Modeling method of thermal elastohydrodynamic lubrication contact model considering tooth surface morphology

Abstract

The invention belongs to the technical field of gear mechanical analysis and kinetic research, and discloses a thermal elastohydrodynamic lubrication contact model modeling method considering tooth surface morphology. According to oil film pressure, oil film thickness, temperature and tooth surface morphology, obtaining tooth surface load distribution, inter-tooth friction coefficient and engaged tooth surface temperature rise, solving rough contact stiffness, oil film stiffness and gear thermal stiffness, and replacing Hertz contact stiffness in a traditional model; and the bending rigidity, the shearing rigidity, the axial compression rigidity and the tooth base rigidity are combined to obtain the comprehensive meshing rigidity of the gear. According to the model, the tooth surface morphology, the lubricating performance and the heat effect under thermal elastohydrodynamic lubrication are considered. The fractal theory and the thermal elastohydrodynamic lubrication theory are combined, and the tooth surface microcosmic contact rigidity and thermal rigidity are introduced. On the basis, the necessity of considering the tooth surface morphology when the comprehensive rigidity of the gear is analyzed is verified. Compared with the prior art, the method has the advantages that the rough tooth surface contact rigidity and the comprehensive rigidity can be calculated more accurately, and a new method is provided for calculating the rigidity of the gear teeth.

Description

Technical Field

[0001] The present invention relates to the technical field of gear mechanics analysis and dynamics research, and in particular to a method for modeling a thermal elastohydrodynamic lubrication contact model taking tooth surface morphology into consideration. Background Art

[0002] Currently, thermal stiffness, caused by thermal effects such as tooth surface friction, is often overlooked. These thermal effects directly impact lubricant performance and tooth surface topography. Conversely, lubrication conditions and tooth surface topography play a decisive role in tooth surface friction and heat generation. In light of this, the present invention establishes a method for modeling a thermal elastohydrodynamic lubrication contact model that considers tooth surface topography.

[0003] CN114969616A uses the potential energy method to analytically calculate the equivalent spur gear meshing stiffness of a single-piece spur bevel gear, obtains the meshing stiffness of the single-piece spur bevel gear, calculates the single-tooth meshing stiffness of the spiral bevel gear, and superimposes the single-tooth meshing stiffness according to the meshing process to obtain the time-varying meshing stiffness of the spiral bevel gear.

[0004] US20180128710A1 provides a passive vibration isolation platform and a method for calculating the three-dimensional contact stiffness of spur gears based on a rough surface.

[0005] Due to the widespread use of gears in aerospace, automotive, marine, and other high-end mechanical equipment, gear systems often operate in complex, changing, and harsh environments. Furthermore, the manufacturing process creates a microstructure of irregularities on the tooth surface with random shapes, heights, and densities. This directly affects inter-tooth load distribution, lubrication characteristics, friction / wear, transmission efficiency, and thermal effects, thereby impacting the meshing characteristics and contact performance of the meshing area. This, in turn, affects gear vibration noise, meshing shock, safety, reliability, and service life through stiffness and error excitation. Therefore, calculating the integrated time-varying mesh stiffness while considering the thermal elastohydrodynamic lubrication of gear teeth is particularly important. The elastic deformation and lubrication state of gear teeth play a crucial role in the gear meshing process. Tooth stiffness and contact stiffness directly influence the time-varying mesh stiffness, a key factor in determining the vibration characteristics of a gear system. Different machining or surface strengthening processes can produce different tooth morphologies. Due to the influence of the gear's operating environment, tooth surface roughness and oil film thickness typically remain at or above the same order of magnitude during gear meshing. This complicates the contact behavior at the gear meshing interface, impacting lubrication performance, friction characteristics, and meshing stability of the gear system. Furthermore, frequent contact between tooth surfaces can lead to lubrication failures such as stress concentration, micropitting, and oil film breakdown. Therefore, it is necessary to consider the influence of tooth surface topography when analyzing thermal elastohydrodynamic lubrication (TEHL) of gears.

[0006] Existing technologies fail to consider the TEHL contact characteristics during gear meshing during design and analysis. Therefore, this paper analyzes the tooth surface roughness and TEHL, and proposes a TEHL contact modeling method that considers tooth surface topography. Summary of the Invention

[0007] The purpose of the present invention is to provide a modeling method of a thermal elastic hydrodynamic lubrication contact model that takes into account the tooth surface morphology, establish a more accurate modeling method that conforms to the gear contact characteristics, and break through the current calculation technology of the comprehensive stiffness of the gear.

[0008] The technical solution of the present invention is as follows: a modeling method of a thermal elastic hydrodynamic lubrication contact model taking into account the tooth surface morphology, which obtains the tooth surface load distribution, inter-tooth friction coefficient and meshing tooth surface temperature rise based on the oil film pressure, oil film thickness, temperature and tooth surface morphology, and solves the rough contact stiffness, oil film stiffness and gear thermal stiffness to replace the Hertz contact stiffness in the traditional model; then combines the bending stiffness, shear stiffness, axial compression stiffness and tooth base stiffness to obtain the comprehensive gear meshing stiffness.

[0009] Using the modified WM fractal function W M (x, y) is used to simulate and characterize the tooth surface morphology; V is obtained based on the tooth surface morphology generated by the WM fractal function. M (x, t), calculate the real-time oil film thickness h(x, t), use the Reynolds equation to establish the gear thermal elastic hydrodynamic lubrication contact model, obtain the oil film stiffness and roughness stiffness of the gear during meshing; establish the fluid energy equation to obtain the gear temperature, and obtain the thermal stiffness of the gear during meshing according to the gear temperature; the comprehensive meshing stiffness k of the gear cm From the tooth base stiffness k f , tooth bending stiffness k b , shear stiffness k s , axial compression stiffness k a , contact stiffness k c and thermal stiffness k T Composition; the comprehensive meshing stiffness expression is;

[0010]

[0011] The middle position and edge position of the tooth surface are selected as the detection objects, marked as a and b respectively; the surface morphometer is used to detect the local area of ​​the detection object. The detection results show that the gear surface morphology has certain fractal characteristics, so the modified WM fractal function is used to generate the three-dimensional fractal tooth surface morphology; the random profile height W of the rough surface of the three-dimensional fractal tooth surface M (x, y) is expressed as:

[0012]

[0013] Where L represents the length of the tooth surface, D represents the fractal dimension of the rough surface, which is related to the density of surface protrusions, G is the characteristic scale parameter, which is related to the height amplitude of the surface protrusions, n is the frequency index, m represents the number of superimposed ridges, x is the measurement distance in the x direction, y is the measurement distance in the y direction, γ is the scaling parameter, and M is the total number of superimposed ridges used to construct the tooth surface. represents random phase, θ = tan -1 (y / x).

[0014] The process of establishing the gear thermal elastohydrodynamic lubrication contact model is as follows:

[0015] Based on the tooth surface contact state under the condition of thermal elastohydrodynamic lubrication, the Reynolds equation under the condition of thermal elastohydrodynamic lubrication is obtained as follows:

[0016]

[0017] Among them, u r (t) is the entrainment velocity between the gear teeth, p represents the oil film pressure, h(x,t) represents the oil film thickness, ρ represents the density of the lubricating oil, η represents the viscosity of the lubricating oil, x0 is the rolling direction, and t is time;

[0018] The oil film thickness is composed of surface elastic deformation and surface roughness, which can be expressed as:

[0019]

[0020] Where h0(t) is the central film thickness of the rigid body in the contact area, that is, the oil film thickness between the two gear teeth in meshing, R(t) is the radius of curvature, and E e is the equivalent elastic modulus, x in is the entrance boundary of the contact area, x out is the exit boundary of the contact area, s is the coordinate of a point on the rough surface; V M (x, t) represents the tooth surface morphology at the tth moment, which is obtained by the modified WM fractal function.

[0021] When the protrusion of the tooth surface exceeds the oil film thickness, the meshing teeth are considered to be in the rough peak contact state; in the rough peak contact state, the load in the tooth contact area is shared by the oil film and the rough peak; the Hertz contact stiffness is replaced by the rough contact stiffness and the oil film stiffness, that is,

[0022] k c =k r +k o

[0023] The rough contact stiffness is expressed as;

[0024]

[0025] Where A n, n0, E, β and σ are the nominal contact area, asperity density, equivalent elastic modulus, equivalent curvature radius of asperity and standard deviation of surface roughness, respectively; is the average film thickness, z represents the distance between the rough surface height and the average height line of the rough peak, and l represents the distance between the average height line of the rough surface and the average height line of the rough peak;

[0026] The oil film stiffness is determined by the oil film thickness and the average pressure, and its expression is:

[0027]

[0028] Where γ0 is the ratio of the bump contact area to the entire area, and B is the bulk modulus of the lubricant, which is expressed as;

[0029]

[0030] Where B0 represents the bulk modulus at ambient pressure; B′0 is the rate of change of the bulk modulus.

[0031] After the oil film pressure and oil film load converge, the real-time temperature is calculated according to the fluid energy equation. The judgment standard is that the oil film pressure iteration error is less than 10 -4 , the oil film load iteration error is less than 10 -3 If the judgment criteria are not met, the initial oil film parameters are updated and the oil film pressure and oil film load are recalculated.

[0032] Due to the shear effect and compression effect between the oil film layers, the contact area of ​​the gear teeth generates a certain amount of heat, which in turn causes the oil film temperature to change. To study the thermal effect of the contact area, the fluid energy equation is rewritten as;

[0033]

[0034] Among them, z i 、c i 、k i and ρ i are the position coordinates, specific heat capacity, thermal conductivity and density of the gear part in contact with the lubricating oil, i = 1, 2;

[0035] Assuming that the temperature of the interface between the oil film and the solid is continuous, the heat flow at the oil film-solid interface satisfies the following conditions:

[0036]

[0037] Where k1 and k2 are the heat transfer coefficients of the driving wheel and the driven wheel respectively; k l is the thermal conductivity of the lubricating oil;

[0038] Assuming that the temperature rise of the intermediate oil film is equal to the temperature rise of the tooth surface, the tooth profile deformation caused by the temperature rise of the tooth surface is expressed as σi , i=1, 2;

[0039]

[0040] Where, L i , i=1, 2 is the tooth thickness, α ai is the tooth top pressure angle, α is the gear pressure angle, r bi is the base circle radius, δ bi represents the steady-state thermal deformation of the base circle, ξ is the linear expansion coefficient, T t Refers to the temperature difference of the tooth surface;

[0041] T t =T M +ΔT-T0

[0042]

[0043] Where r ci , i=1, 2 represents the distance from the meshing point to the center of the driving / driven gear, T roi and T rbi is the temperature of the driving / driven gear shaft and the temperature of the driving / driven gear base circle, μ is the temperature rise coefficient; T M represents the ambient temperature of the meshing area, ΔT represents the temperature rise of the gear surface, T0 represents the internal temperature of the gear material, r bi Indicates the base circle radius of the driving / driven wheel, r oi Indicates the root radius of the driving / driven gear, α ci Indicates the pressure angle of the driving / driven gear at the meshing point. The thermal stiffness of the gear teeth is a series relationship, and the thermal stiffness of a single tooth of the gear teeth is k Ti , i = 1, 2 and meshing thermal stiffness k T for

[0044]

[0045] Calculate the real-time temperature based on the fluid energy equation and judge whether the temperature converges. The judgment standard is that the temperature iteration error is less than 10 -5 If the standard is not met, update the initial temperature and recalculate the real-time temperature based on the fluid energy equation.

[0046] The beneficial effect of the present invention is that it provides a method for modeling a thermal elastohydrodynamic lubrication contact model that takes into account the tooth surface morphology. The model takes into account the tooth surface morphology, lubrication performance, and thermal effects under thermal elastohydrodynamic lubrication. Combining fractal theory with thermal elastohydrodynamic lubrication theory, the microscopic contact stiffness and thermal stiffness of the tooth surface are introduced. On this basis, the necessity of considering the tooth surface morphology when analyzing the comprehensive stiffness of gears is verified. Compared with the existing technology, the present invention can more accurately calculate the contact stiffness and comprehensive stiffness of rough tooth surfaces, thereby providing a new method for calculating the stiffness of gear teeth. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Tooth surface topography measurement. (a) Measurement results for sample a; (b) 3D cloud image of the measurement results for sample a; (c) Schematic diagram of the tooth surface topography for sample a in the X direction; (d) Schematic diagram of the tooth surface topography for sample a in the Y direction; (e) Measurement results for sample b; (f) 3D cloud image of the measurement results for sample b; (g) Schematic diagram of the tooth surface topography for sample b in the X direction; (h) Schematic diagram of the tooth surface topography for sample b in the Y direction.

[0048] Figure 2 The three-dimensional morphology of the surface with different G (D = 2.4). (a) G = 1.02 × 10 8 (b) G = 1.25 × 10 8 (c) G = 1.30 × 10 8 (d) G = 1.42 × 10 8 ; (e) Comparison of surface 3D morphologies of different G;

[0049] Figure 3 The three-dimensional morphology of the surface with different D (G = 1.23 × 10 8 ). (a) D = 2.2, (b) D = 2.4, (c) D = 2.6, (d) D = 2.8; (e) Comparison of surface three-dimensional morphologies at different D;

[0050] Figure 4 is the stiffness model of the gear with rough tooth surface;

[0051] Figure 5 Flowchart for solving the comprehensive meshing stiffness;

[0052] Figure 6 Comparison results of smooth and rough tooth surfaces. (a)-(b) 3D oil film pressure; (c)-(d) 3D oil film thickness; (e)-(f) 3D oil film temperature rise; (g)-(h) 2D oil film pressure and thickness.

[0053] Figure 7 is the gear tooth contact stiffness and combined stiffness. (a)-(b)G=1.02×10 8 ; (c)-(d)G=1.30×10 8 ;(e)-(f)G=1.42×10 8 . DETAILED DESCRIPTION

[0054] Reference Figure 1 The present invention provides a method for modeling a thermal elastohydrodynamic lubrication contact model taking into account the tooth surface morphology, the method comprising the following steps:

[0055] Step 1: Select the tooth surface at the middle and edge of the tooth surface as the test object, and mark them as a and b. Use Newview 9000 3D surface morphometer to test the area of ​​1mm×1mm, and use the modified WM fractal function to generate the three-dimensional fractal tooth surface morphology. The three-dimensional fractal tooth surface morphology is the random contour height W of the rough surface. M (x, y) can be expressed as:

[0056]

[0057] Where L represents the sample length, D represents the fractal dimension of the rough tooth surface, which is related to the density of surface protrusions, G is the characteristic scale parameter, which is related to the height amplitude of the protrusions. n is the frequency index, m represents the number of superimposed ridges. x and y are the measurement distances in the x / y direction, γ is the scaling parameter, and M is the number of superimposed ridges used to construct the surface. stands for random phase.

[0058] In order to clarify the influence of fractal parameters D and G on surface morphology, Figure 2 and Figure 3 The three-dimensional surface morphology under different D and G is given, and the measured length and width are both 1mm. Figure 2 In the experiment, the fractal dimension D remains unchanged (D = 2.4), and the parameter G increases from 1.02×10 8 Increased to 1.42×10 8 It can be noticed that the fractal parameter G has a significant effect on the peak value of the surface. In other words, as G increases, the peak value of the surface increases significantly. By comparing Figure 3 From the surface morphology in the figure, it can be found that the fractal dimension D determines the peak density and surface smoothness. As D decreases and G increases (i.e., the roughness Ra increases), the tooth surface morphology presents a more complex shape, reduced smoothness and higher peaks. Therefore, W M (x, y) can be used to simulate and characterize the tooth surface morphology.

[0059] Step 2: Based on the tooth surface contact state under the TEHL condition, the Reynolds equation under the TEHL condition is derived as follows:

[0060]

[0061] Among them, u r (t) is the entrainment velocity between gear teeth, p, h, ρ and η represent the oil film pressure, oil film thickness, density and viscosity of lubricating oil respectively, ρ e and ρ* represent the characteristic parameters of the fluid in the film thickness direction, x is the rolling direction, and t is the time.

[0062] The oil film thickness is composed of surface elastic deformation and surface roughness and can be expressed as:

[0063]

[0064] Where h0(t) is the displacement of the rigid body, R(t) is the radius of curvature, and E e is the equivalent elastic modulus, x in and x out are the inlet and outlet boundaries of the contact area respectively, and s is the coordinate of a point on the surface.

[0065] Considering the thermal effect in the contact area, the viscosity-pressure-temperature equation proposed by Roelands and the density-pressure-temperature equation derived by Dowson-Higginson can be expressed as:

[0066]

[0067] Where ρ0, η0, and T0 are the initial values ​​of the oil density, viscosity, and ambient temperature, respectively; T(x, t) is the surface temperature rise; s0 represents the viscosity-temperature coefficient; and z0 is the viscosity-pressure coefficient.

[0068] Due to the shear and compression effects between the oil film layers, the contact area of ​​the gear teeth will generate a certain amount of heat, which will cause the oil film temperature to change. To study the thermal effect of the contact area, the fluid energy equation can be written as

[0069]

[0070] Among them, k f and c f Represent the thermal coefficient and specific heat capacity of lubricating oil, u x represents the velocity of the lubricating oil in the x direction.

[0071] Simplifying equation (6), it can be rewritten as

[0072]

[0073] Among them, z i 、c i 、k i and ρ i (i=1, 2) are the solid position coordinates, specific heat capacity, thermal coefficient and density respectively.

[0074] Assuming that the temperature of the interface between the oil film and the solid is continuous, the heat flow at the oil-solid interface should satisfy

[0075]

[0076] Where k1 and k2 are the solid thermal conductivity coefficients respectively.

[0077] Step 3: Since the tooth surface inevitably produces rough morphology during the machining process, under the thermal elastic hydrodynamic lubrication, rough contact and oil film exist in the contact area at the same time, and the contact stiffness is composed of the oil film stiffness and the roughness stiffness. In the present invention, the comprehensive meshing stiffness k of the gear is cm From the tooth base stiffness k f , tooth bending stiffness k b , shear stiffness k s , axial compression stiffness k a and contact stiffness k c (From the rough stiffness k r and oil film stiffness k o ) consists of several parts. Figure 4 The equivalent contact model with rough tooth surface and the schematic diagram of gear comprehensive stiffness are given. The comprehensive stiffness expression is:

[0078]

[0079] Due to different tooth surface processing techniques, when the micro-protrusions on the tooth surface exceed the oil film thickness, the meshing teeth are considered to be in a rough peak contact state. At this time, according to the Johnson load sharing concept in hybrid TEHL, the load in the tooth contact area is shared by the oil film and the rough peak. Therefore, the Hertz contact stiffness is replaced by the rough contact stiffness and the oil film stiffness, that is,

[0080] k c =k r +k o (10)

[0081] The roughness stiffness can be expressed as

[0082]

[0083] Where A n , n, E, β, and σ are the nominal contact area, asperity density, equivalent elastic modulus, equivalent curvature radius of asperity, and surface roughness standard deviation, respectively. h is the average film thickness, z represents the distance between the asperity height and the average height line of the asperity peaks, and l represents the distance between the average height line of the asperity surface and the average height line of the asperity peaks.

[0084] The oil film stiffness is determined by the oil film thickness and the average pressure, and its expression is:

[0085]

[0086] Where γ is the ratio of the bump contact area to the entire area, and B is the bulk modulus of the lubricant, which can be expressed as,

[0087]

[0088] Where B0 is the bulk modulus at ambient pressure and B'0 is the rate of change of the bulk modulus.

[0089] Step 4: To facilitate the calculation of tooth surface thermal deformation, it is assumed that the temperature rise of the intermediate oil film is approximately equal to the temperature rise of the tooth surface. Therefore, the tooth profile deformation caused by the temperature rise of the tooth surface can be expressed as σ i (i=1, 2)

[0090]

[0091] Where, L i (i=1, 2) is the tooth thickness, α ai is the tooth top pressure angle, α is the gear pressure angle, r bi is the base circle radius, δ bi represents the steady-state thermal deformation of the base circle, ξ is the linear expansion coefficient, T t Refers to the temperature difference between the tooth surfaces.

[0092]

[0093] Where r ci (i=1, 2) represents the distance from the meshing point to the center of the driving / driven gear, T roi and T rbi is the temperature of the driving / driven gear shaft and base circle, and μ is the temperature rise coefficient.

[0094] Since the thermal stiffness of gear teeth is in series relationship, the thermal stiffness of a single gear tooth k Ti (i=1, 2) and meshing thermal stiffness k T for

[0095]

[0096] Based on the above analysis, Figure 5 A detailed flow chart for solving the comprehensive meshing stiffness under the condition of thermal elastohydrodynamic lubrication is given.

[0097] Step 5: In order to verify the influence of tooth surface morphology on gear tooth contact characteristics, Figure 6 A comparison of the oil film pressure, oil film thickness, and center temperature rise of the oil film was conducted on smooth and rough tooth surfaces. This comparison revealed that due to the alternating meshing of single and double teeth during gear meshing, all graphs exhibit significant fluctuations along the meshing line. Furthermore, the maximum oil film pressure, temperature rise, and minimum oil film thickness all occur in the single-tooth meshing region, which is closely related to the load distribution on the tooth surface. For rough tooth surfaces, the oil film pressure, oil film thickness, and temperature rise exhibit significant fluctuations. Significantly affected by the elastic deformation and random distribution of local roughness, the pressure and temperature are significantly greater than those on smooth tooth surfaces, while the oil film thickness exhibits the opposite trend. This indicates that roughness significantly influences the contact state of gear tooth surfaces, and the influence of tooth surface topography must be considered in subsequent analysis.

[0098] Step 6, solve the gear tooth contact stiffness k for different characteristic scale parameters G c and comprehensive stiffness k cm . Figure 7 The changes in contact stiffness and combined stiffness for different G parameters are presented. Since the fractal parameter G is closely related to the peak value of tooth surface roughness, smaller G values ​​yield smaller fluctuations in the amplitude of the tooth surface basic stiffness and combined stiffness. However, as G increases, the fluctuations in the contact stiffness and combined stiffness become more pronounced, indicating that the gear teeth are in a mixed thermal elastohydrodynamic lubrication state during meshing.

Claims

1. A method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology, characterized in that: According to the oil film pressure, oil film thickness, temperature and tooth surface morphology, the tooth surface load distribution, inter-tooth friction coefficient and meshing tooth surface temperature rise are obtained, and the rough contact stiffness, oil film stiffness and gear thermal stiffness are solved to replace the Hertzian contact stiffness in the traditional model; then the bending stiffness, shear stiffness, axial compression stiffness and tooth base stiffness are combined to obtain the comprehensive gear meshing stiffness.

2. The method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology according to claim 1, characterized in that: Using the modified WM fractal function W M (x, y) is used to simulate and characterize the tooth surface morphology; V is obtained based on the tooth surface morphology generated by the WM fractal function. M (x, t), calculate the real-time oil film thickness h(x, t), use the Reynolds equation to establish the gear thermal elastohydrodynamic lubrication contact model, and obtain the oil film stiffness and rough contact stiffness of the gear during meshing; Establish the fluid energy equation to obtain the gear temperature, and obtain the thermal stiffness of the gear during the meshing process based on the gear temperature; the gear comprehensive meshing stiffness k cm From the tooth base stiffness k f , tooth bending stiffness k b , shear stiffness k s , axial compression stiffness k a , contact stiffness k c and thermal stiffness k T Composition; the comprehensive meshing stiffness expression is; 3. The method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology according to claim 2, characterized in that: The middle position and edge position of the tooth surface are selected as the detection objects, marked as a and b respectively; the surface morphometer is used to detect the local area of ​​the detection object. The detection results show that the gear surface morphology has certain fractal characteristics, so the modified WM fractal function is used to generate the three-dimensional fractal tooth surface morphology; the random profile height W of the rough surface of the three-dimensional fractal tooth surface M (x, y) is expressed as: Where L represents the length of the tooth surface, D represents the fractal dimension of the rough surface, which is related to the density of surface protrusions, G is the characteristic scale parameter, which is related to the height amplitude of the surface protrusions, n is the frequency index, m represents the number of superimposed ridges, x is the measurement distance in the x direction, y is the measurement distance in the y direction, γ is the scaling parameter, and M is the total number of superimposed ridges used to construct the tooth surface. represents random phase, θ = tan -1 (y / x).

4. The method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology according to claim 3, characterized in that: The process of establishing the gear thermal elastohydrodynamic lubrication contact model is as follows: Based on the tooth surface contact state under the condition of thermal elastohydrodynamic lubrication, the Reynolds equation under the condition of thermal elastohydrodynamic lubrication is obtained as follows: Among them, u r (t) is the entrainment velocity between the gear teeth, p represents the oil film pressure, h(x,t) represents the oil film thickness, ρ represents the density of the lubricating oil, η represents the viscosity of the lubricating oil, x0 is the rolling direction, and t is time; The oil film thickness is composed of surface elastic deformation and surface roughness, which can be expressed as: Where h0(t) is the central film thickness of the rigid body in the contact area, that is, the oil film thickness between the two gear teeth in meshing, R(t) is the radius of curvature, and E e is the equivalent elastic modulus, x in is the entrance boundary of the contact area, x out is the exit boundary of the contact area, s is the coordinate of a point on the rough surface; V M (x, t) represents the tooth surface morphology at the tth moment, which is obtained by the modified WM fractal function.

5. The method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology according to claim 4, characterized in that: When the protrusion of the tooth surface exceeds the oil film thickness, the meshing teeth are considered to be in the rough peak contact state; in the rough peak contact state, the load in the tooth contact area is shared by the oil film and the rough peak; the Hertz contact stiffness is replaced by the rough contact stiffness and the oil film stiffness, that is, k c =k r +k o The rough contact stiffness is expressed as; Where A n , n0, E, β and σ are the nominal contact area, asperity density, equivalent elastic modulus, equivalent curvature radius of asperity and standard deviation of surface roughness, respectively; is the average film thickness, z represents the distance between the rough surface height and the average height line of the rough peak, and l represents the distance between the average height line of the rough surface and the average height line of the rough peak; The oil film stiffness is determined by the oil film thickness and the average pressure, and its expression is: Where γ0 is the ratio of the bump contact area to the entire area, and B is the bulk modulus of the lubricant, which is expressed as; Where B0 represents the bulk modulus at ambient pressure; B′0 is the rate of change of the bulk modulus.

6. The method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology according to claim 4, characterized in that: After the oil film pressure and oil film load converge, the real-time temperature is calculated according to the fluid energy equation. The judgment standard is that the oil film pressure iteration error is less than 10 -4 , the oil film load iteration error is less than 10 -3 If the judgment criteria are not met, the initial oil film parameters are updated and the oil film pressure and oil film load are recalculated.

7. The method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology according to claim 2, characterized in that: Due to the shear effect and compression effect between the oil film layers, the contact area of ​​the gear teeth generates a certain amount of heat, which in turn causes the oil film temperature to change. To study the thermal effect of the contact area, the fluid energy equation is rewritten as; Among them, z i 、c i 、k i and ρ i are the position coordinates, specific heat capacity, thermal conductivity and density of the gear part in contact with the lubricating oil, i = 1, 2; Assuming that the temperature of the interface between the oil film and the solid is continuous, the heat flow at the oil film-solid interface satisfies the following conditions: Where k1 and k2 are the heat transfer coefficients of the driving wheel and the driven wheel respectively; k l is the thermal conductivity of the lubricating oil; Assuming that the temperature rise of the intermediate oil film is equal to the temperature rise of the tooth surface, the tooth profile deformation caused by the temperature rise of the tooth surface is expressed as σ i , i=1, 2; Where, L i , i=1, 2 is the tooth thickness, α ai is the tooth top pressure angle, α is the gear pressure angle, r bi is the base circle radius, δ bi represents the steady-state thermal deformation of the base circle, ξ is the linear expansion coefficient, T t Refers to the temperature difference of the tooth surface; T t =T M +ΔT-T0 Where r ci , i=1, 2 represents the distance from the meshing point to the center of the driving / driven gear, T roi and T rbi is the temperature of the driving / driven gear shaft and the temperature of the driving / driven gear base circle, μ is the temperature rise coefficient; T M represents the ambient temperature of the meshing area, ΔT represents the temperature rise of the gear surface, T0 represents the internal temperature of the gear material, r bi Indicates the base circle radius of the driving / driven wheel, r oi Indicates the root radius of the driving / driven gear, α ci Indicates the pressure angle of the driving / driven gear at the meshing point; The thermal stiffness of the gear teeth is in series relationship, and the thermal stiffness of a single gear tooth k Ti , i = 1, 2 and meshing thermal stiffness k T for 8. The method for modeling a thermal elastohydrodynamic lubrication contact model considering tooth surface morphology according to claim 7, characterized in that: Calculate the real-time temperature based on the fluid energy equation and judge whether the temperature converges. The judgment standard is that the temperature iteration error is less than 10 -5 ; If the standard is not met, the initial temperature is updated and the real-time temperature is recalculated based on the fluid energy equation.

Images