Method and system for predicting temperature of asymmetric helical gear contact surface based on thermal network

Abstract

The present application relates to the field of gear transmission system thermal analysis, and more particularly to a kind of asymmetric helical gear contact surface temperature prediction method and system based on thermal network, the method comprises: S1, the basic parameters of asymmetric helical gear are acquired, and gear thermal network model is constructed, S2, the friction heat flow is calculated, S3, the heat conduction thermal resistance and heat convection thermal resistance are calculated, S4, the thermal network topological structure is constructed, and the body temperature value of each node of driving wheel and the body temperature value of each node of driven wheel are obtained by solving, S5, the contact surface body temperature is solved. Realize the quick analysis of asymmetric helical gear body temperature, it is favorable to more quickly solve.

Description

Technical Field

[0001] This invention relates to the field of thermal analysis of gear transmission systems, and in particular to a method and system for predicting the contact surface temperature of asymmetric helical gears based on thermal networks. Background Technology

[0002] The asymmetric gear design concept aligns with the modern trend towards lightweight and high-power-density mechanical equipment. It effectively reduces gear mass while maintaining transmission performance, thereby lowering energy consumption.

[0003] Currently, the traditional finite element method (FEM) is a commonly used approach for gear temperature field analysis. However, the geometry and boundary conditions of asymmetric helical gears are complex. The asymmetry of their tooth profile necessitates more refined meshing when building the finite element model to ensure accuracy. This not only increases the model's complexity but also significantly raises the computational load. Furthermore, obtaining accurate temperature distribution results requires numerous iterative calculations, further extending the computation time. In practical engineering, rapid acquisition of gear temperature information is often necessary for timely adjustments to design and operating parameters. The traditional finite element method struggles to meet these requirements for real-time performance and efficiency, making it unable to quickly analyze the body temperature of asymmetric helical gears.

[0004] In conclusion, developing a method and system for rapidly and accurately predicting the body temperature of the contact surface of asymmetric helical gears is of great practical significance for promoting the widespread application of asymmetric helical gears in high-speed transmission systems and improving the performance and reliability of gear transmission systems. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] The main objective of this invention is to provide a method and system for predicting the contact surface temperature of asymmetric helical gears based on thermal networks, so as to solve the above-mentioned technical problems.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, this invention provides a method for predicting the contact surface temperature of asymmetric helical gears based on thermal networks, comprising the following steps:

[0009] S1. Obtain the basic parameters of the asymmetric helical gear and construct a gear thermal network model. The basic parameters include geometric parameters, transmission parameters, and thermal property parameters.

[0010] S2, Calculate frictional heat flow: Based on the basic parameters provided in step S1, calculate the half-width of the helical gear's linear contact zone using Hertzian contact theory. and average contact stress pThe relative sliding velocity is solved by combining the meshing geometry. V c Based on the mixed lubrication model, the heat flux density is distributed to obtain the frictional heat flow of the driving wheel tooth surface at the meshing point C between the driving wheel and the driven wheel. Heat flow from friction between driven gear teeth ;

[0011] S3, Calculate the thermal conduction resistance and thermal convection resistance: Based on the gear thermal network model in step S1, discretize the gear thermal network model and define temperature nodes. Calculate the thermal conduction resistance and thermal convection resistance of relevant parts of the gear according to the geometric parameters of the divided regions, including:

[0012] S31, based on the gear thermal network model in step S1, the three-dimensional gear meshing region is discretized into average values. N Each region is defined as described. N Each meshing point on the surface of a region and the midpoint of the tooth thickness along the tooth thickness direction of the meshing point are temperature nodes, and the three-dimensional gear is divided into regions along the tooth thickness, tooth width, tooth height directions and spokes.

[0013] S32, based on the geometric parameters of the defined thermal resistance boundary region, calculate the thermal conduction resistance along the tooth thickness direction on the working tooth surface. Thermal resistance of non-working tooth surface along tooth thickness direction Thermal resistance along the tooth height direction Thermal resistance along the tooth width direction Thermal conduction and thermal resistance in the direction of the spokes And calculate the thermal resistance of heat convection between the tooth tip and the lubricating oil. Thermal resistance of heat convection between gear end face and lubricating oil Thermal resistance of heat convection between meshing tooth surfaces and lubricating oil Thermal resistance of non-meshing tooth surfaces and lubricating oil ;

[0014] S4, construct the thermal network topology and solve for the body temperature values ​​of each node of the driving wheel and each node of the driven wheel:

[0015] S41, associate the nodes set in step S3 with the divided regions, connect adjacent nodes through thermal resistance to form heat transfer paths, and construct a thermal network topology, wherein each divided region is connected to at least one node.

[0016] S42, based on the ambient temperature, the frictional heat flow in step S2, and the thermal resistance parameter in step S3, and according to the law of conservation of energy, the body temperature values ​​of each node of the driving wheel and each node of the driven wheel are calculated through the thermal balance equations of the driving wheel temperature node and the driven wheel temperature node.

[0017] S5, Solve for the contact surface body temperature: Based on the body temperature values ​​of each node of the driving wheel and each node of the driven wheel obtained in step S4, select the body temperature of the contact surface of two contact wheel teeth. and The average value is used to calculate the body temperature of the contact surface. The calculation formula is as follows:

[0018]

[0019] in, This represents the tangential velocity of the driving wheel at the node. This indicates the tangential velocity of the driven wheel at the node; Indicates the thermal contact coefficient of the driving wheel. This represents the thermal contact coefficient of the driven wheel.

[0020] Preferably, the basic parameters in step S1 include:

[0021] The geometric parameters include: number of gear teeth, gear normal module, helix angle, tooth width, pressure angle of gear working tooth surface, pressure angle of gear non-working tooth surface, tooth tip height and total tooth height, gear displacement coefficient, shaft outer diameter, Poisson's ratio of gear material, elastic modulus and surface roughness.

[0022] The transmission parameters include: rotational speed, gear input power, and center distance;

[0023] The thermophysical parameters include: the thermal conductivity coefficient of the gear material, the density of the gear material, the specific heat capacity of the gear material, the dynamic viscosity of the lubricating oil, the thermal conductivity coefficient of the lubricating oil, the density of the lubricating oil, and the specific heat capacity of the lubricating oil.

[0024] Preferably, the half-width of the helical gear line contact area in step S2 and average contact stress p Calculated using the following formula:

[0025] p

[0026]

[0027] in, B represents the normal load, and B represents the tooth width. Represents the equivalent elastic modulus. This represents the combined radius of curvature at the meshing point c. This represents the total length of the contact line at the engagement point c.

[0028] Preferably, the relative sliding speed in step S2 The calculation formula is as follows:

[0029]

[0030] in, This represents the relative sliding velocity at any meshing point C. This represents the tangential velocity of the driving wheel at the meshing point c. This represents the tangential velocity of the driven wheel at the meshing point c.

[0031] Preferably, the heat flux density distribution of the hybrid lubrication model in step S2 includes:

[0032] Under mixed lubrication conditions, the formulas for calculating the frictional heat flux density of the tooth surfaces of the driving and driven gears are as follows:

[0033]

[0034]

[0035] in, γ Indicates the heat conversion coefficient. Indicates the heat flux density distribution coefficient. Let be the tangential velocity at the meshing point c;

[0036] The heat flow rate of friction on the tooth surface of the driving gear in step S2 Heat flow from friction between driven gear teeth Calculated using the following formula:

[0037]

[0038]

[0039] in, This represents the area of ​​the contact surface of the driving wheel at the meshing point c. This represents the area of ​​the contact surface of the driven wheel at the meshing point c.

[0040] Preferably, step S31 further includes: discretizing a single tooth along the tooth thickness and tooth height directions into N Each three-dimensional element divides the tooth end face area into i blocks, whose areas are denoted as follows: .

[0041] Preferably, in step S32, the thermal resistance of the working tooth surface along the tooth thickness direction is calculated using the following formula. The thermal resistance of the non-working tooth surface along the tooth thickness direction. The thermal resistance along the tooth height direction. The thermal resistance along the tooth width direction. Thermal resistance in the spoke direction The thermal resistance of heat convection between the tooth tip and the lubricating oil The thermal resistance of heat convection between the gear end face and the lubricating oil The thermal resistance of the meshing tooth surface and the lubricating oil during heat convection. Thermal resistance of non-meshing tooth surfaces and lubricating oil :

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] in, This represents the heat transfer coefficient of the tooth tip and the non-working tooth surface of the gear. This represents the heat transfer coefficient of the gear end face via convection. This represents the thermal convection heat transfer coefficient of the working tooth surface of the gear. This represents the convective heat transfer area of ​​the tooth tip surface. This represents the convective heat transfer area of ​​the working tooth surface of the gear. This represents the convective heat transfer area of ​​the non-working tooth surface of the gear.

[0052] Preferably, the thermal balance equation of the active wheel temperature node includes:

[0053]

[0054] in, Indicates ambient temperature. Indicates the active round node from Frictional heat flow rate input at each node; This represents the temperature at various temperature points on the meshing tooth surface. This indicates the temperature at various temperature nodes inside the tooth core.

[0055] Preferably, the thermal balance equation of the driven wheel temperature node has the same form as the thermal balance equation of the driving wheel, and the specific parameters are replaced with the equivalent parameters of the driven wheel. The replaced equivalent parameters include the frictional heat flow, thermal resistance and ambient temperature of the driven wheel.

[0056] The present invention also provides a thermal network-based asymmetric helical gear contact surface temperature prediction system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the thermal network-based asymmetric helical gear contact surface temperature prediction method as described in any of the preceding claims.

[0057] (III) Beneficial Effects

[0058] The proposed method for predicting the contact surface temperature of asymmetric helical gears based on thermal networks considers not only the meshing behavior of the asymmetric helical gear pair during meshing but also the influence of the asymmetric gear structure on heat transfer and convective heat transfer during gear thermal network model construction, resulting in more accurate predictions. Its calculation steps are simple, computationally inexpensive, and fast. It can solve for the body temperature value of any point on the gear independently, accurately predicting the body temperature of the contact surface of the asymmetric helical gear. This allows for rapid analysis of the body temperature of the asymmetric helical gear, facilitating faster solutions. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating a method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network, as provided in this embodiment.

[0060] Figure 2 A flowchart illustrating a method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network, provided for another embodiment;

[0061] Figure 3 This embodiment provides a schematic diagram (a) illustrating the local tooth surface parameters of an asymmetric helical gear, which is based on a thermal network for predicting the contact surface temperature of an asymmetric helical gear.

[0062] Figure 4 This embodiment provides a schematic diagram (b) illustrating the local tooth surface parameters of an asymmetric helical gear, which is based on a thermal network for predicting the contact surface temperature of an asymmetric helical gear.

[0063] Figure 5This embodiment provides a schematic diagram of an asymmetric bevel gear with labeled angles and tooth surface regions, representing an asymmetric bevel gear for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network.

[0064] Figure 6 This embodiment provides a hardware structure diagram of an asymmetric helical gear contact surface temperature prediction system based on a thermal network. Detailed Implementation

[0065] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0066] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0067] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0068] In this invention, unless otherwise explicitly specified and limited, the terms "connection" and "fixed" should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; "connection" can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0069] like Figure 1 and Figure 2 As shown, this embodiment provides a method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network. The method includes steps S1 to S5.

[0070] S1. Obtain the basic parameters of the asymmetric helical gear and construct a gear thermal network model. The basic parameters include geometric parameters, transmission parameters, and thermal property parameters. The basic parameters provide basic data support for the entire prediction process. The basic parameters can be set according to the actual situation and may include, for example, geometric parameters, transmission parameters, thermal property parameters, and operating condition parameters. The obtained basic parameters are a key prerequisite for subsequent calculations to reflect the actual situation.

[0071] In other embodiments, the gear thermal network model is based on M The ATLAB computational model, built upon gear geometry and heat transfer theory, can transform input basic parameters into thermal resistance network nodes of the gear system and solve for the temperature field distribution of the gear system.

[0072] S2, Calculate frictional heat flow: Based on the basic parameters provided in step S1, calculate the half-width of the helical gear's linear contact zone using Hertzian contact theory. and average contact stress p The relative sliding velocity is solved by combining the meshing geometry. V c Based on the mixed lubrication model, the heat flux density is distributed to obtain the frictional heat flow of the driving wheel tooth surface at the meshing point C between the driving wheel and the driven wheel. Heat flow from friction between driven gear teeth Based on the basic parameters obtained in step S1, combined with the gear meshing principle and tribology, the heat generated on the gear contact surface per unit time is calculated, clarifying the source and intensity of the heat, providing basic heat source conditions for subsequent heat transfer analysis, and facilitating accurate simulation of temperature changes inside the gear.

[0073] Specifically, the half width of the helical gear line contact area The lateral dimension of the contact area affects the distribution range of the heat source; the average contact stress p The pressure per unit area of ​​the contact zone determines the intensity of the frictional heat source.

[0074] S3, Calculate the thermal conduction resistance and thermal convection resistance: Based on the gear thermal network model in step S1, discretize the gear thermal network model and define temperature nodes. Calculate the thermal conduction resistance and thermal convection resistance of relevant parts of the gear according to the geometric parameters of the divided regions, including:

[0075] S31, based on the gear thermal network model in step S1, the three-dimensional gear meshing region is discretized into average values. N Each region is defined as described. NEach meshing point on the surface of a region and the midpoint of the tooth thickness along the tooth thickness direction of the meshing point are temperature nodes. The three-dimensional gear is divided into regions along the tooth thickness, tooth width, tooth height and spokes. The tooth surface area directly affects the thermal resistance: the larger the area, the smaller the convective thermal resistance. The conduction thermal resistance is related to both the area and the path length. Based on the geometric parameters of the divided thermal resistance boundary regions, it is helpful to calculate the heat transfer thermal resistance of the gear.

[0076] Specifically, in other embodiments, the step of discretizing the three-dimensional gear meshing region into average values ​​is... N The regions include:

[0077] S311, Discretization of the meshing region, uniformly dividing the gear meshing region along the tooth thickness, tooth width, and tooth height directions. N A hexahedral subregion or N Each of the given tetrahedral units depends on the mesh type; wherein, the volume of each sub-region is... satisfy For example, For helical gears, the meshing contact line is finely divided along the helical direction, with the node spacing along the contact line direction being... satisfy To capture local heat flux density gradients.

[0078] S312, Mesh division of spoke and tooth root regions: The spoke portion is meshed radially and circumferentially, with the radial node spacing dynamically adjusted according to the heat flux gradient. For example, the tooth root transition region can be fined to [a specific mesh size]. .

[0079] S313, Define meshing point temperature nodes: Temperature nodes are set on the meshing surface of each sub-region, with node positions covering the actual meshing points (i.e., tooth surface contact trajectory points). Temperature nodes are added along the tooth thickness direction at corresponding positions on the mid-section of the tooth thickness to reflect the temperature gradient between the tooth surface and the tooth center. Total number of temperature nodes. M With the number of discrete regions N Relevant, satisfy For example, This indicates that nodes are set on the surface and inside of each region.

[0080] S32, based on the geometric parameters of the defined thermal resistance boundary region, calculate the thermal conduction resistance along the tooth thickness direction on the working tooth surface. Thermal resistance of non-working tooth surface along tooth thickness direction Thermal resistance along the tooth height direction Thermal resistance along the tooth width direction Thermal conduction and thermal resistance in the direction of the spokes And calculate the thermal resistance of heat convection between the tooth tip and the lubricating oil. Thermal resistance of heat convection between gear end face and lubricating oil Thermal resistance of heat convection between meshing tooth surfaces and lubricating oil Thermal resistance of non-meshing tooth surfaces and lubricating oil It distinguishes the thermal resistance of the working tooth surface from that of the non-working tooth surface, reflects the actual heat flow asymmetry, and significantly improves the accuracy and adaptability of gear thermal resistance prediction.

[0081] S4, construct the thermal network topology and solve for the body temperature values ​​of each node of the driving wheel and each node of the driven wheel:

[0082] S41, associate the nodes set in step S3 with the divided regions, connect adjacent nodes through thermal resistance to form a heat transfer path, and construct a thermal network topology, wherein each divided region is connected to at least one node; the asymmetric helical gear is abstracted as a thermal network composed of multiple nodes and thermal resistance, each node represents a specific region of the gear (such as tooth surface, tooth root, tooth tip, etc.), and the thermal resistance represents the resistance to heat transfer between different regions and between the region and the outside world, so as to intuitively show the heat transfer path and distribution inside the gear;

[0083] S42, based on the ambient temperature, the frictional heat flow from step S2, and the thermal resistance parameters from step S3, and according to the law of conservation of energy, the body temperature values ​​of each node of the driving wheel and each node of the driven wheel are calculated using the thermal balance equations of the driving wheel temperature node and the driven wheel temperature node. The thermal balance equations describe the relationship between heat input, output, and storage at the nodes. By solving the thermal balance equations, the temperature changes at each node can be obtained, i.e., the temperature distribution of the gear at different times. This integrates the previous calculations of frictional heat flow and thermal resistance to solve for the gear's thermal balance state.

[0084] S5, Solve for the contact surface body temperature to predict the contact surface body temperature of the asymmetric helical gear: Based on the body temperature values ​​of each node of the driving gear and each node of the driven gear obtained in step S4, select the body temperature of the contact surface of two contacting gear teeth. and The average value is used to calculate the body temperature of the contact surface. The calculation formula is as follows:

[0085]

[0086] in, This represents the tangential velocity of the driving wheel at the node. This indicates the tangential velocity of the driven wheel at the node; Indicates the thermal contact coefficient of the driving wheel. This represents the thermal contact coefficient of the driven gear. After obtaining the thermal balance solution, the temperature value at the contact surface is extracted from the temperature data of all thermal nodes, i.e., the body temperature of the contact surface of the asymmetric helical gear. The body temperature of the contact surface is crucial for studying problems such as gear scuffing failure and is beneficial for gear design, optimization, and fault diagnosis.

[0087] Specifically, the thermal contact coefficient of the drive wheel The thermal contact coefficient of the driven wheel The calculation formula is as follows:

[0088]

[0089] .

[0090] Preferably, in this embodiment, the basic parameters in step S1 include:

[0091] The geometric parameters include: the number of teeth on the driving gear. Number of teeth on the driven gear Gear normal module helix angle Tooth width B, gear working tooth surface pressure angle Pressure angle of non-working tooth surface of gear Addendum ha and total height h, and the displacement coefficient of the driving gear. Driven gear displacement coefficient outer diameter of the drive shaft Outer diameter of driven wheel shaft Poisson's ratio of the driving gear material Poisson's ratio of the driven gear material , elastic modulus of the drive wheel elastic modulus of driven wheel Surface roughness of the drive wheel Surface roughness of driven wheel ;

[0092] The transmission parameters include: the rotational speed of the drive wheel. The speed of the driven wheel Gear input power The center distance 'a' between the driving wheel and the driven wheel;

[0093] The thermal properties include: the thermal conductivity coefficient of the driving gear material. Thermal conductivity coefficient of driven gear material Density of the material of the drive gear Density of driven gear material Specific heat capacity per unit mass of the drive wheel material Specific heat capacity per unit mass of driven wheel material Lubricating oil dynamic viscosity Lubricating oil thermal conductivity Lubricating oil density Specific heat capacity per unit mass of lubricating oil .

[0094] Preferably, the half-width of the helical gear line contact area in step S2 and average contact stress p Calculated using the following formula:

[0095] p

[0096]

[0097] in, B represents the normal load, and B represents the tooth width. Represents the equivalent elastic modulus. This represents the combined radius of curvature at the meshing point c. This represents the total length of the contact line at the engagement point c.

[0098] Specifically, the equivalent elastic modulus The combined radius of curvature at the meshing point c ， and the total length of the contact line at the engagement point c. It is calculated using the following formula:

[0099]

[0100]

[0101]

[0102] in, This represents the elastic modulus of the driving wheel. This represents the elastic modulus of the driven wheel. The Poisson's ratio represents the material of the driving gear. The Poisson's ratio represents the material of the driven gear. Indicates the overlap coefficient; Indicates the base circle helix angle; This represents the radius of curvature of the driving wheel at the meshing point C. This represents the radius of curvature of the driven wheel at the meshing point C.

[0103] Furthermore, the radius of curvature of the driving wheel at the meshing point C The radius of curvature of the driven wheel at the meshing point C The calculation formula is as follows:

[0104]

[0105]

[0106] in, This represents the base circle radius of the driving wheel. This represents the base circle radius of the driven gear. This represents the pressure angle of the driving wheel at any engagement point C. This represents the pressure angle of the driven wheel at any meshing point C.

[0107] Preferably, the relative sliding speed in step S2 The calculation formula is as follows:

[0108]

[0109] in, This represents the relative sliding velocity at any meshing point C. This represents the tangential velocity of the driving wheel at the meshing point c. This represents the tangential velocity of the driven wheel at the meshing point c.

[0110] Optionally, the tangential velocity of the driving wheel at the meshing point c The tangential velocity of the driven wheel at the meshing point c The calculation formula is as follows:

[0111]

[0112]

[0113] in, This is expressed as the rotational speed of the drive wheel. This represents the rotational speed of the driven wheel.

[0114] In a preferred embodiment of the present invention, the heat flux density distribution of the hybrid lubrication model in step S2 includes:

[0115] Under mixed lubrication conditions, the formulas for calculating the frictional heat flux density of the tooth surfaces of the driving and driven gears are as follows:

[0116]

[0117]

[0118] in, γ Indicates the heat conversion coefficient. Indicates the heat flux density distribution coefficient. Let be the tangential velocity at the meshing point c;

[0119] Specifically, based on the study of energy conversion efficiency of metal friction pairs, the value range of the thermal energy conversion coefficient γ is 0.9~0.97. Specifically, in this embodiment, the value of the thermal energy conversion coefficient γ is 0.95 to conservatively estimate energy loss.

[0120] The heat flux density distribution coefficient It is calculated using the following formula:

[0121]

[0122] in, This represents the thermal conductivity coefficient of the driving gear material. This represents the thermal conductivity coefficient of the driven gear material. This indicates the density of the material of the driving gear. This indicates the density of the driven gear material. This indicates the specific heat capacity per unit mass of the drive wheel material. This indicates the specific heat capacity per unit mass of the driven wheel material.

[0123] Furthermore, the coefficient of friction of the hybrid lubrication The calculation formula is as follows:

[0124]

[0125] in, This represents the coefficient of friction between the contact surfaces of the teeth under elastohydrodynamic lubrication. This represents the coefficient of friction of the contact tooth surface under boundary lubrication. This represents the load-carrying coefficient of the elastohydrodynamic oil film, indicating the ratio of elastohydrodynamic lubrication to boundary lubrication on the tooth surface. Specifically, the load-carrying coefficient of the elastohydrodynamic oil film... It can be set according to the actual situation, for example, 0.8.

[0126] Specifically, the coefficient of friction of the lower contact tooth surface under the elastohydrodynamic lubrication The coefficient of friction of the tooth surface in contact with the boundary lubrication line It can be obtained using the following formula:

[0127]

[0128]

[0129] in, Indicates the dynamic viscosity of the mixed lubricating medium. This represents the tooth surface roughness factor.

[0130] Specifically, the tooth surface roughness factor The calculation formula is as follows:

[0131]

[0132] in, Indicates the surface roughness of the driving wheel. This indicates the surface roughness of the driven wheel.

[0133] Preferably, the frictional heat flow of the driving gear tooth surface in step S2 is... Heat flow from friction between driven gear teeth Calculated using the following formula:

[0134]

[0135]

[0136] in, This represents the area of ​​the contact surface of the driving wheel at the meshing point c. This represents the area of ​​the contact surface of the driven wheel at the meshing point c.

[0137] In a preferred embodiment of the present invention, step S31 further includes: discretizing a single gear tooth along the tooth thickness and tooth height directions into... N Each three-dimensional element divides the tooth end face area into i blocks, whose areas are denoted as follows: .

[0138] Specifically, the area of ​​the asymmetric helical gear end face region :

[0139]

[0140] in, This represents the area of ​​the working side end face of an asymmetric helical gear. This represents the area of ​​the central end face of a symmetrical helical gear. This represents the area of ​​the non-working end face of a symmetrical helical gear.

[0141] like Figure 5 As shown, optionally, in this embodiment, the working side end face area of ​​the asymmetric helical gear of the driving wheel is calculated. , area of ​​the central end face of a symmetrical helical gear and the area of ​​the non-working side end face of the symmetrical helical gear The calculation formula is as follows:

[0142]

[0143]

[0144]

[0145] in, This represents the base circle radius of the working surface of an asymmetric helical gear. This represents the radius of the base circle of the non-working surface of an asymmetric helical gear. This indicates the pressure angle of the working end face of an asymmetric helical gear. This indicates the pressure angle of the non-working end face of an asymmetric helical gear. This indicates the thickness of the pitch circle teeth on the working end face of the drive wheel. This indicates the thickness of the pitch circle teeth on the non-working end face of the drive wheel, where, and The correspondence is as follows:

[0146] .

[0147] In other embodiments, the working side end face area of ​​the driven gear's asymmetric helical gear , area of ​​the central end face of a symmetrical helical gear and the area of ​​the non-working side end face of the symmetrical helical gear The calculation formula for the driving wheel has the same form as that for the driving wheel, with the specific parameters replaced by the equivalent parameters of the driven wheel.

[0148] Optionally, the heat transfer area of ​​the tooth tip of the asymmetric helical gear can be expressed as:

[0149]

[0150] in, This indicates the tooth thickness of the addendum circle on the working end face of an asymmetric helical gear. This indicates the tooth thickness of the addendum circle on the non-working end face of an asymmetric helical gear.

[0151] Specifically, taking the driving wheel as an example, the tooth thickness of any circular end face can be expressed as:

[0152] .

[0153] Optionally, the working surface of the asymmetric helical gear non-working surface heat transfer area The calculation formula is as follows:

[0154]

[0155]

[0156] in, This represents the involute length of the working surface of an asymmetric helical gear. The length of the involute curve on the non-working surface of an asymmetric helical gear is expressed by the following formula:

[0157]

[0158]

[0159] Preferably, in step S32, the thermal resistance of the working tooth surface along the tooth thickness direction is calculated using the following formula. The thermal resistance of the non-working tooth surface along the tooth thickness direction. The thermal resistance along the tooth height direction. The thermal resistance along the tooth width direction. Thermal resistance in the spoke direction The thermal resistance of heat convection between the tooth tip and the lubricating oil The thermal resistance of heat convection between the gear end face and the lubricating oil The thermal resistance of the meshing tooth surface and the lubricating oil during heat convection. Thermal resistance of non-meshing tooth surfaces and lubricating oil :

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169] in, This represents the heat transfer coefficient of the tooth tip and the non-working tooth surface of the gear. This represents the heat transfer coefficient of the gear end face via convection. This represents the thermal convection heat transfer coefficient of the working tooth surface of the gear. This represents the convective heat transfer area of ​​the tooth tip surface. This represents the convective heat transfer area of ​​the working tooth surface of the gear. This represents the convective heat transfer area of ​​the non-working tooth surface of the gear.

[0170] like Figure 3 and Figure 4 As shown, optionally, the heat conduction area along the tooth height direction... With the heat conduction area along the tooth thickness direction The specific calculation formula is as follows:

[0171]

[0172]

[0173] Furthermore, the thermal balance equation for the active wheel temperature node includes:

[0174]

[0175] in, This indicates the ambient temperature of the driving wheel, expressed in degrees Celsius or Kelvin. Indicates the active round node from Frictional heat flow rate input at each node; This represents the temperature at the i-th temperature node on the meshing tooth surface of the driving gear. This represents the temperature of the i-th temperature node inside the core of the driving gear tooth;

[0176] Preferably, the thermal balance equation for the driven wheel temperature node has the same form as the thermal balance equation for the driving wheel, with specific parameters replaced by equivalent parameters of the driven wheel. These equivalent parameters include the frictional heat flow, thermal resistance, and ambient temperature of the driven wheel. This significantly simplifies modeling complexity and improves computational efficiency for engineers performing thermal analysis of transmission systems.

[0177] Specifically, the thermal balance equation for the driven wheel temperature node includes:

[0178]

[0179] in, This indicates the ambient temperature of the driven wheel. Indicates the driven wheel node from Frictional heat flow rate input at each node; This represents the temperature at the i-th temperature node on the meshing tooth surface of the driven gear. This represents the temperature of the i-th temperature node inside the driven gear tooth core.

[0180] like Figure 6 As shown, the present invention also provides a thermal network-based asymmetric helical gear contact surface temperature prediction system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the thermal network-based asymmetric helical gear contact surface temperature prediction method as described in any of the above claims.

[0181] Figure 6This is a schematic diagram of the hardware structure for running a method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network, according to an embodiment of the present invention. Figure 6 As shown, this embodiment / computer 6 includes: a processor 60, a memory 61, and a computer program 62 stored in the memory 61 and executable on the processor 60, such as a program for running a method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network. When the processor 60 executes the computer program 62, it implements the steps described in the embodiments of running a method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network. Alternatively, when the processor 60 executes the computer program 62, it implements the functions of each module / unit in the aforementioned device embodiments.

[0182] For example, the computer program 62 may be divided into one or more modules / units, which are stored in the memory 61 and executed by the processor 60 to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program 62 in the computer 6.

[0183] The computer 6 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. The computer 6 may include, but is not limited to, a processor 60 and a memory 61. Those skilled in the art will understand that... Figure 6 This is merely an example of computer 6 and does not constitute a limitation on computer 6. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer 6 may also include input / output devices, network access devices, buses, etc.

[0184] The processor 60 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0185] The memory 61 can be an internal storage unit of the computer 6, such as a hard drive or memory. The memory 61 can also be an external storage device of the computer 6, such as a plug-in hard drive, smart media card (SMC), secure digital (SD) card, flash card, etc., equipped on the terminal device. Furthermore, the memory 61 can include both internal storage units and external storage devices of the computer 6. The memory 61 is used to store the computer program and other programs and data required by the terminal device. The memory 61 can also be used to temporarily store data that has been output or will be output.

[0186] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0187] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0188] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0189] In the embodiments provided by this invention, it should be understood that the disclosed apparatus / terminal devices and methods can be implemented in other ways. For example, the apparatus / terminal device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0190] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0191] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0192] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0193] The above are merely specific application examples of the present invention and do not constitute any limitation on the scope of protection of the present invention. In addition to the above embodiments, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the scope of protection claimed by the present invention.

Claims

1. A method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network, characterized in that, Including the following steps: S1. Obtain the basic parameters of the asymmetric helical gear and construct a gear thermal network model. The basic parameters include geometric parameters, transmission parameters, and thermal property parameters. S2, Calculate frictional heat flow: Based on the basic parameters provided in step S1, calculate the half-width of the helical gear's linear contact zone using Hertzian contact theory. and average contact stress p The relative sliding velocity is solved by combining the meshing geometry. V c Based on the mixed lubrication model, the heat flux density is distributed to obtain the frictional heat flow of the driving wheel tooth surface at the meshing point C between the driving wheel and the driven wheel. Heat flow from friction between driven gear teeth ; S3, Calculate the thermal conduction resistance and thermal convection resistance: Based on the gear thermal network model in step S1, discretize the gear thermal network model and define temperature nodes. Calculate the thermal conduction resistance and thermal convection resistance of relevant parts of the gear according to the geometric parameters of the divided regions, including: S31, based on the gear thermal network model in step S1, the three-dimensional gear meshing region is discretized into average values. N Each region is defined as described. N Each meshing point on the surface of a region and the midpoint of the tooth thickness along the tooth thickness direction of the meshing point are temperature nodes, and the three-dimensional gear is divided into regions along the tooth thickness, tooth width, tooth height directions and spokes. S32, based on the geometric parameters of the defined thermal resistance boundary region, calculate the thermal conduction resistance along the tooth thickness direction on the working tooth surface. Thermal resistance of non-working tooth surface along tooth thickness direction Thermal resistance along the tooth height direction Thermal resistance along the tooth width direction Thermal conduction and thermal resistance in the direction of the spokes And calculate the thermal resistance of heat convection between the tooth tip and the lubricating oil. Thermal resistance of heat convection between gear end face and lubricating oil Thermal resistance of heat convection between meshing tooth surfaces and lubricating oil Thermal resistance of non-meshing tooth surfaces and lubricating oil ; S4, construct the thermal network topology and solve for the body temperature values ​​of each node of the driving wheel and each node of the driven wheel: S41, associate the nodes set in step S3 with the divided regions, connect adjacent nodes through thermal resistance to form heat transfer paths, and construct a thermal network topology, wherein each divided region is connected to at least one node. S42, based on the ambient temperature, the frictional heat flow in step S2, and the thermal resistance parameter in step S3, and according to the law of conservation of energy, the body temperature values ​​of each node of the driving wheel and each node of the driven wheel are calculated through the thermal balance equations of the driving wheel temperature node and the driven wheel temperature node. S5, Solve for the contact surface body temperature: Based on the body temperature values ​​of each node of the driving wheel and each node of the driven wheel obtained in step S4, select the body temperature of the contact surface of two contact wheel teeth. and The average value is used to calculate the body temperature of the contact surface. The calculation formula is as follows: in, This represents the tangential velocity of the driving wheel at the node. This indicates the tangential velocity of the driven wheel at the node; Indicates the thermal contact coefficient of the driving wheel. This represents the thermal contact coefficient of the driven wheel.

2. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 1, characterized in that, The basic parameters in step S1 include: The geometric parameters include: number of gear teeth, gear normal module, helix angle, tooth width, pressure angle of gear working tooth surface, pressure angle of gear non-working tooth surface, tooth tip height and total tooth height, gear displacement coefficient, shaft outer diameter, Poisson's ratio of gear material, elastic modulus and surface roughness. The transmission parameters include: rotational speed, gear input power, and center distance; The thermophysical parameters include: the thermal conductivity coefficient of the gear material, the density of the gear material, the specific heat capacity of the gear material, the dynamic viscosity of the lubricating oil, the thermal conductivity coefficient of the lubricating oil, the density of the lubricating oil, and the specific heat capacity of the lubricating oil.

3. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 2, characterized in that, The half-width of the helical gear line contact area in step S2 and average contact stress p Calculated using the following formula: p in, Indicates normal load, B Indicates tooth width. Represents the equivalent elastic modulus. This represents the elastic modulus of the driven wheel. This represents the combined radius of curvature at the meshing point c. This represents the total length of the contact line at the engagement point c.

4. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 3, characterized in that, The relative sliding speed in step S2 The calculation formula is as follows: in, This represents the relative sliding velocity at any meshing point C. This represents the tangential velocity of the driving wheel at the meshing point c. This represents the tangential velocity of the driven wheel at the meshing point c.

5. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 4, characterized in that, The heat flux density distribution in the hybrid lubrication model in step S2 includes: Under mixed lubrication conditions, the frictional heat flux density of the tooth surface of the driving wheel is... Heat flux density due to friction between the tooth surfaces of the driven gear and the driven gear The calculation formula is as follows: in, γ Indicates the heat conversion coefficient. Indicates the heat flux density distribution coefficient. The coefficient of friction for mixed lubrication. and These are the rotational speeds of the driving wheel and the driven wheel, respectively. Let be the tangential velocity at the meshing point c; The heat flow rate of friction on the tooth surface of the driving gear in step S2 Heat flow from friction between driven gear teeth Calculated using the following formula: in, This represents the area of ​​the contact surface of the driving wheel at the meshing point c. This represents the area of ​​the contact surface of the driven wheel at the meshing point c.

6. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 5, characterized in that, Step S31 further includes: discretizing a single tooth along the tooth thickness and tooth height directions. N Each three-dimensional element divides the tooth end face area into i blocks, whose areas are denoted as follows: .

7. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 6, characterized in that, In step S32, the thermal resistance of the working tooth surface along the tooth thickness direction is calculated using the following formula. The thermal resistance of the non-working tooth surface along the tooth thickness direction. The thermal resistance along the tooth height direction. The thermal resistance along the tooth width direction. Thermal resistance in the spoke direction The thermal resistance of heat convection between the tooth tip and the lubricating oil The thermal resistance of heat convection between the gear end face and the lubricating oil The thermal resistance of the meshing tooth surface and the lubricating oil during heat convection. Thermal resistance of non-meshing tooth surfaces and lubricating oil : in, This represents the heat transfer coefficient of the tooth tip and the non-working tooth surface of the gear. This represents the heat transfer coefficient of the gear end face via convection. This represents the thermal convection heat transfer coefficient of the working tooth surface of the gear. This represents the convective heat transfer area of ​​the tooth tip surface. This represents the convective heat transfer area of ​​the working tooth surface of the gear. This represents the convective heat transfer area of ​​the non-working tooth surface of the gear.

8. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 7, characterized in that, The thermal balance equation for the temperature node of the driving wheel includes: in, Indicates ambient temperature. Indicates the active round node from Frictional heat flow rate input at each node; This represents the temperature at various temperature points on the meshing tooth surface. This indicates the temperature at various temperature nodes inside the tooth core.

9. The method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network according to claim 8, characterized in that, The thermal balance equation of the driven wheel temperature node has the same form as the thermal balance equation of the driving wheel, with the specific parameters replaced by the equivalent parameters of the driven wheel. The replaced equivalent parameters include the frictional heat flow, thermal resistance, and ambient temperature of the driven wheel.

10. A temperature prediction system for the contact surface of an asymmetric helical gear based on a thermal network, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for predicting the contact surface temperature of an asymmetric helical gear based on a thermal network as described in any one of claims 1 to 9.

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