A method for predicting the temperature field of the double-arc bevel gear nutating transmission body

Abstract

The present invention provides a method for predicting the temperature field of a double-arc bevel gear nutating transmission body, comprising the following steps: step s1: making a gear meshing model; step s2: finding the contact points on the tooth surface of the double-arc bevel gear according to the tooth surface contact analysis principle TCA; step s3: calculating the relative sliding speed v 12 , maximum contact stress P max , Tooth surface friction factors f Step s4: Calculate the interpolation function for q; Step s5: Discretize the convex and concave meshing surfaces into a single contact meshing region; Step s6: Calculate the command stream; Step s7: Calculate the convective heat transfer coefficient h for different gear surfaces; Step s8: Finally, calculate the temperature field of the double-arc bevel gear with nutating transmission. This technical solution innovatively incorporates the principles of gear TCA contact analysis and APDL programming into temperature field simulation analysis. This method offers the advantages of simplicity, high efficiency, and minimal memory usage.

Description

Technical Field

[0001] The invention relates to the technical field of gear application, in particular to a method for predicting the temperature field of a double-arc spiral bevel gear nutating transmission body. Background Art

[0002] High-speed, heavily loaded gears generate considerable temperatures and non-uniform temperature fields. The resulting thermal deformation can seriously affect the gear's load-bearing capacity and transmission performance, leading to a series of problems such as vibration, noise, and shortened life. Therefore, temperature field analysis of double-arc bevel gear nutating transmissions is one of the fundamental tasks to ensure their working performance and load-bearing capacity. It involves knowledge from multiple disciplines such as heat transfer, tribology, mechanical transmission theory, and finite element analysis, and is the basis for thermal deformation analysis, bond strength calculation, and lubrication failure analysis. However, the heat flux density distribution on the meshing surface of high-speed gears is very complex. Not only is the heat flux density span large, but due to the presence of multiple contact meshing zones, there are heat flux steps at the transition points of the multiple contact meshing zones, which brings great difficulties to the simulation of the gear temperature field. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method for predicting the temperature field of the double-arc bevel gear nutating transmission body, innovatively introducing the gear TCA contact analysis principle and APDL language programming into the temperature field simulation analysis. This method has the advantages of simplicity, high efficiency and small memory usage.

[0004] To achieve the above object, the present invention adopts the following technical solution: a method for predicting the temperature field of a double-arc bevel gear nutating transmission body, comprising the following steps:

[0005] Step s1: Based on the basic parameters of the gear and the transmission requirements, a three-dimensional model is constructed for the double-arc bevel gear to create a gear meshing model;

[0006] Step s2: According to the tooth contact analysis principle TCA, the meshing contact points of the double-arc bevel gears in the nutating transmission process have the same position vector and normal vector. The calculation formula is as follows:

[0007]

[0008] Among them, r m1 and r m2 is the position vector in the fixed coordinate system, n m1 and n m2 is the normal vector in the fixed coordinate system, α1 and α2 are the arc angles of the double-arc bevel gear, θ1 and θ2 are the tooth line angles of the double-arc bevel gear, and is the angle of rotation of the two gears; Discretize and calculate the remaining five parameters to determine the meshing point coordinates. Select 15 meshing points on the convex and concave tooth surfaces of the double-arc bevel gear from the large end to the small end of the gear.

[0009] Step s3: Calculate the relative sliding velocity v 12 , maximum contact stress P max , tooth surface friction factor f, and then solve the average heat flux density q according to Hertz theory. The calculation formula is as follows:

[0010]

[0011] Where v1 and v2 are the movement speeds of the outer bevel gear and the inner bevel gear respectively; w1 and w2 are the angular velocities of the outer bevel gear and the inner bevel gear respectively; r1 and r2 are the radial vectors in the coordinate system respectively; F n is the normal contact force; a, b are the major and minor axes of the contact ellipse; σ is the average contact stress; R a is the tooth surface roughness; η d is the dynamic viscosity of the lubricating oil; η s is the sum of sliding velocities; b b contact half-width; β is the friction heat flow distribution coefficient;

[0012] Step s4: Using the Matlab tool Curve Fitting Tool, find the interpolation function of q, which is the contact trace distance function, denoted as q(x), where x is the distance from any point on the contact trace to the gear end;

[0013] Step s5: Create a three-dimensional model in Ansys software and assign gear material properties and various physical parameters. Then, based on the discretization concept, discretize the convex tooth surface and the concave tooth surface of the meshing surface into a contact meshing area.

[0014] Step s6: In the Ansys classic interface, use the q(x) function calculated in step 4 to calculate the command stream. Return to Ansys Workbench, set the reference coordinates, and apply the calculated APDL command stream as a moving heat source to the discrete area, that is, the contact meshing area. The heat source is applied starting from the large end of the gear and ending at the small end of the gear.

[0015] Step s7: Calculate the convective heat transfer coefficient h of different gear surfaces, and number the meshing surfaces, non-meshing surfaces, and gear end faces in Ansys software. Use the APDL command stream to select the corresponding surfaces according to the numbers, and load the convective heat transfer coefficient h onto the selected surfaces. The calculation formula is as follows:

[0016]

[0017] Where N u Nuschel number; material thermal conductivity λ; ω is the angular velocity of the gear; v f is the kinematic viscosity of the lubricating oil; α is the semi-cone angle of the spiral bevel gear; c f Specific heat of lubricating oil; ρ f Lubricating oil density; z Number of teeth on external bevel gear;

[0018] Step s8: In the finite element software, the boundary conditions in s5, s6, and s7 are combined and the temperature field of the high-speed gear is finally calculated according to the boundary formula.

[0019] Compared with the existing technology, the present invention has the following beneficial effects: a method for predicting the temperature field of the double-arc bevel gear nutating transmission body, innovatively introducing the tooth surface contact analysis principle TCA and APDL language programming into the temperature field simulation analysis, the method has the advantages of simplicity, high efficiency and small memory usage. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flow chart illustrating the implementation of the temperature field in a preferred embodiment of the present invention;

[0021] Figure 2 Schematic diagram of a solid model of a double-arc spiral bevel gear according to a preferred embodiment of the present invention;

[0022] Figure 3 Schematic diagram of heat flux density on the meshing surface of a double-arc spiral bevel gear according to a preferred embodiment of the present invention;

[0023] Figure 4 A schematic diagram of a mesh three-dimensional model of a double-arc spiral bevel gear according to a preferred embodiment of the present invention;

[0024] Figure 5 Schematic diagram of the temperature field analysis results of the double-arc spiral bevel gear according to the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0027] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form, and it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0028] A method for predicting the temperature field of the double arc bevel gear nutating transmission body; Figures 1 to 5 , the technical solution adopted includes the following steps:

[0029] Step s1: Based on the basic parameters of the gear and the transmission requirements, a three-dimensional model is performed on the double-arc bevel gear to create a gear meshing model.

[0030] Step s2: According to the Tooth Contact Analysis (TCA) principle, the meshing contact points of the double-arc bevel gears have the same position vector and normal vector during the nutating transmission process. The calculation formula is as follows:

[0031]

[0032] Among them, r m1 and r m2 is the position vector in the fixed coordinate system, n m1 and n m2 is the normal vector in the fixed coordinate system, α1 and α2 are the arc angles of the double-arc bevel gear, θ1 and θ2 are the tooth line angles of the double-arc bevel gear, and is the angle that the two gears rotate. By discretizing, the remaining five parameters can be obtained, and then the coordinates of the meshing points can be determined. 15 meshing points on the convex tooth surface and concave tooth surface of the double-arc bevel gear are selected from the large end to the small end of the gear.

[0033] Step s3: Calculate the relative sliding velocity v 12 , maximum contact stress P max , tooth surface friction factor f, and then solve the average heat flux density q according to Hertz theory. The calculation formula is as follows:

[0034]

[0035] Where v1 and v2 are the movement speeds of the outer bevel gear and the inner bevel gear respectively; w1 and w2 are the angular velocities of the outer bevel gear and the inner bevel gear respectively; r1 and r2 are the radial vectors in the coordinate system respectively; F nis the normal contact force; a, b are the major and minor axes of the contact ellipse; σ is the average contact stress; R a is the tooth surface roughness; η d is the dynamic viscosity of the lubricating oil; η s is the sum of sliding velocities; b b contact half-width; β is the friction heat flux distribution coefficient.

[0036] Step s4: Use the Matlab tool Curve Fitting Tool to find the interpolation function of q, where q is the contact trace distance function, denoted as q(x), where x is the distance from any point on the contact trace to the gear end.

[0037] Step s5: Create a three-dimensional model in Ansys software and assign gear material properties and various physical parameters. Then, based on the discretization concept, discretize the convex tooth surface and the concave tooth surface of the meshing surface into a contact meshing area.

[0038] Step s6: In the Ansys Classic interface, use the q(x) function calculated in step 4 to calculate the command stream. Return to Ansys Workbench, set the reference coordinates, and apply the calculated APDL command stream as a moving heat source to the discrete area, namely the contact meshing area. The heat source is applied starting from the large end of the gear and ending at the small end.

[0039] Step s7: Calculate the convective heat transfer coefficient h of different gear surfaces, and number the meshing surfaces, non-meshing surfaces, and gear end faces in Ansys software. Use the APDL command stream to select the corresponding surfaces according to the numbers, and load the convective heat transfer coefficient h onto the selected surfaces. The calculation formula is as follows:

[0040]

[0041] Where N u Nuschel number; material thermal conductivity λ; ω is the angular velocity of the gear; v f is the kinematic viscosity of the lubricating oil; α is the semi-cone angle of the spiral bevel gear; c f Specific heat of lubricating oil; ρ f Lubricating oil density; z Number of teeth on external bevel gear.

[0042] Step s8: In the finite element software, the boundary conditions in s5, s6, and s7 are combined and the temperature field of the high-speed gear is finally calculated according to the boundary formula.

Claims

1. A method for predicting the temperature field of a double-arc bevel gear nutating transmission body, characterized in that: The steps include: Step s1: Based on the basic parameters of the gear and the transmission requirements, a three-dimensional model is constructed for the double-arc bevel gear to create a gear meshing model; Step s2: According to the tooth contact analysis principle TCA, the meshing contact points of the double-arc bevel gears in the nutating transmission process have the same position vector and normal vector. The calculation formula is as follows: Among them, r m1 and r m2 is the position vector in the fixed coordinate system, n m1 and n m2 is the normal vector in the fixed coordinate system, α1 and α2 are the arc angles of the double-arc bevel gear, θ1 and θ2 are the tooth line angles of the double-arc bevel gear, and is the angle of rotation of the two gears; Discretize and calculate the remaining five parameters to determine the meshing point coordinates. Select 15 meshing points on the convex and concave tooth surfaces of the double-arc bevel gear from the large end to the small end of the gear. Step s3: Calculate the relative sliding velocity v 12 , maximum contact stress P max , tooth surface friction factor f, and then solve the average heat flux density q according to Hertz theory. The calculation formula is as follows: Where v1 and v2 are the movement speeds of the outer bevel gear and the inner bevel gear respectively; w1 and w2 are the angular velocities of the outer bevel gear and the inner bevel gear respectively; r1 and r2 are the radial vectors in the coordinate system respectively; F n is the normal contact force; a, b are the major and minor axes of the contact ellipse; σ is the average contact stress; R a is the tooth surface roughness; η d is the dynamic viscosity of the lubricating oil; η s is the sum of sliding velocities; b b contact half-width; β is the friction heat flow distribution coefficient; Step s4: Using the Matlab tool Curve Fitting Tool, find the interpolation function of q, which is the contact trace distance function, denoted as q(x), where x is the distance from any point on the contact trace to the gear end; Step s5: Create a three-dimensional model in Ansys software and assign gear material properties and various physical parameters. Then, based on the discretization concept, discretize the convex tooth surface and the concave tooth surface of the meshing surface into a contact meshing area. Step s6: In the Ansys classic interface, use the q(x) function calculated in step 4 to calculate the command stream. Return to Ansys Workbench, set the reference coordinates, and apply the calculated APDL command stream as a moving heat source to the discrete area, that is, the contact meshing area. The heat source is applied starting from the large end of the gear and ending at the small end of the gear. Step s7: Calculate the convective heat transfer coefficient h of different gear surfaces, and number the meshing surfaces, non-meshing surfaces, and gear end faces in Ansys software. Use the APDL command stream to select the corresponding surfaces according to the numbers, and load the convective heat transfer coefficient h onto the selected surfaces. The calculation formula is as follows: Where N u Nuschel number; material thermal conductivity λ; ω is the angular velocity of the gear; v f is the kinematic viscosity of the lubricating oil; α is the semi-cone angle of the spiral bevel gear; c f Specific heat of lubricating oil; ρ f Lubricating oil density; z Number of teeth on external bevel gear; Step s8: In the finite element software, the boundary conditions in s5, s6, and s7 are combined and the temperature field of the double-arc bevel gear based on the nutating transmission is finally calculated according to the boundary formula.

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