A method and system for predicting dry running time of spiral bevel gears

Abstract

The present invention discloses a method and system for predicting the dry-running time of a spiral bevel gear, relating to the field of gear monitoring. The method comprises: calculating the pressure distribution, film thickness distribution, and temperature distribution of the contact area of the spiral bevel gear to be predicted during EHD lubrication based on key EHD lubrication parameters; obtaining the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during the transition from EHD lubrication to dry friction; establishing a multi-dimensional simulation model of the gearbox based on the pressure distribution, film thickness distribution, and temperature distribution of the contact area of the spiral bevel gear to be predicted during EHD lubrication, as well as the time-varying friction coefficient; the simulation model includes a tooth surface EHD lubrication dimension, a gear tooth meshing dimension, and a gear system heat transfer dimension; performing a multi-dimensional coupled simulation based on the multi-dimensional gearbox simulation model to obtain the time-varying temperature variation of the spiral bevel gear to be predicted; and predicting the dry-running time based on the time-varying temperature variation of the spiral bevel gear to be predicted. The present invention reduces the cost of monitoring the dry-running state of gears.

Description

Technical Field

[0001] The present invention relates to the technical field of gear detection, and in particular to a method and system for predicting the dry running time of a spiral bevel gear. Background Art

[0002] To ensure that the pilot has enough time to return safely after the helicopter oil system suffers irreversible damage, the helicopter transmission system must have the ability to run dry for at least 30 minutes. Therefore, a method to predict the dry running time of the spiral bevel gears in the transmission system under oil loss state is extremely necessary.

[0003] Currently, the prediction of gear dry running in the oil-loss state mainly relies on experimental methods, which explore its operating characteristics by stopping the oil supply. However, during the test, it is impossible to dynamically monitor the micro-lubrication state of the gear meshing. In addition, such destructive tests have certain risks and are extremely costly. Summary of the Invention

[0004] The purpose of the present invention is to provide a method and system for predicting the dry running time of a spiral bevel gear, thereby reducing the monitoring cost of the gear dry running state.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for predicting dry running time of a spiral bevel gear, comprising:

[0007] Calculating key elastohydrodynamic lubrication parameters of the spiral bevel gear to be predicted based on the structural parameters and processing parameters of the spiral bevel gear to be predicted;

[0008] Calculating the pressure distribution, film thickness distribution and temperature distribution of the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters;

[0009] Obtaining a time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during a process from elastohydrodynamic lubrication to dry friction under an oil loss state;

[0010] Based on the pressure distribution, film thickness distribution, and temperature distribution in the contact area of the spiral bevel gear under elastohydrodynamic lubrication to be predicted, as well as the time-varying friction coefficient, a multi-dimensional simulation model of the gearbox is established; the multi-dimensional simulation model of the gearbox includes the elastohydrodynamic lubrication dimension of the tooth surface, the gear meshing dimension, and the gear system heat transfer dimension;

[0011] Performing a multi-dimensional coupling simulation based on the multi-dimensional simulation model of the gearbox to obtain the change of the temperature of the spiral bevel gear to be predicted over time;

[0012] The dry running time is predicted according to the change of the temperature of the spiral bevel gear to be predicted over time.

[0013] Optionally, the key parameters of elastohydrodynamic lubrication include load distribution, contact area ellipse major axis size, contact area ellipse minor axis size, entrainment speed and direction angle; the direction angle is the angle between the entrainment speed and the direction of the contact area ellipse minor axis.

[0014] Optionally, calculating the pressure distribution, film thickness distribution, and temperature distribution of the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters specifically includes:

[0015] Based on the key parameters of EHL, the progressive grid refinement method and the multigrid integration method are used to numerically calculate the control equations of the EHL theory of spiral bevel gears, and the pressure distribution, film thickness distribution and temperature distribution in the contact area are obtained.

[0016] Optionally, the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during the process from elastohydrodynamic lubrication to dry friction state is expressed as:

[0017]

[0018] Where f represents the time-varying friction coefficient, ε is the proportion of elastic fluid dynamic lubrication; f D is the friction coefficient in dry friction state; f B is the average friction coefficient in the boundary lubrication state; f EHL is the friction coefficient in the fully lubricated state, ω represents the speed of the spiral bevel gear to be predicted, t represents time, and γ is the oil film maintenance parameter.

[0019] Optionally, in the multi-dimensional simulation model of the gearbox, the friction heat source generated by the tooth surface elastohydrodynamic lubrication dimension is transmitted to the gear tooth meshing dimension and the gear system heat transfer dimension respectively, the ambient temperatures of the gear tooth meshing dimension and the gear system heat transfer dimension are both transmitted to the tooth surface elastohydrodynamic lubrication dimension, the heat source of the gear tooth meshing dimension is transmitted to the gear system heat transfer dimension, and the ambient temperature of the gear system heat transfer dimension is transmitted to the gear tooth meshing dimension.

[0020] Optionally, performing a multi-dimensional coupled simulation based on the multi-dimensional simulation model of the gearbox to obtain the change of the temperature of the spiral bevel gear to be predicted over time specifically includes:

[0021] In the elastohydrodynamic lubrication dimension of the tooth surface, the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the elastohydrodynamic lubrication state, i.e., the oil loss process, is calculated;

[0022] Substituting the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the elastohydrodynamic lubrication state, i.e., the oil loss process, into the gear meshing dimension, calculating the time-varying friction heat source in the gear meshing process, and combining the time-varying friction heat source with the windage power loss to obtain the total heat generation of the gear;

[0023] According to the different heat generating locations, the total heat generated is applied to the corresponding locations of the heat transfer dimension of the gear system for simulation to obtain the temperature distribution of the internal flow domain of the spiral bevel gear to be predicted;

[0024] The average temperature of the internal flow domain is used as the ambient temperature for the gear meshing dimension simulation to obtain the temperature change of the spiral bevel gear to be predicted over time.

[0025] Optionally, the temperature change over time includes the temperature change of the large wheel over time, the temperature change of the small wheel over time, the temperature change in the cavity over time, and the temperature change of the casing over time.

[0026] Optionally, predicting the dry running time according to the change of the temperature of the spiral bevel gear to be predicted over time specifically includes:

[0027] The time corresponding to when the temperature of the small wheel reaches the preset temperature is recorded as the failure time of the spiral bevel gear to be predicted;

[0028] The dry running time is determined according to the failure time of the spiral bevel gear to be predicted.

[0029] The present invention discloses a spiral bevel gear dry running time prediction system, comprising:

[0030] an elastohydrodynamic lubrication key parameter determination module, configured to calculate the elastohydrodynamic lubrication key parameters of the spiral bevel gear to be predicted based on the structural parameters and processing parameters of the spiral bevel gear to be predicted;

[0031] A spiral bevel gear elastohydrodynamic lubrication calculation module is used to calculate the pressure distribution, film thickness distribution and temperature distribution of the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters;

[0032] A time-varying friction coefficient determination module is used to obtain the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during the process from elastohydrodynamic lubrication to dry friction state in the oil loss state;

[0033] a gearbox multi-dimensional simulation model establishment module, configured to establish a gearbox multi-dimensional simulation model based on the pressure distribution, film thickness distribution, and temperature distribution in the contact area of the spiral bevel gear under elastohydrodynamic lubrication to be predicted, as well as the time-varying friction coefficient; the gearbox multi-dimensional simulation model includes a tooth surface elastohydrodynamic lubrication dimension, a gear tooth meshing dimension, and a gear system heat transfer dimension;

[0034] a module for determining temperature changes over time, configured to perform a multi-dimensional coupled simulation based on the multi-dimensional simulation model of the gearbox to obtain temperature changes over time of the spiral bevel gear to be predicted;

[0035] The dry running time prediction module is used to predict the dry running time according to the change of the temperature of the spiral bevel gear to be predicted over time.

[0036] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0037] The present invention establishes a multi-dimensional simulation model of the gearbox, performs multi-dimensional coupling simulation based on the multi-dimensional simulation model of the gearbox, obtains the temperature change of the to-be-predicted spiral bevel gear over time, and predicts the dry running time based on the temperature change of the to-be-predicted spiral bevel gear over time, thereby avoiding the influence of destructive tests on the gear motion state and reducing the monitoring cost of the gear dry running state. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention 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 invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1 A schematic flow chart of a method for predicting dry running time of spiral bevel gears provided by an embodiment of the present invention;

[0040] Figure 2 A schematic diagram of the time-varying friction coefficient of the tooth surface under the oil loss state provided by an embodiment of the present invention;

[0041] Figure 3 A schematic diagram of multi-dimensional coupling prediction provided by an embodiment of the present invention;

[0042] Figure 4 A schematic diagram of the data transmission relationship between different dimensions in a multi-dimensional simulation model of a gearbox provided by an embodiment of the present invention;

[0043] Figure 5 A schematic diagram of gear tooth meshing dimensions provided by an embodiment of the present invention;

[0044] Figure 6 A schematic diagram of a multi-scale parameter coupling concept provided by an embodiment of the present invention;

[0045] Figure 7 A schematic diagram showing the change of meshing friction heat source over time during an oil loss process provided by an embodiment of the present invention;

[0046] Figure 8 A schematic diagram of the temperature field of a gear system during an oil loss process provided by an embodiment of the present invention;

[0047] Figure 9A schematic diagram of the structure of a spiral bevel gear dry running time prediction system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0049] The purpose of the present invention is to provide a method and system for predicting the dry-running time of spiral bevel gears, thereby reducing the cost of monitoring the dry-running state of the gears.

[0050] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Example 1

[0052] like Figure 1 As shown, the present invention provides a method for predicting the dry running time of a spiral bevel gear, comprising the following steps.

[0053] Step 101: Calculating key elastohydrodynamic lubrication parameters of the spiral bevel gear to be predicted based on the structural parameters and processing parameters of the spiral bevel gear to be predicted.

[0054] The key parameters of elastohydrodynamic lubrication include load distribution F m , the major axis size of the contact area ellipse ρ x , the minor axis size of the contact area ellipse ρ y , suction speed u m And the direction angle θ; the direction angle is the angle between the suction velocity and the minor axis direction of the contact area ellipse.

[0055] As a specific implementation, the main structural parameters and processing parameters of the spiral bevel gear to be predicted are shown in Table 1 and Table 2.

[0056] Table 1 Main structural parameters of spiral bevel gears

[0057]

[0058]

[0059] Table 2 Processing parameters of large wheel

[0060]

[0061] The tooth surface equation of the spiral bevel gear is established according to the meshing principle of the spiral bevel gear, the tooth surface flexibility matrix is established using the finite element theory, and the curvature and load of the spiral bevel gear are calculated through load-bearing contact analysis.

[0062] The entrainment speed and direction θ can be calculated according to formulas (1) and (2). m The size is:

[0063]

[0064] Among them, u 1η is the projection of the velocity at the meshing point of the large gear tooth surface in the direction of the long axis, u 1ζ is the projection of the velocity at the meshing point of the large gear tooth surface in the direction of the minor axis, u 2η is the projection of the velocity at the meshing point of the pinion tooth surface in the long axis direction, u 2ζ is the projection of the velocity at the meshing point of the pinion tooth surface in the direction of the minor axis, η and ζ are the spatial vectors of the major axis and minor axis of the contact ellipse in the tangent plane, respectively.

[0065] The angle θ between the entrainment velocity and the x-direction of the minor axis of the contact ellipse is:

[0066]

[0067] The meshing of spiral bevel gears satisfies the Hertz contact theory of point contact, and the major radius of the contact ellipse is ρ x and the short radius ρ y It can be calculated according to formula (3):

[0068]

[0069] Among them, F m is the load, ρ 11 and ρ 12 is the principal curvature of the large wheel at the meshing point on the orthogonal principal plane, ρ 21 and ρ 22 is the principal curvature of the small wheel at the meshing point on the orthogonal principal plane, θ1 and θ2 are the elastic coefficients determined by the elastic modulus of the two meshing gear materials, θ1 is the elastic coefficient corresponding to the large wheel material, and θ2 is the elastic coefficient corresponding to the small wheel material. The calculation method is:

[0070]

[0071] Among them, m1 is the coefficient of the ratio of longitudinal extension and transverse compression of the large wheel material, m2 is the coefficient of the ratio of longitudinal extension and transverse compression of the small wheel material, μ and v are the elliptic integral coefficients, and their values are determined by τ(ρ).

[0072]

[0073] Where ω′ is the angle between the principal planes of the two contact bodies, ρ ij represents the principal curvature of the elastic surface at the meshing point, with the subscripts representing the large wheel surface and the small wheel surface, respectively. After calculating τ(ρ), μ and v can be found by looking up the table. Some of the data are shown in Table 3.

[0074] Table 3 μ, v coefficients

[0075]

[0076] Step 102: Calculate the pressure distribution, film thickness distribution, and temperature distribution in the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters.

[0077] Pressure distribution, film thickness distribution and temperature distribution refer to spatial distribution.

[0078] Wherein, step 102 specifically includes:

[0079] Based on the key parameters of EHL, the progressive grid refinement method and the multigrid integration method are used to numerically calculate the control equations of the EHL theory of spiral bevel gears, and the pressure distribution, film thickness distribution and temperature distribution in the contact area are obtained.

[0080] As a specific implementation, the time-varying elastohydrodynamic lubrication model for spiral bevel gears is simplified into a series of local steady-state elastohydrodynamic lubrication models. The steady-state thermal elastohydrodynamics at different meshing positions of spiral bevel gears can be equivalent to ball-on-disc contact, thus establishing the governing equations for the elastohydrodynamic lubrication of spiral bevel gears. These equations include the Reynolds equation, the film thickness equation, the viscosity equation, the density equation, the load balance equation, the oil film energy equation, the solid energy equation, the interface continuity equation, the oil film velocity equation, the shear force equation, and the friction coefficient calculation equation.

[0081] The Reynolds equation is:

[0082]

[0083] Where x is the direction of the minor axis with the positive direction of the x-axis forming an acute angle with the entrainment velocity, y is the direction of the major axis with the positive direction of the y-axis forming an acute angle with the entrainment velocity, η is the equivalent oil viscosity, u and v are the entrainment velocities of the lubricating medium along the major and minor axes of the ellipse, respectively, p is the oil film pressure, h is the oil film thickness, and ρ is the oil density.

[0084] The film thickness equation is:

[0085]

[0086] Among them, h0 is the center film thickness, which will be determined according to the load balance condition; R x , Ry are the equivalent curvature radii of the two surfaces in the x and y directions; E' is the comprehensive elastic modulus of the upper and lower contact surfaces; x' represents the derivative of x, and y' represents the derivative of y.

[0087] The viscosity equation is:

[0088]

[0089] Among them, Z=α / [5.1×10-9(lnη0+9.67)], S=β T ×(T0-138) / (lnη0+9.67), where T0 is the initial temperature, α is the viscosity-pressure coefficient, η0 is the environmental viscosity of the lubricating oil (Pa·S), β T is the viscosity-temperature coefficient, unit is K -1 , T represents the oil film temperature.

[0090] The density equation is:

[0091]

[0092] Among them, ρ0 is the initial density, β f is a constant, β f =0.0007K -1 .

[0093] The load balance equation is:

[0094] F=∫∫ Ω p(x,y)dxdy (10);

[0095] Where Ω is the contact area, and F is the load borne by the gear teeth at the meshing point at different meshing moments.

[0096] The oil film energy equation is:

[0097]

[0098] in, c and k are the specific heat and thermal conductivity of the fluid, z represents the coordinate in the z-axis direction, and z' represents the derivative of z.

[0099] The solid energy equation is:

[0100]

[0101] Among them, k1 and k2 are the thermal conductivity coefficients of the solid, c1 and c2 are the specific heats of the solid, z1 and z2 are the z-coordinates of the solid, and ρ1 and ρ2 are the densities of the solid.

[0102] The interface continuity equation is:

[0103]

[0104] The oil film flow velocity equation is:

[0105]

[0106]

[0107] The shear force equation is:

[0108]

[0109]

[0110] Among them, τ x and τ y are the shear stresses along the x and y directions respectively, and τ is the resultant force.

[0111] The friction coefficient calculation equation is:

[0112]

[0113] Where μ is the friction coefficient, F l Friction

[0114] By non-dimensionalizing the above equations and performing numerical calculations using the progressive grid refinement method and the multi-grid integration method, the numerical solution of the elastohydrodynamic lubrication of spiral bevel gears can be obtained.

[0115] The numerical solution includes the pressure distribution, film thickness distribution, temperature distribution, and friction coefficient in the contact area.

[0116] Step 103: Obtaining the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during the process from elastohydrodynamic lubrication to dry friction state in the oil loss state.

[0117] In the oil loss state, the lubrication state of the spiral bevel gear meshing gradually changes, from complete elastic fluid dynamic lubrication (elastohydrodynamic lubrication) to dry friction state. Finally, the parts fail due to the disappearance of tooth side clearance, zero film thickness or excessive temperature rise. During this period, it will experience intermediate states such as mixed lubrication and boundary lubrication. The mixed lubrication state is further divided into mild mixed lubrication and severe mixed lubrication.

[0118] Usually, the lubrication state of the contact area is judged by the film thickness ratio. The expression of the film thickness ratio λ is:

[0119]

[0120] Among them, h min is the minimum oil film thickness; R1 and R2 are the roughness values of the two contact surfaces, R aIndicates the average roughness of the two contacting surfaces. In the elastic hydrodynamic lubrication region, λ>3, in the mixed lubrication region, 0.8<λ<3, and in the boundary lubrication region, λ<0.8.

[0121] In the oil loss state, the lubricating oil between the teeth gradually decreases, so the study of this process first needs to consider the problem of side flow between the teeth. In point contact elastohydrodynamic lubrication, the following relationship exists:

[0122]

[0123] Where n is the number of gear rotations, n = ω·t, where ω is the speed and t is the time; γ is the oil film maintenance parameter; r0 is the ratio of the film thickness in the inlet area at the first meshing to the central film thickness under fully lubricated conditions; R(n) is the central film thickness after n revolutions h c The center film thickness h under fully lubricated condition EHL ratio.

[0124] Therefore, the relationship between film thickness and time is:

[0125] h c =h EHL ·(ω·t) -1 / γ (20);

[0126] Oil film maintenance parameters It depends on the load parameter M and the material parameter L, and is calculated as follows:

[0127]

[0128] Where W, G, and U are the dimensionless load parameters, dimensionless material parameters, and dimensionless velocity parameters in the elastohydrodynamic lubrication model.

[0129] For spiral bevel gears with different surface processing accuracy, according to formula (18), the definition of their lubrication state is related to the surface average roughness Ra. By calculating the ratio of film thickness ratio λ to Ra, the minimum film thickness h is obtained. min The relationship with Ra, through analogy calculation, the center film thickness h can be obtained c The relationship between Ra and friction coefficient f can be obtained.

[0130] Taking the average surface roughness Ra = 0.2μm as an example, if the boundary lubrication state is entered, the minimum film thickness h c =0.16μm. According to the calculation of thermal elastic hydrodynamic lubrication of spiral bevel gear, the minimum film thickness of the gear is h min =0.5μm. Therefore, when R(n)=0.32, the system can be considered to have entered the boundary lubrication state; and when R(n)<1%, the system is generally considered to have entered the dry friction state, from which the corresponding friction coefficient f is derived as:

[0131]

[0132] Where f represents the time-varying friction coefficient, ε is the proportion of elastic fluid dynamic lubrication; f D The friction coefficient in dry friction state is usually taken as f D =0.6; f B is the average friction coefficient of the boundary lubrication state, usually taken as f B =0.11; f EHL is the friction coefficient in the fully lubricated state, which is calculated by elastohydrodynamic lubrication, ω represents the speed of the spiral bevel gear to be predicted, t represents time, and γ is the oil film maintenance parameter.

[0133] Assuming that the inter-tooth asperities are in uniform contact with the boundary film during the thinning of the oil film, then df∝dh c ,ε∝dh c , calculated using the example parameters described in this embodiment, we can obtain γ=3.

[0134] In summary, the variation law of the time-varying friction coefficient f of the spiral bevel gear in the oil-loss state is as follows: Figure 2 shown.

[0135] The time-varying friction coefficient provides accurate boundary conditions for the subsequent simulation of gear thermal characteristics under oil loss conditions.

[0136] Step 104: Based on the pressure distribution, film thickness distribution, and temperature distribution in the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication, as well as the time-varying friction coefficient, a multi-dimensional simulation model of the gearbox is established; the multi-dimensional simulation model of the gearbox includes a tooth surface elastohydrodynamic lubrication dimension, a gear tooth meshing dimension, and a gear system heat transfer dimension.

[0137] In the elastohydrodynamic lubrication dimension (step 102), a thermal elastohydrodynamic lubrication model for spiral bevel gears is established to calculate the oil film thickness and friction coefficient in the microscopic contact area of the tooth surface, thereby providing a time-varying friction heat source for the gear meshing dimension and the gear system heat transfer dimension.

[0138] In helicopter transmission systems, spiral bevel gears are usually made of metal with high heat capacity. Heat is transferred by convection and conduction during rotation. The time scale depends on the gear speed. The input speed level is O(10 3 -10 4 )r / min, gear diameter grade is O(10 -1 )m, the contact stress level is O(10 0 )GPa, the system transient thermal response time level is O(10 -2 -10 0 )s.

[0139] During the meshing process of gear teeth, the friction heat generated by the tooth surface is the main heat source, and the high-speed rotating gear will generate greater wind resistance heat. The contact width level is O(10 -4 )m, the sliding speed level is O(10 0 -10 1 )m / s, the number of teeth is O(10 1 -10 2 ), the meshing time scale is O(10 -4 -10 -3 )s, the wind resistance simulation calculation length level is O(10 -6 )m.

[0140] For the elastohydrodynamic lubrication characteristics of the tooth surface micro-contact, its time scale is several orders of magnitude smaller than the thermodynamic time scale of the gear meshing process, which is O(10 -6 -10 -5 )s, the film thickness grade is O(10 -6 )m.

[0141] Based on this, a multi-dimensional simulation model of the gearbox is established, and its time scale and space scale are shown in Table 4.

[0142] Table 4 Time scale and space scale of different dimensions

[0143]

[0144] During the transmission process of spiral bevel gears, various thermophysical effects occur constantly within the system at different time and space scales, such as Figure 3 shown.

[0145] The data transmission relationship between different dimensions is as follows Figure 4 As shown, in the multi-dimensional simulation model of the gearbox, the friction heat source generated by the tooth surface elastohydrodynamic lubrication dimension is transmitted to the gear tooth meshing dimension and the gear system heat transfer dimension respectively, the ambient temperatures of the gear tooth meshing dimension and the gear system heat transfer dimension are both transmitted to the tooth surface elastohydrodynamic lubrication dimension, the heat source of the gear tooth meshing dimension is transmitted to the gear system heat transfer dimension, and the ambient temperature of the gear system heat transfer dimension is transmitted to the gear tooth meshing dimension.

[0146] Step 105: Perform a multi-dimensional coupling simulation based on the multi-dimensional simulation model of the gearbox to obtain the change of the temperature of the spiral bevel gear to be predicted over time.

[0147] Wherein, step 105 specifically includes:

[0148] In the tooth surface elastohydrodynamic lubrication dimension, the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the elastohydrodynamic lubrication state, that is, the oil loss process, is calculated.

[0149] The time-varying friction coefficient of the spiral bevel gear tooth surface to be predicted in the elastohydrodynamic lubrication state, i.e., during the oil loss process, is substituted into the gear meshing dimension, and the time-varying friction heat source during the gear meshing process is calculated. The time-varying friction heat source is combined with the windage power loss to obtain the total heat generation of the gear.

[0150] According to the different heat generating locations, each heat source (overall heat generation of the gear) is applied to the corresponding position of the heat transfer dimension of the gear system for simulation to obtain the internal flow domain temperature distribution of the spiral bevel gear to be predicted.

[0151] The average temperature of the internal flow domain is used as the ambient temperature for the gear meshing dimension simulation to obtain the temperature change of the spiral bevel gear to be predicted over time.

[0152] The temperature changes over time include the temperature changes over time of the large wheel, the temperature changes over time of the small wheel, the temperature changes over time in the cavity and the temperature changes over time of the casing.

[0153] As a specific implementation method: (1) The steps for simulation analysis of gear tooth meshing dimensions are as follows.

[0154] The gear meshing dimension characterizes the physical characteristics of gear meshing heat generation, wind resistance heat generation, convection heat transfer, etc. Figure 5 Considering that the time scale at this level is still very small, transient thermal analysis cannot be implemented due to the high time cost. Therefore, the CFD steady-state simulation analysis method is used to calculate the gear meshing dimension.

[0155] When performing finite element simulation calculations on the gear meshing dimension, only the flow field and temperature field of the gear and its adjacent area are considered, so its boundary conditions are mainly the meshing power loss, windage power loss and convection heat transfer coefficient.

[0156] The average value of the dynamic meshing power loss of spiral bevel gears is:

[0157]

[0158] Among them, z is the number of teeth, Q N It represents the heat generated by single tooth meshing, in W, T is the single tooth meshing period, in s; m is the number of discrete points of a single tooth; i is the discrete point number; f i is the friction coefficient corresponding to the i-th discrete point; F i is the normal load corresponding to the i-th discrete point, in N; v si is the sliding velocity corresponding to the i-th discrete point, in m / s.

[0159] The windage power loss of spiral bevel gears is calculated through CFD simulation. A thin flow region is set near the tooth wall, and the dimensionless drag torque coefficient is calculated using the Multiple Reference Frame (MRF) method:

[0160]

[0161] Where Cm is the dimensionless drag moment coefficient; ρ is the reference density in kg / m 3 ; v is the reference velocity, unit is m / s; A is the reference area, unit is m / s 2 L is the reference characteristic length, in m / s; M is the drag torque, in N·m. MRF is a multi-region computational model with a steady-state approximation. During the calculation process, each unit region can be assigned a different rotational or translational velocity. Local reference coordinate transformations are required at the interfaces between unit regions.

[0162] The windage power loss of spiral bevel gear is calculated as follows:

[0163] P w =Mω (25);

[0164] Where, P w is the wind resistance power loss, in W; ω is the angular velocity, in rad / s.

[0165] The convective heat transfer in the gear tooth meshing dimension includes: convective heat transfer between the gear meshing surface and the oil-gas two-phase mixture, convective heat transfer between the gear tooth side and the oil-gas two-phase mixture, convective heat transfer between other gear surfaces and the oil-gas two-phase mixture, and convective heat transfer of the bearings. However, these convective heat transfers can be automatically analyzed and calculated by simulation calculation software in the gear system heat transfer dimension.

[0166] (2) The steps for simulation analysis of the heat transfer dimension of the gear system are as follows.

[0167] Compared to the tooth meshing dimension and the tooth surface elastohydrodynamic lubrication dimension, the time and spatial scale response of heat transfer in a gear system is significantly larger. Therefore, when simulating this, a transient simulation method can be used to relate the system's temperature changes to time. Considering the time cost of transient simulation analysis and the near-wall layer used in the tooth meshing dimension analysis, the two gears can be approximated as two disks in the gear system dimension.

[0168] When performing transient thermal simulation calculations on a gear system, the boundary conditions include the heat source and the convective heat transfer coefficient. The thermal effect inside the disk is calculated from the meshing heat generated by the gear meshing dimension and the windage heat generated by the windage. Convective heat transfer includes not only the convective heat transfer between the gear meshing surface, gear end face, and other gear surfaces and the oil-gas two-phase mixture, but also the convective heat transfer between the outer surface of the housing and the air.

[0169] The calculation method of the convection heat transfer coefficient between the outer surface of the box and the air is:

[0170]

[0171] Among them, L j is the diameter of the box shell, in m, represents the Reynolds number, k represents the thermal conductivity of air, and the unit is W / (mK).

[0172] (3) The steps of multi-dimensional coupling optimization are as follows.

[0173] In order to make the coupled simulation prediction of the dry running time of spiral bevel gears more accurate, the coupled predictions among the elastohydrodynamic lubrication dimension of the tooth surface, the gear meshing dimension, and the gear system heat transfer dimension are optimized. The parameter transfer relationship among the three is as follows: Figure 6 shown.

[0174] In the tooth surface elastohydrodynamic lubrication dimension, the friction coefficient of the spiral bevel gear tooth surface under full lubrication and oil loss processes is calculated; after substituting it into the gear meshing dimension, the time-varying friction heat source in the gear meshing process is calculated, and then the total heat generation of the gear is obtained by combining it with the wind resistance power loss. According to the different heat generation locations, each heat source is applied to the corresponding position of the gear system heat transfer dimension for simulation to obtain the temperature distribution of the flow field inside the gear system; then the average temperature of the flow field in the box is used as the ambient temperature for the gear meshing dimension simulation to obtain the gear temperature distribution.

[0175] In the tooth surface elastohydrodynamic lubrication dimension, the friction coefficient of the spiral bevel gear tooth surface under full lubrication and oil loss processes is calculated; after substituting it into the gear meshing dimension, the time-varying friction heat source in the gear meshing process is calculated, and then the total heat generation of the gear is obtained by combining it with the wind resistance power loss. According to the different heat generation locations, each heat source is applied to the corresponding position of the gear system heat transfer dimension for simulation to obtain the temperature distribution of the flow field inside the gear system; then the average temperature of the flow field in the box is used as the ambient temperature for the gear meshing dimension simulation to obtain the gear temperature distribution.

[0176] Step 106: Predicting the dry running time according to the change of the temperature of the spiral bevel gear to be predicted over time.

[0177] Wherein, step 106 specifically includes:

[0178] The time corresponding to when the temperature of the pinion reaches the preset temperature is recorded as the failure time of the spiral bevel gear to be predicted.

[0179] The dry running time is determined according to the failure time of the spiral bevel gear to be predicted.

[0180] As a specific implementation method, the time-varying friction coefficient of the spiral bevel gear is calculated according to formula (17), and then the time-varying friction heat source during the oil loss process is obtained. Figure 7 It is the source of frictional heat between the meshing of the large and small wheels.

[0181] The multi-dimensional coupling prediction model is used to simulate the gear system, and the temperature variation over time is as follows: Figure 8 As shown in the figure, it can be seen that the temperature rise of each component in the system shows a trend of first rising sharply, then rising slowly, and finally gradually stabilizing, and the temperature rise trend of the small wheel is the most significant.

[0182] Will Figure 7 and Figure 8 By comparison, it can be seen that the overall temperature rise of the gear system is closely related to the increase of friction heat source, but Figure 2 Compared with the increase curve of friction coefficient, the temperature rise curve has obvious hysteresis.

[0183] Generally, under boundary lubrication conditions, the adsorption film fails at around 150°C, while the chemical reaction film can withstand high temperatures of around 300°C. Therefore, when the chemical reaction film also fails, the gear meshing enters a completely dry friction state. Figure 8 It can be seen that after the spiral bevel gear enters the oil-loss state for about 1.5 hours, the lubrication effect of the small wheel tooth surface disappears and it completely enters the dry friction state. After that, the small wheel will wear and glue rapidly until it fails.

[0184] The present invention discretizes the entire gearbox into the tooth surface elastohydrodynamic lubrication scale, the gear tooth meshing scale and the gearbox heat transfer scale according to the relationship between time and space. Considering the coupling relationship between each scale level, an overall multi-scale (dimensional) calculation model is derived, and the dry running time is predicted based on the multi-scale calculation model.

[0185] The present invention analyzes the change of friction heat source and temperature over time based on the coupling simulation among the tooth surface elastic-hydrodynamic lubrication dimension, gear tooth meshing dimension and gear system heat transfer dimension, and obtains the predicted dry running time of the spiral bevel gear to be predicted.

[0186] This paper proposes a research idea of "lubrication status prediction method for spiral bevel gears facing dry operation needs". It combines the tooth surface load contact theory, elastohydrodynamic lubrication theory and computational fluid dynamics simulation analysis, and establishes a multi-dimensional coupling prediction method of tooth surface elastohydrodynamic lubrication-tooth meshing-gear system heat transfer, revealing the transient evolution mechanism between microscopic elastohydrodynamic lubrication and macroscopic flow field / temperature field during oil loss.

[0187] The present invention addresses the huge time cost issue of applying CFD simulation to analyze the transient temperature field of gears during oil loss. By coupling the steady-state temperature field of the gear meshing scale with the transient temperature field of the gear system, the simulation time is effectively shortened and parameter transfer in three dimensions is achieved.

[0188] Based on the established multi-dimensional coupled prediction model of tooth surface elastohydrodynamic lubrication, gear meshing, and gear system heat transfer, the present invention obtains the transient evolution mechanism of the temperature field of spiral bevel gears during oil loss. Based on the failure temperature of the chemical reaction film under boundary lubrication conditions and the change of temperature over time during the oil loss process, it is determined that the gear meshing has entered a completely dry friction state, thereby realizing dynamic prediction of the dry running time.

[0189] Example 2

[0190] The present invention also discloses a spiral bevel gear dry running time prediction system, such as Figure 9 As shown, a spiral bevel gear dry running time prediction system includes:

[0191] The elastohydrodynamic lubrication key parameter determination module 201 is used to calculate the elastohydrodynamic lubrication key parameters of the spiral bevel gear to be predicted based on the structural parameters and processing parameters of the spiral bevel gear to be predicted.

[0192] The spiral bevel gear elastohydrodynamic lubrication calculation module 202 is used to calculate the pressure distribution, film thickness distribution and temperature distribution of the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters.

[0193] The time-varying friction coefficient determination module 203 is used to obtain the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the process of changing from elastohydrodynamic lubrication to dry friction state under the oil loss state.

[0194] The gearbox multi-dimensional simulation model establishment module 204 is used to establish a gearbox multi-dimensional simulation model based on the pressure distribution, film thickness distribution and temperature distribution in the contact area of the spiral bevel gear during elastohydrodynamic lubrication to be predicted, as well as the time-varying friction coefficient; the gearbox multi-dimensional simulation model includes the tooth surface elastohydrodynamic lubrication dimension, the gear tooth meshing dimension and the gear system heat transfer dimension.

[0195] The temperature change determination module 205 is used to perform a multi-dimensional coupling simulation based on the multi-dimensional simulation model of the gearbox to obtain the temperature change of the spiral bevel gear to be predicted over time.

[0196] The dry running time prediction module 206 is configured to predict the dry running time according to the change in the temperature of the spiral bevel gear to be predicted over time.

[0197] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0198] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for predicting dry running time of spiral bevel gears, characterized in that: include: Calculating key elastohydrodynamic lubrication parameters of the spiral bevel gear to be predicted based on the structural parameters and processing parameters of the spiral bevel gear to be predicted; Calculating the pressure distribution, film thickness distribution and temperature distribution of the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters; Obtaining a time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during a process from elastohydrodynamic lubrication to dry friction under an oil loss state; Based on the pressure distribution, film thickness distribution, and temperature distribution in the contact area of the spiral bevel gear under elastohydrodynamic lubrication to be predicted, as well as the time-varying friction coefficient, a multi-dimensional simulation model of the gearbox is established; the multi-dimensional simulation model of the gearbox includes the elastohydrodynamic lubrication dimension of the tooth surface, the gear meshing dimension, and the gear system heat transfer dimension; Performing a multi-dimensional coupling simulation based on the multi-dimensional simulation model of the gearbox to obtain the change of the temperature of the spiral bevel gear to be predicted over time; Predicting the dry running time according to the change of the temperature of the spiral bevel gear to be predicted over time; The key parameters of elastohydrodynamic lubrication include load distribution, contact area ellipse major axis size, contact area ellipse minor axis size, entrainment velocity and direction angle; The direction clamp is the angle between the entrainment velocity and the direction of the minor axis of the contact area ellipse; The time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during the process from elastohydrodynamic lubrication to dry friction state is expressed as: ； in, f represents the time-varying friction coefficient, is the proportion of elastic fluid dynamic lubrication; f D is the friction coefficient in dry friction state; f B is the average friction coefficient in the boundary lubrication state; f EHL is the friction coefficient in fully lubricated state, Indicates the speed of the spiral bevel gear to be predicted, t Indicates time, Maintain parameters for oil film; Performing a multi-dimensional coupled simulation based on the multi-dimensional simulation model of the gearbox to obtain the change of the temperature of the spiral bevel gear to be predicted over time specifically includes: In the elastohydrodynamic lubrication dimension of the tooth surface, the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the elastohydrodynamic lubrication state, i.e., the oil loss process, is calculated; Substituting the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the elastohydrodynamic lubrication state, i.e., the oil loss process, into the gear meshing dimension, calculating the time-varying friction heat source in the gear meshing process, and combining the time-varying friction heat source with the windage power loss to obtain the total heat generation of the gear; According to the different heat generating locations, the total heat generated is applied to the corresponding locations of the heat transfer dimension of the gear system for simulation to obtain the temperature distribution of the internal flow domain of the spiral bevel gear to be predicted; The average temperature of the internal flow domain is used as the ambient temperature for the gear meshing dimension simulation to obtain the temperature change of the spiral bevel gear to be predicted over time.

2. The method for predicting dry running time of spiral bevel gears according to claim 1, characterized in that: Calculating the pressure distribution, film thickness distribution, and temperature distribution of the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters specifically includes: Based on the key parameters of EHL, the progressive grid refinement method and the multigrid integration method are used to numerically calculate the control equations of the EHL theory of spiral bevel gears, and the pressure distribution, film thickness distribution and temperature distribution in the contact area are obtained.

3. The method for predicting dry running time of spiral bevel gears according to claim 1, characterized in that: In the multi-dimensional simulation model of the gearbox, the friction heat source generated by the tooth surface elastohydrodynamic lubrication dimension is transmitted to the gear tooth meshing dimension and the gear system heat transfer dimension respectively, the ambient temperatures of the gear tooth meshing dimension and the gear system heat transfer dimension are both transmitted to the tooth surface elastohydrodynamic lubrication dimension, the heat source of the gear tooth meshing dimension is transmitted to the gear system heat transfer dimension, and the ambient temperature of the gear system heat transfer dimension is transmitted to the gear tooth meshing dimension.

4. The method for predicting dry running time of spiral bevel gears according to claim 1, characterized in that: The temperature changes over time include the temperature changes over time of the large wheel, the temperature changes over time of the small wheel, the temperature changes over time in the cavity and the temperature changes over time of the casing.

5. The method for predicting dry running time of spiral bevel gears according to claim 4, characterized in that: Predicting the dry running time according to the change of the temperature of the spiral bevel gear to be predicted over time specifically includes: The time corresponding to when the temperature of the small wheel reaches the preset temperature is recorded as the failure time of the spiral bevel gear to be predicted; The dry running time is determined according to the failure time of the spiral bevel gear to be predicted.

6. A spiral bevel gear dry running time prediction system, characterized in that: include: an elastohydrodynamic lubrication key parameter determination module, configured to calculate the elastohydrodynamic lubrication key parameters of the spiral bevel gear to be predicted based on the structural parameters and processing parameters of the spiral bevel gear to be predicted; A spiral bevel gear elastohydrodynamic lubrication calculation module is used to calculate the pressure distribution, film thickness distribution and temperature distribution of the contact area of the spiral bevel gear to be predicted during elastohydrodynamic lubrication based on the key elastohydrodynamic lubrication parameters; A time-varying friction coefficient determination module is used to obtain the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during the process from elastohydrodynamic lubrication to dry friction state in the oil loss state; a gearbox multi-dimensional simulation model establishment module, configured to establish a gearbox multi-dimensional simulation model based on the pressure distribution, film thickness distribution, and temperature distribution in the contact area of the spiral bevel gear under elastohydrodynamic lubrication to be predicted, as well as the time-varying friction coefficient; the gearbox multi-dimensional simulation model includes a tooth surface elastohydrodynamic lubrication dimension, a gear tooth meshing dimension, and a gear system heat transfer dimension; a module for determining temperature changes over time, configured to perform a multi-dimensional coupled simulation based on the multi-dimensional simulation model of the gearbox to obtain temperature changes over time of the spiral bevel gear to be predicted; A dry running time prediction module, configured to predict the dry running time according to the change in temperature of the spiral bevel gear to be predicted over time; The key parameters of elastohydrodynamic lubrication include load distribution, contact area ellipse major axis size, contact area ellipse minor axis size, entrainment velocity and direction angle; The direction clamp is the angle between the entrainment velocity and the direction of the minor axis of the contact area ellipse; The time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted during the process from elastohydrodynamic lubrication to dry friction state is expressed as: ； in, f represents the time-varying friction coefficient, is the proportion of elastic fluid dynamic lubrication; f D is the friction coefficient in dry friction state; f B is the average friction coefficient in the boundary lubrication state; f EHL is the friction coefficient in fully lubricated state, Indicates the speed of the spiral bevel gear to be predicted, t Indicates time, Maintain parameters for oil film; Performing a multi-dimensional coupled simulation based on the multi-dimensional simulation model of the gearbox to obtain the change of the temperature of the spiral bevel gear to be predicted over time specifically includes: In the elastohydrodynamic lubrication dimension of the tooth surface, the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the elastohydrodynamic lubrication state, i.e., the oil loss process, is calculated; Substituting the time-varying friction coefficient of the tooth surface of the spiral bevel gear to be predicted in the elastohydrodynamic lubrication state, i.e., the oil loss process, into the gear meshing dimension, calculating the time-varying friction heat source in the gear meshing process, and combining the time-varying friction heat source with the windage power loss to obtain the total heat generation of the gear; According to the different heat generating locations, the total heat generated is applied to the corresponding locations of the heat transfer dimension of the gear system for simulation to obtain the temperature distribution of the internal flow domain of the spiral bevel gear to be predicted; The average temperature of the internal flow domain is used as the ambient temperature for the gear meshing dimension simulation to obtain the temperature change of the spiral bevel gear to be predicted over time.

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