Gear transient thermal grid temperature detection method and system considering single-tooth and double-tooth alternate meshing

Abstract

The invention specifically discloses a gear transient thermal grid temperature detection method and system considering single-tooth and double-tooth alternate meshing, and the method comprises the following steps: collecting the basic parameters of the thermal resistance of a gear, the meshing time ratio of single teeth and double teeth in each rotation of the gear teeth, the contact half width during meshing of the gear teeth, the tooth profile involute arc length of the gear teeth and the conduction thermal resistance of each temperature gradient layer in the radial direction and the circumferential direction are calculated, and the conduction thermal resistance, the tooth crest tooth thickness and the tooth crest surface heat exchange area of a gear pair during meshing alternation of the single teeth and the double teeth of the gear teeth are considered; the gear teeth have a convective heat exchange area in a non-contact area; calculating a convective heat transfer coefficient and convective heat transfer heat resistance of each non-contact surface and heat flux generated by friction at a gear tooth meshing position; and listing an instantaneous heat balance equation, and calculating to obtain the real-time temperature of each node of the gear in the movement process of the gear pair. By means of the technical scheme, changes of conduction thermal resistance and convection thermal resistance in the gear tooth meshing process and influences on gear tooth heat transfer are studied, and the gear temperature calculation accuracy is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear temperature detection, and relates to a gear transient thermal grid temperature detection method and system considering the alternating meshing of single and double teeth. Background Art

[0002] As the demand for temperature calculation accuracy increases, the temperature analysis method based on the overall heat source method combined with the steady-state thermal grid method is insufficient to meet the simulation accuracy requirements. Researchers focus on the heat exchange at the gear meshing point and the impact of thermal expansion on gear performance. During the gear meshing process, the temperature of the gear pair changes periodically in real time as the single and double teeth alternately mesh. Therefore, it is necessary to establish a transient thermal grid model that considers the alternating meshing of single and double teeth to achieve more accurate prediction of the gear pair temperature distribution.

[0003] During gear meshing, the cyclical variation in the non-contact area of ​​the tooth profile causes a change in the convective thermal resistance, affecting heat convection between the teeth. Simultaneously, the alternation between single and double meshing alters the conductive thermal resistance, affecting heat conduction between the teeth. Therefore, it is necessary to develop a calculation method for the convective thermal resistance that accounts for the cyclical variation in the non-contact area of ​​the tooth profile, as well as a calculation method for the conductive thermal resistance that accounts for the alternating single and double meshing.

[0004] Previous research has focused on using steady-state thermal mesh methods to calculate the contact temperature caused by frictional heat flow in gear transmissions, as well as the contact temperature of gear teeth to prevent scuffing and failure. However, this approach ignores the impact of cyclical changes in thermal resistance on gear heating during the meshing process. This approach does not meet the requirements of gear transmissions with high precision. Therefore, further work is needed to develop thermal mesh models that consider the meshing process. Summary of the Invention

[0005] The purpose of the present invention is to provide a gear transient thermal grid temperature detection method and system considering the alternating meshing of single and double teeth, which ensures the accuracy of gear temperature calculation while being closer to reality.

[0006] In order to achieve the above-mentioned object, the basic scheme of the present invention is: a method for detecting the transient thermal grid temperature of a gear considering the alternating meshing of single and double teeth, comprising the following steps:

[0007] S1, collecting basic parameters of the gear thermal resistance to be calculated;

[0008] S2, according to the definition of overlap, calculate the proportion of the meshing time of single teeth and double teeth in each rotation of the gear teeth;

[0009] Based on Hertz contact theory, calculate the contact half-width when the gear teeth are meshing;

[0010] Calculate the involute arc length of the gear tooth profile based on the involute parametric equation and calculus theory;

[0011] S3, based on the proportion of the meshing time of single teeth and double teeth and the arc length of the tooth profile involute, the areas corresponding to the meshing of single teeth and double teeth in the tooth profile arc length are divided, and the gear teeth are divided into multiple temperature gradient layers along the radial direction;

[0012] According to the thin-walled ring theory, the conduction thermal resistance of each temperature gradient layer along the radial and circumferential directions is calculated;

[0013] S4, calculate the conduction thermal resistance of the gear pair when considering the alternating meshing of single and double teeth;

[0014] S5, using the basic parameters in step S1 to calculate the tooth top thickness and the tooth top surface heat exchange area;

[0015] Calculate the convective heat transfer area of ​​the gear teeth in the non-contact region using the contact half-width and the involute arc length of the gear tooth profile obtained in step S2;

[0016] S6, calculate the Reynolds number based on the basic parameters of S1 and divide the lubricating oil into laminar flow and turbulent flow, and calculate the convective heat transfer coefficient and convective heat transfer thermal resistance of each non-contact surface;

[0017] S7, calculating the heat flux generated by friction at the gear meshing position based on the basic parameters in step S1 and the contact half-width in step S2;

[0018] S8, using the conduction heat resistance of step S4 and the convection heat transfer heat resistance of step S6, the instantaneous heat balance equation at each grid node is listed to calculate the real-time temperature of each gear node during the gear pair movement process.

[0019] The working principle and beneficial effects of this basic solution are as follows: This technical solution considers the changes in the non-contact area of ​​the tooth profile to calculate the convective thermal resistance. It also considers the alternation of single and double tooth meshing to calculate the conductive thermal resistance. Furthermore, it considers the changes in the gear meshing state to establish a transient thermal grid model. This allows the study of the changes in conductive and convective thermal resistance during gear meshing and their impact on gear heat transfer, ensuring the accuracy of gear temperature calculations while being closer to reality.

[0020] Further, in step S2, according to the definition of overlap, the proportion of the gear single tooth meshing time η is calculated. single and the proportion of double-tooth meshing time η double ,for:

[0021] η single =mod(ε)

[0022] η double =1-mod(ε)

[0023] Among them, ε represents the degree of coincidence, 1<ε<2, and mod represents the remainder;

[0024] Based on Hertz contact theory, calculate the contact half-width a when the gear teeth are meshing H ,for:

[0025]

[0026] Among them, F represents the normal meshing force, B represents the tooth width, μ p 、μ g are the Poisson's ratios of the driving wheel and the driven wheel, E p 、E g are the elastic moduli of the driving wheel and the driven wheel respectively, R1 and R2 are the equivalent curvature radii of the two tooth surfaces at the contact point respectively;

[0027] Based on the involute parametric equation and calculus theory, the involute arc length L of the gear tooth profile is calculated as:

[0028]

[0029] The rectangular coordinate equation of the involute is expressed as x(θ)=r b (cosθ+θs inθ), y(θ)=r b (si nθ-θcosθ), θ is the involute expansion angle, r b is the base circle radius.

[0030] According to the definition of overlap, the proportion of single-tooth meshing time and double-tooth meshing time of gear teeth are calculated with simple operation.

[0031] Furthermore, in step S3, the gear teeth are divided into multiple temperature gradient layers along the radial direction, and the specific method for calculating the conduction thermal resistance of each temperature gradient layer along the radial direction and the circumferential direction is:

[0032] S301, according to the proportion of single tooth meshing time η single and the proportion of double-tooth meshing time η double , and the involute arc length L of the tooth profile, based on the definition of overlap, calculate the arc length L of the area where single tooth meshing and double tooth meshing are located single and L double ,for:

[0033]

[0034] Among them, ε represents the degree of coincidence, 1<ε<2, and mod represents the remainder;

[0035] S302, according to the arc length of the area where the single tooth meshing and double tooth meshing are located calculated in step S301, set the tooth top to the initial position, then the single tooth meshing area area s Double tooth meshing area d Divided into:

[0036]

[0037] S303, based on the thin-walled ring theory, calculate the radial conduction thermal resistance R between each temperature gradient layer of the gear teeth ri and circumferential thermal resistance R ci ,for:

[0038] Among them, δ ri is the thickness of the i-th temperature gradient layer, S ri is the average surface area of ​​the i-th temperature gradient layer, S ri =s i ·B,s i is the average tooth thickness, B is the tooth width; S c is the gear tooth contact area, S c =2a H B; λ is the thermal conductivity that changes with temperature.

[0039] The tooth profile arc length is divided into areas corresponding to single tooth and double tooth meshing, and the gear teeth are divided into multiple temperature gradient layers along the radial direction according to the areas, which facilitates data analysis and acquisition of corresponding parameters.

[0040] Further, step S4 is based on the radial conduction thermal resistance R between each temperature gradient layer of the gear teeth. ri and circumferential thermal resistance R ci , calculate the conduction thermal resistance R of the gear pair when considering the alternating meshing of single and double teeth si The collection is:

[0041]

[0042] Among them, n start Indicates the position where the second pair of gear teeth engages with the corresponding gradient layer, n end Indicates the position where the first pair of gear teeth engage the corresponding gradient layer.

[0043] Considering that single and double tooth meshing will change the connection mode of thermal resistance in the thermal grid, the conduction thermal resistance R on a single tooth is calculated. si gather.

[0044] Furthermore, step S5 calculates the tooth top thickness s using the basic parameters in step S1. a , tooth top surface heat exchange area S a ,for:

[0045]

[0046] S a =s a B

[0047] Among them, da is the tooth top diameter, s is the pitch circle tooth thickness, d is the pitch circle diameter, α is the pitch circle pressure angle, α a is the tooth tip circle pressure angle, invα is the involute function, invα=tanα-α; B represents the tooth width;

[0048] The convective heat transfer area S of the gear teeth in the non-contact area is calculated by using the contact half-width and the involute arc length of the gear tooth profile obtained in step S2. nc ,for:

[0049] S nc =(L-2a H )B

[0050] Where L is the involute arc length of the gear tooth profile, a H is the contact half-width when the gear teeth are meshing.

[0051] Based on the corresponding parameters, the required heat exchange area is obtained, which is beneficial for subsequent use.

[0052] Furthermore, in step S6, the Reynolds number is calculated based on the basic parameters of S1 and the lubricating oil is divided into laminar flow and turbulent flow. The steps of calculating the convective heat transfer coefficient and convective heat transfer thermal resistance of each non-contact surface are as follows:

[0053] S601, calculate the Reynolds number Re, which is:

[0054]

[0055] Among them, ρ eff is the density of the oil-gas mixture, ρ eff =Xρ oil +(1-X)ρ air , X is the oil-gas ratio coefficient, ρ oil is the density of oil, ρ air is the density of the gas; η eff is the dynamic viscosity of the oil-gas mixture, η eff =η oil / (η oil / η air (1-X)+X), η oil is the dynamic viscosity of the oil, η air is the dynamic viscosity of the gas; ω is the angular velocity of the gear, r b is the base circle radius;

[0056] S602, based on the fluid cross-plane theory, taking into account the key factors of the nozzle diameter and angle, calculate the average convective heat transfer coefficient h of the gear surface s ,for:

[0057]

[0058] Where ν is the pitch circle speed, S oil is the injection port area, ψ is the injection port angle; S nc is the convective heat transfer area of ​​the gear teeth in the non-contact area;

[0059] S603, according to the Reynolds number calculated in step S601, the lubricating oil is divided into laminar flow, transition flow and turbulent flow, and the convective heat transfer coefficient h of the tooth top surface is calculated. a ,for:

[0060]

[0061] Where Pr is the Prandtl number, Pr = η eff c p / k D , c p is the specific heat capacity of lubricating oil, k D is the thermal conductivity of lubricating oil;

[0062] S604: Calculate the convection thermal resistance R of each non-contact surface based on the convection heat transfer coefficient and heat transfer theory. s 、R a ,for:

[0063]

[0064] Among them, S a is the heat transfer area of ​​the tooth top surface.

[0065] Based on relevant theories, the convection heat transfer coefficient and convection heat transfer thermal resistance are obtained with simple operation.

[0066] Furthermore, step S7 calculates the heat flux generated by friction at the gear meshing position based on the basic parameters in step S1 and the contact half-width in step S2, specifically:

[0067] S701, calculate the contact pressure p of the gear teeth at the meshing point, which is:

[0068]

[0069] Among them, E eq is the equivalent elastic modulus of the contact point, F NC is the normal force, r eq is the curvature radius of the contact point; B is the tooth width;

[0070] S702, calculate the heat flux Q generated by the meshing of the driving and driven gears p , Q g ,for:

[0071]

[0072] Among them, a His the contact half-width when the gear teeth are meshing, v c1 、v c2 are the linear velocities of the master and driven gears at the contact point C, n1 and n2 are the rotational speeds of the master and driven gears, β is the heat flux distribution coefficient, γ is the heat conversion coefficient, μ c is the friction coefficient, v c is the relative sliding velocity, v c =|v c1 -v c2 |.

[0073] According to the relevant parameters obtained above, the heat flux generated by the meshing of the driving and driven gear teeth is obtained.

[0074] Furthermore, in step S8, the instantaneous heat balance equation at each grid node is listed, and the specific steps for calculating the real-time temperature of each gear node during the gear pair movement are as follows:

[0075] S801, based on Kirchhoff's law, the net heat flow of a single node is equal to the increment of the corresponding internal energy of the volume. The expression between the net heat flow and the temperature increment of the jth node is q j for:

[0076]

[0077] Among them, c j is the specific heat capacity of the jth node, ρ j is the density of the jth node, V j is the volume of the jth node, T j is the temperature of the jth node, t is the time;

[0078] S802: Based on the basic parameters, conduction thermal resistance, convection thermal resistance, and the heat flux generated by the meshing of the master and slave gears, and assuming that the heat flux flowing into and out of each node is equal, the instantaneous thermal balance at the jth grid node is:

[0079]

[0080] Among them, Q j represents the heat flux generated at the jth node, and is 0 if no heat is generated; T j represents the temperature at the jth node; R k-j It represents the total thermal resistance between nodes k and j; k represents the node number;

[0081] S803, considering the presence of heat sources on both sides of the gear teeth when double teeth are meshed, the temperature of each node of the gear teeth is calculated jointly through heat transfer on both sides. The instantaneous heat balance equation is rewritten as:

[0082]

[0083] Among them, c d is the specific heat capacity of the dth node, ρ d is the density of the dth node, V d is the volume of the dth node, T d is the temperature of the dth node; node d represents the node in the gear teeth when the double teeth are meshing, Q e and Q f Represent the heat flux generated at contact point e and contact point f respectively; R di Indicates that there are i radial thermal resistances from contact point e to node d, R d(n-i) It indicates that there are (ni) radial thermal resistances from contact point f to node d, and n indicates the total number of radial thermal resistances from contact point e to contact point f;

[0084] In S804, the transient thermal equations of each node established in S803 are combined, and the transient thermal grid equations constructed by using the Runge-Kutta method are solved in MTALAB to calculate the real-time temperature of each gear node during the gear meshing process.

[0085] Based on the instantaneous heat balance equation at the mesh nodes, the real-time temperature of each gear node during the gear meshing process is obtained.

[0086] The present invention also provides a gear transient thermal grid temperature detection system considering the alternating meshing of single and double teeth, comprising a data acquisition module and a processing module, wherein the data acquisition module is used to collect basic parameters of the gear thermal resistance to be calculated;

[0087] The input end of the processing module is connected to the output end of the data acquisition module, and the processing module executes the method of the present invention to obtain the real-time temperature of each node of the gear during the movement of the gear pair.

[0088] This system addresses the shortcomings of existing technologies and obtains the real-time temperature of each gear node during the movement of the gear pair, ensuring the accuracy of gear temperature calculation while being closer to reality. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 1 is a flow chart of a method for detecting transient thermal grid temperature of a gear in which single and double teeth are alternately meshed;

[0090] Figure 2 Schematic diagram of the structure of the tooth temperature gradient layer division of the gear transient thermal grid temperature detection method considering the alternating meshing of single and double teeth of the present invention;

[0091] Figure 3 It is a structural schematic diagram of a double-tooth meshing thermal grid of a gear transient thermal grid temperature detection method considering alternating meshing of single and double teeth according to the present invention. DETAILED DESCRIPTION

[0092] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0093] In the description of the present invention, it should be understood that the terms "longitudinal", "transverse", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention.

[0094] In the description of the present invention, unless otherwise specified and limited, it should be noted that the terms "installed", "connected" and "connected" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the internal communication between two components. It can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to the specific circumstances.

[0095] The present invention discloses a gear transient thermal grid temperature detection method considering the alternating meshing of single and double teeth, taking into account the change of the non-contact area of ​​the tooth profile, the alternating meshing of single and double teeth, and the change of the gear meshing state, ensuring the accuracy of the gear temperature calculation while being closer to reality. Figure 1 As shown in FIG, the transient thermal grid temperature detection method for gears considering alternating meshing of single and double teeth includes the following steps:

[0096] S1, collect the basic parameters of the gear thermal resistance to be calculated, including gear speed, contact ratio, tooth width, tooth top circle thickness, thermal conductivity, lubricating oil density, lubricating oil dynamic viscosity, etc.

[0097] S2, according to the definition of overlap, calculate the proportion of the meshing time of single teeth and double teeth in each rotation of the gear teeth;

[0098] Based on Hertz contact theory, calculate the contact half-width when the gear teeth are meshing;

[0099] Calculate the involute arc length of the gear tooth profile based on the involute parametric equation and calculus theory;

[0100] S3, based on the proportion of the meshing time of single teeth and double teeth and the arc length of the tooth profile involute, the areas corresponding to the meshing of single teeth and double teeth in the tooth profile arc length are divided, and the gear teeth are divided into multiple temperature gradient layers along the radial direction;

[0101] According to the thin-walled ring theory, the conduction thermal resistance of each temperature gradient layer along the radial and circumferential directions is calculated;

[0102] S4, calculate the conduction thermal resistance of the gear pair when considering the alternating meshing of single and double teeth;

[0103] S5, using the basic parameters in step S1 to calculate the tooth top thickness and the tooth top surface heat exchange area;

[0104] Calculate the convective heat transfer area of ​​the gear teeth in the non-contact region using the contact half-width and the involute arc length of the gear tooth profile obtained in step S2;

[0105] S6, calculate the Reynolds number based on the basic parameters of S1 and divide the lubricating oil into laminar flow and turbulent flow, and calculate the convective heat transfer coefficient and convective heat transfer thermal resistance of each non-contact surface;

[0106] S7, calculating the heat flux generated by friction at the gear meshing position based on the basic parameters in step S1 and the contact half-width in step S2;

[0107] S8, using the conduction heat resistance of step S4 and the convection heat transfer heat resistance of step S6, the instantaneous heat balance equation at each grid node is listed to calculate the real-time temperature of each gear node during the gear pair movement process.

[0108] In a preferred embodiment of the present invention, in step S2, according to the definition of overlap, the proportion of the gear single tooth engagement time η is calculated. single and the proportion of double-tooth meshing time η double ,for:

[0109] η single =mod(ε)

[0110] η double =1-mod(ε)

[0111] Among them, ε represents the degree of coincidence, 1<ε<2, and mod represents the remainder;

[0112] Based on Hertz contact theory, calculate the contact half-width a when the gear teeth are meshing H ,for:

[0113]

[0114] Among them, F represents the normal meshing force, B represents the tooth width, μ p 、μ g are the Poisson's ratios of the driving wheel and the driven wheel, E p 、E g are the elastic moduli of the driving wheel and the driven wheel respectively, R1 and R2 are the equivalent curvature radii of the two tooth surfaces at the contact point respectively;

[0115] Based on the involute parametric equation and calculus theory, the involute arc length L of the gear tooth profile is calculated as:

[0116]

[0117] The rectangular coordinate equation of the involute is expressed as x(θ)=r b (cosθ+θs inθ), y(θ)=r b (si nθ-θcosθ), θ is the involute expansion angle, r b is the base circle radius.

[0118] In a preferred embodiment of the present invention, Figure 2 As shown, in step S3, the gear teeth are divided into multiple temperature gradient layers along the radial direction. The specific method for calculating the conduction thermal resistance of each temperature gradient layer along the radial direction and the circumferential direction is:

[0119] S301, according to the proportion of single tooth meshing time η single and the proportion of double-tooth meshing time η double , and the involute arc length L of the tooth profile, based on the definition of overlap, calculate the arc length L of the area where single tooth meshing and double tooth meshing are located single and L double ,for:

[0120]

[0121] Among them, ε represents the degree of coincidence, 1<ε<2, and mod represents the remainder;

[0122] S302, according to the arc length of the area where the single tooth meshing and double tooth meshing are located calculated in step S301, set the tooth top to the initial position, then the single tooth meshing area area s Double tooth meshing area d Divided into:

[0123]

[0124] S303, based on the thin-walled ring theory, calculate the radial conduction thermal resistance R between each temperature gradient layer of the gear teeth ri and circumferential thermal resistance R ci ,for:

[0125]

[0126] Among them, δ ri is the thickness of the i-th temperature gradient layer, S ri is the average surface area of ​​the i-th temperature gradient layer, S ri =s i ·B,s iis the average tooth thickness, B is the tooth width; S c is the gear tooth contact area, S c =2a H B; λ is the thermal conductivity that changes with temperature.

[0127] In a preferred embodiment of the present invention, step S4 is based on the radial conduction thermal resistance R between each temperature gradient layer of the gear teeth. ri and circumferential thermal resistance R ci , calculate the conduction thermal resistance R of the gear pair when considering the alternating meshing of single and double teeth si The collection is:

[0128]

[0129] Among them, n start Indicates the position where the second pair of gear teeth engages with the corresponding gradient layer, n end Indicates the position where the first pair of gear teeth engage the corresponding gradient layer.

[0130] In a preferred embodiment of the present invention, step S5 uses the basic parameters in step S1 to calculate the tooth top thickness s a , tooth top surface heat exchange area S a ,for:

[0131]

[0132] S a =s a B

[0133] Among them, d a is the tooth top diameter, s is the pitch circle tooth thickness, d is the pitch circle diameter, α is the pitch circle pressure angle, α a is the tooth tip circle pressure angle, invα is the involute function, invα=tanα-α; B represents the tooth width;

[0134] The convective heat transfer area S of the gear teeth in the non-contact area is calculated by using the contact half-width and the involute arc length of the gear tooth profile obtained in step S2. nc ,for:

[0135] S nc =(L-2a H )B

[0136] Where L is the involute arc length of the gear tooth profile, a H is the contact half-width when the gear teeth are meshing.

[0137] In a preferred embodiment of the present invention, in step S6, the Reynolds number is calculated based on the basic parameters of S1 and the lubricating oil is divided into laminar flow and turbulent flow. The convective heat transfer coefficient and convective heat transfer thermal resistance of each non-contact surface are calculated as follows:

[0138] S601, calculate the Reynolds number Re, which is:

[0139]

[0140] Among them, ρ eff is the density of the oil-gas mixture, ρ eff =Xρ oil +(1-X)ρ air , X is the oil-gas ratio coefficient, ρ oil is the density of oil, ρ air is the density of the gas; η eff is the dynamic viscosity of the oil-gas mixture, η eff =η oil / (η oil / η air (1-X)+X), η oil is the dynamic viscosity of the oil, η air is the dynamic viscosity of the gas; ω is the angular velocity of the gear, r b is the base circle radius;

[0141] S602, based on the fluid cross-plane theory, taking into account the key factors of the nozzle diameter and angle, calculate the average convective heat transfer coefficient h of the gear surface s ,for:

[0142]

[0143] Where ν is the pitch circle speed, S oil is the injection port area, ψ is the injection port angle; S nc is the convective heat transfer area of ​​the gear teeth in the non-contact area;

[0144] S603, according to the Reynolds number calculated in step S601, the lubricating oil is divided into laminar flow, transition flow and turbulent flow, and the convective heat transfer coefficient h of the tooth top surface is calculated. a ,for:

[0145]

[0146] Where Pr is the Prandtl number, Pr = η eff c p / k D , c p is the specific heat capacity of lubricating oil, k D is the thermal conductivity of lubricating oil;

[0147] S604: Calculate the convection thermal resistance R of each non-contact surface based on the convection heat transfer coefficient and heat transfer theory. s 、R a ,for:

[0148]

[0149] Among them, S a is the heat transfer area of ​​the tooth top surface.

[0150] In a preferred embodiment of the present invention, step S7 calculates the heat flux generated by friction at the meshing of the gear teeth based on the basic parameters in step S1 and the contact half-width in step S2, specifically:

[0151] S701, calculate the contact pressure p of the gear teeth at the meshing point, which is:

[0152]

[0153] Among them, E eq is the equivalent elastic modulus of the contact point, F NC is the normal force, r eq is the curvature radius of the contact point; B is the tooth width;

[0154] S702, calculate the heat flux Q generated by the meshing of the driving and driven gears p , Q g ,for:

[0155]

[0156] Among them, a H is the contact half-width when the gear teeth are meshing, v c1 、v c2 are the linear velocities of the master and driven gears at the contact point C, n1 and n2 are the rotational speeds of the master and driven gears, β is the heat flux distribution coefficient, γ is the heat conversion coefficient, μ c is the friction coefficient, v c is the relative sliding velocity, v c =|v c1 -v c2 |.

[0157] In a preferred embodiment of the present invention, Figure 3 As shown, in step S8, the instantaneous heat balance equation at each grid node is listed, and the specific steps for calculating the real-time temperature of each gear node during the gear pair movement are as follows:

[0158] S801, based on Kirchhoff's law, the net heat flow of a single node is equal to the increment of the corresponding internal energy of the volume. The expression between the net heat flow and the temperature increment of the jth node is q j for:

[0159]

[0160] Among them, c j is the specific heat capacity of the jth node, ρ j is the density of the jth node, Vj is the volume of the jth node, T j is the temperature of the jth node, t is the time;

[0161] S802: Based on the basic parameters, conduction thermal resistance, convection thermal resistance, and the heat flux generated by the meshing of the master and slave gears, and assuming that the heat flux flowing into and out of each node is equal, the instantaneous thermal balance at the jth grid node is:

[0162]

[0163] Among them, Q j represents the heat flux generated at the jth node, and is 0 if no heat is generated; T j represents the temperature at the jth node; R k-j It represents the total thermal resistance between nodes k and j; k represents the node number;

[0164] S803, considering the presence of heat sources on both sides of the gear teeth when double teeth are meshed, the temperature of each node of the gear teeth is calculated jointly through heat transfer on both sides. The instantaneous heat balance equation is rewritten as:

[0165]

[0166] Among them, c d is the specific heat capacity of the dth node, ρ d is the density of the dth node, V d is the volume of the dth node, T d is the temperature of the dth node; node d represents the node in the gear teeth when the double teeth are meshing, Q e and Q f Respectively expressed in Figure 3 The heat flux generated at the contact point e and the contact point f; R di Indicates attachment Figure 3 There are i radial thermal resistances from contact point e to node d, R d(n-i) Indicates attachment Figure 3 There are (ni) radial thermal resistances from the contact point f to the node d, n represents the radial thermal resistance from the adjacent Figure 3 The total radial thermal resistance between contact point e and contact point f;

[0167] S804: Combine the transient thermal equations of each node established in step S803, solve the transient thermal grid equations constructed using the Runge-Kutta method based on MTALAB, and calculate the real-time temperature of each gear node during the gear meshing process.

[0168] The present invention also provides a gear transient thermal grid temperature detection system considering the alternating meshing of single and double teeth, comprising a data acquisition module and a processing module. The data acquisition module is used to collect basic parameters of the gear thermal resistance to be calculated.

[0169] The input end of the processing module is electrically connected to the output end of the data acquisition module. The processing module executes the method of the present invention to obtain the real-time temperature of each node of the gear during the movement of the gear pair.

[0170] This system addresses the shortcomings of existing technologies and obtains the real-time temperature of each gear node during the movement of the gear pair, ensuring the accuracy of gear temperature calculation while being closer to reality.

[0171] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0172] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A method for detecting the transient thermal grid temperature of a gear considering the alternating meshing of single and double teeth, characterized in that: The steps include: S1, collecting basic parameters of the gear thermal resistance to be calculated; S2, according to the definition of overlap, calculate the proportion of the meshing time of single teeth and double teeth in each rotation of the gear teeth; Based on Hertz contact theory, calculate the contact half-width when the gear teeth are meshing; Calculate the involute arc length of the gear tooth profile based on the involute parametric equation and calculus theory; S3, based on the proportion of the meshing time of single teeth and double teeth and the arc length of the tooth profile involute, the areas corresponding to the meshing of single teeth and double teeth in the tooth profile arc length are divided, and the gear teeth are divided into multiple temperature gradient layers along the radial direction; According to the thin-walled ring theory, the conduction thermal resistance of each temperature gradient layer along the radial and circumferential directions is calculated; S4, calculate the conduction thermal resistance of the gear pair when considering the alternating meshing of single and double teeth; S5, using the basic parameters in step S1 to calculate the tooth top thickness and the tooth top surface heat exchange area; Calculate the convective heat transfer area of ​​the gear teeth in the non-contact region using the contact half-width and the involute arc length of the gear tooth profile obtained in step S2; S6, calculate the Reynolds number based on the basic parameters of S1 and divide the lubricating oil into laminar flow and turbulent flow, and calculate the convective heat transfer coefficient and convective heat transfer thermal resistance of each non-contact surface; S7, calculating the heat flux generated by friction at the gear meshing position based on the basic parameters in step S1 and the contact half-width in step S2; S8, using the conduction heat resistance of step S4 and the convection heat transfer heat resistance of step S6, the instantaneous heat balance equation at each grid node is listed to calculate the real-time temperature of each gear node during the gear pair movement process.

2. The method for detecting transient thermal grid temperature of gears considering alternating meshing of single and double teeth according to claim 1, characterized in that: In step S2, according to the definition of overlap, the proportion of the gear tooth single tooth meshing time η is calculated. single and the proportion of double-tooth meshing time η double ,for: or single =mod(e) or double =1-mod(e) Among them, ε represents the degree of coincidence, 1<ε<2, and mod represents the remainder; Based on Hertz contact theory, calculate the contact half-width a when the gear teeth are meshing H ,for: Among them, F represents the normal meshing force, B represents the tooth width, μ p 、μ g are the Poisson's ratios of the driving wheel and the driven wheel, E p 、E g are the elastic moduli of the driving wheel and the driven wheel respectively, R1 and R2 are the equivalent curvature radii of the two tooth surfaces at the contact point respectively; Based on the involute parametric equation and calculus theory, the involute arc length L of the gear tooth profile is calculated as: The rectangular coordinate equation of the involute is expressed as x(θ)=r b (cosθ+θs inθ), y(θ)=r b (si nθ-θcosθ), θ is the involute expansion angle, r b is the base circle radius.

3. The method for detecting transient thermal grid temperature of gears considering alternating meshing of single and double teeth according to claim 1, characterized in that: In step S3, the gear teeth are divided into multiple temperature gradient layers along the radial direction. The specific method for calculating the conduction thermal resistance of each temperature gradient layer along the radial direction and the circumferential direction is as follows: S301, according to the proportion of single tooth meshing time η single and the proportion of double-tooth meshing time η double , and the involute arc length L of the tooth profile, based on the definition of overlap, calculate the arc length L of the area where single tooth meshing and double tooth meshing are located single and L double ,for: Among them, ε represents the degree of coincidence, 1<ε<2, and mod represents the remainder; S302, according to the arc length of the area where the single tooth meshing and double tooth meshing are located calculated in step S301, set the tooth top to the initial position, then the single tooth meshing area area s Double tooth meshing area d Divided into: S303, based on the thin-walled ring theory, calculate the radial conduction thermal resistance R between each temperature gradient layer of the gear teeth ri and circumferential thermal resistance R ci ,for: Among them, δ ri is the thickness of the i-th temperature gradient layer, S ri is the average surface area of ​​the i-th temperature gradient layer, S ri =s i ·B,s i is the average tooth thickness, B is the tooth width; S c is the gear tooth contact area, S c =2a H B; λ is the thermal conductivity that changes with temperature.

4. The method for detecting transient thermal grid temperature of gears considering alternating meshing of single and double teeth according to claim 1, characterized in that: Step S4 is based on the radial conduction thermal resistance R between each temperature gradient layer of the gear teeth ri and circumferential thermal resistance R ci , calculate the conduction thermal resistance R of the gear pair when considering the alternating meshing of single and double teeth si The collection is: Among them, n start Indicates the position where the second pair of gear teeth engages with the corresponding gradient layer, n end Indicates the position where the first pair of gear teeth engage the corresponding gradient layer.

5. The method for detecting transient thermal grid temperature of gears considering alternating meshing of single and double teeth according to claim 1, characterized in that: Step S5 uses the basic parameters in step S1 to calculate the tooth top thickness s a , tooth top surface heat exchange area S a ,for: S a =s a B Among them, d a is the tooth top diameter, s is the pitch circle tooth thickness, d is the pitch circle diameter, α is the pitch circle pressure angle, α a is the tooth tip circle pressure angle, invα is the involute function, invα=tanα-α; B represents the tooth width; The convective heat transfer area S of the gear teeth in the non-contact area is calculated by using the contact half-width and the involute arc length of the gear tooth profile obtained in step S2. nc ,for: S nc =(L-2a H )B Where L is the involute arc length of the gear tooth profile, a H is the contact half-width when the gear teeth are meshing.

6. The method for detecting transient thermal grid temperature of gears considering alternating meshing of single and double teeth according to claim 1, characterized in that: In step S6, the Reynolds number is calculated based on the basic parameters of S1 and the lubricating oil is divided into laminar flow and turbulent flow. The steps of calculating the convective heat transfer coefficient and convective heat transfer thermal resistance of each non-contact surface are as follows: S601, calculate the Reynolds number Re, which is: Among them, ρ eff is the density of the oil-gas mixture, ρ eff =Xρ oil +(1-X)ρ air , X is the oil-gas ratio coefficient, ρ oil is the density of oil, ρ air is the density of the gas; η eff is the dynamic viscosity of the oil-gas mixture, η eff =η oil / (η oil / η air (1-X)+X), η oil is the dynamic viscosity of the oil, η air is the dynamic viscosity of the gas; ω is the angular velocity of the gear, r b is the base circle radius; S602, based on the fluid cross-plane theory, taking into account the key factors of the nozzle diameter and angle, calculate the average convective heat transfer coefficient h of the gear surface s ,for: Among them, ν is the pitch circle speed, S oil is the injection port area, ψ is the injection port angle; S nc is the convective heat transfer area of ​​the gear teeth in the non-contact area; S603, according to the Reynolds number calculated in step S601, the lubricating oil is divided into laminar flow, transition flow and turbulent flow, and the convective heat transfer coefficient h of the tooth top surface is calculated. a ,for: Where Pr is the Prandtl number, Pr = η eff c p / k D , c p is the specific heat capacity of lubricating oil, k D is the thermal conductivity of lubricating oil; S604: Calculate the convection thermal resistance R of each non-contact surface based on the convection heat transfer coefficient and heat transfer theory. s 、R a ,for: Among them, S a is the heat transfer area of ​​the tooth top surface.

7. The method for detecting transient thermal grid temperature of gears considering alternating meshing of single and double teeth according to claim 1, characterized in that: Step S7 calculates the heat flux generated by friction at the gear meshing point based on the basic parameters in step S1 and the contact half-width in step S2, specifically: S701, calculate the contact pressure p of the gear teeth at the meshing point, which is: Among them, E eq is the equivalent elastic modulus of the contact point, F NC is the normal force, r eq is the curvature radius of the contact point; B is the tooth width; S702, calculate the heat flux Q generated by the meshing of the driving and driven gears p , Q g ,for: Among them, a H is the contact half-width when the gear teeth are meshing, v c1 、v c2 are the linear velocities of the master and driven gears at the contact point C, n1 and n2 are the rotational speeds of the master and driven gears, β is the heat flux distribution coefficient, γ is the heat conversion coefficient, μ c is the friction coefficient, v c is the relative sliding velocity, v c =|v c1 -v c2 |.

8. The method for detecting transient thermal grid temperature of gears considering alternating meshing of single and double teeth according to claim 1, characterized in that: In step S8, the instantaneous heat balance equation at each grid node is listed, and the specific steps for calculating the real-time temperature of each gear node during the gear pair movement are as follows: S801, based on Kirchhoff's law, the net heat flow of a single node is equal to the increment of the corresponding internal energy of the volume. The expression between the net heat flow and the temperature increment of the jth node is q j for: Among them, c j is the specific heat capacity of the jth node, ρ j is the density of the jth node, V j is the volume of the jth node, T j is the temperature of the jth node, and t is the time; S802: Based on the basic parameters, conduction thermal resistance, convection thermal resistance, and the heat flux generated by the meshing of the master and slave gears, and assuming that the heat flux flowing into and out of each node is equal, the instantaneous thermal balance at the jth grid node is: Among them, Q j represents the heat flux generated at the jth node, and is 0 if no heat is generated; T j represents the temperature at the jth node; R k-j It represents the total thermal resistance between nodes k and j; k represents the node number; S803, considering the presence of heat sources on both sides of the gear teeth when double teeth are meshed, the temperature of each node of the gear teeth is calculated jointly through heat transfer on both sides. The instantaneous heat balance equation is rewritten as: Among them, c d is the specific heat capacity of the dth node, ρ d is the density of the dth node, V d is the volume of the dth node, T d is the temperature of the dth node; node d represents the node in the gear teeth when the double teeth are meshing, Q e and Q f Represent the heat flux generated at contact point e and contact point f respectively; R di Indicates that there are i radial thermal resistances from contact point e to node d, R d(n-i) It indicates that there are (ni) radial thermal resistances from contact point f to node d, and n indicates the total number of radial thermal resistances from contact point e to contact point f; S804: Combine the transient thermal equations of each node established in step S803, solve the transient thermal grid equations constructed based on MTALAB using the Runge-Kutta method, and calculate the real-time temperature of each gear node during the gear meshing process.

9. A gear transient thermal grid temperature detection system considering alternating meshing of single and double teeth, characterized in that: It includes a data acquisition module and a processing module, wherein the data acquisition module is used to collect basic parameters of the gear thermal resistance to be calculated; The input end of the processing module is connected to the output end of the data acquisition module, and the processing module executes the method described in any one of claims 1 to 8 to obtain the real-time temperature of each node of the gear during the movement of the gear pair.

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