Gear contact fatigue life prediction method considering macro-micro geometric parameter influence

Abstract

The invention provides a gear contact fatigue life prediction method considering macro-micro geometric parameter influence. The method comprises the following steps: firstly, establishing a tooth surface contact-dynamics analysis model considering macro-micro geometric parameter influence, and calculating tooth surface dynamic load distribution; secondly, establishing a calculation model of the stress on the surface and below the surface of the gear considering the influence of lubrication and surface roughness, and calculating the oil film pressure and the stress on the surface and below the surface of the gear; and finally, establishing a gear contact fatigue life prediction model considering the influence of macro and micro geometric parameters, and calculating the contact fatigue life of the gear. According to the method, the influence of the rigidity change of the gear on the contact fatigue life of the gear is considered, the contact fatigue life of gears with different web structures is predicted, and the deviation between the contact fatigue life obtained through theoretical calculation and the actual contact fatigue life is reduced. Meanwhile, the method considers the influence of the error on the contact fatigue life of the gear, so that the prediction of the contact fatigue life of the gear with the modification and the error is realized.

Description

Technical Field

[0001] This invention relates to the field of mechanical parametric design, and more specifically, to a method for predicting gear contact fatigue life that takes into account the influence of macroscopic and microscopic geometric parameters. Background Technology

[0002] Gear contact fatigue life has always been a hot topic in the machinery industry. Gear systems experience complex dynamic responses due to the meshing of gears subjected to various internal and external excitations. Studying the impact of these excitations on gear contact fatigue life is of guiding significance for improving the reliability and fatigue life of gear systems.

[0003] During the actual operation of a gear system, the tooth surface load varies due to changes in the gear web structure, tooth surface profile, and tooth surface errors. In actual meshing, factors affecting gear contact fatigue life include not only the impact and deformation generated during gear meshing, but also variations in tooth surface profile, meshing errors, and gear web structure resulting from design, manufacturing, and installation. Calculating gear contact fatigue life without considering the influence of gear structure and errors cannot eliminate the interference of gear structure and errors on the results, inevitably affecting the accuracy of the results.

[0004] Most current research neglects the influence of web structure, tooth surface modification, and tooth surface errors on gear contact fatigue life. In the actual load working environment of a gear system, the structure and errors of system components will inevitably cause changes in the load conditions of the gear tooth surface, resulting in a deviation between the actual load conditions and the theoretical load conditions, and thus causing a deviation between the prediction and the actual gear contact fatigue life. Summary of the Invention

[0005] The purpose of this application is to provide a method for predicting gear contact fatigue life that considers the influence of macroscopic and microscopic geometric parameters. This method establishes an analytical model for gear contact fatigue life that takes into account the influence of these parameters. By incorporating the effect of gear stiffness variations on gear contact fatigue life, this method enables the prediction of contact fatigue life for gears with different web structures, reducing the deviation between theoretically calculated and actual contact fatigue life. Furthermore, because this method considers the influence of errors on gear contact fatigue life, it also enables the prediction of contact fatigue life for modified and error-laden gears.

[0006] The technical solution of this invention is as follows:

[0007] A method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters includes the following steps:

[0008] Step 1: Establish a tooth surface contact-dynamic analysis model that considers the influence of macroscopic and microscopic geometric parameters and calculate the dynamic load distribution on the tooth surface;

[0009] Step 2: Establish a calculation model for the stress on and below the gear surface, taking into account the effects of lubrication and surface roughness. Utilize the dynamic load distribution on the tooth surface to calculate the oil film pressure, surface stress, and stress below the gear surface based on the calculation model.

[0010] Step 3: Establish a gear contact fatigue life prediction model that considers the influence of macroscopic and microscopic geometric parameters, and calculate the gear contact fatigue life based on the prediction model using the surface and subsurface stresses.

[0011] Furthermore, step one specifically includes the following steps:

[0012] 1.1 Establish a tooth surface contact-dynamic analysis model, including the tooth surface bearing contact equation and the gear motion differential equation;

[0013] 1.2 The static load distribution, static transmission error, comprehensive meshing stiffness, and comprehensive meshing error of the tooth surface are obtained by solving the tooth surface bearing contact equation;

[0014] 1.3. Solve the tooth surface contact-dynamic analysis model established in step 1.1 in the time domain using the Newmark integral method to obtain the dynamic load distribution on the tooth surface.

[0015] Furthermore, in step 1.1, the tooth surface contact-dynamic analysis model includes:

[0016] Tooth surface bearing contact equation

[0017] { [ λ G ] { F } − { u L } + { ε } − STE − { d } = 0 ∑ i = 1 n F i = { I } { F } = P When F i > 0 ， d i = 0 When F i = 0 ， d i > 0

[0018] and the differential equation of gear motion

[0019] { m p x ¨ p + { c τ ˙ + k ( t )[ τ − e ( t )]}sin φ = 0 m p y ¨ p + { c τ ˙ + k ( t )[ τ − e ( t )]}cos φ = 0 m p z ¨ p = 0 I xp θ ¨ xp = 0 I yp θ ¨ yp = 0 I zp θ ¨ zp + { c τ ˙ + k ( t )[ τ − e ( t )]} r p = T p m g x ¨ g − { c τ ˙ + k ( t )[ τ − e ( t )]}sin φ = 0 m g y ¨ g − { c τ ˙ + k ( t )[ τ − e ( t )]}cos φ = 0 m g z ¨ g = 0 I xg θ ¨ xg = 0 I yg θ ¨ yg = 0 I zg θ ¨ zg + { c τ ˙ + k ( t )[ τ − e ( t )]} r g = T g

[0020] in: [ λ G ] This represents the macroscopic deformation compliance coefficient matrix of the contact points on the tooth surface. The applied load vector, Let be the local contact deformation vector at the contact point. Let be the initial gap vector at the contact point. Let STE be the remaining gap vector at the contact points, and n be the static transmission error. Let {I} be the load applied to the i-th contact point. The vector has elements of 1, and P is the external load vector. The remaining gap at the i-th contact point;

[0021] In the differential equation of gear motion, Let the masses of the driving wheel and the driven wheel be... These are the moments of inertia of the driving wheel and the driven wheel, respectively. The overall meshing stiffness of the gear pair varies with q. The overall meshing error of the gear pair varies with q. For the meshing damping of the gear pair; Let x represent the displacement of the driving wheel and the driven wheel in the x-axis direction. The rotation angle of the driving wheel and the driven wheel in the x-axis direction; This refers to the relative displacement of the gear pair along the normal line of meshing. , The meshing angle of the gear pair. To install the phase angle; and These are the base circle radii of the driving wheel and the driven wheel, respectively. The torque applied to the drive wheel, Let q be the torque applied to the driven gear, and q be the gear pitch coordinate.

[0022]

[0023] Relative displacement of the gear pair along the normal meshing line ;

[0024] In the formula, Let the projection vector of any nodal displacement onto the normal meshing line direction be:

[0025] { V } = [sin φ , ± cos φ , 0 , 0 , 0 , ± r p , − sin φ , ∓ cos φ , 0 , 0 , 0 , ± r g ]

[0026] In the formula, and These are the base circle radii of the driving and driven wheels, respectively. and Take the upper half when the drive wheel rotates counterclockwise, and take the lower half when it rotates clockwise.

[0027] Furthermore, in step 1.2, the static load distribution of the tooth surface is obtained by solving the tooth surface bearing contact equation. And the static transmission error STE, then solve for the combined meshing stiffness k and the combined meshing error e:

[0028]

[0029] .

[0030] Furthermore, in step 1.3, the combined meshing stiffness k and combined meshing error e are substituted into the gear motion differential equation and the dynamic displacement, velocity, and acceleration of the contact point are obtained through the Newmark numerical integration method; the dynamic transmission error is then solved based on the obtained dynamic displacement and velocity. and its derivative The meshing dynamic load can be calculated based on the dynamic transmission error.

[0031] F d = k [ DTE ( t ) − e ( t )] + c [ D T ˙ E ( t ) − e ˙ ( t )]

[0032] The dynamic load distribution on the tooth surface is recalculated using the meshing dynamic load and the bearing contact equation; the Hertzian stress distribution on the tooth surface is then solved using the dynamic load distribution on the tooth surface and the Hertzian stress formula.

[0033]

[0034] In the formula, The effective contact length of the contact point. The dynamic load at the contact point. , The density of the two gears, , Let be the elastic modulus of the two gears. , Let be the radius of curvature of the tooth profile at the pitch circle of the two gears, expressed as:

[0035]

[0036]

[0037] In the formula, , Let be the pitch circle diameter of the two gears. This is the pressure angle.

[0038] Furthermore, in step two, the calculation model is composed of the Reynolds equation, the viscosity-pressure relationship equation, the pressure-density equation, the load equation, as well as the boundary conditions, the film thickness equation, and the WM fractal function. By using the Hertzian contact stress as the initial value of the oil film pressure and solving the calculation model using the multigrid integration method, the lubricating oil film pressure and oil film thickness are obtained. Based on the lubricating oil film pressure and oil film thickness, the shear stress is calculated. By convolving the oil film pressure and shear stress with the influence coefficient, the influence relationship between the gear surface stress and the stress below the surface is established, and the surface and subsurface stresses are calculated.

[0039] Furthermore, the computational model consists of:

[0040] Reynolds equations

[0041]

[0042] Viscosity-pressure relationship:

[0043] η = η 0 exp { (ln η 0 + 9 . 67 ) [ ( 1 + 5 . 1 × 10 − 9 p ) Z ] − 1 }

[0044] Pressure Compressibility Equation:

[0045]

[0046] Load equations and boundary conditions:

[0047]

[0048]

[0049] Film thickness equation:

[0050]

[0051] WM fractal function:

[0052]

[0053] S '( m , n ) = s 1 { s 2 − cos s 3 ⋅ s 4 + ϕ m , n ] }

[0054] { s 1 = γ ( D − 3 ) n s 2 = cos ϕ m , n s 3 = [ 2 πγ n ( x 2 + y 2 ) ] / L s 4 = cos[arctan( y x ) − π m M ]

[0055] Composed of two elements;

[0056] in: For the density of lubricating oil, The viscosity of the lubricating oil. Where U is the thickness of the lubricating oil film, and U is the lubricating oil entrainment speed; This refers to the dynamic viscosity of the lubricating oil. Z = α / [ 5 . 1 × 10 − 9 (ln η 0 + 9 . 67 )] , This refers to the viscosity-pressure coefficient of the lubricating oil. This refers to the lubricating oil film pressure. The density of the lubricating oil at room temperature; and These are the coordinates of the oil film inlet and outlet positions, respectively. Where V is the thickness of the central oil film, and V is the elastic deformation matrix. The rough surface random profile generated by the WM fractal function at point The height of the location denoted by , where is the combined radius of curvature of the two tooth profiles at the meshing point; M is the number of overlapping surface ridges; and D is the fractal dimension. The spatial frequency of the roughness surface profile. Here, L is the random profile frequency index, and L is the sampling length. n is a constant. max This represents the upper limit of the frequency exponent. It is a random phase.

[0057] Furthermore, in step two, the Hertzian contact stress is used as the initial value of the oil film pressure. The calculation model is solved using the multigrid integration method to obtain the lubricating oil film pressure p and the oil film thickness h.

[0058] The shear stress is calculated using the oil film pressure p and oil film thickness h according to the oil film shear stress calculation formula:

[0059]

[0060] In the formula, This refers to the equivalent viscosity of the lubricating oil. , These are the velocities of the two contact surfaces along the tooth profile direction, The oil film thickness at the current position is taken as follows: and The shear stress distribution on the surfaces of the two gears is obtained;

[0061] The stress components of the subsurface are the convolution sum of the oil film pressure and shear stress at any gear unit and the influence coefficient on the current unit:

[0062]

[0063] In the formula, the influence coefficient

[0064] D S / N , qr i − ξ , j − η , l = 1 2 π [ T S / N , qr ( x i − x ξ + dx 2 , y j − y η + dy 2 , z l ) + T S / N , qr ( x i − x ξ − dx 2 , y j − y η − dy 2 , z l ) − T S / N , qr ( x i − x ξ + dx 2 , y j − y η − dy 2 , z l ) − T S / N , qr ( x i − x ξ − dx 2 , y j − y η + dy 2 , z l ) ]

[0065] This is the influence coefficient under the action of normal stress and tangential stress;

[0066] The stress at any point in space, calculated using the above method, is:

[0067] σ ⇀ = [ σ xx τ xy τ xz τ yx σ yy τ yz τ zx τ zy σ zz ]

[0068] Based on the existing stress distribution on and below the surface, the stress history of each point is obtained by iteratively solving the stress distribution along the perpendicular direction of the contact line.

[0069] Furthermore, in step three, the gear contact fatigue life prediction model is as follows:

[0070] 1 β [ σ a , c Ψ ] 2 + ( f Nf t Nf ) 2 ( τ a , c ) 2 + k s ( σ a , c H ) 2 = f Nf

[0071] In the formula, The normal stress amplitude on the characteristic plane, The mean normal stress on the characteristic plane, The shear stress amplitude on the characteristic plane, The hydrostatic stress amplitude is defined on the characteristic plane, which is defined as the plane containing the maximum normal stress amplitude. The plane of the angle, and The stress-life curves of the material under pure bending and pure torsion states represent the fatigue strength at a lifetime of Nf. , These are the material parameters at the current fatigue limit. The mean stress correction factor is:

[0072]

[0073] In the formula, These are the material parameters in the correction factor.

[0074] Beneficial effects

[0075] The gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters provided in this application establishes a gear contact fatigue life analysis model that takes into account the influence of gear stiffness variations on gear contact fatigue life. This enables the prediction of contact fatigue life for gears with different web structures, reducing the deviation between theoretically calculated and actual contact fatigue life. Furthermore, because this method considers the influence of errors on gear contact fatigue life, it also enables the prediction of contact fatigue life for modified and error-infected gears.

[0076] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0077] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0078] Figure 1 A schematic diagram of the calculation process for the gear contact fatigue life prediction and analysis method considering the influence of macro- and micro-geometric parameters provided in the embodiments of this application;

[0079] Figure 2 This is a schematic diagram of the gear pair meshing dynamics model;

[0080] Figure 3 A schematic flowchart of a tooth surface contact-dynamic analysis method considering the influence of macro- and micro-geometric parameters provided in this application embodiment;

[0081] Figure 4 is a schematic diagram of different gear web structures provided in the embodiments of this application;

[0082] Figure 5 The gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters provided in the embodiments of this application calculates the meshing dynamic load of different web gears;

[0083] Figure 6 The gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters provided in the embodiments of this application calculates the oil film pressure of different web gears;

[0084] Figure 7 The gear contact fatigue life analysis method considering the influence of macro and micro geometric parameters provided in the embodiments of this application calculates the surface and subsurface Von-mises stress of different web gears.

[0085] Figure 8 The gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters provided in the embodiments of this application calculates the contact fatigue life of different web gears. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0087] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0088] This application provides a method for analyzing gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters, including the following steps:

[0089] Step 1: Establish a tooth surface contact-dynamic analysis model considering the influence of macroscopic and microscopic geometric parameters and calculate the dynamic load distribution on the tooth surface; specifically, this includes the following steps:

[0090] 1.1 Establish a tooth surface contact-dynamic analysis model, including the tooth surface bearing contact equation and the gear motion differential equation;

[0091] 1.2 The static load distribution, static transmission error, comprehensive meshing stiffness, and comprehensive meshing error of the tooth surface are obtained by solving the tooth surface bearing contact equation;

[0092] 1.3 The tooth surface contact-dynamic analysis model established in step 1.1 is solved in the time domain using the Newmark integral method to obtain the dynamic load distribution on the tooth surface.

[0093] Step 2: Establish a calculation model for the stress on and below the gear surface, taking into account the effects of lubrication and surface roughness, and calculate the oil film pressure, surface stress, and stress below the gear surface.

[0094] The main idea is:

[0095] An elastohydrodynamic lubrication model was established, and the influence of surface roughness was introduced into the film thickness equation using the WM fractal function;

[0096] The tooth surface contact stress distribution is calculated by dynamic load distribution on the tooth surface as the initial value of oil film pressure in the elastohydrodynamic lubrication model. The center oil film thickness calculated by load and gear surface velocity is used as the initial value of oil film thickness in the elastohydrodynamic lubrication model. The Gauss–Seidel iterative method is used to solve the Reynolds equation in the inner layer iteratively, and the multigrid integration method is used in the outer layer iteratively to ensure the accuracy of the results and the computational efficiency. Finally, the convergent solution of gear oil film pressure and oil film thickness is obtained, and the oil film shear stress of the gear is calculated by oil film pressure.

[0097] The pressure and shear stress on the gear surface are obtained by measuring the oil film pressure and shear stress of the gear. The influence relationship between the pressure and shear stress on the gear surface and the stress below the surface is established by convolving the pressure and shear stress on the gear surface with the influence coefficient, and the stress on the surface and below the surface is calculated.

[0098] The final computational model consists of the Reynolds equation, the viscosity-pressure relationship equation, the pressure-density equation, the load equation, the boundary conditions, the film thickness equation, and the WM fractal function. Then, the Hertzian contact stress is used as the initial value of the oil film pressure. The computational model is solved using the multigrid integration method to obtain the lubricating oil film pressure and the oil film thickness. Based on the lubricating oil film pressure and the oil film thickness, the shear stress is calculated. By convolving the oil film pressure and shear stress with the influence coefficient, the influence relationship between the gear surface stress and the stress below the surface is established, and the surface and subsurface stresses are calculated.

[0099] Step 3: Establish a gear contact fatigue life prediction model that considers the influence of macroscopic and microscopic geometric parameters, and calculate the gear contact fatigue life. The main idea is:

[0100] The gear contact fatigue life prediction model is solved by using the gear stress history obtained by iterative calculation within the Hertzian contact half-width range of the surface and subsurface stresses. The location of the maximum normal stress amplitude plane is determined by stress history search. The relationship between the maximum normal stress amplitude plane and the characteristic plane is calculated based on the material properties of the gear (bending fatigue limit and torsional fatigue limit) to determine the location of the characteristic plane. The maximum normal stress amplitude and maximum shear stress amplitude are calculated on the characteristic plane to obtain the contact fatigue equivalent stress considering the average stress effect and the influence of material properties. The contact fatigue equivalent stress is compared with the stress life curves obtained by the gear material under full bending and full torsion conditions to obtain two initial contact fatigue life values ​​under full bending and full torsion conditions. The two initial contact fatigue life values ​​are used as the updated values ​​of the bending fatigue limit and torsional fatigue limit. The above process is repeated iteratively until the two contact fatigue life values ​​under full bending and full torsion conditions are equal, and the contact fatigue life of the gear at this contact point is obtained. The contact fatigue life of the gear is obtained by traversing all contact points.

[0101] The following detailed description of the features and performance of the gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters of this application, in conjunction with embodiments, provides further insight into its characteristics and performance.

[0102] like Figure 1 As shown in the figure, this application provides a method for analyzing gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters. The specific steps are as follows:

[0103] In this embodiment, the macro- and micro-geometric parameters are the position of the gear web, tooth surface modification, and tooth surface error. The gear stiffness is calculated using the finite element substructure method, taking into account the influence of the web structure. The influence of tooth surface modification and tooth surface error is considered by establishing a contact-dynamic analysis model of the gear.

[0104] Step 1: Establish a tooth surface contact-dynamic analysis model that considers the influence of macroscopic and microscopic geometric parameters and calculate the dynamic load distribution on the tooth surface;

[0105] The tooth surface contact-dynamic analysis model includes:

[0106] Tooth surface bearing contact equation

[0107] { [ λ G ] { F } − { u L } + { ε } − STE − { d } = 0 ∑ i = 1 n F i = { I } { F } = P When F i > 0 ， d i = 0 When F i = 0 ， d i > 0

[0108] and the differential equation of gear motion

[0109] { m p x ¨ p + { c τ ˙ + k ( t )[ τ − e ( t )]}sin φ = 0 m p y ¨ p + { c τ ˙ + k ( t )[ τ − e ( t )]}cos φ = 0 m p z ¨ p = 0 I xp θ ¨ xp = 0 I yp θ ¨ yp = 0 I zp θ ¨ zp + { c τ ˙ + k ( t )[ τ − e ( t )]} r p = T p m g x ¨ g − { c τ ˙ + k ( t )[ τ − e ( t )]}sin φ = 0 m g y ¨ g − { c τ ˙ + k ( t )[ τ − e ( t )]}cos φ = 0 m g z ¨ g = 0 I xg θ ¨ xg = 0 I yg θ ¨ yg = 0 I zg θ ¨ zg + { c τ ˙ + k ( t )[ τ − e ( t )]} r g = T g

[0110] in: [ λ G ] This represents the macroscopic deformation compliance coefficient matrix of the contact points on the tooth surface. The applied load vector, Let be the local contact deformation vector at the contact point. Let be the initial gap vector at the contact point. Let STE be the remaining gap vector at the contact points, and n be the static transmission error. Let {I} be the load applied to the i-th contact point. The vector has elements of 1, and P is the external load vector. Let be the remaining gap at the i-th contact point.

[0111] In the differential equation of gear motion, Let the masses of the driving wheel and the driven wheel be... These are the moments of inertia of the driving wheel and the driven wheel, respectively. The overall meshing stiffness of the gear pair varies with q. The overall meshing error of the gear pair varies with q. For the meshing damping of the gear pair; Let x represent the displacement of the driving wheel and the driven wheel in the x-axis direction. The rotation angle of the driving wheel and the driven wheel in the x-axis direction; This refers to the relative displacement of the gear pair along the normal line of meshing. , The meshing angle of the gear pair. To install the phase angle; and These are the base circle radii of the driving wheel and the driven wheel, respectively. The torque applied to the drive wheel, Let q be the torque applied to the driven gear, and q be the gear pitch coordinate.

[0112]

[0113] Relative displacement of the gear pair along the normal meshing line ;

[0114] In the formula, Let the projection vector of any nodal displacement onto the normal meshing line direction be:

[0115] { V } = [sin φ , ± cos φ , 0 , 0 , 0 , ± r p , − sin φ , ∓ cos φ , 0 , 0 , 0 , ± r g ]

[0116] In the formula, and These are the base circle radii of the driving and driven wheels, respectively. and Take the upper half when the drive wheel rotates counterclockwise, and take the lower half when it rotates clockwise.

[0117] The static load distribution on the tooth surface is obtained by solving the contact equation for tooth surface bearing. And the static transmission error STE, and then solve for the combined meshing stiffness k and the combined meshing error e.

[0118]

[0119]

[0120] Substituting the combined meshing stiffness k and the combined meshing error e into the gear motion differential equation, the dynamic displacement, velocity and acceleration of the contact point are obtained by Newmark numerical integration method.

[0121] The dynamic transmission error is calculated based on the obtained dynamic displacement and velocity. and its derivative ;

[0122] The meshing dynamic load can be calculated based on the dynamic transmission error.

[0123] F d = k [ DTE ( t ) − e ( t )] + c [ D T ˙ E ( t ) − e ˙ ( t )]

[0124] The dynamic load distribution on the tooth surface is recalculated using meshing dynamic loads and the bearing contact equation.

[0125] The Hertzian stress distribution on the tooth surface is solved using the dynamic load distribution on the tooth surface and the Hertzian stress formula:

[0126]

[0127] In the formula, The effective contact length of the contact point. The dynamic load at the contact point. , The density of the two gears, , Let be the elastic modulus of the two gears. , Let be the radius of curvature of the tooth profile at the pitch circle of the two gears, which can be expressed as:

[0128]

[0129]

[0130] In the formula, , Let be the pitch circle diameter of the two gears. This is the pressure angle.

[0131] Step 2: Establish a calculation model for gear surface stress and secondary surface stress considering the effects of lubrication and surface roughness, and calculate the gear oil film pressure, surface stress, and secondary surface stress:

[0132] The computational model consists of:

[0133] Reynolds equations

[0134]

[0135] Viscosity-pressure relationship:

[0136] η = η 0 exp { (ln η 0 + 9 . 67 ) [ ( 1 + 5 . 1 × 10 − 9 p ) Z ] − 1 }

[0137] Pressure Compressibility Equation:

[0138]

[0139] Load equations and boundary conditions:

[0140]

[0141]

[0142] Film thickness equation:

[0143]

[0144] WM fractal function:

[0145]

[0146] S '( m , n ) = s 1 { s 2 − cos s 3 ⋅ s 4 + ϕ m , n ] }

[0147] { s 1 = γ ( D − 3 ) n s 2 = cos ϕ m , n s 3 = [ 2 πγ n ( x 2 + y 2 ) ] / L s 4 = cos[arctan( y x ) − π m M ]

[0148] Composed of two elements;

[0149] in: For the density of lubricating oil, The viscosity of the lubricating oil. Where U is the thickness of the lubricating oil film, and U is the lubricating oil entrainment speed; This refers to the dynamic viscosity of the lubricating oil. Z = α / [ 5 . 1 × 10 − 9 (ln η 0 + 9 . 67 )] , This is the viscosity-pressure coefficient of the lubricating oil. This refers to the lubricating oil film pressure. The density of the lubricating oil at room temperature; and These are the coordinates of the oil film inlet and outlet positions, respectively. Where V is the thickness of the central oil film, and V is the elastic deformation matrix. The rough surface random profile generated by the WM fractal function at point The height of the location is the combined radius of curvature of the two tooth profiles at the meshing point; M is the number of overlapping surface ridges; and D is the fractal dimension, typically taken as 2 to 3. The spatial frequency of the roughness surface profile is generally taken as 1.5. Here, L is the random profile frequency index, and L is the sampling length. n is a constant. max This represents the upper limit of the frequency exponent. It is a random phase;

[0150] By using the Hertzian contact stress as the initial value of the oil film pressure and solving the above equations using the multigrid integration method, the lubricating oil film pressure p and oil film thickness h are obtained.

[0151] The shear stress is calculated using the oil film pressure p and oil film thickness h according to the oil film shear stress calculation formula:

[0152]

[0153] In the formula, The equivalent viscosity of the lubricating oil (Pa·s) , These are the velocities of the two contact surfaces along the tooth profile direction, The oil film thickness at the current position is taken as follows: and This allows us to obtain the shear stress distribution on the surfaces of the two gears;

[0154] The stress components of the subsurface are the convolution sum of the oil film pressure and shear stress at any gear unit and the influence coefficient on the current unit:

[0155]

[0156] In the formula, the influence coefficient

[0157] D S / N , qr i − ξ , j − η , l = 1 2 π [ T S / N , qr ( x i − x ξ + dx 2 , y j − y η + dy 2 , z l ) + T S / N , qr ( x i − x ξ − dx 2 , y j − y η − dy 2 , z l ) − T S / N , qr ( x i − x ξ + dx 2 , y j − y η − dy 2 , z l ) − T S / N , qr ( x i − x ξ − dx 2 , y j − y η + dy 2 , z l ) ]

[0158] The influence coefficients under normal stress and tangential stress The material's Poisson's ratio, (i,j) and ( , The distance between the two nodes and the different independent variables in the above formula are obtained by solving.

[0159] The stress at any point in space, calculated using the above method, is:

[0160] σ ⇀ = [ σ xx τ xy τ xz τ yx σ yy τ yz τ zx τ zy σ zz ]

[0161] Based on the existing stress distribution on and below the surface, the stress history of each point is obtained by iteratively solving the stress distribution along the perpendicular direction of the contact line.

[0162] Step 3: Establish a gear contact fatigue life prediction model that considers the influence of macroscopic and microscopic geometric parameters and calculate the contact fatigue life of the gear.

[0163] The gear contact fatigue life prediction model is as follows:

[0164] 1 β [ σ a , c Ψ ] 2 + ( f Nf t Nf ) 2 ( τ a , c ) 2 + k s ( σ a , c H ) 2 = f Nf

[0165] In the formula, The normal stress amplitude on the characteristic plane, The mean normal stress on the characteristic plane, The shear stress amplitude on the characteristic plane, The hydrostatic stress amplitude is defined on the characteristic plane, which is defined as the plane containing the maximum normal stress amplitude. The plane of the angle, and The stress-life curves of the material under pure bending and pure torsion states represent the fatigue strength at a lifetime of Nf. , These are the material parameters at the current fatigue limit.

[0166]

[0167]

[0168]

[0169] In the formula, and These represent the fatigue limits of the material under pure bending and pure torsion conditions, respectively.

[0170] The mean stress correction factor is:

[0171]

[0172] In the formula, The material parameters in the correction factor can be calculated using the following simplified formula:

[0173]

[0174] In the solution, first according to and calculate , and Then, based on the stress history obtained in step two, calculate the plane of maximum normal stress amplitude, and then based on the included angle... Determine the characteristic plane;

[0175] The stress history is transformed onto the characteristic plane to solve for the maximum normal stress amplitude. mean normal stress and hydrostatic stress amplitude (The average of the three principal stresses);

[0176] The maximum shear stress amplitude is determined using the least circumcircle method. Using the mean normal stress Solving for the mean stress correction factor ;

[0177] Will and As and The initial value is combined with the stress-life curves of the material obtained under complete bending and complete torsion conditions. The above process is repeated iteratively to solve the problem until the left and right sides of the equation of the gear contact fatigue life prediction model are equal. At this time, the corresponding stress cycle number Nf is the final gear contact fatigue life obtained by the solution.

[0178] In the initial calculation, the bending fatigue limit and the torsional fatigue limit of the material are used as... and The initial value is used to calculate the equivalent stress of contact fatigue life through the above process. This equivalent stress is then substituted into the stress-life curves of the material under complete bending and complete torsion to obtain the initial values ​​of contact fatigue life under the corresponding complete bending and complete torsion conditions. The fatigue limit corresponding to these two initial values ​​of contact fatigue life is taken as... and The updated value is repeated in the above calculation process until the two contact fatigue life values ​​under the conditions of complete bending and complete torsion are equal, and the contact fatigue life at the current position is obtained. By traversing all positions, the calculation of the gear contact fatigue life prediction model considering the influence of macro and micro geometric parameters is completed.

[0179] The gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters proposed in this application uses an input speed of 1500 r / min and a load torque of 5100 N∙m. Compared with other gear contact fatigue life analysis methods, the method used in this application can consider the influence of gear macro- and micro-geometric parameters such as gear web structure and tooth surface error. The gear web structure used in this example is as follows: Figure 4 The contact fatigue life of a rough surface with Ra=0.6μm was calculated using fractal function simulation, with the web structure centered and offset to the left by 15mm, respectively.

[0180] Table 1. Parameters of the gears calculated using the method of the embodiments of this application.

[0181]

[0182] Table 2. Bearing parameters calculated using the method described in the embodiments of this application.

[0183]

[0184] Figure 5 The gear contact fatigue life analysis method considering the influence of macro and micro geometric parameters provided in the embodiments of this application calculates the dynamic load distribution of gears with different web plates. It can be seen that the dynamic load distribution of the gear tooth surface is skewed along the tooth width direction due to the offset of the web plate. This is because the stiffness of the gear changes with the change of the web plate position.

[0185] Figure 6 The gear contact fatigue life analysis method considering the influence of macro and micro geometric parameters provided in the embodiments of this application calculates the oil film pressure of different web-type gears. It can be seen that the gear oil film pressure is reduced on the offset side due to the change in the web structure. This is because the tooth surface load itself is unbalanced.

[0186] Figure 7 The gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters provided in the embodiments of this application calculates the Von-mises stress on and below the surface of different web-type gears. The figure shows a cross-sectional view of the side with larger tooth surface load. It can be seen that the stress distribution on and below the gear surface is clearly obtained through the load on the tooth surface.

[0187] Figure 8 The gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters provided in this application calculates the contact fatigue life of different web gears. The result in the figure is a cross-sectional view along the tooth width at a certain contact line position. It can be seen that the load deviation is well reflected in the contact fatigue life, which also confirms the effectiveness of the gear contact fatigue life analysis method considering the influence of macro- and micro-geometric parameters.

[0188] The embodiments described above are some, but not all, of the embodiments of this application. The detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters, characterized in that: Includes the following steps: Step 1: Establish a tooth surface contact-dynamic analysis model that considers the influence of macroscopic and microscopic geometric parameters and calculate the dynamic load distribution on the tooth surface; Step 2: Establish a calculation model for the stress on and below the gear surface, taking into account the effects of lubrication and surface roughness. Utilize the dynamic load distribution on the tooth surface to calculate the oil film pressure, surface stress, and stress below the gear surface based on the calculation model. Step 3: Establish a gear contact fatigue life prediction model that considers the influence of macroscopic and microscopic geometric parameters, and calculate the gear contact fatigue life based on the prediction model using the surface and subsurface stresses.

2. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 1, characterized in that: Step one specifically includes the following steps: 1.1 Establish a tooth surface contact-dynamic analysis model, including the tooth surface bearing contact equation and the gear motion differential equation; 1.2 The static load distribution, static transmission error, comprehensive meshing stiffness, and comprehensive meshing error of the tooth surface are obtained by solving the tooth surface bearing contact equation; 1.

3. Solve the tooth surface contact-dynamic analysis model established in step 1.1 in the time domain using the Newmark integral method to obtain the dynamic load distribution on the tooth surface.

3. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 2, characterized in that: In step 1.1, The tooth surface contact-dynamic analysis model includes: Tooth surface bearing contact equation and the differential equation of gear motion in: This represents the macroscopic deformation compliance coefficient matrix of the contact points on the tooth surface. The applied load vector, Let be the local contact deformation vector at the contact point. Let be the initial gap vector at the contact point. Let STE be the remaining gap vector at the contact points, and n be the static transmission error. Let {I} be the load applied to the i-th contact point. The vector has elements of 1, and P is the external load vector. The remaining gap at the i-th contact point; In the differential equation of gear motion, Let the masses of the driving wheel and the driven wheel be... These are the moments of inertia of the driving wheel and the driven wheel, respectively. The overall meshing stiffness of the gear pair varies with q. The overall meshing error of the gear pair varies with q. For the meshing damping of the gear pair; Let x represent the displacement of the driving wheel and the driven wheel in the x-axis direction. The rotation angle of the driving wheel and the driven wheel in the x-axis direction; This refers to the relative displacement of the gear pair along the normal line of meshing. , The meshing angle of the gear pair. To install the phase angle; and These are the base circle radii of the driving wheel and the driven wheel, respectively. The torque applied to the drive wheel, Let q be the torque applied to the driven gear, and q be the gear pitch coordinate. Relative displacement of the gear pair along the normal meshing line ; In the formula, Let the projection vector of any nodal displacement onto the normal meshing line direction be: In the formula, and These are the base circle radii of the driving and driven wheels, respectively. and Take the upper half when the drive wheel rotates counterclockwise, and take the lower half when it rotates clockwise.

4. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 2, characterized in that: In step 1.2, the static load distribution of the tooth surface is obtained by solving the tooth surface bearing contact equation. And the static transmission error STE, then solve for the combined meshing stiffness k and the combined meshing error e: 。 5. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 2, characterized in that: In step 1.3, the combined meshing stiffness k and combined meshing error e are substituted into the gear motion differential equation and the dynamic displacement, velocity, and acceleration of the contact point are obtained through the Newmark numerical integration method; the dynamic transmission error is then solved based on the obtained dynamic displacement and velocity. and its derivative The meshing dynamic load can be calculated based on the dynamic transmission error. The dynamic load distribution on the tooth surface is recalculated using the meshing dynamic load and the bearing contact equation; the Hertzian stress distribution on the tooth surface is then solved using the dynamic load distribution on the tooth surface and the Hertzian stress formula. In the formula, The effective contact length of the contact point. The dynamic load at the contact point. , Let the density of the two gears be... , Let be the elastic modulus of the two gears. , Let be the radius of curvature of the tooth profile at the pitch circle of the two gears, expressed as: In the formula, , Let be the pitch circle diameter of the two gears. This is the pressure angle.

6. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 1, characterized in that: In step two, the calculation model is composed of the Reynolds equation, the viscosity-pressure relationship equation, the pressure-density equation, the load equation, as well as the boundary conditions, the film thickness equation, and the WM fractal function. By using the Hertzian contact stress as the initial value of the oil film pressure and solving the calculation model using the multigrid integration method, the lubricating oil film pressure and oil film thickness are obtained. Based on the lubricating oil film pressure and oil film thickness, the shear stress is calculated. By convolving the oil film pressure and shear stress with the influence coefficient, the influence relationship between the gear surface stress and the stress below the surface is established, and the surface and subsurface stresses are calculated.

7. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 6, characterized in that: The computational model consists of: Reynolds equations Viscosity-pressure relationship: Pressure Compressibility Equation: Load equations and boundary conditions: Film thickness equation: WM fractal function: Composed of two elements; in: For the density of lubricating oil, The viscosity of the lubricating oil. Where U is the thickness of the lubricating oil film, and U is the lubricating oil entrainment speed; This refers to the dynamic viscosity of the lubricating oil. , This refers to the viscosity-pressure coefficient of the lubricating oil. This refers to the lubricating oil film pressure. The density of the lubricating oil at room temperature; and These are the coordinates of the oil film inlet and outlet positions, respectively. Where V is the thickness of the central oil film, and V is the elastic deformation matrix. The rough surface random profile generated by the WM fractal function at point The height of the location denoted by , where is the combined radius of curvature of the two tooth profiles at the meshing point; M is the number of overlapping surface ridges; and D is the fractal dimension. The spatial frequency of the roughness surface profile. Here, L is the random profile frequency index, and L is the sampling length. n is a constant. max This represents the upper limit of the frequency exponent. It is a random phase.

8. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 7, characterized in that: In step two, the Hertzian contact stress is used as the initial value of the oil film pressure. The calculation model is solved using the multigrid integration method to obtain the lubricating oil film pressure p and the oil film thickness h. The shear stress is calculated using the oil film pressure p and oil film thickness h according to the oil film shear stress calculation formula: In the formula, This refers to the equivalent viscosity of the lubricating oil. , These are the velocities of the two contact surfaces along the tooth profile direction, The oil film thickness at the current position is taken as follows: and The shear stress distribution on the surfaces of the two gears is obtained; The stress components of the subsurface are the convolution sum of the oil film pressure and shear stress at any gear unit and the influence coefficient on the current unit: In the formula, the influence coefficient This is the influence coefficient under the action of normal stress and tangential stress; The stress at any point in space, calculated using the above method, is: Based on the existing stress distribution on and below the surface, the stress history of each point is obtained by iteratively solving the stress distribution along the perpendicular direction of the contact line.

9. The method for predicting gear contact fatigue life considering the influence of macroscopic and microscopic geometric parameters according to claim 1, characterized in that: In step three, the gear contact fatigue life prediction model is as follows: In the formula, The normal stress amplitude on the characteristic plane, The mean normal stress on the characteristic plane, The shear stress amplitude on the characteristic plane, The hydrostatic stress amplitude is defined on the characteristic plane, which is defined as the plane containing the maximum normal stress amplitude. The plane of the angle, and The stress-life curves of the material under pure bending and pure torsion states represent the fatigue strength at a lifetime of Nf. , These are the material parameters at the current fatigue limit. The mean stress correction factor is: In the formula, These are the material parameters in the correction factor.

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