradigm equivalent stress and the material yield strength is used as the yield function; the paradigm equivalent stress is determined based on the initial value of the equivalent stress at the nth iteration step.

[0155] Determine whether the yield function is lower than the set value at the nth iteration step. If so, output the current equivalent plastic strain component; otherwise, calculate the equivalent plastic strain increment based on the yield function.

[0156] The sum of equivalent plastic strain increments, the total equivalent plastic strain, and the plastic strain components are calculated based on the equivalent plastic strain increments at the (n+1)th iteration step. The sum of equivalent plastic strain increments is used to calculate the paradigm equivalent stress and perform the (n+1)th iteration.

[0157] In an exemplary embodiment, step 206 includes the calculation of initial plastic deformation and residual stress, specifically including:

[0158] Calculate the plastic strain components Then, the surface plastic deformation can be calculated using the following expression:

[0159]

[0160] Among them, u z (α,β) represents the plastic deformation at node (α,β), D zst For each component of plastic strain with respect to u z The influence coefficients of (α,β), ξ, η These are Gaussian points in the x, y, and z directions, respectively.

[0161] Plastic deformation region and solution space rectangular mesh as follows Figure 10 As shown, the distribution of plastic deformation is as follows: Figure 11 As shown, where, Figure 11 In the middle (a), the three-dimensional distribution of plastic deformation is shown. Figure 11 (b) is a contour map of plastic deformation.

[0162] After determining the plastic strain, the components of the residual stress caused by the intrinsic strain are calculated, and the expressions are as follows:

[0163]

[0164] in, Let μ and υ represent the components of the residual stress, respectively, and let μ and υ be the shear modulus and Poisson's ratio of the spiral bevel gear material. The plastic strain component under pressure. This is the influence coefficient of intrinsic strain and stress disturbance. and These are the influence coefficients of surface load and subsurface stress, respectively, τ zz τ zx and τ zy These are the tangential loads along the z, x, and y directions, respectively, and (α, β, γ) are the specific coordinate values ​​in the x, y, z spatial coordinate axes.

[0165] Figure 10 The diagram shows the plastic deformation region and the rectangular mesh for the solution space. The number of nodes in the x, y, and z directions are set as M, N, and L, respectively.

[0166] Residual stress distribution as follows Figure 12 As shown, the three-dimensional diagram of residual stress is as follows: Figure 12 As shown in (a), the residual stress contour map is as follows: Figure 12 As shown in (b).

[0167] In an exemplary embodiment, step 207 involves superimposing each stress component with each component of the residual stress. Considering the influence of plastic behavior on the subsurface stress field, each stress component should include the corresponding component of the residual stress. The process returns to step 203, where the stress components calculated in step 203 under the initial pressure without considering residual stress are superimposed. The expression for each stress component then changes as follows:

[0168]

[0169] Where, σ qr Indicates the stress components after superposition. This represents the stress components of the subsurface obtained by applying contact pressure p and shear stress τ. This represents the stress components of the subsurface obtained by the application of residual stress.

[0170] This application repeats steps 203 to 207 to calculate the plastic deformation u considering the combined action of residual stress and subsurface stress. z The convergence accuracy of plastic deformation is set to 1.0 × 10⁻⁶. -3 When the convergence accuracy requirement is not met, return to step 201. At this point, the plastic deformation is no longer zero, which means it is elastoplastic hydrodynamic lubrication. By solving the elastoplastic hydrodynamic lubrication control equation, the micromorphology of the tooth surface is updated to obtain a new amount of plastic deformation until the convergence accuracy requirement is met, and the elastoplastic lubrication convergence solution is obtained.

[0171] Figure 13 The oil film pressure, film thickness and temperature distribution in the contact area obtained from the elasto-plastic hydrodynamic lubrication model of spiral bevel gears. The presence of plastic deformation changes the elasto-hydrodynamic lubrication characteristics under mixed lubrication conditions, producing additional pressure peaks and temperature peaks as shown in the figure.

[0172] This application combines iterative calculation of plastic deformation with lubrication contact analysis to establish a dynamic contact model that considers material work hardening and surface morphology evolution. By introducing a subsurface stress field analysis module and a tooth surface morphology update mechanism, a two-way coupling between elasto-plastic deformation and lubrication behavior is achieved, significantly improving the prediction accuracy of gear pair contact fatigue life under harsh working conditions.

[0173] Based on the same inventive concept, this application also provides a device for calculating the elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears, used to implement the aforementioned method for calculating the elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the elasto-plastic hydrodynamic lubrication contact analysis device for spiral bevel gears provided below can be found in the limitations of the elasto-plastic hydrodynamic lubrication contact analysis method for spiral bevel gears described above, and will not be repeated here.

[0174] In an exemplary embodiment, Figure 14 As shown, a calculation device for elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears is provided. This device applies the aforementioned calculation method for elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears. The device includes:

[0175] The elastodynamic parameter calculation module is used to calculate the elastodynamic parameters during gear meshing; the gear is a spiral bevel gear.

[0176] The elastic deformation calculation module is used to calculate the elastic deformation of the gear tooth surface during gear meshing based on the elastohydrodynamic parameters.

[0177] The tooth surface roughness distribution calculation module is used to calculate the tooth surface roughness distribution of the gear.

[0178] A hybrid time-varying thermo-elastohydrodynamic lubrication model construction module for spiral bevel gears is used to construct a hybrid time-varying thermo-elastohydrodynamic lubrication model for spiral bevel gears based on the elastic deformation and the tooth surface roughness distribution.

[0179] The elasto-plastic hydrodynamic lubrication calculation module for spiral bevel gears is used to perform bidirectional coupled iterative calculations of plastic deformation and lubrication behavior based on a hybrid time-varying thermo-elasto-hydrodynamic lubrication model of spiral bevel gears. It introduces subsurface stress field analysis and tooth surface morphology update to obtain coupled solution results of pressure field, oil film thickness distribution and temperature field in the tooth surface contact area.

[0180] 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 15As 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 database stores calculation data for the elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears.

[0181] Those skilled in the art will understand that Figure 15 The structures shown are merely block diagrams of some structures related to the present application and do 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 shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0182] 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.

[0183] 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.

[0184] 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, stored data, displayed data, 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 relevant data must comply with relevant regulations.

[0185] 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).

[0186] 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 units, data processing logic units, etc., and are not limited to these.

[0187] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, 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.

[0188] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears, characterized in that, The method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears includes: Calculate the elastohydrodynamic parameters during gear meshing; the gear is an arc bevel gear; The elastic deformation of the gear tooth surface during gear meshing is calculated based on the aforementioned elastohydrodynamic parameters; Calculate the surface roughness distribution of the gear teeth; A hybrid time-varying thermo-elasto-hydrodynamic lubrication model for spiral bevel gears is constructed based on the elastic deformation and the tooth surface roughness distribution. Based on the hybrid time-varying thermo-elastohydrodynamic lubrication model of spiral bevel gears, subsurface stress field analysis and tooth surface morphology update are introduced to perform bidirectional coupled iterative calculation of plastic deformation and lubrication behavior, and obtain coupled solution results of pressure field, oil film thickness distribution and temperature field in tooth surface contact area.

2. The method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears according to claim 1, characterized in that, Based on a hybrid time-varying thermo-elasto-hydrodynamic lubrication model for spiral bevel gears, subsurface stress field analysis and tooth surface morphology updates are introduced. A two-way coupled iterative calculation of plastic deformation and lubrication behavior is performed to obtain coupled solution results for the pressure field, oil film thickness distribution, and temperature field within the tooth surface contact area. Specifically, these results include: Based on the zero plastic deformation, the current elastic deformation is substituted into the hybrid time-varying thermo-elasto-hydrodynamic lubrication model of the spiral bevel gear to calculate the current tooth surface contact pressure and tooth surface contact shear stress. Based on the current tooth surface contact pressure and tooth surface contact shear stress, calculate the stress components on the corresponding subsurface of the tooth surface. The equivalent stress of the paradigm is calculated based on the stress components on the subsurface. Based on the stress components and equivalent stress of each subsurface, the radial return algorithm is used to calculate the equivalent plastic strain components. Calculate the residual stress on the subsurface based on the equivalent plastic strain components; The stress components on the subsurface are superimposed with the stress components on the subsurface obtained by the action of residual stress to obtain superimposed stress components. The plastic deformation of the subsurface is calculated based on the superimposed stress components. The calculated plastic deformation is substituted into the film thickness equation of the hybrid time-varying thermo-elastohydrodynamic lubrication model of the spiral bevel gear to obtain new tooth surface contact pressure and tooth surface contact shear stress. The new tooth surface contact pressure and tooth surface contact shear stress are used as the current tooth surface contact pressure and tooth surface contact shear stress. The process returns to the step of "calculate the stress components on the corresponding subsurface of the tooth surface based on the current tooth surface contact pressure and tooth surface contact shear stress" until the plastic deformation, pressure field, oil film thickness distribution and temperature field in the tooth surface contact area all reach the convergence condition. Finally, the plastic deformation, pressure field, oil film thickness distribution and temperature field in the tooth surface contact area are output.

3. The method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears according to claim 1, characterized in that, The calculation of elastohydrodynamic parameters during gear meshing includes: Based on the contact analysis of spiral bevel gear tooth surfaces and Hertz contact theory for point contact, the elastohydrodynamic parameters during gear meshing are calculated. The elastodynamic parameters include the combined radius of curvature of the tooth surface in the x-direction, the combined radius of curvature in the y-direction, the entrainment speed, the major axis of the contact ellipse, and the minor axis of the contact ellipse during gear meshing; the elastodynamic parameters change with time during the meshing process from gear engagement to disengagement.

4. The method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears according to claim 1, characterized in that, The expression for calculating the elastic deformation of the gear tooth surface during gear meshing is: Where v(x,y) is the elastic deformation at the target point (x,y), E' is the combined elastic modulus of the upper and lower contact surfaces during gear meshing, p(x',y') is the pressure at the load application point (x',y'), Ω is the elliptical contact area, x' and y' are the x-axis coordinates and y-axis coordinates of the load application point (x',y') respectively, and x and y are the x-axis coordinates and y-axis coordinates of the target point (x,y) respectively.

5. The method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears according to claim 1, characterized in that, The calculation of the tooth surface roughness distribution of the gear specifically includes: Generate a two-dimensional random sequence of Gaussian-distributed white noise; The surface roughness distribution of the gear tooth is obtained by passing a two-dimensional random sequence of Gaussian distributed white noise through a two-dimensional filter.

6. The method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears according to claim 1, characterized in that, The film thickness equation for the hybrid time-varying thermo-elastohydrodynamic lubrication model of the spiral bevel gear is expressed as: Where h is the oil film thickness, h0 is the film thickness at the rigid body center, and R x and R y Let be the combined radii of curvature in the x and y directions, respectively; v(x,y) be the elastic deformation at point (x,y); z(x,y) be the tooth surface roughness at point (x,y); and u be the tooth surface roughness. z (x,y) represents the plastic deformation at point (x,y).

7. The method for analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears according to claim 2, characterized in that, Based on the stress components and normative equivalent stress on the subsurface, the equivalent plastic strain components are calculated using a radial return algorithm, specifically including: Each stress component and the equivalent stress of the paradigm on the subsurface are taken as the initial values ​​of each stress component and the equivalent stress, respectively. At the nth iteration step of the radial return algorithm: The difference between the paradigm equivalent stress and the material yield strength is used as the yield function; the paradigm equivalent stress is determined based on the initial value of the equivalent stress at the nth iteration step. Determine whether the yield function is lower than the set value at the nth iteration step. If so, output the current equivalent plastic strain component; otherwise, calculate the equivalent plastic strain increment based on the yield function. The sum of equivalent plastic strain increments, the total equivalent plastic strain, and the plastic strain components are calculated based on the equivalent plastic strain increments at the (n+1)th iteration step. The sum of equivalent plastic strain increments is used to calculate the paradigm equivalent stress and perform the (n+1)th iteration.

8. A calculation device for elasto-plastic hydrodynamic lubrication contact analysis of spiral bevel gears, characterized in that, The spiral bevel gear elasto-plastic hydrodynamic lubrication contact analysis and calculation device applies the spiral bevel gear elasto-plastic hydrodynamic lubrication contact analysis and calculation method according to any one of claims 1-7, and the spiral bevel gear elasto-plastic hydrodynamic lubrication contact analysis and calculation device comprises: The elastohydrodynamic parameter calculation module is used to calculate the elastohydrodynamic parameters during gear meshing. The elastic deformation calculation module is used to calculate the elastic deformation of the tooth surface during gear meshing based on the elastohydrodynamic parameters. A tooth surface roughness distribution calculation module is used to calculate the tooth surface roughness distribution of the gear. A hybrid time-varying thermo-elastohydrodynamic lubrication model construction module for spiral bevel gears is used to construct a hybrid time-varying thermo-elastohydrodynamic lubrication model for spiral bevel gears based on the elastic deformation and the tooth surface roughness distribution. The elasto-plastic hydrodynamic lubrication calculation module for spiral bevel gears is used to perform bidirectional coupled iterative calculations of plastic deformation and lubrication behavior based on a hybrid time-varying thermo-elasto-hydrodynamic lubrication model of spiral bevel gears. It introduces subsurface stress field analysis and tooth surface morphology update to obtain coupled solution results of pressure field, oil film thickness distribution and temperature field in the tooth surface contact area.

9. 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 elastoplastic hydrodynamic lubrication contact analysis calculation of spiral bevel gears according to any one of claims 1-7.

10. 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 analyzing and calculating the elasto-plastic hydrodynamic lubrication contact of spiral bevel gears as described in any one of claims 1-7.

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