Dynamic analysis method of face gear considering coupling of hybrid thermo-elastohydrodynamic lubrication and micro-texture

Abstract

The application discloses a kind of surface gear dynamics analysis method considering mixed thermoelastohydrodynamic lubrication and micro-texture coupling, comprising the following steps: step one: based on gear dynamics theory, construct eight degrees of freedom surface gear-rotor system dynamics model;Step two: establish the finite element analysis model of micro-texture surface gear transmission pair, solve time-varying mesh stiffness and coupled into system dynamics equation;Step three: the micro-texture item of film thickness equation is coupled with the film thickness equation of mixed thermoelastohydrodynamic lubrication;Step four: coupling is carried out between mixed and thermal effect and elastohydrodynamic lubrication basic equation, and mixed thermoelastohydrodynamic lubrication model is established;Step five: the mixed thermoelastohydrodynamic lubrication and micro-texture coupling equation are iteratively solved, and the friction force and friction coefficient of the solution domain are output, and they are input as parameters into system dynamics equation;Step six: the system dynamics equation after coupling is solved using Runge-Kutta numerical integration method, and the dynamic response of surface gear transmission system is obtained.

Description

Technical Field

[0001] This invention belongs to the field of face gear transmission technology, specifically a face gear dynamics analysis method that considers the coupling of hybrid thermo-elasto-fluidic lubrication and microtexture. Background Technology

[0002] Face gear drives, due to their high overlap ratio, good stability, and ability to meet high-speed, heavy-load requirements, have gradually become a more advanced transmission method in the aerospace field, fulfilling the gear transmission requirements under extreme operating conditions such as those in aviation. However, face gears operating under high-speed, heavy-load conditions are prone to high tooth surface temperatures and greater elastic deformation during long-term tooth surface friction, easily leading to pitting and scuffing failures. Simultaneously, the system will generate significant vibration and noise. Therefore, performance prediction, analysis, and improvement of face gears operating under extreme conditions are currently a hot and challenging research topic in the field of gear transmission.

[0003] Existing research indicates that surface microtexturing can induce hydrodynamic lubrication during surface flow, significantly improving oil film load-bearing capacity while reducing the coefficient of friction. This method, which enhances lubrication performance by altering surface morphology, has mature theoretical and practical applications in machining tools, sliding bearings, and washers. However, research on gears is still in its early stages. Texturing the tooth surfaces of face gears can effectively improve lubrication performance between tooth contacts, reduce tooth surface friction excitation, and is expected to improve the dynamic performance of face gear transmissions, extending their applicability and service life under extreme high-speed and heavy-load conditions. Summary of the Invention

[0004] The dynamic analysis of face gears under extreme conditions of high speed and heavy load is very complex, and high-precision predictive analysis methods often need to consider the influence of mixed thermo-elastohydrodynamic lubrication. Research on the dynamic performance of face gear transmissions due to microtexturing of the tooth surface is still immature; the mechanism of the coupling effect of changes in surface morphology caused by microtexturing on tooth surface lubrication and system dynamic parameters is lacking. In view of this, this invention proposes a face gear dynamic analysis method that considers the coupling of mixed thermo-elastohydrodynamic lubrication and microtexturing, based on the combined theory of microtexturing and lubrication, and microtexturing and dynamics in the field of face gear transmission dynamics. This method achieves high-precision predictive analysis of the dynamic performance of face gear transmissions under extreme operating conditions, taking into account multiple factors.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture includes the following steps: Step 1: Based on gear dynamics theory, construct an eight-degree-of-freedom surface gear-rotor system dynamic model including prime mover, spur gear, surface gear and load, and derive the system dynamic equations; Step 2: Establish a finite element analysis model of the microtextured gear transmission pair using the finite element method, solve for the time-varying meshing stiffness containing the microtexture, and couple the time-varying meshing stiffness into the system dynamic equations; Step 3: Construct the microtexture geometry design and the mathematical expression of the microtexture region of the flow domain to be solved, characterize the microtexture term of the film thickness equation and couple it with the film thickness equation of hybrid thermo-elasto-fluidic lubrication; Step 4: Based on the elastohydrodynamic lubrication theory, define a hybrid lubrication characterization method, couple the hybrid lubrication effects and thermal effects with the basic equations of elastohydrodynamic lubrication, and establish a hybrid thermo-elastohydrodynamic lubrication model that includes the Reynolds equation for point contact two-dimensional elastohydrodynamic lubrication, the viscosity-temperature-viscosity equation, the density-temperature-density-density equation, and the energy equation. Step 5: The coupling equation of hybrid thermo-elasto-fluidic lubrication and microtexture is solved iteratively using the finite difference method. The tooth surface friction force and friction coefficient in the solution domain are output and used as parameters to input the system dynamic equation. Step 6: Solve the coupled system dynamic equations using the Runge-Kutta numerical integration method to obtain the dynamic response of the face gear transmission system.

[0006] Furthermore, in step one, the eight degrees of freedom include four torsional angular displacements of the prime mover, spur gear, face gear, and load, as well as three lateral displacements and one axial displacement of the spur gear and face gear. Its generalized displacement matrix is ​​expressed as:

[0007] in: It is an eight-degree-of-freedom generalized displacement matrix; in Cartesian coordinates, Cylindrical gear Axial vibration displacement; Cylindrical gear Axial vibration displacement; For cylindrical gears around its Rotational displacement in the axial direction; For the prime mover around it Rotational displacement in the axial direction; For face gears Axial vibration displacement; For face gears Axial vibration displacement; For the face gear around it Rotational displacement in the axial direction; For the load around it Rotational displacement in the axial direction.

[0008] The dynamic model of the eight-degree-of-freedom surface gear-rotor system is expressed as follows:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] in: The concentrated mass of the driving and driven wheels; The moment of inertia of the prime mover, driving wheel, driven wheel, and load; For the torsional damping and torsional stiffness of the drive shaft in the torsional direction; The radius of rotation of the dynamic meshing force and tooth surface friction force of the gear teeth around the rotation center of the driving and driven gears; The combined equivalent damping and stiffness of the drive shaft and support bearings for the gear in the lateral vibration direction; The dynamic meshing force and tooth surface friction force are the two-dimensional components of the driving gear Cartesian coordinate system and the driven gear Cartesian coordinate system, respectively. For driving torque and load torque.

[0017] Furthermore, in step two, the time-varying meshing stiffness of the gear teeth during the gear transmission process is simulated using the finite element method. The time-varying meshing stiffness is expressed as:

[0018] in: The rotation angles of the driving and driven wheels under load; The rotation angles of the driving and driven gears under no-load conditions are given; the discrete rotation angle data are obtained through face gear dynamics simulation results. This is the load torque; and These are the base circle radii of the face gear and the cylindrical gear, respectively. The time-varying meshing stiffness of the face gear is fitted to the discrete data using a Fourier series expansion, yielding:

[0019] in: Let be the order of the Fourier series expansion; The gear tooth meshing frequency is related to the number of gear teeth. and rotational speed Related, and ; is the amplitude constant of sine and cosine.

[0020] Furthermore, in step three, the two-dimensional film thickness equation for the point contact of the microtextured tooth surface, considering elastic deformation, is expressed as:

[0021] in: The thickness of the oil film at the center is determined by the load balance conditions. The equivalent radius is the radius of curvature of the two spheres used for point contact analysis. and Related, and radius of curvature and Obtained through 3D modeling or simulation of surface gear transmission pairs; For microtexture terms, a corresponding mathematical model is constructed to represent the microtexture based on its specific geometric shape. This is the elastic deformation term, obtained from the formula for surface elastic deformation under normal load in elasticity mechanics.

[0022] Furthermore, in step four, the elastohydrodynamic lubrication theory states that: a geometric surface located in an ideally smooth plane is used as the tolerance base surface, and a certain section of the actual rough surface is used as the tolerance baseline. The deviation between the two surfaces in the height direction is [missing information - likely a specific value]. The geometric line serves as the tolerance boundary. The portion of the actual rough surface exceeding the upper tolerance boundary is considered non-elastohydrodynamic lubrication, while the portion within the tolerance boundary is considered elastohydrodynamic lubrication. Offset Generally, the value can be taken as the calculated oil film thickness. .

[0023] Furthermore, in step four, the Reynolds equation for point-contact two-dimensional elastohydrodynamic lubrication based on surface gear transmission is expressed as:

[0024] in: The density of the lubricating oil; The viscosity of the lubricating oil; Oil film pressure; The thickness of the lubricating oil film; For the fluid between the contact tooth surfaces The average velocity along the axis is determined by the upper boundary velocity. With lower boundary velocity Decide: ; For fluid in The average velocity along the axis is determined by the upper boundary velocity. With lower boundary velocity Decide: ; The viscosity-temperature-viscosity-pressure equation is expressed as:

[0025] in: Zero pressure and initial temperature The viscosity of the lubricating oil is as follows; The viscosity coefficient is the pressure viscosity coefficient. The coefficients in the viscosity-pressure formula; The current temperature; The dense temperature and dense pressure equation is expressed as:

[0026] in: Zero pressure and initial temperature The density of the lubricating oil below; It is the density temperature coefficient; The energy equation is expressed as:

[0027]

[0028]

[0029] in: The specific heat capacity of the lubricating oil at constant pressure; The thermal conductivity coefficient of the lubricating oil; and These are the upper and lower boundary temperature conditions of the watershed to be calculated, used to solve the energy equation. item; , , The fluid in sequence axis, axis, Flow velocity in the three axial directions.

[0030] Furthermore, in step five, the tooth surface friction force under mixed lubrication conditions and the friction coefficient under lubrication conditions are expressed as follows:

[0031] in: The load can be calculated using the load balance equation; This is the non-elastohydro lubrication proportional coefficient, determined by the characterization method of mixed elastohydro and non-elastohydro lubrication. The coefficient of friction of the tooth surface under non-elastohydrodynamic lubrication conditions; Let be the shear stress under elastohydrodynamic lubrication; the shear stress under elastohydrodynamic lubrication is expressed as:

[0032] in: This represents the velocity difference between the upper and lower boundaries of the watershed.

[0033] The beneficial effects of this invention are as follows: This invention considers a face gear dynamics analysis method that couples hybrid thermo-elastohydrodynamic lubrication with microtexture. Through a multi-factor coupling analysis method, it significantly improves the accuracy and reliability of predicting the dynamic performance of face gears under extreme conditions, including: (1) Multiphysics coupling modeling improves analysis accuracy By coupling the hybrid thermo-elastohydrodynamic lubrication model with the time-varying meshing stiffness of the microtexture to the dynamic model of an eight-DOF face gear-rotor system, and by coupling the microtexture term of the film thickness equation with the film thickness equation of hybrid thermo-elastohydrodynamic lubrication, the synergistic effect of lubrication state, thermal effect, elastic deformation, and surface microtexture is simultaneously incorporated into the dynamic analysis of face gears for the first time. This multiphysics coupling modeling effectively overcomes the limitations of traditional methods that only consider a single factor in isolation (such as only lubrication or only stiffness change), and solves the problem of "unclear coupling mechanism between microtexture and lubrication and dynamics" mentioned in the background art. This significantly improves the prediction accuracy of tooth surface contact meshing force, oil film thickness, and friction excitation, thereby enabling more accurate adjustment and optimization of system parameter design through this predictive analysis method, reducing the risk of failures such as pitting and scuffing on the tooth surface.

[0034] (2) Microtexture optimizes lubrication performance and reduces friction excitation By constructing a microtexture mathematical model, a controllable hydrodynamic pressure effect is introduced into the tooth surface contact area. Combined with the friction force calculation under mixed lubrication conditions, the contribution of microtexture to the improvement of oil film bearing capacity and the reduction of non-elastohydrodynamic lubrication ratio can be quantified, which can effectively reduce the reduction of tooth surface friction coefficient, thereby reducing system vibration and noise.

[0035] (3) Efficient numerical methods to realize simulation of complex working conditions A multi-scale solution strategy combining the finite difference method and Runge-Kutta numerical integration is adopted, which significantly improves computational efficiency while ensuring the stability of the solution of the hybrid thermo-elastohydrodynamic lubrication equation and the dynamic equation.

[0036] (4) Extend service life and expand application scenarios The output system dynamic response (such as vibration amplitude, vibration signal frequency components, and dynamic meshing force) can directly guide the coordinated design of microtexture parameters (such as array spacing and aspect ratio) and lubrication conditions. Attached Figure Description

[0037] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 A flowchart of the dynamic analysis method for face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture in this invention; Figure 2 is a schematic diagram of the dynamic model of an eight-degree-of-freedom surface gear-rotor system; Figure 3 is a simulation diagram of the time-varying meshing stiffness of the micro-textured gear. Figure 4 shows the geometric model of the diamond-shaped microtexture; Figure 5 shows the characterization method for mixed elastohydrodynamic and non-elastohydrodynamic lubrication. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0039] like Figure 1 As shown, this embodiment considers a face gear dynamics analysis method that couples hybrid thermo-elastohydrodynamic lubrication with microtexture, and includes the following steps.

[0040] Step 1: Based on gear dynamics theory, construct an eight-degree-of-freedom surface gear-rotor system dynamic model including prime mover, spur gear, surface gear and load, and derive the system dynamic equations.

[0041] In this embodiment, an eight-degree-of-freedom surface gear-rotor system dynamic model is constructed using the lumped parameter method. The prime mover (drive motor), spur gear, surface gear, and load are considered as four elements with rotational inertia, such as... Figure 2 As shown. The system dynamics model considers factors including time-varying meshing stiffness of gear teeth, meshing damping, static transmission error, torsional damping and torsional stiffness of the transmission shaft, damping and stiffness of the support bearing, and tooth surface friction. The damping and stiffness of the input and output transmission shafts and gear support bearings are respectively considered as equivalent damping and equivalent stiffness. The system has eight generalized displacements: four torsional angular displacements of the prime mover, spur gear, face gear, and load; three lateral displacements and one axial displacement of the spur gear and face gear. That is, in this embodiment, the eight degrees of freedom include four torsional angular displacements of the prime mover, spur gear, face gear, and load; and three lateral displacements and one axial displacement of the spur gear and face gear. Its generalized displacement matrix is ​​expressed as:

[0042] in: For an eight-degree-of-freedom generalized displacement matrix; in Figure 2 In the Cartesian coordinate system defined in China, Cylindrical gear Axial vibration displacement; Cylindrical gear Axial vibration displacement; For cylindrical gears around its Rotational displacement in the axial direction; For the prime mover around it Rotational displacement in the axial direction; For face gears Axial vibration displacement; For face gears Axial vibration displacement; For the face gear around it Rotational displacement in the axial direction; For the load around it Rotational displacement in the axial direction.

[0043] Based on this dynamic model, the system meshing coupling dynamic equations are established according to Newton's laws. The dynamic model of the eight-degree-of-freedom surface gear-rotor system is expressed as follows:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] in: The concentrated mass of the driving and driven wheels; The moment of inertia of the prime mover, driving wheel, driven wheel, and load; For the torsional damping and torsional stiffness of the drive shaft in the torsional direction; The radius of rotation of the dynamic meshing force and tooth surface friction force of the gear teeth around the rotation center of the driving and driven gears; The combined equivalent damping and stiffness of the drive shaft and support bearings for the gear in the lateral vibration direction; The dynamic meshing force and tooth surface friction force are the two-dimensional components of the driving gear Cartesian coordinate system and the driven gear Cartesian coordinate system, respectively. For driving torque and load torque.

[0052] Step 2: Establish a finite element analysis model of the microtextured gear transmission pair using the finite element method, solve for the time-varying meshing stiffness containing the microtexture, and couple the time-varying meshing stiffness into the system dynamic equations.

[0053] Based on the above face gear dynamics equations, the microtexture factor is coupled with face gear dynamics. The coupling method considering microtexture is as follows: Since the structural changes caused by microtextured tooth surfaces have an effect on face gear transmission, from the perspective of dynamic excitation, an important and significant influence of microtextured tooth surfaces on face gear dynamics is "time-varying meshing stiffness". Therefore, the effect of microtexture on face gear dynamics can be characterized by "time-varying meshing stiffness".

[0054] Given that face gear drives are more complex than ordinary gear drives, their time-varying meshing stiffness is not suitable for direct calculation using the relevant formulas for ordinary gear meshing stiffness. This embodiment uses the finite element method to simulate the time-varying meshing stiffness of the face gear teeth during the transmission process. Then, considering its periodicity, Fourier series expansion is used to fit the discrete data results. Specifically, the time-varying meshing stiffness can be calculated using the following formula:

[0055] in: The rotation angles of the driving and driven wheels under load; The rotation angles of the driving and driven wheels under no-load conditions; This is the load torque; and These represent the base circle radii of the face gear and the cylindrical gear, respectively. The discrete rotation angle data are obtained from the dynamic simulation results of the face gear.

[0056] The time-varying meshing stiffness of the face gear is fitted to the discrete data using a Fourier series expansion, yielding:

[0057] in: Let be the order of the Fourier series expansion; The gear tooth meshing frequency is related to the number of gear teeth. and rotational speed Related, and ; is the amplitude constant of sine and cosine.

[0058] The finite element method (FEM) was used to simulate the micro-textured gear transmission pair model. A diamond-shaped microtexture was coupled into the gear transmission pair, with the microtexture added near the contact trace of the transmission pair. The time-varying meshing stiffness of the micro-textured gear can be obtained using the above formula. The simulation method for the time-varying meshing stiffness of the micro-textured gear is as follows: Figure 3 As shown.

[0059] Step 3: Construct the microtexture geometry design and the mathematical expression of the microtexture region of the flow domain to be solved, characterize the microtexture term of the film thickness equation and couple it with the film thickness equation of hybrid thermo-elasto-fluidic lubrication.

[0060] The coupling between microtexture and elastohydrodynamic lubrication is achieved through the microtexture term in the film thickness equation and the microtexture mathematical model. The key to constructing the microtexture tooth surface film thickness equation considering elastic deformation lies in adding elastic deformation and microtexture terms to the original point-contact two-dimensional film thickness equation. The microtexture tooth surface point-contact two-dimensional film thickness equation considering elastic deformation can be expressed as:

[0061] in: The thickness of the oil film at the center is determined by the load balance conditions. The equivalent radius is the radius of curvature of the two spheres used for point contact analysis. and Related, and radius of curvature and Obtained through 3D modeling or simulation of surface gear transmission pairs; For microtexture terms, a corresponding mathematical model is constructed to represent the microtexture based on its specific geometric shape. This is the elastic deformation term, obtained from the formula for surface elastic deformation under normal load in elasticity mechanics.

[0062] Specifically, elastic deformation term Represented as:

[0063] in: The combined elastic modulus of the two contact surfaces is expressed as a function of the Poisson's ratio of the contact surface materials. , and elastic modulus , The relationship is as follows: ; This is the region of elastic deformation integration. and These are the coordinates of the load application point and the coordinates of the point to be calculated, respectively. This is the two-dimensional load distribution function.

[0064] The film thickness equation for microtextured tooth surfaces needs to additionally consider the change in the original elastic deformation point contact two-dimensional film thickness caused by the microtextured region. Therefore, a microtexture term is added to the actual film thickness equation. This embodiment proposes an asymmetric "diamond-shaped" microtexture and uses it as an example to express the microtexture term in the watershed film thickness equation containing this microtexture. The main structural parameters of the "diamond-shaped" microtexture include: principal axis parameters. minor axis parameters Transition parameters Lateral center-to-center spacing parameters and longitudinal center spacing parameters . Figure 4 It showcases the geometry of the "diamond-shaped" microtexture and its aspect ratio of... Furthermore, it includes six rectangular oil film flow domains of this microtexture to be calculated. The microtexture of the membrane thickness in this watershed It can be represented as:

[0065] in: This is represented as a non-microtextured region, and its representation can be obtained by subtracting the whole watershed from the microtextured region. Specifically, the microtextured region... The mathematical expression is:

[0066] in: and For microtexture apexes near the origin of the coordinate system and shaft and The perpendicular distance of the axis; the "diamond-shaped" microtexture is composed of triangular and elliptical halves. and These represent the triangular and elliptical halves of the microtextured region in the longitudinal direction, respectively. and They represent the current The lower bound of the range of values. , ; The linear array coefficients of the microtexture within the watershed are given for the rectangular oil film watershed in this embodiment. , .

[0067] Step 4: Based on elastohydrodynamic lubrication theory, define a hybrid lubrication characterization method, couple the effects of hybrid lubrication and thermal effects with the basic equations of elastohydrodynamic lubrication, and establish a hybrid thermo-elastohydrodynamic lubrication model that includes the Reynolds equation for point contact two-dimensional elastohydrodynamic lubrication, the viscosity-temperature-viscosity equation, the density-temperature-density-density equation, and the energy equation.

[0068] Due to manufacturing errors in gear tooth surfaces, sharp peaks with high roughness and abrupt surface transitions can easily lead to oil film breakdown, resulting in a mixed elastohydrodynamic (ETD) lubrication state. The ETD lubrication theory defined in this embodiment is as follows: The geometric surface representing the mixed elastohydrodynamic (ETD) lubrication state at the contact interface of the face gear pair is used as the tolerance baseline. A cross-section of the actual rough surface is used as the tolerance baseline, and the deviation (or tolerance value) from the tolerance baseline in the height direction is defined as follows: The geometric line serves as the tolerance boundary. The portion of the actual rough surface exceeding the upper tolerance boundary is considered to be in a "non-elastohydrodynamic lubrication" state, while the portion within the tolerance boundary is considered to be in a "elastohydrodynamic lubrication" state. The offset is... Generally, the value can be taken as the calculated oil film thickness. Methods for characterizing elastohydrodynamic and non-elastohydrodynamic mixed lubrication include... Figure 5 As shown.

[0069] For this method of characterizing mixed elastohydrodynamic and non-elastohydrodynamic lubrication, the actual rough surface can be obtained by measuring the tooth surface using the white light interference experiment of an optical profilometer, or by simulating it using mathematical methods of probability distribution.

[0070] (1) Reynolds equation for point contact two-dimensional elastohydrodynamic lubrication The contact form of a cylindrical gear-face gear transmission pair is "point contact," and the transmission process involves a contact ellipse. Typically, the combined velocity of the lubricating oil flow forms a certain angle with the major axis of the ellipse; that is, the combined velocity is not collinear with the principal axis of the contact ellipse. Therefore, if the major axis of the contact ellipse is defined as... When considering the two-dimensional elastohydrodynamic lubrication of a shaft in a "point contact" manner, attention must be paid to its speed. shaft and The axis has components in both directions. The Reynolds equation for "point contact" two-dimensional elastohydrodynamic lubrication, applicable to face gear drives, can be expressed as:

[0071] in: The density of the lubricating oil; The viscosity of the lubricating oil; Oil film pressure; The thickness of the lubricating oil film; For the fluid between the contact tooth surfaces The average velocity along the axis is determined by the upper boundary velocity. With lower boundary velocity Decide: ; For fluid in The average velocity along the axis is determined by the upper boundary velocity. With lower boundary velocity Decide: .

[0072] (2) Load balance equation The correctness of the numerical solution for elastohydrodynamic pressure needs to be verified by the load-pressure balance equation. Theoretically, the magnitude of the pressure in the region should be consistent with the magnitude of the load on the region. For point contact, the load-pressure balance equation can be expressed as:

[0073] in: It is a point contact load; This is point contact pressure.

[0074] (3) Viscosity-temperature-viscosity-pressure equation For face gear drives under high-speed, heavy-load extreme conditions, the tooth contact area is often under high pressure and high temperature. When the temperature and pressure of the lubricating oil change, the viscosity and density of the lubricating oil will also change. Especially for face gear drives under high-speed, heavy-load conditions, the viscosity-pressure characteristics, viscosity-temperature characteristics, pressure-density characteristics, and temperature-density characteristics of the oil will be important factors affecting the elastohydrodynamic lubrication performance of the inter-tooth lubricating oil.

[0075] Roelands' viscosity-pressure and viscosity-temperature coupling equations can be expressed as follows:

[0076] in: Zero pressure and initial temperature The viscosity of the lubricating oil is as follows; The viscosity coefficient is the pressure viscosity coefficient. The coefficients in the viscosity-pressure formula; The current temperature is expressed in Kelvin (SI). It can be solved using the energy equation; Pressure, unit: In this embodiment, .

[0077] (4) The equation of temperature and pressure The coupling equations of pressure and temperature can be expressed as:

[0078] in: Zero pressure and initial temperature The density of the lubricating oil below; This is the density coefficient.

[0079] (5) Energy equation The effect of heat on lubrication is mainly reflected in the change in the viscosity and density of lubricating oil due to temperature, and the solution for the temperature distribution relies on the energy equation. For the tooth surface of a point-contact gear, its energy equation can be expressed as:

[0080]

[0081]

[0082] in: The specific heat capacity of the lubricating oil at constant pressure; The thermal conductivity coefficient of the lubricating oil; and These are the upper and lower boundary temperature conditions of the watershed to be calculated, used to solve the energy equation. item; , , The fluid in sequence axis, axis, Flow velocity in the three axial directions.

[0083] Step 5: The finite difference method is used to iteratively solve the coupling equation of hybrid thermo-elasto-fluidic lubrication and microtexture, outputting the tooth surface friction force and friction coefficient in the solution domain, and inputting them as parameters into the system dynamic equation.

[0084] By integrating the above-mentioned hybrid thermo-elastohydrodynamic lubrication theory and microtexture characterization methods, a series of equations coupling hybrid thermo-elastohydrodynamic lubrication and microtexture can be obtained. Subsequently, the input parameters needed to calculate tooth surface friction and friction coefficient can be obtained by iteratively solving these equations using the finite difference method. Hybrid thermo-elastohydrodynamic lubrication and face gear dynamics are coupled through tooth surface friction and friction coefficient. The calculation method for tooth surface friction and friction coefficient under hybrid lubrication conditions is as follows:

[0085] in: The load can be calculated using the load balance equation; This is the non-elastohydro lubrication proportional coefficient, determined by the characterization method of mixed elastohydro and non-elastohydro lubrication. The coefficient of friction of the tooth surface under non-elastohydrodynamic lubrication conditions; Let be the shear stress under elastohydrodynamic lubrication; the shear stress under elastohydrodynamic lubrication is expressed as:

[0086] in: This represents the velocity difference between the upper and lower boundaries of the watershed.

[0087] The calculated tooth surface friction force and friction coefficient can be used as parameter input for the subsequent face gear-rotor system dynamic equations, completing the coupling of "hybrid thermo-elastohydrodynamic lubrication" and "face gear dynamics".

[0088] Step Six: Solve the coupled system dynamic equations using the Runge-Kutta numerical integration method to obtain the dynamic response of the face gear transmission system. That is, substitute the calculation formulas for each parameter of the dynamic equations back into the original system dynamic equations, and use the Runge-Kutta numerical integration method to solve the dynamic equations of the face gear-rotor system considering multi-factor coupling, thus obtaining the system's dynamic response.

[0089] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture, characterized in that: Includes the following steps: Step 1: Based on gear dynamics theory, construct an eight-degree-of-freedom surface gear-rotor system dynamic model including prime mover, spur gear, surface gear and load, and derive the system dynamic equations; Step 2: Establish a finite element analysis model of the microtextured gear transmission pair using the finite element method, solve for the time-varying meshing stiffness containing the microtexture, and couple the time-varying meshing stiffness into the system dynamic equations; Step 3: Construct the microtexture geometry design and the mathematical expression of the microtexture region of the flow domain to be solved, characterize the microtexture term of the film thickness equation and couple it with the film thickness equation of hybrid thermo-elasto-fluidic lubrication; Step 4: Based on the elastohydrodynamic lubrication theory, define a hybrid lubrication characterization method, couple the hybrid lubrication effects and thermal effects with the basic equations of elastohydrodynamic lubrication, and establish a hybrid thermo-elastohydrodynamic lubrication model that includes the Reynolds equation for point contact two-dimensional elastohydrodynamic lubrication, the viscosity-temperature-viscosity equation, the density-temperature-density-density equation, and the energy equation. Step 5: The coupling equation of hybrid thermo-elasto-fluidic lubrication and microtexture is solved iteratively using the finite difference method. The tooth surface friction force and friction coefficient in the solution domain are output and used as parameters to input the system dynamic equation. Step 6: Solve the coupled system dynamic equations using the Runge-Kutta numerical integration method to obtain the dynamic response of the face gear transmission system.

2. The method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture as described in claim 1, characterized in that: In step one, the eight degrees of freedom include four torsional angular displacements of the prime mover, spur gear, face gear, and load, as well as three lateral displacements and one axial displacement of the spur gear and face gear. The generalized displacement matrix is ​​expressed as: in: It is an eight-degree-of-freedom generalized displacement matrix; in Cartesian coordinates, Cylindrical gear Axial vibration displacement; Cylindrical gear Axial vibration displacement; For cylindrical gears around its Rotational displacement in the axial direction; For the prime mover around it Rotational displacement in the axial direction; For face gears Axial vibration displacement; For face gears Axial vibration displacement; For the face gear around it Rotational displacement in the axial direction; For the load around it Rotational displacement in the axial direction; The dynamic model of the eight-degree-of-freedom surface gear-rotor system is expressed as follows: in, and These are the concentrated masses of the driving wheel and the driven wheel, respectively. , , and These are the moments of inertia of the prime mover, driving wheel, driven wheel, and load, respectively. , These are the torsional damping and torsional stiffness of the drive shaft on the drive wheel side in the torsional direction, respectively. and These are the torsional damping and torsional stiffness of the driven shaft on the driven wheel side in the torsional direction, respectively. Dynamic meshing force of gear teeth The radius of rotation about the center of rotation of the driving wheel; Dynamic meshing force of gear teeth The radius of rotation about the center of rotation of the driven wheel; For tooth surface friction The radius of rotation about the center of rotation of the driving wheel; , , , , , , , These are the combined equivalent damping and stiffness of the gears in the corresponding lateral vibration directions, respectively, provided by the drive shaft and the support bearings. , , , Dynamic meshing force of gear teeth Two component forces in the Cartesian coordinate system for the driving and driven wheels, respectively; , , , For tooth surface friction Two component forces in the Cartesian coordinate system for the driving and driven wheels, respectively; and These are the driving torque and the load torque, respectively.

3. The method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture as described in claim 2, characterized in that: In step two, the time-varying meshing stiffness of the gear teeth during the gear transmission process is simulated using the finite element method. The time-varying meshing stiffness is expressed as: in: This represents the rotation angle of the drive wheel under load. This represents the rotation angle of the driven wheel under load. This represents the rotation angle of the drive wheel under unloaded conditions. The rotation angle is the value of the driven gear under no-load conditions; the discrete rotation angle data are obtained from the dynamic simulation results of the face gear. This is the load torque; and These are the base circle radii of the face gear and the cylindrical gear, respectively. The time-varying meshing stiffness of the face gear is fitted to the discrete data using a Fourier series expansion, yielding: in: Let be the order of the Fourier series expansion; The gear tooth meshing frequency is related to the number of gear teeth. and rotational speed Related, and ; The amplitude constants of the sine and cosine waves are... .

4. The method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture as described in claim 1, characterized in that: In step three, the two-dimensional film thickness equation for point contact of the microtextured tooth surface considering elastic deformation is expressed as: in: The thickness of the oil film at the center is determined by the load balance conditions. The equivalent radius is the radius of curvature of the two spheres used for point contact analysis. and Related, and radius of curvature and Obtained through 3D modeling or simulation of surface gear transmission pairs; For microtexture terms, a corresponding mathematical model is constructed to represent the microtexture based on its specific geometric shape. This is the elastic deformation term, obtained from the formula for surface elastic deformation under normal load in elasticity mechanics; The coordinates of the point to be calculated are denoted as .

5. The method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture as described in claim 1, characterized in that: In step four, the elastohydrodynamic lubrication theory states that: a geometric surface in an ideally smooth plane is used as the tolerance baseline, and a cross-section of the actual rough surface is used as the tolerance baseline. The deviation from the tolerance baseline in the height direction is [missing information]. The geometric line serves as the tolerance boundary. The portion of the actual rough surface exceeding the upper tolerance boundary is considered non-elastohydrodynamic lubrication, while the portion within the tolerance boundary is considered elastohydrodynamic lubrication. Offset amount. The value is the calculated oil film thickness. .

6. The method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture as described in claim 1, characterized in that: In step four, the Reynolds equation for point-contact two-dimensional elastohydrodynamic lubrication based on surface gear transmission is expressed as: in: The density of the lubricating oil; The viscosity of the lubricating oil; Oil film pressure; The thickness of the lubricating oil film; For the fluid between the contact tooth surfaces The average velocity along the axis is determined by the upper boundary velocity. With lower boundary velocity Decide: ; For fluid in The average velocity along the axis is determined by the upper boundary velocity. With lower boundary velocity Decide: ; The viscosity-temperature-viscosity-pressure equation is expressed as: in: Zero pressure and initial temperature The viscosity of the lubricating oil is as follows; The pressure viscosity coefficient; The coefficients in the viscosity-pressure formula; The current temperature; The dense temperature and dense pressure equation is expressed as: in: Zero pressure and initial temperature The density of the lubricating oil below; It is the density temperature coefficient; The energy equation is expressed as: in: The specific heat capacity of the lubricating oil at constant pressure; The thermal conductivity coefficient of the lubricating oil; and These are the upper and lower boundary temperature conditions of the watershed to be calculated, used to solve the energy equation. item; , , The fluid in sequence axis, axis, Flow velocity in the three axial directions.

7. The method for dynamic analysis of face gears considering the coupling of hybrid thermo-elasto-fluid lubrication and microtexture as described in claim 1, characterized in that: In step five, the tooth surface friction force under mixed lubrication and the friction coefficient under lubrication are expressed as follows: in: This refers to the frictional force on the tooth surface. The load can be calculated using the load balance equation; This is the non-elastohydro lubrication proportional coefficient, determined by the characterization method of mixed elastohydro and non-elastohydro lubrication. The coefficient of friction of the tooth surface under non-elastohydrodynamic lubrication conditions; This refers to the shear stress under elastohydrolubrication conditions. The shear stress under elastohydrolubrication is expressed as: in: The velocity difference between the upper and lower boundaries of the watershed; The viscosity of the lubricating oil; The thickness of the lubricating oil film; This refers to the oil film pressure.

Images