Gear tooth surface wear prediction method based on interface characteristics

Abstract

The invention discloses a gear tooth surface wear prediction method based on interface characteristics, and belongs to the technical field of gears. According to the gear tooth surface wear prediction method based on the interface characteristics, the tooth surface morphology evolution is dynamically represented through the fractal theory, and the roughness change in the wear process is quantified; contact interface parameters and interface characteristics are introduced, a time-varying friction model and a translation-torsion coupling dynamic model are combined, the coupling effect of tooth surface morphology, lubricating conditions and dynamic loads is comprehensively considered, the limitation that a traditional model ignores multi-factor coupling is broken through, and a scientific basis is provided for reliability design and service life prediction of a gear system; and the method has important engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of gears, and particularly to a method for predicting gear tooth surface wear based on interface characteristics. Background Technique

[0002] During the actual operation process, gears are in complex working conditions such as high speed, heavy load, and poor lubrication for a long time, and inevitably, tooth surface friction and wear problems will occur. Among them, slight wear, as the initial process of wear failure, its progressive development often leads to more serious failure forms. During the operation of the gear transmission system, the metal contact surfaces of the meshing pairs are not ideally smooth, and there is still local contact between asperities even under lubricated conditions. This microscopic-scale contact behavior will significantly affect the interface characteristics of the system. Therefore, in-depth study of tooth surface contact and friction characteristics has important engineering application value for accurate prediction of tooth surface wear.

[0003] Compared with experimental research with high cost and long cycle, many scholars have adopted an economical and efficient research method of calculating the tooth surface wear amount through theoretical modeling, and have carried out a lot of meaningful work on tooth surface wear prediction. However, most of the current work separately considers the effects of tooth surface topography, lubrication, and dynamic load on tooth surface wear, but rarely comprehensively considers the coupling effects among tooth surface topography, lubrication, dynamic load, and tooth surface wear, making it difficult to accurately characterize the interface characteristics and their evolution under the tooth surface wear state, resulting in a large difference between the predicted tooth surface wear and the actual tooth surface wear damage phenomenon.

[0004] Based on this, a method for predicting gear tooth surface wear based on interface characteristics is proposed, which comprehensively considers the coupling effects among tooth surface topography, lubrication, dynamic load, and tooth surface wear. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting gear tooth surface wear based on interface characteristics to solve the problems in the background technique.

[0006] To achieve the above purpose, the present invention provides a method for predicting gear tooth surface wear based on interface characteristics, including the following steps:

[0007] S1. For the gear transmission system composed of gear pairs, set geometric parameters, working condition parameters, and lubrication parameters;

[0008] Among them, the geometric parameters include the number of teeth, mass, module, pressure angle, Young's modulus, tooth width, addendum coefficient, clearance coefficient, and Poisson's ratio; the working condition parameters include the input rotational speed and load torque; the lubrication parameters include dynamic viscosity and viscosity-pressure coefficient;

[0009] S2. Based on the fractal theory, use the tooth surface topography characterization function to simulate the evolution in the process of tooth surface wear accumulation, obtain the numerical characterization of the tooth surface topography, and further obtain the tooth surface roughness;

[0010] S3. Introduce the dynamic relationship between the contact interface parameters and the friction coefficient, construct a time-varying friction model that comprehensively considers the tooth surface topography evolution, lubrication conditions and dynamic loads, and calculate the tooth surface friction force arm and the friction coefficient and friction force based on the tooth surface contact load;

[0011] The contact interface parameters include fractal dimension, characteristic scale coefficient, composite roughness, equivalent tooth surface roughness, lubricating film thickness ratio, viscosity-pressure coefficient, dynamic viscosity, equivalent elastic modulus, dimensionless load parameter, dimensionless material parameter, dimensionless tooth surface topography parameter, unit normal load;

[0012] S4. Incorporate the contact interface characteristics and their evolution into the tooth surface wear effect, establish a translational-torsional coupling dynamic model of the gear transmission system based on the tooth surface wear effect, and calculate the tooth surface contact load;

[0013] The contact interface characteristics are the comprehensive characteristics exhibited by the gear contact interface during the wear process, including topography roughening, lubrication state transition, non-uniform wear distribution, friction characteristics, and dynamic load effect;

[0014] S5. Comprehensively consider the effects of tooth surface topography, lubrication conditions and dynamic loads, construct a tooth surface wear prediction model to predict the tooth surface wear amount at all meshing points;

[0015] S6. Gradually increase the number of wear cycles until the tooth surface wear amount reaches the preset threshold;

[0016] S7. Update the tooth surface topography, loop through S1-S6, and superimpose the tooth surface wear amounts obtained from each update of the tooth surface topography until the wear amount at any meshing point on the tooth surface reaches the allowable maximum wear amount, realizing the prediction of the gear tooth surface wear amount.

[0017] Preferably, the tooth surface topography characterization function in S2 is:

[0018]

[0019] In the formula, z(x) is the tooth surface profile height, x is the position coordinate along the tooth profile direction, D is the fractal dimension, G is the characteristic scale coefficient of the profile height value, R ai represents the initial machining surface roughness, n is the spatial frequency coefficient, n s is the ordinal number corresponding to the lowest cut-off frequency, γ is a constant with a value of 1.5, ψ n is a random phase between 0 and 2π.

[0020] Preferably, in S3, for different teeth of the driving wheel and different teeth of the driven wheel in the gear transmission system, the calculation of the friction force arm on the tooth surface is carried out, and the calculation formula is:

[0021]

[0022] In the formula, L p1 (t) and L p2 (t) are both the friction force arms of the tooth surface friction force on the driving wheel relative to the center of the wheel shaft at time t, L g1 (t) and L g2 (t) are both the friction force arms of the tooth surface friction force on the driven wheel relative to the center of the wheel shaft at time t, r bi , i = p, g represents the base circle radius of the driving wheel or the driven wheel, mod(·) represents the modulo operation, ω p is the rotational speed of the driving wheel; α jp , j = B, D, E represents the pressure angle of the driving wheel at point j.

[0023] Preferably, in S3, considering the influence of tooth surface topography evolution, lubrication conditions and dynamic loads, the calculation of the time-varying friction coefficient and friction force on the tooth surface based on the tooth surface contact load is carried out, and the calculation formula is:

[0024]

[0025] In the formula, f(t) is the time-varying tooth surface friction force, μ(t) is the time-varying friction coefficient, F′(t) is the tooth surface contact load, R ae (t) is the equivalent tooth surface roughness, η is the dynamic viscosity of the lubricating oil, w e (t) represents the unit normal load at the meshing point, v s (t) represents the tooth surface slip speed, v e (t) is the entrainment speed.

[0026] Preferably, the calculation formulas for the equivalent tooth surface roughness, the unit normal load at the meshing point, the tooth surface slip speed, and the entrainment speed are:

[0027]

[0028] In the formula, R ap (t) is the tooth surface roughness of the driving wheel, E ag (t) is the tooth surface roughness of the driven wheel, B represents the tooth width, V p (t) and V g (t) respectively represent the circumferential speeds of the driving wheel and the driven wheel at the meshing point; ω i , i = p, g is the rotational speed of the driving wheel or the driven wheel; ρ i(t), where \(i = p, g\) represents the instantaneous radius of curvature at the contact position of the driving or driven gear; \(r\) bi , where \(i = p, g\) represents the base circle radius of the driving or driven gear; \(\alpha\) i (t), where \(i = p, g\) represents the pressure angle corresponding to the meshing point of the driving or driven gear.

[0029] Preferably, in the said S4, the tooth surface wear effect includes the static transmission error, dynamic transmission error and dynamic meshing force of the gear pair, and the calculation formulas are respectively:

[0030]

[0031] In the formula, \(e(t)\) is the static transmission error, \(\delta\) h is the dynamic transmission error, \(F\) is the dynamic meshing force, \(h\) pi (t), \(h\) gi (t) respectively represent the tooth surface wear depth of the driving and driven gears at the \(i\)-th point, \(y\) p and \(y\) g respectively represent the vibration displacements of the driving and driven gears along the meshing line direction, \(\theta\) p and \(\theta\) g respectively represent the rotational displacements of the driving and driven gears along the axis direction, \(r\) bi , where \(i = p, g\) represents the base circle radius of the driving or driven gear, \(k\) h and \(c\) h are respectively the time-varying meshing stiffness and damping of the gear pair.

[0032] Preferably, in the said S4, the motion differential equation of the translational-torsional coupling dynamic model of the gear transmission system is:

[0033]

[0034] In the formula, \(x\) j (t), \(y\) j (t), where \(j = p, g\) are the vibration displacements of the driving or driven gear, \(\theta\) j , where \(j = p, g\) is the rotational displacement of the driving or driven gear, \(m\) j , where \(j = p, g\) represents the masses of the driving and driven gears, \(I\) j , where \(j = p, g\) represents the moments of inertia of the driving and driven gears, \(k\) jx , \(k\) jy , where \(j = p, g\) are respectively the support stiffnesses of the driving and driven gears, \(c\) jx , \(c\) jy , where \(j = p, g\) is the corresponding damping, \(f\) ji , where \(j = p, g\); \(i = 1, 2\) respectively represent the frictions received by different teeth of the driving and driven gears, \(T\) j , where \(j = p, g\) is the input torque or load torque.

[0035] Preferably, in S5, let the meshing point be A, and the prediction formula for the tooth surface wear amount is:

[0036]

[0037] In the formula, h A (t) represents the tooth surface wear amount at point A, and k A (t) is the dimensionless wear factor at point A, and p A (t) represents the tooth surface contact pressure at point A, and s A represents the relative slip distance at point A.

[0038] Preferably, the calculation formula for the dimensionless wear factor is:

[0039]

[0040] In the formula, λ is the lubricant film thickness ratio, and k0 is the dimensionless wear factor in the boundary lubrication state.

[0041] Preferably, the calculation formulas for the lubricant film thickness ratio and the dimensionless wear factor are:

[0042]

[0043] In the formula, h min is the minimum oil film thickness, and E c , W * , G * and S * are the equivalent elastic modulus, dimensionless load parameter, dimensionless material parameter, and dimensionless tooth surface topography parameter respectively, R ap , R ag are the tooth surface roughnesses of the driving and driven wheels respectively; E p and E g represent the elastic moduli of the driving and driven wheels respectively, v p and v g are the Poisson's ratios of the driving and driven wheels respectively, α represents the viscosity-pressure coefficient, and ρ e represents the equivalent curvature radius at the contact point; ρ i , i = p, and g represents the instantaneous curvature radius at the contact position of the driving or driven wheel.

[0044] Preferably, the calculation formula for the tooth surface contact pressure is:

[0045]

[0046] In the formula, a H is the half-width of the contact area, ρ e represents the equivalent curvature radius at the contact point, and Ec is the equivalent elastic modulus.

[0047] Preferably, the calculation formula for the relative slip distance is:

[0048]

[0049] In the formula, s p and s g are the relative slip distances of the driving wheel and the driven wheel respectively, and V p and V g represent the circumferential speeds of the driving wheel and the driven wheel at the meshing point respectively.

[0050] Therefore, a gear tooth surface wear prediction method based on interface characteristics of the present invention has the following beneficial effects:

[0051] (1) By dynamically characterizing the evolution process of the tooth surface topography through the fractal theory, the cumulative effect of tooth surface wear can be more accurately simulated, and the accuracy of wear amount prediction is significantly improved.

[0052] (2) By introducing contact interface parameters and interface characteristics, a time-varying friction model considering tooth surface topography evolution, lubrication conditions and dynamic loads, and a translational-torsional coupling dynamic model considering interface characteristic evolution are constructed, comprehensively revealing the coupling mechanism between tooth surface topography, lubrication, dynamic loads and wear.

[0053] (3) Through the phased parameter update strategy and iterative loop calculation, key parameters such as tooth surface topography, friction coefficient and contact load are dynamically updated to ensure that the model can reflect the change of interface state during the wear process in real time and enhance the reliability of prediction.

[0054] (4) It provides a theoretical basis for the condition monitoring, life prediction and optimal design of the gear transmission system, helps to identify potential failure risks in advance, and thus improves the safety and operation reliability of the gear transmission system.

[0055] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Description of the Drawings

[0056] Figure 1 is the flowchart of the embodiment of the present invention;

[0057] Figure 2 is the schematic diagram of the meshing contact of the rough tooth surface in the embodiment of the present invention;

[0058] Figure 3 is the tooth surface contour curve of the driving wheel in the embodiment of the present invention; where (a) is the contour curve of the healthy tooth surface (S1); (b) is the meshing N m = 3×10 6The contour curve after (S2); (c) is the meshing N m = 6×10 6 The contour curve after (S3); (d) is the meshing N m = 9×10 6 The contour curve after (S4);

[0059] Figure 4 is the contour curve of the tooth surface of the driven wheel in the embodiment of the present invention; where (a) to (d) are the contour curves in the S1 to S4 stages in sequence;

[0060] Figure 5 is the schematic diagram of the gear pair meshing in the embodiment of the present invention;

[0061] Figure 6 is the tooth surface friction coefficient diagram in the healthy and different wear states in the embodiment of the present invention;

[0062] Figure 7 is the calculation result diagram of the time-varying meshing stiffness in the embodiment of the present invention;

[0063] Figure 8 is the schematic diagram of the translational-torsional coupling dynamic model of the gear transmission system in the embodiment of the present invention;

[0064] Figure 9 is the tooth surface contact load diagram in the healthy and different wear states in the embodiment of the present invention;

[0065] Figure 10 is the experimental verification diagram of the maximum wear amount of the driving wheel in the embodiment of the present invention;

[0066] Figure 11 is the lubricating film thickness ratio diagram in the healthy and different wear states in the embodiment of the present invention;

[0067] Figure 12 is the tooth surface wear factor diagram in the healthy and different wear states in the embodiment of the present invention;

[0068] Figure 13 is the tooth surface contact pressure diagram in the healthy and different wear states in the embodiment of the present invention; where (a) is the comparison diagram of different stages; (b) is the comparison diagram of the S1 stage and the S4 stage;

[0069] Figure 14 is the tooth surface wear amount prediction diagram in the embodiment of the present invention; where (a) is the tooth surface wear amount of the driving wheel; (b) is the tooth surface wear amount of the driven wheel. Detailed implementation manners

[0070] The technical solution of the present invention will be further described below with reference to the drawings and embodiments.

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments.

[0072] Embodiment

[0073] As Figure 1 shown, a gear tooth surface wear prediction method based on interface characteristics provided by the present invention includes the following steps:

[0074] S1. As shown in Table 1, for a gear transmission system composed of a gear pair, set geometric parameters, operating parameters, and lubrication parameters;

[0075] Table 1 Related parameters of the gear transmission system

[0076] Parameter Driver / Driven wheel Number of teeth z 23 / 84 Mass M / kg 0.10 / 2.18 Module m / mm 1.5 Pressure angle α / (°) 20 Young's modulus E / GPa 206 Tooth width B / mm 25 <![CDATA[Addendum coefficient h a > 1 Clearance coefficient c 0.25 Poisson's ratio v 0.3 Input speed n / r / min 1500 Load torque T / N·m 40 Dynamic viscosity η / Pa·s 0.15 <![CDATA[Adhesion pressure coefficient α / m 2 / N]]> <![CDATA[1.4×10 -8 >

[0077] S2. Based on the fractal theory, use the tooth surface topography characterization function to simulate the evolution in the process of tooth surface wear accumulation, obtain the numerical characterization of the tooth surface topography, and further obtain the tooth surface roughness. Specifically:

[0078] As Figure 2 shown, the meshing of the gear pair is actually a dynamic contact process of two rough tooth surfaces, which will inevitably lead to tooth surface wear accumulation. As the tooth surface wear accumulates gradually, the microscopic rough profile of the tooth surface topography will gradually change, thereby causing dynamic changes in the tooth surface roughness characteristics.

[0079] Since the irregularity change of the tooth surface topography is not significant in the mild wear stage, the fractal dimension D mainly depends on the initial machining accuracy of the tooth surface. Set the initial machining surface roughness R ai = 0.2 μm; the characteristic scale coefficient G shows a dynamic attenuation characteristic with the increase of the meshing times N m of the gear pair, and its value can be measured by contour measurement. For the convenience of calculation, in this embodiment, it is specifically set as: N m = 0, N m = 3×10 6 , N m = 6×10 6 and N m = 9×10 6 corresponding characteristic scale coefficients G are taken as 2×10 -6 , 1.75×10 -6 , 1.5×10 -6 and 1.25×10 -6 . The tooth surface topographies of the driving and driven wheels obtained through numerical simulation are as Figure 3 , Figure 4 shown. The specific steps include:

[0080] (1) The tooth surface topography characterization function is as follows:

[0081]

[0082] In the formula, z(x) is the tooth surface profile height, x is the position coordinate along the tooth profile direction, D is the fractal dimension, R ai represents the initial machining surface roughness, G is the characteristic scale coefficient of the profile height value, n is the spatial frequency coefficient, n s is the ordinal number corresponding to the lowest cut-off frequency, γ is a constant with a value of 1.5, ψ n is a random phase between 0 and 2π, making the generated tooth surface profile curve have randomness.

[0083] (2) To balance computational efficiency and prediction accuracy, the present invention adopts a phased parameter update strategy to simulate and characterize the evolution of the tooth surface topography during the tooth surface wear accumulation process: after every N m = 3×10 6 meshing calculations, key parameters such as tooth surface roughness and dynamic load are dynamically iteratively updated. The tooth surface roughness R ap of the driving gear tooth surface and the tooth surface roughness R ag of the driven gear tooth surface are obtained through the numerically characterized tooth surface topography.

[0084] S3. Introduce the dynamic relationship between the contact interface parameters and the friction coefficient, construct a time-varying friction model that comprehensively considers the evolution of the tooth surface topography, lubrication conditions, and dynamic load, and calculate the tooth surface friction arm and the friction coefficient and friction force based on the tooth surface contact load F′(t);

[0085] Figure 5 shows the meshing process of the gear pair along the meshing line direction. The first meshing tooth is subjected to the normal meshing force and the tangential friction force f p1 in the EB section, and the second meshing tooth is subjected to the normal meshing force and the tangential friction force f p2 in the BA section. The direction of the friction force is always opposite to the direction of the relative sliding speed of the contact point, along the tangent direction of the meshing point. It should be noted that when the meshing point passes through the node C, due to the change in the relative sliding direction of the tooth surfaces of the driving and driven gears, the direction of f p1 changes. Figure 6 shows the change of the friction coefficient at each meshing point in different wear stages. The specific steps include:

[0086] (1) For different teeth of the driving gear and different teeth of the driven gear in the gear transmission system, calculate the tooth surface friction arm. The calculation formula is:

[0087]

[0088] Wherein, L p1 (t) and L p2 (t) are both the friction arms of the tooth surface friction force on the driving wheel with respect to the center o of the wheel shaft at time t p , L g1 (t) and L g2 (t) are both the friction arms of the tooth surface friction force on the driven wheel with respect to the center o of the wheel shaft at time t g , r bi , i = p, g represents the base circle radius of the driving wheel or the driven wheel, mod(·) represents the modulo operation, ω p is the rotational speed of the driving wheel; α jp , j = B, D, E represents the pressure angle of the driving wheel at point j.

[0089] (2) Considering comprehensively the influence of tooth surface topography evolution, lubrication conditions and dynamic loads, calculate the time-varying friction coefficient and friction force of the tooth surface based on the tooth surface contact load, and the calculation formula is:

[0090]

[0091] Wherein, f(t) is the time-varying tooth surface friction force, μ(t) is the time-varying friction coefficient, F′ is the tooth surface contact load, R ae (t) is the equivalent tooth surface roughness, R ap (t) is the tooth surface roughness of the driving wheel, R ag (t) is the tooth surface roughness of the driven wheel, η is the dynamic viscosity of the lubricating oil, w e (t) represents the unit normal load at the meshing point, v s (t) represents the tooth surface slip speed, v e (t) is the entrainment speed, B represents the tooth width, V p (t) and V g (t) respectively represent the circumferential speeds of the driving wheel and the driven wheel at the meshing point; ω i , i = p, g is the rotational speed of the driving wheel or the driven wheel; ρ i (t), i = p, g represents the instantaneous curvature radius of the contact position of the driving wheel or the driven wheel; r bi , i = p, g represents the base circle radius of the driving wheel or the driven wheel; α i (t), i = p, g represents the pressure angle corresponding to the meshing point of the driving wheel or the driven wheel.

[0092] S4. Incorporate the contact interface characteristics and their evolution into the tooth surface wear effect, establish a translational-torsional coupling dynamic model of the gear transmission system based on the tooth surface wear effect, and its schematic diagram is as Figure 8 shown, and calculate the tooth surface contact load. Among them, the tooth surface wear effect includes the time-varying meshing stiffness, static transmission error, dynamic transmission error and dynamic meshing force of the gear pair.

[0093] Based on the geometric parameters and working conditions of the gear transmission system, the present invention determines the quasi-static tooth surface contact load of the gear teeth during the meshing period through the tooth load distribution coefficient. On this basis, the dynamic meshing force of the gear transmission system is decomposed to each meshing point, and the obtained dynamic tooth surface contact load is as Figure 9 shown. The specific steps include:

[0094] (1) The present invention comprehensively considers factors such as the coupling effect of the gear matrix and the tooth root transition curve, and uses the potential energy method to calculate the time-varying meshing stiffness of the gear pair. During the running-in stage, the tooth surface wear amount is small, and its influence on the time-varying meshing stiffness is not significant. Therefore, ignoring the change in the time-varying meshing stiffness caused by the cumulative tooth surface wear, the calculated result of the time-varying meshing stiffness of the gear pair is as Figure 7 shown.

[0095] (2) The calculation formulas for the static transmission error, dynamic transmission error, and dynamic meshing force are respectively:

[0096]

[0097] wherein, e(t) is the static transmission error, δ h is the dynamic transmission error, F is the dynamic meshing force, h pi (t), h gi (t) respectively represent the tooth surface wear depths of the driving wheel and the driven wheel at the i-th point, y p and y g respectively represent the vibration displacements of the driving wheel and the driven wheel along the meshing line direction, θ p and θ g respectively represent the rotational displacements of the driving wheel and the driven wheel along the axis direction, r bi , i = p, g represents the base circle radius of the driving wheel or the driven wheel, k h and c h are respectively the time-varying meshing stiffness and damping of the gear pair.

[0098] (3) Establish a translational-torsional coupling dynamic model of the gear transmission system considering the tooth surface wear effect, and the corresponding motion differential equation is:

[0099]

[0100] wherein, x j (t), y j (t), j = p, g are all the vibration displacements of the driving wheel or the driven wheel, θ j , j = p, g is the rotational displacement of the driving wheel or the driven wheel, m j , j = p, g represents the masses of the driving wheel and the driven wheel, I j , j = p, g represents the moments of inertia of the driving wheel and the driven wheel, k jx, k jy , where \(j = p, g\) are the support stiffnesses of the driving and driven wheels respectively, and \(c\) jx , \(c\) jy , where \(j = p, g\) are the corresponding damping, and \(f\) ji , where \(j = p, g\); \(i = 1, 2\) represent the frictions on different teeth of the driving and driven wheels respectively, and \(T\) j , where \(j = p, g\) is the input torque or load torque.

[0101] S5. Considering the influences of tooth surface topography, lubrication conditions and dynamic loads comprehensively, a tooth surface wear prediction model is constructed to predict the tooth surface wear amount at all meshing points. Specifically:

[0102] On the one hand, tooth surface wear is affected by the coupling of factors such as tooth surface topography, lubrication state and dynamic load. On the other hand, with the gradual accumulation of tooth surface wear, tooth surface topography, lubrication state, dynamic load, etc. will also change, which will in turn affect the accumulation of tooth surface wear. To accurately calculate the tooth surface wear amount, the above coupling effects must be taken into account. Based on this, this method establishes a gear tooth surface wear prediction model that comprehensively considers the influences of tooth surface topography, lubrication conditions and dynamic loads. As Figure 10 shown, experimental verification shows that the gear tooth surface wear prediction method proposed in the present invention that comprehensively considers interface characteristics has high accuracy. The specific steps include:

[0103] (1) Preset the tooth surface wear amount threshold as the criterion for tooth surface topography update;

[0104] (2) The lubricant film thickness ratio can quantitatively describe the lubrication conditions of the tooth surface. The lubricant film thickness ratios in the healthy and different wear stages are as Figure 11 shown. As a key parameter for tooth surface wear prediction, the dimensionless wear factor \(k\) can comprehensively characterize the coupling effects such as tooth surface topography evolution, lubrication characteristics and load fluctuation during the dynamic contact process. The dimensionless wear factors in the healthy and different wear stages are as Figure 12 shown.

[0105] The calculation formula of the dimensionless wear factor \(k\) is:[[]]

[0106]

[0107] In the formula, \(\lambda\) is the lubricant film thickness ratio, \(k_0\) is the dimensionless wear factor in the boundary lubrication state, \(h\) min is the minimum oil film thickness; \(R\) ac is the composite roughness; \(E\) c , \(W\) * , \(G\) * and \(S\) * are the equivalent elastic modulus, dimensionless load parameter, dimensionless material parameter and dimensionless tooth surface topography parameter respectively; \(R\) ap , \(R\)ag are the surface roughnesses of the driving and driven wheels respectively; E p and E g represent the elastic moduli of the driving and driven wheels respectively; v p and v g are the Poisson's ratios of the driving and driven wheels respectively; w e represents the unit normal load at the meshing point; α represents the coefficient of viscosity and pressure; ρ e represents the equivalent radius of curvature at the contact point; ρ i , i = p, g represents the instantaneous radius of curvature at the contact position of the driving or driven wheel.

[0108] (3) The tooth surface contact pressure at a certain point can be simplified to the average pressure within the contact area at this point through Hertz contact theory. Figure 13 Shows the tooth surface contact pressure in the healthy and different wear stages. The calculation formula for the tooth surface contact pressure is:

[0109]

[0110] In the formula, x r is the radial distance from the Hertz contact center, a H is the half-width of the contact area;

[0111] (4) The calculation formula for the relative slip distance of the driving and driven wheels corresponding to the meshing point is:

[0112]

[0113] In the formula, s p , s g are the relative slip distances of the driving and driven wheels respectively, V p and V g represent the circumferential speeds of the driving and driven wheels at the meshing point respectively.

[0114] (5) For the prediction calculation of the tooth surface wear amount, the improved Archard formula can be used to numerically predict the wear amount at the meshing point. Let the meshing point be A, and the prediction formula for the tooth surface wear amount is:

[0115]

[0116] In the formula, h A (t) represents the tooth surface wear amount at point A, k A (t) is the dimensionless wear factor at point A, p A (t) represents the tooth surface contact pressure at point A, s A represents the relative slip distance at point A.

[0117] S6. Gradually increase the number of wear cycles (number of meshing circles) q until the tooth surface wear amount reaches the preset threshold ξ;

[0118] S7, update the tooth surface morphology, execute S1 to S6 cyclically, and add the tooth surface wear amount obtained from each tooth surface morphology update until the accumulated wear amount of any meshing point on the tooth surface reaches the maximum allowable wear amount ζ t , to realize the prediction of gear tooth surface wear.

[0119] Figure 14 The prediction results of tooth surface wear are shown. The distribution law of tooth surface wear of the driving and driven wheels is similar, and there is only a difference in the values of tooth surface wear between the two. Since the driving wheel undergoes more wear cycles in the same time, the tooth surface wear of the driving wheel is generally greater than that of the driven wheel. During the gear meshing process, the wear factor, tooth surface contact pressure and relative slip distance are non-uniformly distributed along the tooth profile direction, resulting in the non-uniform distribution of tooth surface wear of the driving and driven wheels along the tooth profile direction. In addition, since the wear factor, tooth surface contact pressure and relative slip distance are all larger at the meshing point of the first double-tooth meshing area, the tooth surface wear is the largest at the meshing point of the first double-tooth meshing area, corresponding to the root of the driving wheel and the top of the driven wheel. Near the gear node, the relative sliding speed of the driving and driven wheels is close to zero, so the tooth surface wear near the node is very small. At the meshing point of the first double-tooth meshing area, the wear of the driving wheel is greater than that of the driven wheel, while at the meshing point of the second double-tooth meshing area, the wear of the driven wheel is greater than that of the driving wheel. At the point where single and double teeth mesh alternately, the wear on the tooth surface changes suddenly. The number of wear cycles directly affects the cumulative wear process and wear amount of the tooth surface, but has little effect on the distribution of tooth surface wear. With the increase in the number of wear cycles, the wear on the tooth surface of the driving and driven wheels gradually increases, especially at the root and top of the gear, where the distribution of wear along the tooth profile changes more dramatically.

[0120] Therefore, the present invention provides a gear tooth surface wear prediction method based on interface characteristics, which dynamically characterizes the evolution of tooth surface morphology through fractal theory and quantifies the roughness change during the wear process; introduces contact interface parameters and interface characteristics, combines time-varying friction model and translation-torsion coupling dynamic model, and comprehensively considers the coupling effect of tooth surface morphology, lubrication conditions and dynamic load, breaking through the limitation of traditional models that ignore the coupling of multiple factors, providing a scientific basis for the reliability design and life prediction of gear systems, and has important engineering application value.

[0121] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A gear tooth surface wear prediction method based on interface characteristics, characterized in that, It includes the following steps: S1. Set geometric parameters, operating parameters, and lubrication parameters for a gear transmission system composed of a gear pair; S2. Based on the fractal theory, use the tooth surface topography characterization function to simulate the evolution during the tooth surface wear accumulation process, obtain the numerical characterization of the tooth surface topography, and further obtain the tooth surface roughness; S3. Introduce the dynamic relationship between the contact interface parameters and the friction coefficient, construct a time-varying friction model that comprehensively considers the tooth surface topography evolution, lubrication conditions, and dynamic loads, and calculate the tooth surface friction force arm and the friction coefficient and friction force based on the tooth surface contact load; S4. Incorporate the contact interface characteristics and their evolution into the tooth surface wear effect, establish a translational-torsional coupling dynamic model of the gear transmission system based on the tooth surface wear effect, and calculate the tooth surface contact load; S5. Comprehensively consider the influence of tooth surface topography, lubrication conditions, and dynamic loads, construct a tooth surface wear prediction model to predict the tooth surface wear amount at all meshing points; S6. Gradually increase the number of wear cycles until the tooth surface wear amount reaches a preset threshold; S7. Update the tooth surface topography, loop through S1 - S6, and superimpose the tooth surface wear amounts obtained from each tooth surface topography update until the wear amount at any meshing point on the tooth surface reaches the allowable maximum wear amount to achieve the prediction of the gear tooth surface wear amount.

2. The gear tooth surface wear prediction method based on interface features according to claim 1, wherein The tooth surface topography characterization function in S2 is: where \(z(x)\) is the height of the tooth surface profile, \(x\) is the position coordinate along the tooth profile direction, \(D\) is the fractal dimension, \(G\) is the characteristic scale coefficient of the profile height value, \(R\) ai represents the initial machining surface roughness, \(\varepsilon\), \(\tau\), \(\theta\), \(\beta\) are all constants, \(n\) is the spatial frequency coefficient, \(n\) s is the ordinal number corresponding to the lowest cut-off frequency, \(\gamma\) is a constant with a value of 1.5, \(\psi\) n is a random phase between 0 and \(2\pi\).

3. A gear tooth surface wear prediction method based on interface characteristics according to claim 1, characterized in that: In S3, for different teeth of the driving wheel and different teeth of the driven wheel in the gear transmission system, calculate the tooth surface friction force arm, and the calculation formula is: where L p1 (t) and L p2 (t) are both the friction arms of the tooth surface friction force on the driving wheel with respect to the center of the wheel axis at time t, L g1 (t) and L g2 (t) are both the friction arms of the tooth surface friction force on the driven wheel with respect to the center of the wheel axis at time t, r bi , i = p, g represents the base circle radius of the driving wheel or the driven wheel, mod(·) represents the modulo operation, ω p is the rotational speed of the driving wheel; α jp , j = B, D, E represents the pressure angle of the driving wheel at point j.

4. A method for predicting gear tooth surface wear based on interface characteristics according to claim 1, characterized in that, In S3, comprehensively consider the influence of tooth surface topography evolution, lubrication conditions, and dynamic loads, and calculate the time-varying tooth surface friction coefficient and friction force based on the tooth surface contact load. The calculation formula is: where \(f(t)\) is the time-varying tooth surface friction force, \(\mu(t)\) is the time-varying friction coefficient, \(F'(t)\) is the tooth surface contact load, \(R\) ac (t) is the equivalent tooth surface roughness, \(\eta\) is the dynamic viscosity of the lubricating oil, \(w\) e (t) represents the unit normal load at the meshing point, \(v\) s (t) represents the tooth surface sliding speed, \(v\) e (t) is the entrainment speed.

5. A gear tooth surface wear prediction method based on interface characteristics according to claim 1, characterized in that: In S4, the tooth surface wear effect includes the static transmission error, dynamic transmission error, and dynamic meshing force of the gear pair. The calculation formulas are respectively: where, e(t) is the static transmission error, δ h is the dynamic transmission error, F is the dynamic meshing force, h pi (t), h gi (t) respectively represent the tooth surface wear depths of the driving gear and the driven gear at the i-th point, y p and y g respectively represent the vibration displacements of the driving gear and the driven gear along the meshing line direction, θ p and θ g respectively represent the rotational displacements of the driving gear and the driven gear along the axis direction, r bi , i = p, g represents the base circle radius of the driving gear or the driven gear, k h and c h are respectively the time-varying meshing stiffness and damping of the gear pair.

6. A gear tooth surface wear prediction method based on interface characteristics according to claim 1, characterized in that In S4, the motion differential equation of the translational-torsional coupling dynamic model of the gear transmission system is: where x j (t), y j (t), j = p, g are the vibration displacements of the driving or driven wheels, θ j , j = p, g is the rotational displacement of the driving or driven wheel, m j , j = p, g represents the masses of the driving and driven wheels, I j , j = p, g represents the moments of inertia of the driving and driven wheels, k jx , k jy , j = p, g are the support stiffnesses of the driving and driven wheels respectively, c jx , c jy , j = p, g is the corresponding damping, f ji , j = p, g; i = 1, 2 respectively represent the frictional forces on different teeth of the driving and driven wheels, T j , j = p, g is the input torque or load torque.

7. A method for predicting gear tooth surface wear based on interface characteristics according to claim 1, characterized in that: In S5, assume the meshing point is A, and the prediction formula for the tooth surface wear amount is: where h A (t) represents the tooth surface wear amount at point A, and k A (t) is the dimensionless wear factor at point A, p A (t) represents the tooth surface contact pressure at point A, and s A represents the relative slip distance at point A.

8. A method for predicting gear tooth surface wear based on interface characteristics according to claim 7, characterized in that The calculation formula for the dimensionless wear factor is: In the formula, λ is the lubricating film thickness ratio, and k0 is the dimensionless wear factor in the boundary lubrication state.

9. A gear tooth surface wear prediction method based on interface features according to claim 7, characterized in that The calculation formula for the tooth surface contact pressure is: where a H is the half-width of the contact area, ρ e represents the equivalent radius of curvature of the contact point, and E c is the equivalent elastic modulus.

10. A method for predicting gear tooth surface wear based on interface characteristics according to claim 7, characterized in that The calculation formula for the relative slip distance is: where s p , s g are the relative slip distances of the driving wheel and the driven wheel respectively, and V p and V g represent the circumferential speeds of the driving wheel and the driven wheel at the meshing point respectively.

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