Gear tooth surface wear prediction method based on interface characteristics

Abstract

The present invention discloses a gear tooth surface wear prediction method based on interface features, belonging to the field of gear technology. The present invention's gear tooth surface wear prediction method, based on interface features, dynamically characterizes the evolution of tooth surface morphology through fractal theory and quantifies the change in roughness during wear. By introducing contact interface parameters and interface features, combined with a time-varying friction model and a translation-torsion coupling dynamics model, it comprehensively considers the coupling effects of tooth surface morphology, lubrication conditions, and dynamic loads. This method overcomes the limitation of traditional models that ignore multi-factor coupling, provides a scientific basis for the reliability design and life prediction of gear systems, and has important engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of gears, and in particular to a gear tooth surface wear prediction method based on interface features. Background Art

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

[0003] Compared to costly and time-consuming experimental studies, many researchers have adopted the cost-effective method of calculating tooth wear through theoretical modeling, and have conducted a large amount of meaningful work on tooth wear prediction. However, most current work considers the effects of tooth surface morphology, lubrication, and dynamic load on tooth surface wear separately, but few comprehensively consider the coupling effects between tooth surface morphology, lubrication, dynamic load, and tooth surface wear. This makes it difficult to accurately characterize the interface characteristics and their evolution under the wear state of the tooth surface, resulting in a large discrepancy between the predicted tooth surface wear and the actual tooth surface wear damage phenomenon.

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

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

[0006] To achieve the above object, the present invention provides a gear tooth surface wear prediction method based on interface characteristics, comprising the following steps:

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

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

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

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

[0011] 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, and unit normal load;

[0012] S4. Taking the contact interface characteristics and their evolution into account the tooth surface wear effect, a translation-torsion coupling dynamic model of the gear transmission system based on the tooth surface wear effect is established to calculate the tooth surface contact load;

[0013] The contact interface characteristics are the comprehensive characteristics of the gear contact interface during the wear process, including topographic roughening, lubrication state transition, wear distribution non-uniformity, friction characteristics, and dynamic load effects;

[0014] S5. Considering the influence of tooth surface morphology, lubrication conditions and dynamic load, a tooth surface wear prediction model is constructed to predict the tooth surface wear amount of all meshing points;

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

[0016] S7, update the tooth surface profile, execute S1 to S6 cyclically, and add the tooth surface wear obtained from each tooth surface profile update until the wear of any meshing point on the tooth surface reaches the maximum allowable wear, thereby realizing the prediction of gear tooth surface wear.

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

[0018]

[0019] Where z(x) is the height of the tooth 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 processing surface roughness, n is the spatial frequency coefficient, n s is the ordinal number corresponding to the lowest cutoff frequency, γ is a constant with a value of 1.5, and ψ n is a random phase between 0 and 2π.

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

[0021]

[0022] Where, L p1 (t) and L p2 (t) are the friction arms of the tooth surface friction force of the driving wheel relative to the center of the wheel shaft at time t, L g1 (t) and L g2 (t) is the friction arm of the driven wheel tooth surface friction force relative to the wheel axle center 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 speed of the driving wheel; α jp , j=B, D, E represents the driving wheel pressure angle at point j.

[0023] Preferably, in S3, the influence of tooth surface topography evolution, lubrication conditions and dynamic load is comprehensively considered to 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:

[0024]

[0025] Where 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, and 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 velocity, v e (t) is the entrainment velocity.

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

[0027]

[0028] Where R ap (t) is the roughness of the driving wheel tooth surface, E ag (t) is the roughness of the driven gear tooth surface, B is the tooth width, V p (t) and V g (t) represents the circumferential speed of the driving wheel and the driven wheel at the meshing point; ω i , i = p, g is the 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.

[0029] Preferably, in 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:

[0030]

[0031] 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) represents the wear depth of the tooth surface of the driving wheel and the driven wheel at point i, y p and y g Represents the vibration displacement of the driving wheel and the driven wheel along the meshing line direction, θ p and θ g They represent the rotational displacement of the driving wheel and the driven wheel along the axis, r bi , i=p, g represents the base circle radius of the driving wheel or the driven wheel, k h and c h are the time-varying mesh stiffness and damping of the gear pair, respectively.

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

[0033]

[0034] Where x j (t), y j (t), j = p, g are 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 mass of the driving wheel and the driven wheel, I j , j = p, g represents the moment of inertia of the driving wheel and the driven wheel, k jx , k jy , j = p, g are the supporting stiffness of the driving wheel and the driven wheel respectively, c jx , c jy , j = p, g is the corresponding damping, f ji , j = p, g; i = 1, 2 represent the friction force on different teeth of the driving wheel and the driven wheel respectively, T j , j=p, g is the input torque or load torque.

[0035] Preferably, in S5, assuming that the meshing point is A, the prediction formula for the tooth surface wear is:

[0036]

[0037] Where h A (t) represents the tooth surface wear 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 Indicates the relative slip distance of point A.

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

[0039]

[0040] Where λ is the lubricating film thickness ratio, and k0 is the dimensionless wear factor under boundary lubrication conditions.

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

[0042]

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

[0044] Preferably, the tooth surface contact pressure is calculated as follows:

[0045]

[0046] Where a H is the half-width of the contact area, ρ e Indicates the equivalent curvature radius of the contact point, Ec is the equivalent elastic modulus.

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

[0048]

[0049] Where s p 、s g are the relative slip distances of the driving wheel and the driven wheel, V p and V g Respectively represent the peripheral speeds of the driving wheel and the driven wheel at the meshing point.

[0050] Therefore, the 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 of tooth surface morphology through fractal theory, the cumulative effect of tooth surface wear can be simulated more accurately, significantly improving the accuracy of wear prediction.

[0052] (2) By introducing contact interface parameters and interface characteristics, a time-varying friction model considering the evolution of tooth surface morphology, lubrication conditions and dynamic loads, as well as a translation-torsion coupling dynamic model taking into account the evolution of interface characteristics, were constructed. The coupling mechanism between tooth surface morphology, lubrication, dynamic load and wear was fully revealed.

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

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

[0055] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of an embodiment of the present invention;

[0057] Figure 2 Schematic diagram of meshing contact of rough tooth surfaces according to an embodiment of the present invention;

[0058] Figure 3 The profile curves of the driving gear tooth surface of the embodiment of the present invention are as follows; (a) is the profile curve of the healthy tooth surface (S1); (b) is the profile curve of the meshing N m =3×10 6(c) is the profile curve of meshing N m =6×10 6 (S3) is the contour curve; (d) is the meshing N m =9×10 6 The contour curve of the posterior (S4);

[0059] Figure 4 : The profile curve of the driven gear tooth surface in an embodiment of the present invention; (a) to (d) are the profile curves of stages S1 to S4 respectively;

[0060] Figure 5 A schematic diagram of the meshing of a gear pair according to an embodiment of the present invention;

[0061] Figure 6 Graphs showing tooth surface friction coefficients under healthy and different wear conditions according to an embodiment of the present invention;

[0062] Figure 7 Calculation result diagram of time-varying meshing stiffness according to an embodiment of the present invention;

[0063] Figure 8 Schematic diagram of a translation-torsion coupling dynamic model of a gear transmission system according to an embodiment of the present invention;

[0064] Figure 9 The tooth surface contact load diagram under healthy and different wear states according to an embodiment of the present invention;

[0065] Figure 10 This is a diagram illustrating an experimental verification of the maximum wear of the driving wheel according to an embodiment of the present invention;

[0066] Figure 11 is a graph showing the lubricating film thickness ratio under healthy and different wear states according to an embodiment of the present invention;

[0067] Figure 12 Graph showing tooth surface wear factors under healthy and different wear conditions according to an embodiment of the present invention;

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

[0069] Figure 14 1 is a tooth surface wear prediction diagram of an embodiment of the present invention; (a) is the tooth surface wear of the driving wheel; (b) is the tooth surface wear of the driven wheel. DETAILED DESCRIPTION

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

[0071] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0072] Example

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

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

[0075] Table 1 Gear transmission system related parameters

[0076] parameter Driving wheel / driven wheel Number of teeth z 23 / 84 Mass M / kg 0.10 / 2.18 Modulus 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 Head 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[Coefficient of viscous pressure α / m 2 / N]]> <![CDATA[1.4×10 -8 ]]>

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

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

[0079] Since the irregularity of the tooth surface morphology does not change significantly in the slight wear stage, the fractal dimension D mainly depends on the initial machining accuracy of the tooth surface. The initial machining surface roughness R is set to ai =0.2μm; characteristic scale coefficient G changes with the number of meshing times N of the gear pair m The dynamic attenuation characteristic can be increased and its value can be determined by profile measurement. For the convenience of calculation, this embodiment is specifically set as: N m =0, N m =3×10 6 , N m =6×10 6 and N m =9×10 6 The corresponding characteristic scale coefficient G is 2×10 -6 , 1.75×10 -6 , 1.5×10 -6 and 1.25×10 -6 The tooth surface morphology of the master and driven gears obtained through numerical simulation is as follows: Figure 3 、 Figure 4 The specific steps include:

[0080] (1) The tooth surface morphology characterization function is:

[0081]

[0082] Where z(x) is the height of the tooth profile, x is the position coordinate along the tooth profile direction, D is the fractal dimension, R ai represents the initial processing 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 cutoff frequency, γ is a constant with a value of 1.5, and ψ n It is a random phase between 0 and 2π, which makes the generated tooth surface profile curve random.

[0083] (2) In order to balance computational efficiency and prediction accuracy, the present invention adopts a phased parameter updating strategy to simulate and characterize the evolution of tooth surface morphology during the accumulation of tooth surface wear: m =3×10 6 After the meshing calculation, the key parameters such as tooth surface roughness and dynamic load are dynamically iterated and updated. The tooth surface roughness R of the driving wheel is obtained by numerically characterizing the tooth surface morphology. ap and driven gear tooth surface roughness R ag .

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

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

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

[0087]

[0088] Where, L p1 (t) and L p2 (t) is the friction force on the tooth surface of the driving wheel at time t relative to the center of the wheel shaft o p The friction arm, L g1 (t) and L g2 (t) is the friction force on the tooth surface of the driven wheel relative to the center of the wheel shaft at time t g The friction arm, 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 speed of the driving wheel; α jp , j=B, D, E represents the driving wheel pressure angle at point j.

[0089] (2) Taking into account the influence of tooth surface topography evolution, lubrication conditions and dynamic load, the time-varying friction coefficient and friction force of the tooth surface based on the tooth surface contact load are calculated. The calculation formula is:

[0090]

[0091] Where 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, and R ae (t) is the equivalent tooth surface roughness, R ap (t) is the roughness of the driving wheel tooth surface, R ag (t) is the roughness of the driven gear tooth surface, 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 velocity, v e (t) is the entrainment speed, B is the tooth width, V p (t) and V g (t) represents the circumferential speed of the driving wheel and the driven wheel at the meshing point; ω i , i = p, g is the 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. Taking the contact interface characteristics and their evolution into account the tooth surface wear effect, a translation-torsion coupling dynamic model of the gear transmission system based on the tooth surface wear effect is established, as shown in the schematic diagram. Figure 8 The tooth surface contact load is calculated as shown in Figure 2. 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 cycle through the gear tooth load distribution coefficient. On this basis, the dynamic meshing force of the gear transmission system is decomposed into each meshing point, and the dynamic tooth surface contact load obtained is as follows: Figure 9 The specific steps include:

[0094] (1) The present invention comprehensively considers 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 amount of tooth surface wear is small and its effect on the time-varying meshing stiffness is not significant. Therefore, ignoring the change in the time-varying meshing stiffness caused by the accumulation of tooth surface wear, the time-varying meshing stiffness of the gear pair is calculated as follows: Figure 7 shown.

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

[0096]

[0097] 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) represents the wear depth of the tooth surface of the driving wheel and the driven wheel at point i, y p and y g Represents the vibration displacement of the driving wheel and the driven wheel along the meshing line direction, θ p and θ g They represent the rotational displacement of the driving wheel and the driven wheel along the axis, r bi , i=p, g represents the base circle radius of the driving wheel or the driven wheel, k h and c h are the time-varying mesh stiffness and damping of the gear pair, respectively.

[0098] (3) A translation-torsion coupling dynamic model of the gear transmission system taking into account the tooth surface wear effect is established, and the corresponding differential equation of motion is:

[0099]

[0100] Where x j (t), y j (t), j = p, g are 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 mass of the driving wheel and the driven wheel, I j , j = p, g represents the moment of inertia of the driving wheel and the driven wheel, k jx, k jy , j = p, g are the supporting stiffness of the driving wheel and the driven wheel respectively, c jx , c jy , j = p, g is the corresponding damping, f ji , j = p, g; i = 1, 2 represent the friction force on different teeth of the driving wheel and the driven wheel respectively, T j , j=p, g is the input torque or load torque.

[0101] S5. Considering the influence of tooth surface morphology, lubrication conditions and dynamic load, a tooth surface wear prediction model is constructed to predict the tooth surface wear amount of all meshing points. Specifically:

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

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

[0104] (2) Lubricating film thickness ratio can quantitatively describe the lubrication conditions of the tooth surface. The lubricating film thickness in healthy and different wear stages is as follows: Figure 11 As a key parameter for tooth surface wear prediction, the dimensionless wear factor k can integrate the coupling effects of tooth surface morphology evolution, lubrication characteristics and load fluctuations during dynamic contact. The dimensionless wear factors of healthy and different wear stages are as follows: Figure 12 shown.

[0105] The calculation formula of dimensionless wear factor k is:

[0106]

[0107] Where λ is the lubricating film thickness ratio, k0 is the dimensionless wear factor under boundary lubrication, and 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 、Rag are the tooth surface roughness of the driving and driven wheels respectively; E p and E g Represents the elastic modulus of the driving wheel and the driven wheel 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 viscosity coefficient; ρ e represents the equivalent curvature radius of the contact point; ρ i , i=p, g represents the instantaneous curvature radius of the contact position of the driving wheel or the driven wheel.

[0108] (3) The tooth surface contact pressure at a certain point can be simplified to the average pressure in the contact area of ​​the point through Hertz contact theory. Figure 13 The tooth contact pressure at healthy and different wear stages is shown. The tooth contact pressure is calculated as:

[0109]

[0110] Where 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 between the driving and driven wheels corresponding to the meshing point is:

[0112]

[0113] Where s p 、s g are the relative slip distances of the driving wheel and the driven wheel, V p and V g Respectively represent the peripheral speeds of the driving wheel and the driven wheel at the meshing point.

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

[0115]

[0116] Where h A (t) represents the tooth surface wear 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 Indicates the relative slip distance of point A.

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

[0118] S7, update the tooth surface profile, and execute S1 to S6 in a loop, adding the tooth surface wear obtained from each tooth surface profile update until the accumulated wear 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 for tooth wear are presented. The tooth wear distribution patterns of the driving and driven gears are similar, with only the numerical values ​​of the tooth wear differing. Because the driving gear undergoes more wear cycles in the same timeframe, the tooth wear of the driving gear is generally greater than that of the driven gear. During the gear meshing process, the wear factor, tooth contact pressure, and relative slip distance are non-uniformly distributed along the tooth profile, resulting in a non-uniform distribution of tooth wear along the tooth profile for both the driving and driven gears. Furthermore, because the wear factor, tooth contact pressure, and relative slip distance are all greater at the entry point of the first double-tooth meshing zone, the tooth wear is greatest there, corresponding to the root of the driving gear and the tip of the driven gear. Near the gear pitch point, the relative sliding velocity between the driving and driven gears is close to zero, resulting in minimal tooth wear near the pitch point. At the entry point of the first double-tooth meshing zone, the wear of the driving gear is greater than that of the driven gear, while at the exit point of the second double-tooth meshing zone, the wear of the driven gear is greater than that of the driving gear. At the point where single and double teeth alternate in mesh, tooth wear changes abruptly. The number of wear cycles directly affects the cumulative wear and wear volume, but has little influence on the wear distribution. As the number of wear cycles increases, the wear volume of both the driving and driven gears increases, particularly at the tooth root and tooth tip, where the wear distribution 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 the time-varying friction model and the translation-torsion coupling dynamic model, and comprehensively considers the coupling effect of tooth surface morphology, lubrication conditions and dynamic loads, breaking through the limitation of traditional models that ignore multi-factor coupling, 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 solutions of the present invention rather than to limit the same. 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 solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A gear tooth surface wear prediction method based on interface characteristics, characterized in that: The following steps are involved: S1. For the gear transmission system composed of gear pairs, set the geometric parameters, working condition parameters and lubrication parameters; S2. Based on fractal theory, the tooth surface topography characterization function is used to simulate the evolution of tooth surface wear during the accumulation process, obtain the numerical representation of the tooth surface topography and further obtain the tooth surface roughness; S3. Introducing the dynamic relationship between contact interface parameters and friction coefficient, constructing a time-varying friction model that comprehensively considers the evolution of tooth surface morphology, lubrication conditions, and dynamic loads, and calculating the tooth surface friction arm and the friction coefficient and friction force based on the tooth surface contact load; S4. Taking the contact interface characteristics and their evolution into account the tooth surface wear effect, a translation-torsion coupling dynamic model of the gear transmission system based on the tooth surface wear effect is established to calculate the tooth surface contact load; S5. Considering the influence of tooth surface morphology, lubrication conditions and dynamic load, a tooth surface wear prediction model is constructed to predict the tooth surface wear amount of all meshing points; S6. Gradually increase the number of wear cycles until the tooth surface wear reaches a preset threshold; S7, update the tooth surface profile, execute S1 to S6 cyclically, and add the tooth surface wear obtained from each tooth surface profile update until the wear of any meshing point on the tooth surface reaches the maximum allowable wear, thereby realizing the gear tooth surface wear prediction; In the above S5, the meshing point is set to , the prediction formula for tooth surface wear is: ； Where, express The tooth surface wear amount at point for The dimensionless wear factor of the point, represent Tooth contact pressure at point express Relative sliding distance of the points; The calculation formula of the dimensionless wear factor is: ； Where, is the lubricating film thickness ratio, is the dimensionless wear factor under boundary lubrication; The calculation formula of the tooth surface contact pressure is: ； Where, is the half-width of the contact area, ; represents the equivalent curvature radius of the contact point, is the equivalent elastic modulus; The calculation formula of the relative slip distance is: ； Where, 、 are the relative slip distances of the driving wheel and the driven wheel, and Respectively represent the peripheral speeds of the driving wheel and the driven wheel at the meshing point.

2. The gear tooth surface wear prediction method based on interface features according to claim 1, characterized in that: The tooth surface morphology characterization function in S2 is: ； Where, is the tooth profile height, is the position coordinate along the tooth profile direction, is the fractal dimension, ; is the characteristic scale coefficient of the profile height value, ; represents the initial machining surface roughness, 、 、 、 are all constants, is the spatial frequency coefficient, is the ordinal number corresponding to the lowest cutoff frequency, is a constant with a value of 1.5, is between 0 and Random phases between .

3. The gear tooth surface wear prediction method based on interface features according to claim 1, characterized in that: In S3, the tooth surface friction arm is calculated for different gear teeth of the driving wheel and different gear teeth of the driven wheel in the gear transmission system, and the calculation formula is: ； Where, and Both The friction force arm of the tooth surface friction force of the driving wheel relative to the center of the wheel axle at the moment, and Both The friction arm of the tooth surface friction force of the driven wheel relative to the center of the wheel axle at any moment, , , Indicates the base circle radius of the driving wheel or the driven wheel, represents the modulo operation, is the speed of the driving wheel; , , represent The driving wheel pressure angle at point .

4. The gear tooth surface wear prediction method based on interface features according to claim 1, characterized in that: In S3, the influence of tooth surface topography evolution, lubrication conditions and dynamic load is comprehensively considered to calculate the time-varying friction coefficient and friction force of the tooth surface based on the tooth surface contact load. The calculation formula is: ； Where, is the time-varying tooth surface friction force, is the time-varying friction coefficient, is the tooth contact load, is the equivalent tooth surface roughness, is the dynamic viscosity of the lubricating oil, represents the unit normal load at the meshing point, represents the tooth surface slip velocity, is the suction speed.

5. The gear tooth surface wear prediction method based on interface features 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, and the calculation formulas are: ； Where, is the static transfer error, is the dynamic transmission error, is the dynamic meshing force, 、 Respectively represent the driving wheel and the driven wheel in the The wear depth of tooth surface at point and Respectively represent the vibration displacement of the driving wheel and the driven wheel along the meshing line direction, and They represent the rotational displacement of the driving wheel and the driven wheel along the axis direction, , , Indicates the base circle radius of the driving wheel or the driven wheel, and are the time-varying mesh stiffness and damping of the gear pair, respectively.

6. The gear tooth surface wear prediction method based on interface features according to claim 1, characterized in that: In S4, the motion differential equation of the gear transmission system translation-torsion coupling dynamic model is: ； Where, , , , are the vibration displacements of the driving wheel or the driven wheel, , , is the rotational displacement of the driving wheel or the driven wheel, , , Indicates the mass of the driving wheel and the driven wheel, , , represents the moment of inertia of the driving wheel and the driven wheel, , , , are the supporting stiffness of the driving wheel and the driven wheel respectively, , , , is the corresponding damping, , , ; , 2 represent the friction force on different teeth of the driving wheel and the driven wheel respectively, , , is the input torque or load torque.

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