A gear lubrication reliability evaluation method and system

Abstract

The present invention provides a gear lubrication reliability assessment method and system, which belongs to the technical field of gear lubrication reliability assessment, and includes: respectively obtaining the equivalent radius of curvature, load parameter, speed parameter and material parameter in the gear lubrication system, and further obtaining the minimum film thickness of gear lubrication; constructing a gear lubrication reliability model according to the minimum film thickness and tooth surface roughness; and calculating the failure probability of gear lubrication in the gear lubrication system based on the Monte Carlo method using the gear lubrication reliability model. The present invention solves the minimum film thickness of gear lubrication by using the equivalent radius of curvature, load parameter, speed parameter and material parameter, and constructs a gear lubrication reliability model by combining the minimum film thickness and tooth surface RMS roughness, and uses the model to calculate the failure probability of gear lubrication in the gear lubrication system, without solving complex partial differential equations, and is not only applicable to initial test surfaces that obey Gaussian distribution, but also to non-Gaussian surfaces after wear.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear lubrication reliability assessment, and more specifically, relates to a gear lubrication reliability assessment method and system. Background Art

[0002] It is estimated that about 1 / 2 to 1 / 3 of the world's energy is consumed in various forms of friction. Wear caused by friction is the main cause of mechanical equipment failure, and about 80% of damaged parts are caused by various forms of wear. Effective lubrication is the main way to reduce wear. According to the film thickness ratio, the lubrication state can usually be divided into three types. When λ>3 (λ is the film thickness ratio), the surface roughness peaks do not come into direct contact, and the load is mainly borne by the lubricating oil film, which is called full film lubrication. When 1≤λ≤3, some of the surface roughness peaks come into contact, and the load is borne by the lubricating oil film and the contact surface roughness peaks, which is called mixed lubrication. When λ≤1, most of the surface roughness peaks come into contact, and the load is almost entirely borne by the contact surface roughness peaks. At this time, it is in a boundary lubrication state. In order to reduce wear, reduce friction, and increase service life, the system mechanical transmission works in the full film lubrication range. However, due to the differences in the machining accuracy of the contact surface of the mechanical transmission, the properties of the lubricant, and the changes in the operating conditions, full film lubrication cannot be guaranteed at all times, resulting in lubrication failure.

[0003] The essence of the objective world is uncertainty. The uncertainty of the gear lubrication system is reflected in the structural dimensions of the mechanical transmission, the physical parameters of the material, and external excitations. Under the influence of these uncertain factors, the lubrication state is no longer a definite value, but a random variable or a random process. In order to study the lubrication state of mechanical transmission and the probability of lubrication failure under the action of uncertain parameters, the concept of lubrication reliability needs to be introduced. At present, the existing lubrication reliability evaluation methods, such as CN115310331A, a method for determining the lubrication state of a friction pair under fluid lubrication conditions, rely on a complex elastohydrodynamic lubrication numerical model, which requires solving cumbersome partial differential equations, and is not suitable for non-Gaussian surfaces with wear, and the evaluation effect of lubrication reliability is poor. Summary of the invention

[0004] In order to overcome the deficiencies of the prior art, an object of the present invention is to provide a gear lubrication reliability assessment method and system.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A gear lubrication reliability assessment method, comprising:

[0007] Step 1: Obtain the equivalent radius of the contact point in the gear lubrication system;

[0008] Step 2: Determine an equivalent curvature radius expression according to the contact point equivalent radius;

[0009] Step 3: deriving a load parameter expression in the gear lubrication system using a gear dynamics model;

[0010] Step 4: Determine the speed parameter expression according to the speed in the gear lubrication system;

[0011] Step 5: Determine the material parameter expression according to the equivalent elastic quantity and viscosity-pressure coefficient in the gear lubrication system;

[0012] Step 6: Obtaining the minimum film thickness of gear lubrication according to the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression;

[0013] Step 7: constructing a gear lubrication reliability model using the minimum film thickness of the gear lubrication and the RMS roughness of the tooth surface;

[0014] Step 8: Using the reliability model of gear lubrication, the failure probability of lubrication at each meshing point of the gear is obtained by using the Monte Carlo method from the probability density function of the gear parameters.

[0015] Preferably, the step 2: determining an equivalent curvature radius expression according to the contact point equivalent radius comprises:

[0016] Using the formula:

[0017]

[0018] r1=R b1 tan(α)+S p

[0019] r2=R b2 tan(α)-S p

[0020] Determine the equivalent radius of curvature expression; where r is the equivalent radius of curvature expression, R b1 is the base radius of the driving wheel, R b2 is the base circle radius of the driven wheel, α is the pitch circle pressure angle, S P is the distance from the meshing point to the node.

[0021] Preferably, the step 3: using a gear dynamics model to obtain a load parameter expression in the gear lubrication system includes:

[0022] Step 3.1: Construct the dynamic equation of the gear dynamic model according to Newton's theorem; wherein the dynamic equation is:

[0023]

[0024] Among them, m e is the equivalent mass of the gear pair, x represents the relative displacement of the gear, c is the meshing damping, k(t) is the time-varying meshing stiffness, e represents the static transmission error, g(x) is the nonlinear function of x, and j bn is the side clearance, F m is the equivalent driving force;

[0025] Step 3.2: Solve the dynamic equation to obtain the load parameter expression.

[0026] Preferably, the step 3.2: solving the kinetic equation to obtain a load parameter expression comprises:

[0027] Step 3.2.1: Use Ishikawa method to solve the meshing stiffness;

[0028] Step 3.2.2: Solve the meshing damping based on the meshing stiffness;

[0029] Step 3.2.3: Solve the dynamic equation using the meshing stiffness and the meshing damping to obtain a load parameter expression.

[0030] Preferably, the step 3.2.2: solving the meshing damping based on the meshing stiffness comprises:

[0031] Using the formula:

[0032]

[0033]

[0034] Determine the meshing damping; where c is the meshing damping, ζ is the damping ratio; k m is the average meshing stiffness in one meshing cycle, t c is the meshing period, and k(t) is the time-varying meshing stiffness.

[0035] Preferably, the load parameter expression is:

[0036]

[0037]

[0038] Among them, w t is the meshing force on a single tooth, k1(t) is the meshing stiffness of a single pair of teeth, is the load parameter expression, e′ is the equivalent elastic modulus, and r is the equivalent contact radius.

[0039]

[0040]

[0041] Where r1 and r2 are the curvature radii of the tooth surfaces of the driving wheel and the driven wheel at the contact point, υ1 and υ2 are the Poisson ratios of the driving wheel and the driven wheel on the contact surface, and e1 and e2 are the elastic moduli of the driving wheel and the driven wheel on the contact surface.

[0042] Preferably, the step 4: determining the speed parameter expression according to the rotation speed in the gear lubrication system comprises:

[0043] The speed parameter expression is determined according to the rotation speeds of the driving wheel and the driven wheel in the gear lubrication system; wherein the speed parameter expression is:

[0044]

[0045] u=(u1+u2) / 2

[0046] u1=ω1r1

[0047] u2=ω2r2

[0048] Among them, ω1 is the speed of the driving wheel, ω2 is the speed of the driven wheel, is the speed parameter expression, η0 is the lubricant environmental viscosity.

[0049] Preferably, in step 5, the material parameter expression is:

[0050]

[0051] in, is the material parameter expression, e' is the equivalent elastic quantity, and α is the viscosity-pressure coefficient.

[0052] The above parameters can be used to obtain the minimum film thickness of gear lubrication at each meshing point.

[0053]

[0054] Preferably, the gear lubrication reliability model is:

[0055] g f (H min ,∑)=H min -3Σ

[0056] Substituting the minimum film thickness formula into the formula, it can be written as:

[0057] g f (R,W,U,G,Σ,S k )=3.4RW -0.095 U 0.71 G 0.57[1+0.0027(Σ) 1.075 (S k +2) -0.3744 W 0.09451 U -0.974 G -0.806 ]-3Σ

[0058] Where R is the probability density function of the equivalent curvature radius expression, W is the probability density function of the load parameter expression, U is the probability density function of the velocity parameter expression, G is the probability density function of the material parameter expression, ∑ is the dimensionless comprehensive RMS roughness, S k is the skewness.

[0059] The present invention also provides a gear lubrication reliability evaluation system, comprising:

[0060] A contact point equivalent radius acquisition module is used to obtain the contact point equivalent radius in the gear lubrication system;

[0061] An equivalent curvature radius expression determination module is used to determine an equivalent curvature radius expression according to the contact point equivalent radius;

[0062] A load parameter expression solving module, used for obtaining the load parameter expression in the gear lubrication system by using a gear dynamics model;

[0063] A speed parameter expression determination module, used to determine a speed parameter expression according to a rotation speed in a gear lubrication system;

[0064] A material parameter expression determination module is used to determine the material parameter expression according to the equivalent elastic quantity and the viscosity-pressure coefficient in the gear lubrication system;

[0065] A minimum film thickness determination module, used for obtaining the minimum film thickness according to the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression;

[0066] Reliability model building module, used to build a gear lubrication reliability model based on minimum film thickness and tooth surface roughness;

[0067] The failure probability calculation module is used to calculate the failure probability of gear lubrication in the gear lubrication system using the gear lubrication reliability model.

[0068] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps in the above-mentioned gear lubrication reliability assessment method are implemented.

[0069] The beneficial effect of a gear lubrication reliability evaluation method provided by the present invention is that: compared with the prior art, the present invention solves the minimum film thickness of gear lubrication by utilizing an equivalent curvature radius expression, a load parameter expression, a speed parameter expression and a material parameter expression, constructs a gear lubrication reliability model by utilizing the minimum film thickness and RMS roughness, and utilizes the model to calculate the failure probability of gear lubrication in the gear lubrication system. It does not require solving complex partial differential equations and is not only applicable to initial test surfaces that obey a Gaussian distribution, but also to non-Gaussian surfaces after wear. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.

[0071] Figure 1 A flow chart of a gear lubrication reliability assessment method provided by an embodiment of the present invention;

[0072] Figure 2 A schematic diagram of a gear lubrication reliability assessment method provided by an embodiment of the present invention;

[0073] Figure 3 A schematic diagram of the lubrication state of a gear provided by an embodiment of the present invention;

[0074] Figure 4 A schematic diagram of a gear dynamics model provided by an embodiment of the present invention;

[0075] Figure 5 A schematic diagram of geometric parameters of Ishikawa gears provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0076] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0077] See also Figure 1-2 To achieve the above purpose, the technical solution adopted by the present invention is: a gear lubrication reliability evaluation method, comprising:

[0078] Step 1: Obtain the equivalent radius of the contact point in the gear lubrication system;

[0079] Step 2: Determine an equivalent curvature radius expression according to the contact point equivalent radius;

[0080] Furthermore, the step 2 comprises:

[0081] Using the formula:

[0082]

[0083] r1=R b1 tan(α)+S p

[0084] r2=R b2 tan(α)-S p

[0085] Determine the equivalent radius of curvature expression; where r is the equivalent radius of curvature expression, R b1 is the base radius of the driving wheel, R b2 is the base circle radius of the driven wheel, α is the pitch circle pressure angle, S P is the distance from the meshing point to the node.

[0086] Step 3: deriving a load parameter expression in the gear lubrication system using a gear dynamics model;

[0087] Furthermore, the step 3 comprises:

[0088] Step 3.1: Construct the dynamic equation of the gear dynamic model according to Newton's theorem; wherein the dynamic equation is:

[0089]

[0090] Among them, m e is the equivalent mass of the gear pair, x represents the relative displacement of the gear, c is the meshing damping, k(t) is the time-varying meshing stiffness, e represents the static transmission error, g(x) is the nonlinear function of x, and j bn is the side clearance, F m is the equivalent driving force;

[0091] Step 3.2: Solve the dynamic equation to obtain the load parameter expression.

[0092] Among them, step 3.2 includes:

[0093] Step 3.2.1: Use Ishikawa method to solve the meshing stiffness;

[0094] Step 3.2.2: Solve the meshing damping based on the meshing stiffness; wherein the meshing damping calculation formula is:

[0095]

[0096]

[0097] Where c is the meshing damping, ζ is the damping ratio; k m is the average meshing stiffness in one meshing cycle, t c is the meshing period, and k(t) is the time-varying meshing stiffness.

[0098] Step 3.2.3: Solve the dynamic equation using the meshing stiffness and the meshing damping to obtain a load parameter expression. The load parameter expression is:

[0099]

[0100]

[0101] Among them, w t is the meshing force on a single tooth, k1(t) is the meshing stiffness of a single pair of teeth, is the load parameter expression, e′ is the equivalent elastic modulus, and r is the equivalent contact radius.

[0102]

[0103]

[0104] Where r1 and r2 are the curvature radii of the tooth surfaces of the driving wheel and the driven wheel at the contact point, υ1 and υ2 are the Poisson ratios of the two contact surfaces, and e1 and e2 are the elastic moduli of the two contact surfaces.

[0105] Step 4: Determine a speed parameter expression according to the rotation speed in the gear lubrication system; wherein the speed parameter expression is:

[0106]

[0107] u=(u1+u2) / 2

[0108] u1=ω1r1

[0109] u2=ω2r2

[0110] In the formula, ω1 is the speed of the driving wheel, ω2 is the speed of the driven wheel, is the speed parameter expression, η0 is the lubricant environmental viscosity.

[0111] Step 5: Determine the material parameter expression based on the equivalent elasticity and viscosity-pressure coefficient in the gear lubrication system; the material parameter expression is:

[0112]

[0113] in, is the material parameter expression, e' is the equivalent elastic quantity, and α is the viscosity-pressure coefficient.

[0114] Step 6: Obtaining the minimum film thickness of gear lubrication according to the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression;

[0115] Furthermore, from the above parameters, the minimum film thickness of gear lubrication at each meshing point can be obtained as:

[0116]

[0117] Step 7: constructing a gear lubrication reliability model using the minimum film thickness of the gear lubrication and the RMS roughness of the tooth surface;

[0118] Step 8: Using the reliability model of gear lubrication, the failure probability of lubrication at each meshing point of the gear is obtained by using the Monte Carlo method from the probability density function of the gear parameters.

[0119] It should be noted that the construction of the lubrication reliability model in the present invention utilizes the concept of film thickness ratio in the hybrid elastohydrodynamic lubrication theory. The film thickness ratio refers to the ratio of the film thickness (usually the minimum film thickness) to the comprehensive RMS roughness, which is usually expressed by λ and is expressed as follows:

[0120]

[0121] like Figure 3 As shown in the figure, lubrication can be divided into three states according to the film thickness ratio: full film lubrication, mixed lubrication and boundary lubrication. When λ>3, the surface roughness peaks do not come into direct contact, and the load is mainly borne by the lubricating oil film, which is called full film lubrication. When 1≤λ≤3, some of the surface roughness peaks come into contact, and the load is borne by the lubricating oil film and the contact surface roughness peaks, which is called mixed lubrication. When λ≤1, most of the surface roughness peaks come into contact, and the load is almost entirely borne by the contact surface roughness peaks, which is in the boundary lubrication state. Full film lubrication can completely separate the contact surface. In theory, the contact surface will not produce wear. In engineering, it is hoped that the contact is always in the full film lubrication state. However, due to the time-varying and random nature of external excitation, the geometric characteristics of the contact surface, the performance of the lubricant, etc., full film lubrication is often difficult to guarantee all the time and the lubrication state has a certain randomness.

[0122] Based on the concept of film thickness ratio, the reliability of full film lubrication and mixed lubrication are defined as the ratio of the minimum film thickness to the equivalent RMS roughness. The function of full film lubrication is:

[0123] g f (H min ,∑)=H min -3Σ (2)

[0124] In the formula, Hmin is the minimum film thickness, ∑ is the comprehensive RMS roughness, where the minimum film thickness and comprehensive RMS roughness are capitalized to indicate that they are random variables. In lubrication reliability modeling, the film thickness of the lubricant is equivalent to stress, and the RMS roughness of the rough surface is equivalent to strength.

[0125] The failure probability of full film lubrication is:

[0126] p ff =Pr[g f (H min ,Σ)≤0] (3)

[0127] The functional function of mixed lubrication is:

[0128] g m (H min ,Σ)=H min -∑ (4)

[0129] The failure probability of mixed lubrication is:

[0130] p mf =Pr[g m (H min ,Σ)≤0] (5)

[0131] It can be seen from equations (2) and (4) that if the statistical laws of the minimum film thickness and the comprehensive RMS roughness are known, the failure probability of lubrication can be obtained. The statistical law of the comprehensive RMS roughness of the contact surface can be obtained by measuring and statistically analyzing a large number of samples; the statistical law of the minimum film thickness must be obtained through the hybrid elastohydrodynamic lubrication analysis and the statistical law of basic random variables. In addition, according to the classical lubrication theory, when the film thickness is reduced to the point where the surface roughness peaks come into direct contact, it can be considered that the lubrication fails, that is, the failure of the full film lubrication; therefore, the lubrication failure in the present invention is defined as the failure of the full film lubrication.

[0132] The minimum film thickness of gear lubrication and the definition of lubrication reliability given by the present invention can obtain the functional function of gear lubrication reliability:

[0133] g f (H min ,∑)=H min -3Σ

[0134] Substituting the minimum film thickness formula into the formula, it can be written as:

[0135]

[0136] Where R is the dimensionless equivalent radius of curvature, W is the load parameter, U is the velocity parameter, G is the material parameter, ∑ is the dimensionless comprehensive RMS, S k is the skewness. The parameters here are all capitalized to indicate that they are random variables.

[0137] It should be noted that the equivalent curvature radius r and load parameter given in the above steps are Speed ​​Parameters and material parameters It is a solution method when the gear structure dimensions and material physical parameters are all fixed values, while in reliability analysis these parameters are all random variables. Capital letters are used here to indicate that these parameters are all random variables. Due to the uncertainty in processing and manufacturing, the geometric and material parameters of the gears have a certain randomness. It can be seen from the above-mentioned equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression that these parameters are all functions of the gear material parameters and geometric parameters, so they are all random. This method can solve the reliability of gear lubrication when the gear geometric and material parameters such as module, tooth width, moment of inertia of the master and driven wheels, elastic model of the material, amplitude of static transmission error, RMS roughness, etc. are known. Furthermore, when r is known, and After obtaining the expressions of , gear structure dimensions and probability density functions of material parameters, the probability density functions of R, W, U and G can be obtained by the Monte Carlo method for reliability solution.

[0138] The specific calculation process is as follows:

[0139] (1) The expression of equivalent curvature radius is:

[0140]

[0141] Where r1 and r2 are the equivalent radii of the contact points:

[0142] r1=R b1 tan(α)+S p (8)

[0143] r2=R b2 tan(α)-S p (9)

[0144] In the formula, R b1 and R b2 are the base circle radii of the driving wheel and the driven wheel respectively; α is the pressure angle of the pitch circle; S P is the distance from the meshing point to the node.

[0145] (2) The load parameter expression in the present invention can be obtained through the gear dynamics model.

[0146] like Figure 4As shown, the present invention uses a dynamic model to simplify the gear pair into two discs, the masses of the discs are equal to the masses of the master and driven wheels, and the interaction between the gear teeth is simulated by a massless spring and damper.

[0147] According to Newton's theorem, the dynamic equation of the gear pair can be obtained:

[0148]

[0149] Where I1 and I2 are the moments of inertia of the active and passive gears; θ1 and θ2 represent the torsional displacement of the active and passive gears; ˙ and ¨ represent the first and second order derivatives, respectively; R b1 and R b2 represents the base circle radius of the active and passive gears; c is the meshing damping; e represents the static transmission error; k(t) is the time-varying meshing stiffness; T1 and T2 are the input and output torques, respectively.

[0150] The relative displacement of the gear (hereinafter referred to as displacement, and its first-order and second-order derivatives are referred to as velocity and acceleration respectively) is defined as x = R b1 θ1-R b2 θ2-e, Equation 10) can be written as:

[0151]

[0152] In the formula, m e is the equivalent mass of the gear pair; g(x) is a nonlinear function of x; j bn F is the side clearance, which is used to ensure lubrication and prevent seizure caused by thermal deformation; m is the equivalent driving force, which is a constant value in the present invention. Their expressions are:

[0153]

[0154] The meshing stiffness is solved by the Ishikawa method, and the deformation of the load point along the meshing line can be expressed as:

[0155] δ=δ br +δ bt +δ s +δ g (14)

[0156] Where δ is the deformation at the load point, δ br is the bending deformation of the rectangular part, δ bt is the deformation of the trapezoidal part, δ s is the shear deformation, δ g It is the deformation caused by the tilt of the foundation.

[0157] The bending deformation of the rectangular part can be expressed as:

[0158]

[0159] In the formula, F n represents the normal load, ω x is the load angle, l is the gear tooth width, S F ,h x ,h r are geometric parameters, such as Figure 5 shown.

[0160] The deformation of the trapezoidal part is:

[0161]

[0162] In the formula,

[0163]

[0164]

[0165] Where x is the displacement coefficient, θ is the gear angle, and z is the number of teeth; θ1, z1, and x1 are used to solve the deformation of the driving wheel; θ2, z2, and x2 are used to solve the deformation of the driven wheel; and α is the pressure angle.

[0166] The deformation due to shear can be defined as:

[0167]

[0168] The deformation caused by the tilt of the foundation is:

[0169]

[0170] The total deformation along the meshing line when the gears are meshing is the sum of the deformation of the driving wheel, the deformation of the driven wheel and the contact deformation, which can be expressed as:

[0171] δ Σ =δ1+δ2+δ pv (twenty one)

[0172] In the formula, δ1 and δ2 represent the deformation of the driving wheel and the driven wheel respectively, which are solved by formula (14); δ pv For contact deformation, it can be obtained according to Hertz contact theory:

[0173]

[0174] The position parameters in the above equations can be obtained by geometric analysis of the gear teeth. The detailed analysis process can be found in the following figure. It can be noted that the deformation obtained by the Ishikawa method is a function of the rotation angle θ, which can be converted into a function of time under a given gear speed:

[0175]

[0176] During the meshing process of a gear pair, a damping effect will occur due to the material properties, friction between teeth, and lubrication. The influencing factors of this damping are numerous and complex, and usually cannot be accurately described. It is generally simplified to a function of equivalent mass and average meshing stiffness:

[0177]

[0178] Where ζ is the damping ratio; k m is the average meshing stiffness within a meshing cycle, and its expression is:

[0179]

[0180] Where, t c is the meshing period, and its expression is:

[0181] When the gears are meshing, the deviation between the actual meshing position and the theoretical meshing position along the meshing line is called static transmission error. It is caused by errors in gear processing and assembly and elastic deformation of gear teeth, shafts and bearings, and is a high-frequency internal excitation. In gear dynamics, it can be described as a periodic displacement excitation of the meshing point along the meshing line. It is generally assumed to be a simple harmonic function. This article uses a sine function to describe it:

[0182]

[0183] In the formula, e r is the amplitude of the static transmission error, which is usually between 1 μm and 10 μm and is a random variable obeying a Gaussian distribution in the present invention; is the phase angle.

[0184] After solving the above dynamic equations, the meshing force on a single tooth of the driving wheel can be obtained by the following formula:

[0185]

[0186] In the formula, w t is the meshing force on a single tooth, k1(t) is the meshing stiffness of a single pair of teeth, that is, the stiffness of a single gear tooth from the meshing point to the meshing point, and the load parameter expression is:

[0187]

[0188] (3) Speed ​​parameter expression

[0189] When the gears are meshing, there is relative sliding at each meshing point on the gear teeth, and only at the nodes is there pure rolling. The instantaneous tangential velocity on the master and driven wheels at each meshing point can be obtained by the following formula:

[0190] u1=ω1r1 (28)

[0191] u2=ω2r2 (29)

[0192] Where ω1 and ω2 are the rotation speeds of the driving wheel and the driven wheel respectively.

[0193] The entrainment velocity of lubrication can be obtained by the following formula:

[0194] u=(u1+u2) / 2 (30)

[0195] The speed parameter expression is defined as:

[0196]

[0197] (4) Material parameter expression is:

[0198]

[0199] e' is the equivalent elasticity and α is the viscosity-pressure coefficient.

[0200] The comprehensive RMS roughness and skewness S of the contact surface in the gear lubrication reliability model k Statistical laws are obtained through measurement statistics of a large number of samples.

[0201] The above is the solution method for equivalent curvature radius, speed parameter, load parameter and material parameter when the structural and material parameters are all fixed values. When the gear module, tooth width, moment of inertia of the master and slave wheels, elastic model of the material and amplitude of the static transmission error are all random variables and the probability density function is known, the probability density function of R, W, U and G can be obtained according to the Monte Carlo method. Substituting into the gear lubrication reliability model, the failure probability of gear lubrication can be obtained.

[0202] The present invention constructs a gear lubrication reliability model by utilizing the probability density functions of the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression, and utilizes the model to calculate the failure probability of gear lubrication in the gear lubrication system. The reliability of gear lubrication can be evaluated without solving complex partial differential equations. The model is applicable not only to initial test surfaces that obey Gaussian distribution, but also to non-Gaussian surfaces after wear.

[0203] The present invention also provides a gear lubrication reliability evaluation system, comprising:

[0204] A contact point equivalent radius acquisition module is used to obtain the contact point equivalent radius in the gear lubrication system;

[0205] An equivalent curvature radius expression determination module is used to determine an equivalent curvature radius expression according to the contact point equivalent radius;

[0206] A load parameter expression solving module, used for obtaining the load parameter expression in the gear lubrication system by using a gear dynamics model;

[0207] A speed parameter expression determination module, used to determine a speed parameter expression according to a rotation speed in a gear lubrication system;

[0208] A material parameter expression determination module is used to determine the material parameter expression according to the equivalent elastic quantity and the viscosity-pressure coefficient in the gear lubrication system;

[0209] A probability density function calculation module, used for respectively obtaining the probability density functions of the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression by using the Monte Carlo method;

[0210] A reliability model building module, used to build a gear lubrication reliability model according to the probability density function of the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression;

[0211] The failure probability calculation module is used to calculate the failure probability of gear lubrication in the gear lubrication system using the gear lubrication reliability model.

[0212] Compared with the prior art, the beneficial effects of a gear lubrication reliability assessment system provided by the present invention are the same as the beneficial effects of a gear lubrication reliability assessment method described in the above technical solution, which will not be elaborated here.

[0213] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps in the above-mentioned gear lubrication reliability assessment method are implemented.

[0214] Compared with the prior art, the beneficial effects of a computer-readable storage medium provided by the present invention are the same as the beneficial effects of a gear lubrication reliability assessment method described in the above technical solution, and will not be elaborated here.

[0215] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A gear lubrication reliability assessment method, characterized in that: include: Step 1: Obtain the equivalent radius of the contact point in the gear lubrication system; Step 2: Determine an equivalent curvature radius expression according to the contact point equivalent radius; Step 3: deriving a load parameter expression in the gear lubrication system using a gear dynamics model; Step 4: Determine the speed parameter expression according to the speed in the gear lubrication system; Step 5: Determine the material parameter expression according to the equivalent elastic quantity and viscosity-pressure coefficient in the gear lubrication system; Step 6: Obtaining the minimum film thickness of gear lubrication according to the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression; Step 7: constructing a gear lubrication reliability model using the minimum film thickness of the gear lubrication and the RMS roughness of the tooth surface; The gear lubrication reliability model is: g f (H min ,∑)=H min -3Σ Substituting the minimum film thickness formula into it can be written as: g f (R,W,U,G,Σ,S k )=3.4RW -0.095 U 0.71 G 0.57 [1+0.0027(Σ) 1.075 (S k +2) -0.3744 W 0.09451 U -0.974 G -0.806 ]-3S Where R is the probability density function of the equivalent curvature radius expression, W is the probability density function of the load parameter expression, U is the probability density function of the velocity parameter expression, G is the probability density function of the material parameter expression, ∑ is the dimensionless comprehensive RMS roughness, S k is the skewness, H min is the minimum film thickness, and the probability density functions of R, W, U and G are obtained by Monte Carlo method for reliability solution; Step 8: Using the reliability model of gear lubrication, the failure probability of lubrication at each meshing point of the gear is obtained by using the Monte Carlo method from the probability density function of the gear parameters.

2. A gear lubrication reliability evaluation method according to claim 1, characterized in that: The step 2: determining an equivalent curvature radius expression according to the contact point equivalent radius, comprises: Using the formula: r1=R b1 tan(α)+S p r2=R b2 tan(α)-S p Determine the equivalent radius of curvature expression; where r is the equivalent radius of curvature expression, R b1 is the base radius of the driving wheel, R b2 is the base circle radius of the driven wheel, α is the pitch circle pressure angle, S P is the distance from the meshing point to the node.

3. A gear lubrication reliability evaluation method as claimed in claim 2, characterized in that: The step 3: using the gear dynamics model to obtain the load parameter expression in the gear lubrication system includes: Step 3.1: Construct the dynamic equation of the gear dynamic model according to Newton's theorem; wherein the dynamic equation is: Among them, m e is the equivalent mass of the gear pair, x represents the relative displacement of the gear, c is the meshing damping, k(t) is the time-varying meshing stiffness, e represents the static transmission error, g(x) is the nonlinear function of x, and j bn is the side clearance, F m is the equivalent driving force; Step 3.2: Solve the dynamic equation to obtain the load parameter expression.

4. A gear lubrication reliability evaluation method as claimed in claim 3, characterized in that: The step 3.2: solving the dynamic equation to obtain a load parameter expression includes: Step 3.2.1: Use Ishikawa method to solve the meshing stiffness; Step 3.2.2: Solve the meshing damping based on the meshing stiffness; Step 3.2.3: Solve the dynamic equation using the meshing stiffness and the meshing damping to obtain a load parameter expression.

5. A gear lubrication reliability evaluation method as claimed in claim 4, characterized in that: The step 3.2.2: solving the meshing damping based on the meshing stiffness, comprises: Using the formula: Determine the meshing damping; where c is the meshing damping, ζ is the damping ratio; k m is the average meshing stiffness in one meshing cycle, t c is the meshing period, and k(t) is the time-varying meshing stiffness.

6. A gear lubrication reliability evaluation method as claimed in claim 5, characterized in that: The load parameter expression is: Among them, w t is the meshing force on a single tooth, k1(t) is the meshing stiffness of a single pair of teeth, is the load parameter expression, e′ is the equivalent elastic modulus, r is the equivalent contact radius, Where r1 and r2 are the curvature radii of the tooth surfaces of the driving wheel and the driven wheel at the contact point, υ1 and υ2 are the Poisson ratios of the driving wheel and the driven wheel on the contact surface, and e1 and e2 are the elastic moduli of the driving wheel and the driven wheel on the contact surface.

7. A gear lubrication reliability evaluation method according to claim 6, characterized in that: The step 4: determining a speed parameter expression according to the speed in the gear lubrication system includes: The speed parameter expression is determined according to the rotation speeds of the driving wheel and the driven wheel in the gear lubrication system; wherein the speed parameter expression is: u=(u1+u2) / 2 u1=ω1r1 u2=ω2r2 Among them, ω1 is the speed of the driving wheel, ω2 is the speed of the driven wheel, u is the speed parameter expression, and η0 is the environmental viscosity of the lubricant.

8. A gear lubrication reliability evaluation method according to claim 7, characterized in that: In step 5, the material parameter expression is: in, is the material parameter expression, e' is the equivalent elastic quantity, and α is the viscosity-pressure coefficient.

9. A gear lubrication reliability assessment system, characterized in that: include: A contact point equivalent radius acquisition module is used to obtain the contact point equivalent radius in the gear lubrication system; An equivalent curvature radius determination module is used to determine an equivalent curvature radius expression according to the contact point equivalent radius; A load parameter solving module, used for obtaining a load parameter expression in the gear lubrication system by using a gear dynamics model; A speed parameter determination module, used for determining a speed parameter expression according to a rotation speed in a gear lubrication system; A material parameter determination module is used to determine a material parameter expression according to an equivalent elastic quantity and a viscosity-pressure coefficient in a gear lubrication system; A minimum film thickness determination module, used for obtaining the minimum film thickness according to the equivalent curvature radius expression, the load parameter expression, the speed parameter expression and the material parameter expression; Reliability model building module, used to build a gear lubrication reliability model based on minimum film thickness and tooth surface roughness; The gear lubrication reliability model is: g f (H min ,∑)=H min -3Σ Substituting the minimum film thickness formula into it can be written as: g f (R,W,U,G,Σ,S k )=3.4RW -0.095 U 0.71 G 0.57 [1+0.0027(Σ) 1.075 (S k +2) -0.3744 W 0.09451 U -0.974 G -0.806 ]-3S Where R is the probability density function of the equivalent curvature radius expression, W is the probability density function of the load parameter expression, U is the probability density function of the velocity parameter expression, G is the probability density function of the material parameter expression, ∑ is the dimensionless comprehensive RMS roughness, S k is the skewness, H min is the minimum film thickness, and the probability density functions of R, W, U and G are obtained by Monte Carlo method for reliability solution; The failure probability calculation module is used to calculate the failure probability of gear lubrication in the gear lubrication system using the gear lubrication reliability model.

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