Straight gear meshing rigidity calculation method considering machining process factors and abrasion factors

Abstract

The invention provides a straight gear meshing stiffness calculation method considering machining process factors and wear factors, and relates to the field of gear mechanical analysis. The method comprises the following steps: according to the initial roughness of a gear, constructing a gear rough morphology representation model based on a W-M function of a fractal theory, and obtaining the initial rough morphology of the tooth surface of the straight gear; based on an Archard wear model, constructing a gear tooth surface rough morphology evolution model, and obtaining an evolved tooth surface rough morphology; deducing the relationship between the characterization parameters of the evolved tooth surface rough morphology and the power spectrum density of the gear surface rough morphology; on the basis of an energy method, a fractal theory and an elastohydrodynamic lubrication theory, a straight gear meshing stiffness calculation model considering a lubricating oil film and tooth surface abrasion rough morphology evolution is constructed, the straight gear meshing stiffness under different meshing periods is obtained, and the influence of the tooth surface abrasion rough morphology evolution and the lubricating oil film on the straight gear meshing stiffness is comprehensively considered.

Description

Technical Field

[0001] The invention relates to the field of gear mechanics analysis, and in particular to a method for calculating the meshing stiffness of spur gears taking into account processing factors and wear factors. Background Art

[0002] As an important transmission system in mechanical equipment such as aircraft engines, helicopters, and wind power generation, gear systems often operate in harsh and complex working conditions. With long-term operation, gear tooth surface wear is inevitable. Due to processing factors, gears have a certain degree of roughness, that is, a surface morphology composed of multiple micro-convex bodies. With long-term meshing, the interaction between micro-convex bodies causes the micro-convex body peaks to be removed, and the micro-convex body height and average line of the rough tooth surface change, thereby generating a new tooth profile and surface morphology. In addition to the surface morphology, the gear meshing interface usually has lubricating oil film lubrication. The change of gear tooth profile causes the load-bearing capacity along the tooth profile line to change, and the oil film thickness will also change, thereby affecting the oil film stiffness. The accumulated tooth surface wear changes the meshing characteristics between the gear meshing interfaces. Gear meshing stiffness is an important internal excitation of the gear system. Gear tooth surface wear will lead to a new meshing relationship between gears, resulting in a change in gear meshing stiffness. Therefore, it is of great significance to establish a surface morphology evolution and meshing stiffness calculation model for spur gears under wear considering rough morphology and lubricating oil film.

[0003] Regarding the gear wear modeling method, the existing technologies are as follows: Taking the Chinese invention patent CN112434432A as an example, a meshing stiffness modeling method for external meshing spur gears under wear is disclosed. The wear distribution of the wear amount of the external meshing spur gears on the tooth profile is used to construct a worn gear tooth meshing model, and then the meshing stiffness of the external meshing gear is calculated. Taking the Chinese invention patent CN115795718A as an example, a gear contact fatigue life prediction considering tooth surface wear is disclosed. By constructing a gear finite element model, based on the Archard wear model and the Chaboche continuous cumulative damage model, the gear loss amount of different cycles is obtained, and then the contact fatigue life is predicted. Taking the Chinese invention patent CN110929350A as an example, a friction heat flow prediction method considering tooth surface wear is disclosed. The accumulated amount of tooth surface wear is obtained based on the Archard wear model, and the gear friction heat flow is derived using the friction coefficient. However, the technical solutions disclosed in these patent documents focus on the influence of the distribution of gear wear along the tooth profile line on the gear meshing characteristics, and ignore the influence of the rough morphology and lubricating oil film between the gear meshing interfaces on the meshing characteristics of the gear under wear.

[0004] Regarding the calculation method of gear meshing stiffness considering rough morphology, the existing technologies are as follows: Taking Chinese invention patent CN106844818A as an example, a calculation method of three-dimensional contact stiffness of spur gears based on rough morphology is disclosed, the contact pressure distribution of smooth tooth surface is calculated by dividing hexahedral mesh by finite element, and the contact stiffness of tooth surface considering rough morphology of hexahedral mesh is calculated based on fractal contact theory. Taking Chinese invention patent CN114580092A as an example, an algorithm of dynamic contact stiffness of gear considering tooth surface roughness is disclosed, and the contact stiffness considering rough morphology is obtained based on fractal contact theory instead of the traditional contact stiffness calculated based on smooth Hertz theory, and the gear meshing stiffness considering rough morphology is composed of bending stiffness, shear stiffness, axial compression stiffness and matrix deformation stiffness. Taking the Chinese invention patent CN117454626A as an example, a method for analyzing the fitting characteristics of spur gears with tooth surface wear faults based on improved fractals is disclosed. The gear tooth load contact analysis method is combined with fractal contact theory, and the gear meshing characteristics and wear depth are analyzed based on the Archard wear model. However, the technical methods disclosed in these patent documents focus on the influence of rough morphology on gear contact stiffness, ignoring the influence of gear rough morphology evolution on gear meshing stiffness, and the influence of lubricating oil film on gear meshing stiffness.

[0005] In summary, the technical solutions disclosed in the existing patent documents cannot be fully applicable to the calculation of surface morphology evolution and meshing stiffness of spur gears under wear, and the influence of rough morphology and lubricating oil film on spur gear wear has not been considered. Summary of the invention

[0006] In order to solve a technical problem existing in the prior art, an embodiment of the present invention provides a method for calculating the meshing stiffness of spur gears taking into account processing factors and wear factors, so as to make up for the lack of the tooth surface roughness morphology evolution and meshing stiffness calculation method of spur gears under wear with meshing cycle. The technical solution is as follows:

[0007] A method for calculating the meshing stiffness of spur gears taking into account processing factors and wear factors includes:

[0008] S1, according to the initial roughness R of the gear a , based on the WM function of fractal theory, a gear roughness morphology characterization model is constructed to obtain the initial roughness morphology of the spur gear tooth surface;

[0009] S2. According to the initial rough morphology of the spur gear tooth surface and the involute tooth profile of the gear, based on the Archard wear model, a gear tooth surface rough morphology evolution model is constructed to obtain the evolved tooth surface rough morphology;

[0010] S3. Based on the evolved tooth surface roughness morphology, deriving the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectral density of the gear surface roughness morphology;

[0011] S4. According to the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectral density of the gear surface roughness morphology, based on the energy method, fractal theory and elastohydrodynamic lubrication theory, a spur gear meshing stiffness calculation model considering the evolution of lubricating oil film and tooth surface wear roughness morphology is constructed to obtain the spur gear meshing stiffness under different meshing cycles.

[0012] Optionally, the gear roughness characterization model of S1 is formula (1):

[0013] ; (1)

[0014] Among them, z(x) represents the height of the micro-convex body of the rough morphology, G is the fractal characteristic parameter of the rough morphology, and is related to the roughness R a The relationship is ;

[0015] The initial rough morphology of the tooth surface and the involute tooth profile of the gear are used to construct the gear tooth surface rough morphology evolution model based on the Archard wear model. The evolved tooth surface rough morphology includes:

[0016] S201. Based on the gear roughness characterization model and the gear involute tooth profile, derive a tooth profile with a roughness shape. The tooth profile with a roughness shape is expressed as formula (2):

[0017] ; (2)

[0018] Among them, h ini (x) is the height of the initial tooth profile of the spur gear from the center line of the gear tooth, h inv (x) is the height of the involute tooth profile from the center line of the gear tooth;

[0019] S202. Based on the Archard wear model, the wear distribution of the spur gear along the tooth profile is obtained. The expression of the wear along the tooth profile line is formula (3):

[0020] ; (3)

[0021] Among them, h w (x) is the wear amount along the tooth profile, N is the evolutionary meshing cycle, k w To consider the wear coefficient of friction lubrication, P M is the contact pressure, s M is the relative sliding distance;

[0022] S203. Based on the wear amount along the tooth profile line, the tooth profile of the spur gear after evolution is obtained. The expression of the tooth profile of the spur gear after evolution is formula (4):

[0023] ; (4)

[0024] Among them, h new (x) is the tooth profile of the spur gear after evolution;

[0025] S204, after detrending the evolved tooth profile, the evolved tooth surface roughness morphology of the spur gear is obtained, and the expression of the evolved tooth surface roughness morphology is formula (5):

[0026] ; (5)

[0027] Among them, z new (x) is the tooth surface roughness morphology after evolution, f trend () is the fitting trend of the new tooth profile.

[0028] Optionally, the relationship between the characterization parameter of the tooth surface roughness morphology after the derivation and evolution of S3 and the power spectrum density of the gear surface roughness morphology is formula (6):

[0029] ; (6).

[0030] Optionally, according to the relationship between the characterization parameters of the evolved tooth surface roughness and the power spectral density of the gear surface roughness, the S4 constructs a spur gear meshing stiffness calculation model that considers the evolution of lubricating oil film and tooth surface wear roughness based on the energy method, fractal theory and elastohydrodynamic lubrication theory, and obtains the spur gear meshing stiffness under different meshing cycles, including:

[0031] S401, obtaining a fractal characteristic parameter G of the rough morphology and a fractal dimension D of the rough morphology according to a relationship between the characterization parameters of the evolved tooth surface rough morphology and the power spectrum density of the gear surface rough morphology;

[0032] S402. Based on the energy method, the gear teeth are equivalent to cantilever beams, and the new meshing relationship of the gears after wear is considered. The expressions of the bending stiffness, shear stiffness and axial compression stiffness of the spur gear under wear are derived through the bending energy, shear energy and axial compression energy of the cantilever beam.

[0033] S403. Based on the elastic-plastic deformation theory of micro-convex bodies and combined with the WM function characterization model, a fractal contact model for the evolution of the wear roughness morphology of spur gear tooth surfaces is constructed to obtain the evolved fractal contact stiffness.

[0034] S404, the meshing of the gear teeth is equivalent to two cylinders, and the equivalent curvature radius and entrainment speed of the gear are obtained through the gear structure parameters and working condition parameters;

[0035] S405, using a three-dimensional line contact elastohydrodynamic lubrication model equation to obtain oil film pressure and oil film thickness;

[0036] S406. Based on bending stiffness, shear stiffness, axial compression stiffness, fractal contact stiffness, matrix deformation stiffness and oil film stiffness, the meshing stiffness of the spur gear under wear considering the rough morphology and lubricating oil film is obtained.

[0037] Optionally, the step of obtaining the fractal characteristic parameter G and the fractal dimension D of the rough morphology according to the relationship between the characterization parameter of the evolved tooth surface rough morphology and the power spectrum density of the gear surface rough morphology in S401 includes:

[0038] The rough morphology z after the evolution new (x) Perform power spectrum density analysis, obtain the slope and intercept of the straight line through least squares fitting, and obtain the fractal characteristic parameter G and fractal dimension D of the rough morphology.

[0039] Optionally, in S402, based on the energy method, the gear teeth are equivalent to a cantilever beam, and the new meshing relationship of the gears after wear is considered. The expressions of the bending stiffness, shear stiffness and axial compression stiffness of the spur gear under wear are derived through the bending energy, shear energy and axial compression energy of the cantilever beam, including:

[0040] The bending stiffness of the spur gear under wear is given by formula (7):

[0041] ; (7)

[0042] Among them, k b_wear is the bending stiffness of the spur gear under wear, h w is the wear depth along the tooth profile, R b is the base circle radius of the gear, E is the elastic modulus, L is the tooth width, α is the meshing angle, α1 is the meshing angle where the meshing force is tangent to the base circle, and α2 is the half tooth angle on the base circle;

[0043] The shear stiffness of the spur gear under wear is given by formula (8):

[0044] ; (8)

[0045] Among them, k s_wear is the shear stiffness of the spur gear under wear, ν is the Poisson’s ratio;

[0046] The axial compressive stiffness of the spur gear under wear is given by formula (9):

[0047] ; (9)

[0048] Among them, k a_wear is the axial compressive stiffness of the spur gear under wear.

[0049] Optionally, the S403 is based on the elastoplastic deformation theory of micro-convex bodies and combined with the WM function characterization model to construct a fractal contact model for the evolution of the wear roughness morphology of the spur gear tooth surface, and the formula for obtaining the evolved fractal contact stiffness is formula (10):

[0050] ; (10)

[0051] Among them, k fra is the fractal contact stiffness. E * is the equivalent elastic modulus, a c is the theoretical contact area, a lmax is the maximum contact area, λ c is the surface contact coefficient.

[0052] Optionally, the step S405 of obtaining the oil film pressure and the oil film thickness by using the three-dimensional line contact elastohydrodynamic lubrication model equation comprises:

[0053] The three-dimensional line contact elastohydrodynamic lubrication model includes the Reynolds equation, the film thickness equation, the viscosity-pressure equation, the density-pressure equation and the load equation. The expression of the Reynolds equation is formula (11):

[0054] ; (11)

[0055] Among them, p is the oil film pressure, h is the film thickness, ρ is the density, η * is the viscosity, u r is the suction speed,

[0056] In the three-dimensional line contact elastohydrodynamic lubrication model, the tooth surface roughness morphology that evolves with the meshing cycle is added to the film thickness equation. The expression of the film thickness equation is formula (12):

[0057] ; (12)

[0058] Among them, h0 is the minimum film thickness of the two contact surfaces, R * is the equivalent radius of curvature, v is the elastic change, z new (x) is the rough morphology of the tooth surface after evolution;

[0059] By solving the three-dimensional line contact elastohydrodynamic lubrication model, the oil film pressure p of the spur gear under wear is obtained. _wear and oil film thickness h _wear , the oil film stiffness is obtained, and the expression of the oil film stiffness is formula (13):

[0060] ; (13)

[0061] Among them, k oill_wear is the oil film stiffness of the spur gear under wear, A is the contact area, m and k are the number of grid divisions.

[0062] Optionally, the meshing stiffness of the spur gear under wear considering the rough morphology and lubricating oil film in S406 is expressed as formula (14):

[0063] ; (14)

[0064] Among them, k t_wear k is the mesh stiffness of spur gears under wear considering roughness and lubricating oil film. bp_wear is the bending stiffness of the pinion wear, k bg_wear is the bending stiffness of the large gear due to wear, k sp_wear is the shear stiffness of the pinion wear, k sg_wear is the shear stiffness of the large gear wear, k ap_wear is the axial compression stiffness of the pinion, k ag_wear is the axial compression stiffness of the large gear, k fp is the base deformation stiffness of the pinion, k fg is the deformation stiffness of the large gear matrix.

[0065] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0066] The present invention proposes to calculate the meshing stiffness of spur gears by considering the evolution of the rough morphology of the tooth surface of the spur gear with the meshing cycle, and obtains a method for calculating the fractal contact stiffness that evolves with the meshing cycle, which solves the current problem of lack of modeling of the evolution of the rough morphology of the tooth surface of the spur gear under wear; the present invention incorporates the coupling effect of rough morphology and elastohydrodynamic lubrication into the meshing stiffness calculation method of spur gears under wear, considers the influence of the evolution of rough morphology and the evolution of lubricating oil film under wear, and obtains a more accurate meshing stiffness of spur gears under wear. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0068] Figure 1 A flow chart of the spur gear meshing stiffness method proposed by the present invention taking into account the evolution of lubricating oil film and tooth surface wear roughness morphology;

[0069] Figure 2 Schematic diagram of the interaction between the roughness morphology and lubricating oil film at the meshing interface of spur gears;

[0070] Figure 3 Schematic diagram of the evolution of rough surface and lubricating oil film under wear of spur gears;

[0071] Figure 4 This is a schematic diagram of the cantilever beam model of the worn gear teeth of a spur gear;

[0072] FIG5(a) is a graph showing the relationship between the curvature radius of a spur gear structural parameter and the meshing angle along the tooth profile line; FIG5(b) is a graph showing the relationship between the entrainment speed of a spur gear structural parameter and the meshing angle along the tooth profile line;

[0073] FIG6(a) is a graph showing the relationship between the contact load and the meshing angle of the tooth profile when the spur gear is worn; FIG6(b) is a graph showing the relationship between the Hertzian contact stress and the meshing angle of the tooth profile when the spur gear is worn;

[0074] FIG7 is a relationship diagram of the wear amount along the tooth profile line and the change of the meshing angle along the tooth profile line under the wear of the spur gear; FIG7(a) is a small gear, and FIG7(b) is a large gear;

[0075] Figure 8 This is the relationship diagram of the change of meshing angle along the tooth profile line of the surface roughness of the spur gear under wear;

[0076] Figure 9 is a curve relationship diagram of oil film pressure and oil film thickness of elastohydrodynamic lubrication considering rough morphology of meshing interface of spur gear under wear, Figure 9(a) is oil film pressure, and Figure 9(b) is oil film thickness;

[0077] Fig.10 Mesh stiffness of spur gears considering the evolution of lubricating oil film and tooth surface wear roughness morphology. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0079] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "one", "one" or "the" do not indicate a quantitative limitation, but indicate the existence of at least one. Words such as "include" or "comprise" mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0080] It should be noted that the terms "up", "down", "left", "right", "front", "back", etc. used in the present invention are only used to indicate relative position relationships. When the absolute position of the described object changes, the relative position relationship may also change accordingly.

[0081] like Figure 2 As shown in the figure, due to the processing factors, the gear has a certain degree of roughness, that is, the surface morphology is composed of multiple micro-protrusions. In addition to the surface morphology, the gear meshing interface usually has lubrication by lubricating oil film. Therefore, the gear meshing interface is affected by the combined action of micro-protrusions and oil film.

[0082] A pair of spur gears in a certain type of engine gearbox is taken as a research case, and its structure, working conditions, materials and lubrication performance parameters are shown in Table 1.

[0083] Table 1 Gear structure parameters and lubricating oil parameters

[0084]

[0085] like Figure 1-Figure 4 As shown, the present invention proposes a method for calculating the meshing stiffness of spur gears taking into account processing factors and wear factors, wherein the processing factors include lubricating oil film and tooth surface wear roughness morphology evolution.

[0086] This method specifically comprises the following steps:

[0087] S1, according to the initial roughness R of the gear a , based on the WM function of fractal theory, a gear roughness morphology characterization model is constructed to obtain the initial roughness morphology of the spur gear tooth surface;

[0088] S2. According to the initial rough morphology of the spur gear tooth surface and the involute tooth profile of the gear, based on the Archard wear model, a gear tooth surface rough morphology evolution model is constructed to obtain the evolved tooth surface rough morphology;

[0089] S3. Based on the evolved tooth surface roughness morphology, deriving the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectral density of the gear surface roughness morphology;

[0090] S4. According to the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectral density of the gear surface roughness morphology, based on the energy method, fractal theory and elastohydrodynamic lubrication theory, a spur gear meshing stiffness calculation model considering the evolution of lubricating oil film and tooth surface wear roughness morphology is constructed to obtain the spur gear meshing stiffness under different meshing cycles.

[0091] In a specific implementation mode, S1, according to the initial roughness R of the gear a Based on the WM function of fractal theory, a gear roughness morphology characterization model is constructed to obtain the initial roughness morphology of the spur gear tooth surface:

[0092] The WM function has the mathematical characteristics of continuity and non-differentiability, and can describe the multi-scale characteristics of the rough morphology. The initial rough morphology of the spur gear is characterized by the WM function, and the gear rough morphology characterization model is formula (1):

[0093] ; (1)

[0094] Among them, z(x) represents the height of the micro-convex body of the rough morphology, G is the fractal characteristic parameter of the rough morphology, and is related to the roughness R a The relationship is ;

[0095] D is the fractal dimension of the roughness, which is related to the roughness R a The relationship is ,γ is the spatial frequency of the rough surface, φ n is a random phase.

[0096] In a specific implementation mode, S2, according to the initial rough morphology of the spur gear tooth surface and the gear involute tooth profile, based on the Archard wear model, a gear tooth surface rough morphology evolution model is constructed to obtain the evolved tooth surface rough morphology:

[0097] S201. Based on the initial rough morphology of the spur gear surface characterized by the WM function and the gear involute tooth profile, a tooth profile with a rough morphology is derived. The expression of the tooth profile with a rough morphology is formula (2):

[0098] ; (2)

[0099] Among them, h ini (x) is the height of the initial tooth profile of the spur gear from the center line of the gear tooth, h inv (x) is the height of the involute tooth profile from the center line of the gear tooth;

[0100] S202. As the meshing cycle changes, the tooth surface of the spur gear wears and the height of the micro-convex body on the surface changes, resulting in a change in the tooth profile of the spur gear. The wear distribution of the spur gear along the tooth profile is obtained based on the Archard wear model. The expression of the wear along the tooth profile line is formula (3):

[0101] ; (3)

[0102] Among them, h w (x) is the wear amount along the tooth profile, N is the evolutionary meshing cycle, k w To consider the wear coefficient of friction lubrication, P M is the contact pressure, s M is the relative sliding distance;

[0103] S203. Based on the wear amount along the tooth profile line, the tooth profile of the spur gear after evolution is obtained. The expression of the tooth profile of the spur gear after evolution is formula (4):

[0104] ; (4)

[0105] Among them, h new (x) is the tooth profile of the spur gear after evolution;

[0106] S204, after detrending the evolved tooth profile, the evolved tooth surface roughness morphology of the spur gear is obtained, and the expression of the evolved tooth surface roughness morphology is formula (5):

[0107] ; (5)

[0108] Among them, z new (x) is the tooth surface roughness morphology after evolution, f trend () is the fitting trend of the new tooth profile.

[0109] In a specific implementation manner, S3, based on the evolved tooth surface roughness morphology, the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectrum density of the gear surface roughness morphology is derived, and the relationship is formula (6):

[0110] ; (6)

[0111] P(ω) is the power spectral density of the roughness morphology of the spur gear surface.

[0112] A specific implementation method, S4, according to the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectral density of the gear surface roughness morphology, based on the energy method, fractal theory and elastohydrodynamic lubrication theory, a spur gear meshing stiffness calculation model considering the evolution of lubricating oil film and tooth surface wear roughness morphology is constructed, and the spur gear meshing stiffness under different meshing cycles is obtained, including:

[0113] This step is mainly based on the tooth surface roughness morphology and characterization parameters of the spur gear evolution, based on the energy method, fractal theory and elastohydrodynamic lubrication theory, to construct a spur gear meshing stiffness calculation model that takes into account the evolution of lubricating oil film and tooth surface wear roughness morphology, and obtain the spur gear meshing stiffness under different meshing cycles.

[0114] The meshing stiffness of spur gears considering the coupling effects of roughness morphology and lubricating oil film includes bending stiffness, shear stiffness, axial compression stiffness, fractal contact stiffness, matrix deformation stiffness and oil film stiffness.

[0115] S401, according to the relationship between the characterization parameters of the evolved tooth surface roughness and the power spectrum density of the gear surface roughness, obtain the fractal characteristic parameter G of the roughness and the fractal dimension D of the roughness:

[0116] The rough morphology z after the evolution new (x) Perform power spectrum density analysis, obtain the slope and intercept of the straight line through least squares fitting, and obtain the fractal characteristic parameter G and fractal dimension D of the rough morphology.

[0117] S402. Based on the energy method, the gear teeth are equivalent to cantilever beams, and the new meshing relationship of the gears after wear is considered. The expressions of the bending stiffness, shear stiffness and axial compression stiffness of the spur gear under wear are derived through the bending energy, shear energy and axial compression energy of the cantilever beam.

[0118] The bending stiffness of the spur gear under wear is given by formula (7):

[0119] ; (7)

[0120] Among them, k b_wear is the bending stiffness of the spur gear under wear, h w is the wear depth along the tooth profile, R b is the base circle radius of the gear, E is the elastic modulus, L is the tooth width, α is the meshing angle, α1 is the meshing angle where the meshing force is tangent to the base circle, and α2 is the half tooth angle on the base circle;

[0121] The shear stiffness of the spur gear under wear is given by formula (8):

[0122] ; (8)

[0123] Among them, k s_wear is the shear stiffness of the spur gear under wear, is Poisson's ratio;

[0124] The axial compressive stiffness of the spur gear under wear is given by formula (9):

[0125] ; (9)

[0126] Among them, k a_wear is the axial compressive stiffness of the spur gear under wear.

[0127] S403. Based on the elastic-plastic deformation theory of micro-convex bodies and the WM function characterization model, a fractal contact model for the evolution of the wear roughness morphology of spur gear tooth surfaces is constructed to obtain the evolved fractal contact stiffness:

[0128] ; (10)

[0129] Among them, k fra is the fractal contact stiffness. E * is the equivalent elastic modulus, a c is the theoretical contact area, a lmax is the maximum contact area, λ c is the surface contact coefficient.

[0130] S404, the meshing of the gear teeth is equivalent to two cylinders, and the equivalent curvature radius and entrainment speed of the gear are obtained through the gear structure parameters and working condition parameters;

[0131] S405, using a three-dimensional line contact elastohydrodynamic lubrication model equation to obtain oil film pressure and oil film thickness;

[0132] The three-dimensional line contact elastohydrodynamic lubrication model includes the Reynolds equation, the film thickness equation, the viscosity-pressure equation, the density-pressure equation and the load equation. The expression of the Reynolds equation is formula (11):

[0133] ; (11)

[0134] Among them, p is the oil film pressure, h is the film thickness, ρ is the density, η * is the viscosity, u r is the suction speed,

[0135] In the three-dimensional line contact elastohydrodynamic lubrication model, in order to consider the influence of tooth surface wear, the tooth surface roughness morphology that evolves with the meshing cycle is added to the film thickness equation. The expression of the film thickness equation is formula (12):

[0136] ; (12)

[0137] Among them, h0 is the minimum film thickness of the two contact surfaces, R* is the equivalent radius of curvature, v is the elastic change, z new (x) is the rough morphology of the tooth surface after evolution;

[0138] By solving the three-dimensional line contact elastohydrodynamic lubrication model considering tooth surface wear, the oil film pressure p of the spur gear under wear is obtained. _wear and oil film thickness h _wear , the oil film stiffness is further derived, and the expression of the oil film stiffness is formula (13):

[0139] ; (13)

[0140] Among them, k oill_wear is the oil film stiffness of the spur gear under wear, A is the contact area, m and k are the number of grid divisions.

[0141] S406. Based on bending stiffness, shear stiffness, axial compression stiffness, fractal contact stiffness, matrix deformation stiffness and oil film stiffness, the meshing stiffness of the spur gear under wear considering the rough morphology and lubricating oil film is obtained.

[0142] The expression of the meshing stiffness of the spur gear under wear considering the rough morphology and lubricating oil film is formula (14):

[0143] ; (14)

[0144] Among them, k t_wear k is the mesh stiffness of spur gears under wear considering roughness and lubricating oil film. bp_wear is the bending stiffness of the pinion wear, k bg_wear is the bending stiffness of the large gear due to wear, k sp_wear is the shear stiffness of the pinion wear, k sg_wear is the shear stiffness of the large gear wear, k ap_wear is the axial compression stiffness of the pinion, k ag_wear is the axial compression stiffness of the large gear, k fp is the base deformation stiffness of the pinion, k fg is the deformation stiffness of the large gear matrix.

[0145] In the accompanying drawings, Figure 5(a) shows the relationship between the radius of curvature and the equivalent radius of curvature of the gear along the tooth profile. The equivalent radius of curvature increases along the tooth profile. Figure 5(b) shows the linear velocity of the gear and the suction velocity of the gear. The suction velocity increases along the tooth profile. Figure 6(a) shows the load distribution of the gear teeth before and after wear. Before and after wear, the gears experience an increase or decrease in load at the meshing point, the single and double tooth alternating point, and the meshing point. Figure 6(b) shows the distribution of contact pressure of the gear teeth before and after wear. Before and after wear, the gears experience an increase or decrease in contact pressure at the meshing point and the meshing point. Figures 7(a) and 7(b) show the wear distribution of the pinion and gear along the tooth profile, respectively. As the meshing cycle increases, the wear depth increases. Figure 8 The figure shows the changes in the rough morphology of the tooth surface before and after wear. With long-term meshing, the interaction between the micro-asperities causes the micro-asperity peaks to be removed, and the height and average line of the micro-asperities on the rough tooth surface change, thereby generating a new tooth profile and surface morphology. The height of the micro-asperities decreases or increases after wear. Figure 9(a) and Figure 9(b) show the changes in oil film pressure and oil film thickness before and after wear, respectively. Affected by the evolution of the surface morphology and the oil film, the oil film pressure and oil film thickness after wear increase or decrease in the contact area. Fig.10 The mesh stiffness of spur gears considering the evolution of lubricating oil film and tooth surface wear roughness morphology is shown. The mesh stiffness of gears decreases after wear.

[0146] The present invention constructs a characterization model of the initial tooth surface roughness of spur gears to obtain the initial tooth surface roughness of the gears; based on the initial tooth surface roughness and the gear involute tooth profile, a tooth surface wear roughness evolution model is constructed; based on the evolved tooth surface roughness, the evolved tooth surface roughness characterization parameters are derived; according to the evolved tooth surface roughness and characterization parameters, based on the energy method, fractal theory and elastohydrodynamic lubrication theory, a spur gear meshing stiffness calculation model considering the evolution of lubricating oil film and tooth surface wear roughness is constructed to obtain the meshing stiffness of the spur gear that evolves with the meshing cycle. The present invention comprehensively considers the influence of the evolution of tooth surface wear roughness and lubricating oil film on the meshing stiffness of spur gears, and fills the gap in the current method of calculating the evolution of tooth surface wear roughness and meshing stiffness of spur gears with the meshing cycle.

[0147] The present invention proposes a method for calculating the meshing stiffness of spur gears by considering the evolution of the rough morphology of the tooth surface of the spur gear with the meshing cycle, and obtains a method for calculating the fractal contact stiffness that evolves with the meshing cycle, which solves the current problem of lack of modeling of the evolution of the rough morphology of the tooth surface under wear of spur gears; the present invention incorporates the coupling effect of rough morphology and elastohydrodynamic lubrication into the meshing stiffness calculation method of spur gears under wear, considers the influence of the evolution of rough morphology and the evolution of lubricating oil film under wear, and obtains a more accurate meshing stiffness of spur gears under wear.

[0148] The following points need to be explained:

[0149] (1) The drawings of the embodiments of the present invention only involve structures related to the embodiments of the present invention. Other structures may refer to conventional designs.

[0150] (2) For the sake of clarity, in the drawings used to describe the embodiments of the present invention, the thickness of layers or regions is exaggerated or reduced, that is, these drawings are not drawn according to the actual scale. It is understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element may be "directly" "on" or "under" the other element or there may be intermediate elements.

[0151] (3) In the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other to obtain new embodiments.

[0152] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for calculating the meshing stiffness of spur gears taking into account processing factors and wear factors, characterized in that: include: S1, according to the initial roughness R of the gear a , based on the WM function of fractal theory, a gear roughness morphology characterization model is constructed to obtain the initial roughness morphology of the spur gear tooth surface; S2. According to the initial rough morphology of the spur gear tooth surface and the involute tooth profile of the gear, based on the Archard wear model, a gear tooth surface rough morphology evolution model is constructed to obtain the evolved tooth surface rough morphology; S3. Based on the evolved tooth surface roughness morphology, deriving the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectral density of the gear surface roughness morphology; S4. According to the relationship between the characterization parameters of the evolved tooth surface roughness morphology and the power spectral density of the gear surface roughness morphology, based on the energy method, fractal theory and elastohydrodynamic lubrication theory, a spur gear meshing stiffness calculation model considering the evolution of lubricating oil film and tooth surface wear roughness morphology is constructed to obtain the spur gear meshing stiffness under different meshing cycles.

2. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 1, characterized in that: The gear roughness characterization model of S1 is formula (1): ；（1） Among them, z(x) represents the height of the micro-convex body of the rough morphology, G is the fractal characteristic parameter of the rough morphology, and is related to the roughness R a The relationship is ; D is the fractal dimension of the roughness, which is related to the roughness R a The relationship is ,γ is the spatial frequency of the rough surface, φ n is a random phase.

3. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 2, characterized in that: The S2 constructs a gear tooth surface roughness evolution model based on the Archard wear model according to the initial roughness of the spur gear tooth surface and the gear involute tooth profile, and obtains the evolved tooth surface roughness, including: S201. Based on the gear roughness characterization model and the gear involute tooth profile, derive a tooth profile with a roughness shape. The tooth profile with a roughness shape is expressed as formula (2): ；（2） Among them, h ini (x) is the height of the initial tooth profile of the spur gear from the center line of the gear tooth, h inv (x) is the height of the involute tooth profile from the center line of the gear tooth; S202. Based on the Archard wear model, the wear distribution of the spur gear along the tooth profile is obtained. The expression of the wear along the tooth profile line is formula (3): ；（3） Among them, h w (x) is the wear amount along the tooth profile, N is the evolutionary meshing cycle, k w To consider the wear coefficient of friction lubrication, P M is the contact pressure, s M is the relative sliding distance; S203. Based on the wear amount along the tooth profile line, the tooth profile of the spur gear after evolution is obtained. The expression of the tooth profile of the spur gear after evolution is formula (4): ；（4） Among them, h new (x) is the tooth profile of the spur gear after evolution; S204, after detrending the evolved tooth profile, the evolved tooth surface roughness morphology of the spur gear is obtained, and the expression of the evolved tooth surface roughness morphology is formula (5): ；（5） Among them, z new (x) is the tooth surface roughness morphology after evolution, f trend () is the fitting trend of the new tooth profile.

4. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 3, characterized in that: The relationship between the characterization parameters of the tooth surface roughness after the derivation and evolution of S3 and the power spectrum density of the gear surface roughness is as follows: ；（6）。 5. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 4, characterized in that: According to the relationship between the characterization parameters of the evolved tooth surface roughness and the power spectrum density of the gear surface roughness, S4 constructs a spur gear meshing stiffness calculation model that takes into account the evolution of lubricating oil film and tooth surface wear roughness based on the energy method, fractal theory and elastohydrodynamic lubrication theory, and obtains the spur gear meshing stiffness under different meshing cycles, including: S401, obtaining a fractal characteristic parameter G of the rough morphology and a fractal dimension D of the rough morphology according to a relationship between the characterization parameters of the evolved tooth surface rough morphology and the power spectrum density of the gear surface rough morphology; S402. Based on the energy method, the gear teeth are equivalent to cantilever beams, and the new meshing relationship of the gears after wear is considered. The expressions of the bending stiffness, shear stiffness and axial compression stiffness of the spur gear under wear are derived through the bending energy, shear energy and axial compression energy of the cantilever beam. S403. Based on the elastic-plastic deformation theory of micro-convex bodies and combined with the WM function characterization model, a fractal contact model for the evolution of the wear roughness morphology of spur gear tooth surfaces is constructed to obtain the evolved fractal contact stiffness. S404, the meshing of the gear teeth is equivalent to two cylinders, and the equivalent curvature radius and entrainment speed of the gear are obtained through the gear structure parameters and working condition parameters; S405, using a three-dimensional line contact elastohydrodynamic lubrication model equation to obtain oil film pressure and oil film thickness; S406. Based on bending stiffness, shear stiffness, axial compression stiffness, fractal contact stiffness, matrix deformation stiffness and oil film stiffness, the meshing stiffness of the spur gear under wear considering the rough morphology and lubricating oil film is obtained.

6. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 5, characterized in that: The step S401 of obtaining the fractal characteristic parameter G and the fractal dimension D of the rough morphology according to the relationship between the characterization parameter of the evolved tooth surface rough morphology and the power spectrum density of the gear surface rough morphology includes: The rough morphology z after the evolution new (x) Perform power spectrum density analysis, obtain the slope and intercept of the straight line through least squares fitting, and obtain the fractal characteristic parameter G and fractal dimension D of the rough morphology.

7. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 6, characterized in that: In S402, based on the energy method, the gear teeth are equivalent to a cantilever beam, and the new meshing relationship of the gears after wear is considered. The expressions of the bending stiffness, shear stiffness and axial compression stiffness of the spur gear under wear are derived through the bending energy, shear energy and axial compression energy of the cantilever beam, including: The bending stiffness of the spur gear under wear is given by formula (7): ;（7） Among them, k b_wear is the bending stiffness of the spur gear under wear, h w is the wear depth along the tooth profile, R b is the base circle radius of the gear, E is the elastic modulus, L is the tooth width, α is the meshing angle, α1 is the meshing angle where the meshing force is tangent to the base circle, and α2 is the half tooth angle on the base circle; The shear stiffness of the spur gear under wear is given by formula (8): ;（8） Among them, k s_wear is the shear stiffness of the spur gear under wear, is Poisson’s ratio; The axial compressive stiffness of the spur gear under wear is given by formula (9): ;（9） Among them, k a_wear is the axial compressive stiffness of the spur gear under wear.

8. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 7, characterized in that: The S403 is based on the elastic-plastic deformation theory of micro-convex bodies and combined with the WM function characterization model to construct a fractal contact model for the evolution of the wear roughness morphology of the spur gear tooth surface. The formula for the evolved fractal contact stiffness is obtained as formula (10): ；（10） Among them, k fra is the fractal contact stiffness. E * is the equivalent elastic modulus, a c is the theoretical contact area, a lmax is the maximum contact area, λ c is the surface contact coefficient.

9. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 8, characterized in that: The S405 adopts the three-dimensional line contact elastohydrodynamic lubrication model equation to obtain the oil film pressure and oil film thickness, including: The three-dimensional line contact elastohydrodynamic lubrication model includes the Reynolds equation, the film thickness equation, the viscosity-pressure equation, the density-pressure equation and the load equation. The expression of the Reynolds equation is formula (11): ；（11） Among them, p is the oil film pressure, h is the film thickness, ρ is the density, η * is the viscosity, u r is the suction speed, In the three-dimensional line contact elastohydrodynamic lubrication model, the tooth surface roughness morphology that evolves with the meshing cycle is added to the film thickness equation. The expression of the film thickness equation is formula (12): ；（12） Among them, h0 is the minimum film thickness of the two contact surfaces, R * is the equivalent radius of curvature, v is the elastic change, z new (x) is the rough morphology of the tooth surface after evolution; By solving the three-dimensional line contact elastohydrodynamic lubrication model, the oil film pressure p of the spur gear under wear is obtained. _wear and oil film thickness h _wear , the oil film stiffness is obtained, and the expression of the oil film stiffness is formula (13): ；（13） Among them, k oill_wear is the oil film stiffness of the spur gear under wear, A is the contact area, m and k are the number of grid divisions.

10. The method for calculating the meshing stiffness of spur gears considering processing technology factors and wear factors according to claim 9, characterized in that: The expression of the meshing stiffness of the spur gear under wear considering the rough morphology and lubricating oil film of the S406 is formula (14): ；（14） Among them, k t_wear k is the mesh stiffness of spur gears under wear considering roughness and lubricating oil film. bp_wear is the bending stiffness of the pinion wear, k bg_wear is the bending stiffness of the large gear due to wear, k sp_wear is the shear stiffness of the pinion wear, k sg_wear is the shear stiffness of the large gear wear, k ap_wear is the axial compression stiffness of the pinion, k ag_wear is the axial compression stiffness of the large gear, k fp is the base deformation stiffness of the pinion, k fg is the deformation stiffness of the large gear matrix.

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