Aero high-speed spiral bevel gear tooth surface contact temperature prediction method

Abstract

The application provides a kind of aviation high-speed curved-tooth bevel gear tooth surface contact temperature prediction method, it is related to aviation gear transmission technical field.Input gear geometric parameters, material properties and working condition parameters, establish meshing geometry model in combination with involute profile characteristics, calculate the coincidence degree, divide single-tooth meshing area, determine load distribution coefficient;Using Hertz contact theory to calculate the contact band half-width of meshing point, unit tooth width normal load, combined with gear speed and transmission ratio to solve the relative sliding speed of meshing point, friction heat flux density, tooth surface instantaneous flash temperature, superimposed with the body temperature to obtain total contact temperature;Three-dimensional temperature distribution is constructed through tooth width direction temperature correction model, and key thermal parameters such as full-tooth surface temperature distribution cloud picture are output.The temperature result calculated by the application can effectively restore the temperature distribution characteristics of gear meshing process, and the calculation efficiency and prediction accuracy are improved, which provides reliable data support for the anti-sticking design, material selection and operation and maintenance decision of aviation curved-tooth bevel gear.

Description

Technical Field

[0001] This invention relates to the field of aviation gear transmission technology, and in particular to a method for predicting the contact temperature of the tooth surface of high-speed spiral bevel gears in aviation. Background Technology

[0002] Aircraft spiral bevel gears are core load-bearing components in aircraft transmission systems. They operate under harsh conditions of high temperature, high speed, and alternating heavy loads. Excessive tooth surface contact temperature can easily lead to failures such as scuffing, thermal deformation, and wear. These failures result in increased dynamic load and noise in the gear transmission, accelerated tooth surface temperature rise, and ultimately gear failure, directly impacting the reliability of the aircraft transmission system and flight safety. Accurate prediction of tooth surface contact temperature is a crucial technological foundation for the failure-resistant design, material selection, and maintenance decisions of aircraft spiral bevel gears.

[0003] Current technologies for measuring tooth surface contact temperature have significant shortcomings. Traditional contact measurement methods primarily rely on thermocouple embedding and temperature sensor patch bonding. These methods require direct contact with the tooth surface, inevitably interfering with the normal meshing motion of the gears and disrupting the continuity of the tooth surface's mechanical properties. Furthermore, the enclosed cavity structure of aerospace transmission systems, high-temperature oil and gas media, and high-speed rotating airflow severely affect the stability of sensor signals, leading to a significant increase in measurement errors and an inability to accurately capture the dynamic distribution characteristics of the instantaneous contact temperature of the tooth surface. Non-contact measurement technologies, such as infrared thermometry, can avoid contact interference, but are limited by the spatial obstruction issues inherent in gear transmission, making it difficult to achieve full coverage measurement of the entire tooth surface temperature, thus significantly limiting their application scenarios.

[0004] In the field of simulation prediction, existing technologies also have many shortcomings. To improve computational efficiency, mainstream commercial simulation software often oversimplifies the complex geometric characteristics of gear meshing, such as approximating the spatial involute tooth profile as a planar model and ignoring the load distribution differences during alternating single and double tooth meshing. This leads to discrepancies between calculated meshing mechanical properties and actual operating conditions. Furthermore, most simulation methods fail to achieve deep coupling of multiple theories, relying solely on Hertzian contact theory to calculate contact stress or isolated flash temperature theory to estimate temperature rise. This lack of systematic consideration of thermo-mechanical coupling effects results in significant deviations between temperature predictions and actual engineering measurements. Simultaneously, existing tools primarily focus on theoretical calculations, lacking specialized designs for aerospace spiral bevel gears. They cannot support flexible configuration of geometric parameters, material properties, and operating conditions, and struggle to generate three-dimensional temperature field visualizations along the tooth width and meshing line direction, failing to meet the practical needs of parametric analysis and quantitative evaluation in engineering design.

[0005] Therefore, developing a simulation software capable of accurately predicting the contact temperature of the tooth surface of aerospace spiral bevel gears has become an urgent need in the field of aerospace gear transmission technology. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for predicting the contact temperature of the tooth surface of high-speed spiral bevel gears in aviation, which addresses the shortcomings of the prior art and provides a scientific basis for the design improvement, material selection and operation and maintenance decisions of aviation spiral bevel gears, and has important engineering application value.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A method for predicting the contact temperature of high-speed spiral bevel gear teeth in aviation is proposed. First, the gear's geometric parameters, material properties, and operating parameters are input. Then, a traversal loop of the meshing points is initiated: for each point on the meshing line, the position, length, and overlap ratio of the meshing line are determined through kinematic analysis. The total tangential and normal forces on the tooth surface are derived based on the input torque. Single-tooth / double-tooth meshing regions are divided according to the overlap ratio, and loads are distributed. Then, the half-width of the contact band is calculated based on Hertzian contact theory. The relative sliding velocity is derived from the gear angular velocity and meshing position, and the friction coefficient and unit tooth width are considered. The frictional heat flux density is calculated under load. Then, based on the flash temperature theory, the instantaneous flash temperature is calculated by combining the heat flux density, contact band half-width, and material thermophysical parameters. A heat balance equation is established, taking into account both frictional heat generation and body temperature. The instantaneous flash temperature is superimposed with the initial body temperature to obtain the actual contact temperature at the meshing point. Subsequently, the three-dimensional temperature distribution in the tooth width direction and the meshing line direction is calculated through a double-loop extension. After traversing all positions, the predicted results of the temperature distribution and key parameters of the entire tooth surface are output, providing a scientific basis for gear design improvement, material selection, and operation and maintenance decisions.

[0009] Furthermore, the specific steps of the contact temperature prediction method are as follows:

[0010] Step 1: Input the gear geometry parameters, material properties, and operating parameters; the geometry parameters include the module. / mm, Number of teeth on the drive gear Number of teeth on the driven gear Pressure angle / °, Tooth width / mm; the material properties include elastic modulus E / MPa, Poisson's ratio, etc. coefficient of friction Thermal conductivity ,density / kg / Specific heat capacity c / J / (kg·K), coefficient of thermal expansion Operating parameters include initial body temperature. Input torque Drive wheel speed / r / min;

[0011] Step 2: Based on the input gear geometry parameters, calculate the basic dynamic parameters, including the pitch circle radii of the driving and driven gears. and Base circle radius and , base section The pressure angle of the tooth tip circle is derived from the tooth tip circle radius, and then the contact ratio is calculated. The length and boundary range of the single-tooth meshing area and the double-tooth meshing area are defined based on the degree of overlap.

[0012] Step 3: Construct an array of discrete point positions along the meshing line to input torque. Starting from this point, the total tangential force of gear meshing is derived. With total normal force Discrete points are uniformly selected along the meshing line. Based on the meshing region of each point, the load is distributed using a linear gradient function to obtain the normal load per unit tooth width. Simultaneously, the radii of curvature R1 and R2 of the driving and driven gears at any point C during gear meshing are calculated, along with their relative sliding speeds. And the half-width B of the contact zone, forming a mechanical parameter dataset;

[0013] Step 4: Combine the relative sliding speeds of each meshing point Normal load per unit tooth width and friction coefficient f m Calculate the frictional heat flux density The thermal calculation terms are constructed based on thermal conductivity, material density, specific heat capacity, and relative sliding velocity. The instantaneous flash temperature of the tooth surface at each point is then solved by combining the contact band half-width and frictional heat flux density. ;

[0014] Step 5: Instantaneous flash temperature With initial body temperature The total contact temperature at each meshing point is obtained by superposition. Construct a two-dimensional planar mesh with meshing line and tooth width, and use an interpolation algorithm to complete the discrete point temperature data, simulate the temperature gradient in the tooth width direction, and generate three-dimensional temperature field data of the entire tooth surface.

[0015] Step 6: Output total normal force, maximum sliding speed, maximum normal load per unit tooth width, maximum frictional heat flux density, and maximum flash temperature; generate 7 types of visualization charts, including relative sliding speed distribution, contact band half-width variation over time, normal load per unit tooth width variation over time, frictional heat flux density variation over time, tooth surface contact temperature variation over time, tooth surface flash temperature distribution, and a three-dimensional temperature thermogram of the entire tooth surface.

[0016] Furthermore, in step two, the formulas for calculating the basic dynamic parameters are as follows:

[0017] (1);

[0018] (2);

[0019] (3);

[0020] Where i=1,2, corresponding to the driving wheel and the driven wheel, respectively;

[0021] The addendum circle radius of the driving gear and driven gear and the corresponding pressure angle The calculation formulas are as follows:

[0022] (4);

[0023] (5);

[0024] in, This represents the addendum coefficient of a gear. For a standard gear, ; and These are the pressure angles of the tip circle of the driving gear and the driven gear, respectively.

[0025] Coincidence The calculation formula is:

[0026] (6);

[0027] in, It is the engagement angle;

[0028] The lengths of the single-tooth meshing zone and the double-tooth meshing zone are obtained from the following two formulas:

[0029] (7);

[0030] (8);

[0031] in, The length of the single-tooth meshing zone. This represents the length of the double-tooth meshing zone.

[0032] Furthermore, in step three, the total tangential force With total normal force The calculation formula is as follows:

[0033] (9);

[0034] (10);

[0035] The formation of the mechanical parameter dataset is as follows:

[0036] For any meshing point C during the gear meshing process, the radii of the driving gear and the driven gear at that point are... , Its expression is as follows:

[0037] (11);

[0038] (12);

[0039] The involute pressure angles of the tooth profiles of the driving and driven gears corresponding to the meshing point C are:

[0040] (13);

[0041] Tangential slip velocity of the driving and driven gears at the meshing point C for:

[0042] (14);

[0043] in, Let i be the angular velocities of the driving wheel and the driven wheel, i = 1, 2;

[0044] Relative sliding velocity at engagement point C for:

[0045] (15);

[0046] Based on the properties of involutes, the radii of curvature of the tooth profiles of the driving and driven gears at the meshing point C are... for:

[0047] (16);

[0048] According to Herz contact theory, the half-width of the contact band of the driving and driven gears at the meshing point C is obtained. The expression is:

[0049] (17);

[0050] in, To calculate the coefficients, E is Poisson's ratio; i Let i be the elastic modulus, i = 1, 2;

[0051] The relative sliding velocity, radius of curvature, and half-width of the contact zone corresponding to each meshing point on the meshing line are solved by iterative calculation, and the calculation results are integrated into a meshing mechanical parameter dataset.

[0052] Furthermore, in step four, the frictional heat flux density The calculation formula is:

[0053] (18);

[0054] Based on Blok's flash temperature theory, the instantaneous flash temperature of the tooth surface at each meshing point C is calculated. :

[0055] (19);

[0056] in, For spiral bevel gears, the temperature rise coefficient is... ; The thermal conductivity of the two tooth surfaces; The material density of the two tooth surfaces; The contact band width is half. Specific heat capacity.

[0057] Furthermore, the specific method for step five is as follows:

[0058] Construct a two-dimensional structured mesh: M discrete sampling points are set at equal intervals along the meshing line to cover the complete meshing area of ​​the center of the drive wheel; N sampling points are evenly distributed along the tooth width to cover the full width range from 0 to tooth width B, forming an M×N structured two-dimensional planar mesh;

[0059] Based on this mesh, a body temperature gradient model along the tooth width is constructed to simulate the temperature distribution characteristics of high temperature at the center and low temperature at both ends of the tooth; the specific formula is as follows:

[0060] (twenty one);

[0061] Where w represents the coordinates of the meshing point in the tooth width direction;

[0062] For each discrete node within the grid, the body temperature at the corresponding tooth width position is superimposed with the instantaneous flash temperature at the corresponding point on the meshing line to obtain the total contact temperature data in two-dimensional space. For nodes in the non-meshing region, interpolation constrained by physical laws is used to complete the data, ensuring that the temperature field is continuous and conforms to the laws of heat conduction.

[0063] The beneficial effects of adopting the above technical solution are as follows: The method for predicting the contact temperature of high-speed spiral bevel gear teeth provided by this invention uses a meshing point traversal loop method to achieve accurate calculation of each point within the entire meshing line range, fully covering the tooth surface contact area and solving the problem of incomplete temperature distribution caused by traditional local sampling calculation; it uses a dynamic load distribution method for single / double tooth meshing areas, divides the meshing area according to the overlap ratio and distributes the load through a linear gradient function, avoiding errors caused by fixed load assumptions and improving the accuracy of temperature calculation; it integrates the coupled calculation method of Hertzian contact theory and flash temperature theory, which has a solid theoretical foundation. First, the half-width of the contact band is obtained through Hertzian contact theory, and then the instantaneous flash temperature is calculated by combining flash temperature theory, realizing accurate derivation of thermal parameters and greatly improving the accuracy of contact temperature prediction; it adopts a method of collecting and interpolating the temperature of discrete points on the entire tooth surface, obtains the temperature data of discrete points in the tooth width and meshing line direction through batch loop calculation, and constructs a three-dimensional temperature field through interpolation, fully presenting the details of the tooth surface temperature distribution, and has certain engineering application value. Attached Figure Description

[0064] Figure 1 A flowchart of a method for predicting the contact temperature of the tooth surface of a high-speed spiral bevel gear in aviation, provided in an embodiment of the present invention;

[0065] Figure 2 This is a graph showing the relative sliding velocity of the two tooth surfaces at the meshing point as a function of position, obtained from testing according to an embodiment of the present invention.

[0066] Figure 3 This is a graph showing the change of the contact band half-width over time obtained from testing, provided in an embodiment of the present invention.

[0067] Figure 4 This is a graph showing the variation of the normal load per unit tooth width over time, obtained from testing according to an embodiment of the present invention.

[0068] Figure 5 This is a graph showing the change of frictional heat flux density over time obtained from testing, provided in an embodiment of the present invention.

[0069] Figure 6 This is a graph showing the change of tooth surface contact temperature over time obtained from testing, provided in an embodiment of the present invention.

[0070] Figure 7 This is a graph showing the variation of tooth surface flash temperature with different distances from the center of the drive wheel, obtained from testing according to an embodiment of the present invention.

[0071] Figure 8 This is a three-dimensional thermal distribution map of the tooth surface obtained through testing, provided in an embodiment of the present invention. Detailed Implementation

[0072] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0073] A method for predicting the tooth surface contact temperature of high-speed spiral bevel gears in aviation, such as... Figure 1 As shown, the method of this embodiment is described below.

[0074] Step 1: First, input the gear geometry parameters: module / mm, Number of teeth on the drive gear Number of teeth on the driven gear Pressure angle / °, Tooth width / mm; Material properties: Elastic modulus E / MPa, Poisson's ratio coefficient of friction Thermal conductivity ,density / kg / Specific heat capacity c / J / (kg·K), coefficient of thermal expansion Operating parameters: Initial temperature Input torque Drive wheel speed / r / min.

[0075] Step 2: At the theoretical line of meshing of the gear pair Above, the node between the addendum circle of the driven gear tooth and the line of engagement. It is the starting contact point of meshing, the node between the addendum circle of the driving gear tooth and the line of engagement. It is the point where the engagement ends and disengages. The point is the meshing point of the gears. It is the meshing angle, for standard-mounted gears. ; and These are the pressure angles of the tip circle of the driving gear and the driven gear, respectively. The pitch circle radii are, in order, the driving gear and the driven gear; The base circle radii are, in order, the driving wheel and the driven wheel; Represents the tip circle radius of the driving and driven gears; ω represents the angular velocity of the driving wheel and the driven wheel.

[0076] The pitch circle radius is derived using gear geometry theory. Base circle radius , base section The formula is as follows:

[0077] (1);

[0078] (2);

[0079] (3);

[0080] Next, calculate the addendum circle radius and corresponding pressure angle of the driving and driven gears respectively:

[0081] (4);

[0082] (5);

[0083] in, The addendum coefficient represents the gear contact ratio, which is derived from the following formula:

[0084] (6);

[0085] After calculation, the length of the single and double tooth meshing regions is divided according to the overlap ratio. The start and end positions of the single tooth meshing region are accurately defined, and a digital model of the gear meshing region is generated. The length of the single tooth meshing region is... and the length of the double-tooth meshing area The following formula is used to derive:

[0086] (7);

[0087] (8).

[0088] Step 3: Calculate the total tangential force based on the input torque T. With total normal force The formula is as follows:

[0089] (9);

[0090] (10);

[0091] Take N discrete points along the meshing line and mark the meshing area. In the single-tooth meshing area, all loads are applied to the current tooth. In the double-tooth area, the load is distributed through a linear gradient function. That is, when the two teeth are in full contact, all loads are evenly distributed to the two pairs of teeth. As the meshing position changes, the load share is adjusted according to a linear law until one pair of teeth disengages.

[0092] For any point C during gear meshing, the radii of the driving gear and the driven gear at that point are... Its expression is as follows:

[0093] (11);

[0094] (12);

[0095] The involute pressure angles of the tooth profiles of the driving and driven gears corresponding to the meshing point C are:

[0096] (13);

[0097] Tangential slip velocity of the driving and driven gears at the meshing point C for:

[0098] (14);

[0099] Relative sliding velocity at engagement point C for:

[0100] (15);

[0101] Based on the properties of involute curves, the radius of curvature of the tooth profiles of the driving and driven gears at the meshing point C is... for:

[0102] (16);

[0103] According to Herz's contact theory, the half-width of the contact band between the driving and driven gears at the meshing point C of the tooth profiles can be obtained. The expression is:

[0104] (17);

[0105] In the formula, To calculate the coefficients, E is Poisson's ratio; i It is the elastic modulus.

[0106] The relative sliding velocity and radius of curvature (i.e., half-width of the contact zone) corresponding to each meshing point C on the meshing line are solved by iterative calculation. The calculation results are integrated into a meshing mechanical parameter dataset, and further calculations of related thermal parameters are carried out based on this dataset.

[0107] Step 4: Combine the relative sliding speeds of each meshing point Normal load per unit tooth width Tooth width B and friction coefficient Calculate the frictional heat flux density The formula is as follows:

[0108] (18);

[0109] Based on Blok's flash temperature theory, the instantaneous flash temperature of the tooth surface at each meshing point C is calculated. :

[0110] (19);

[0111] In the formula, For spiral bevel gears, the temperature rise coefficient is... ; The thermal conductivity coefficient of the two tooth surfaces; The material density of the two tooth surfaces; The contact band width is half. Specific heat capacity.

[0112] Step 5: Tooth surface contact temperature From the body temperature Instantaneous flash temperature of tooth surface Composition. The relationship is:

[0113] (20);

[0114] In the formula, the body temperature Once the system reaches a stable operating state, the temperature remains unchanged, at which point the body temperature of the two gears is the same; tooth surface flash temperature. This is because when the two tooth surfaces slide relative to each other, the energy consumed by friction is converted into heat, which in turn causes the local temperature of the tooth surface to rise. By superimposing the instantaneous flash temperature calculated in step four with the body temperature, the variation law of tooth surface contact temperature along the meshing direction can be obtained.

[0115] The temperature distribution characteristics along the tooth width have a critical impact on the thermal reliability design of gears. In actual working conditions, the heat dissipation conditions and load distribution at different locations along the tooth width vary significantly, directly affecting the uniformity of tooth surface temperature. To accurately investigate the distribution law of tooth surface contact temperature along the tooth width, this embodiment first constructs a two-dimensional structured mesh: 50 discrete sampling points are set at equal intervals along the meshing line, covering the complete meshing area at the center of the driving gear; 30 sampling points are evenly distributed along the tooth width, covering the full width range from 0 to tooth width B, forming a 50×30 structured two-dimensional planar mesh.

[0116] Based on this mesh, a body temperature gradient model along the tooth width is constructed using empirical formulas from practical engineering experience. This model simulates the temperature distribution characteristic of high temperature at the center and low temperature at both ends of the tooth. The specific formula is as follows:

[0117] (twenty one);

[0118] Where w represents the coordinates of the meshing point in the tooth width direction.

[0119] For each discrete node within the grid, the body temperature at the corresponding tooth width position is superimposed with the instantaneous flash temperature at the corresponding point on the meshing line to obtain the total contact temperature data in two-dimensional space. Nodes in the non-meshing region are completed using interpolation constrained by physical laws to ensure the temperature field is continuous and conforms to the laws of heat conduction. This method extends the one-dimensional temperature distribution on the meshing line to a two-dimensional temperature field of tooth width-meshing line, thus revealing the contact temperature distribution pattern across the entire tooth surface.

[0120] Step Six: Output key parameters such as total tangential force, total normal force, maximum sliding speed, maximum normal load per unit tooth width, maximum frictional heat flux density, and maximum flash temperature; generate 7 types of visualization charts, including relative sliding speed distribution, contact band half-width variation over time, normal load per unit tooth width variation over time, frictional heat flux density variation over time, tooth surface contact temperature variation over time, tooth surface flash temperature distribution, and a three-dimensional temperature thermogram of the entire tooth surface.

[0121] To verify the engineering applicability and accuracy of this method, the driving and driven spiral bevel gears of the central transmission system of a certain type of aero-engine were selected as the research object. The material used was carburized gear steel for aero-engines, with the grade 16Cr3NiWMoVNbE. This material has the high strength, high wear resistance and good thermal stability required for aero-engine transmission, and is a typical application material for aero-engine gears.

[0122] The seven types of visualization charts obtained using the method in this embodiment are as follows: Figures 2-8 As shown.

[0123] Figure 2 The diagram shows the variation of the relative sliding velocity of the two tooth surfaces at the meshing point with position. The relative sliding velocity is 0 at the gear meshing node (38mm). The sliding velocity in the double-tooth meshing area gradually decreases as the meshing position moves towards the node. The sliding velocity in the single-tooth meshing area and the double-tooth meshing area on the other side gradually increases as the meshing position moves away from the node. This variation is completely consistent with the kinematic theory of involute gear meshing.

[0124] Figure 3 The study shows the variation of the contact band half-width over time. On the meshing trajectory, the contact band half-width increases linearly with time when transitioning from the double-tooth meshing area to the single-tooth meshing area. The single-tooth meshing area maintains a stable peak value of approximately 570 μm, while the half-width decreases linearly when transitioning from the single-tooth to the double-tooth meshing area. This variation is consistent with the Hertzian contact theory's principle that "the greater the load, the greater the contact band half-width," verifying the accuracy of the tooth surface contact mechanics calculations using the method in this embodiment.

[0125] Figure 4The variation law of normal load per unit tooth width with time is shown. On the meshing trajectory, the load is shared by two pairs of teeth in the double-tooth meshing zone, and the normal load per unit tooth width increases linearly with time. After entering the fully single-tooth meshing zone, only one pair of teeth bears the entire load, and the load maintains a stable peak value of about 1300 kN / m. When transitioning from single-tooth to double-tooth meshing zone, the load decreases linearly again. This law is highly consistent with the load distribution theory of gear overlap, proving the engineering rationality of the load distribution logic of the method in this embodiment.

[0126] Figure 5 The variation of frictional heat flux density over time is shown. Along the meshing trajectory, as the double-tooth meshing zone transitions to the node, the frictional heat flux density gradually decreases to zero at the node as the sliding speed decreases. Upon entering the single-tooth meshing zone, only one pair of gears bears the entire load, and with the increase in sliding speed, the frictional heat flux density rises linearly, reaching a peak of approximately 0.035 MW / m² in the later stages of the single-tooth meshing zone. The heat flux density slightly decreases during the transition from the single-tooth to the double-tooth meshing zone. This variation conforms to the theoretical calculation logic of frictional heat flux density, verifying the effectiveness of the calculation results obtained using the method in this embodiment.

[0127] Figure 6 The diagram shows that as the double-tooth meshing zone transitions to the node on the meshing trajectory, the total contact temperature decreases to approximately 50°C at the node due to the decrease in frictional heat flux density. Upon entering the single-tooth meshing zone, only one pair of gears bears the entire load, and the increased frictional heat flux density causes the total contact temperature to rise continuously to a peak of approximately 75°C. The body temperature also gradually increases with the accumulation of frictional heat. Simultaneously, this change conforms to the calculation logic of "total contact temperature = body temperature + tooth surface flash temperature," verifying the effectiveness of the temperature calculation method in this embodiment.

[0128] Figure 7 The variation of tooth surface flash temperature with different distances from the center of the driving gear is shown. On the meshing trajectory, when transitioning from the double-tooth meshing zone to the node (38mm), the tooth surface flash temperature decreases to 0℃ at the node as the sliding speed decreases. After entering the single-tooth meshing zone, only one pair of gears bears the entire load and the sliding speed increases, and the tooth surface flash temperature rises linearly, reaching a peak of about 32℃ at the end of the meshing. This change is consistent with the distribution law of sliding speed and load, verifying the accuracy of the flash temperature calculation results of the method in this embodiment.

[0129] Figure 8 The three-dimensional thermal distribution of the tooth surface is shown. In the direction of the meshing line, the temperature first decreases as it moves towards the node (38mm) from the meshing position, and then increases as it moves towards the end of the meshing line after passing the node. In the direction of the tooth width, the temperature in the middle of the tooth width is higher than that on both sides, showing a "high in the middle and low on both sides" distribution. The temperature peak appears in the middle section of the single tooth meshing area, about 42mm from the center of the driving gear and about 12mm in the direction of the tooth width, with a value of 105.6℃. This feature verifies the rationality of the calculation results of the method in this embodiment.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A method for predicting the contact temperature of the tooth surface of a high-speed spiral bevel gear in aviation, characterized in that: First, input the gear geometry, material properties, and operating parameters. Then, initiate a loop to traverse the meshing points: for each point on the meshing line, first determine the position, length, and overlap of the meshing line through kinematic analysis, derive the total tangential and normal forces on the tooth surface based on the input torque, divide the single-tooth / double-tooth meshing region according to the overlap and distribute the load, then calculate the half-width of the contact band based on Hertzian contact theory, derive the relative sliding velocity through the gear angular velocity and meshing position, and calculate the frictional heat flux density based on the friction coefficient and unit tooth width load. Next, based on flash temperature theory, calculate the instantaneous flash temperature by combining the heat flux density, half-width of the contact band, and material thermophysical parameters, establish a heat balance equation, comprehensively consider frictional heat generation and body temperature, and superimpose the instantaneous flash temperature with the initial body temperature to obtain the actual contact temperature of the meshing point. Then, extend the calculation through a double loop to calculate the three-dimensional temperature distribution in the tooth width direction and the meshing line direction. After traversing all positions, output the predicted results of the full tooth surface temperature distribution and key parameters, providing a scientific basis for gear design improvement, material selection, and operation and maintenance decisions.

2. The method for predicting the contact temperature of the tooth surface of high-speed spiral bevel gears in aviation according to claim 1, characterized in that: The specific steps of the contact temperature prediction method are as follows: Step 1: Input the gear geometry parameters, material properties, and operating parameters; the geometry parameters include the module. / mm, Number of teeth on the drive gear Number of teeth on the driven gear Pressure angle / °, Tooth width / mm; the material properties include elastic modulus E / MPa, Poisson's ratio, etc. coefficient of friction Thermal conductivity ,density / kg / Specific heat capacity c / J / (kg·K), coefficient of thermal expansion ; Operating parameters include initial body temperature Input torque Drive wheel speed / r / min; Step 2: Based on the input gear geometry parameters, calculate the basic dynamic parameters, including the pitch circle radii of the driving and driven gears. and Base circle radius and , base section The pressure angle of the tooth tip circle is derived from the tooth tip circle radius, and then the contact ratio is calculated. The length and boundary range of the single-tooth meshing area and the double-tooth meshing area are defined based on the degree of overlap. Step 3: Construct an array of discrete point positions along the meshing line to input torque. Starting from this point, the total tangential force of gear meshing is derived. With total normal force Discrete points are uniformly selected along the meshing line. Based on the meshing region of each point, the load is distributed using a linear gradient function to obtain the normal load per unit tooth width. Simultaneously, the radii of curvature R1 and R2 of the driving and driven gears at any point C during gear meshing are calculated, along with their relative sliding speeds. And the half-width B of the contact zone, forming a mechanical parameter dataset; Step 4: Combine the relative sliding speeds of each meshing point Normal load per unit tooth width and friction coefficient f m Calculate the frictional heat flux density ; Thermal calculation terms are constructed based on thermal conductivity, material density, specific heat capacity, and relative sliding velocity. The instantaneous flash temperature at each point on the tooth surface is then calculated by combining the contact band half-width and frictional heat flux density. ; Step 5: Instantaneous flash temperature With initial body temperature The total contact temperature of each meshing point is obtained by superposition. Construct a two-dimensional planar mesh with meshing line and tooth width, and use an interpolation algorithm to complete the discrete point temperature data, simulate the temperature gradient in the tooth width direction, and generate three-dimensional temperature field data of the entire tooth surface. Step 6: Output total normal force, maximum sliding speed, maximum normal load per unit tooth width, maximum frictional heat flux density, and maximum flash temperature; generate 7 types of visualization charts, including relative sliding speed distribution, contact band half-width variation over time, normal load per unit tooth width variation over time, frictional heat flux density variation over time, tooth surface contact temperature variation over time, tooth surface flash temperature distribution, and a three-dimensional temperature thermogram of the entire tooth surface.

3. The method for predicting the contact temperature of the tooth surface of high-speed spiral bevel gears in aviation according to claim 2, characterized in that: In step two, the formulas for calculating the basic dynamic parameters are as follows: (1)； (2)； (3)； Where i=1,2, corresponding to the driving wheel and the driven wheel, respectively; The addendum circle radius of the driving gear and driven gear and the corresponding pressure angle The calculation formulas are as follows: (4)； (5)； in, This represents the addendum coefficient of a gear. For a standard gear, ; and These are the pressure angles of the tip circle of the driving gear and the driven gear, respectively. Coincidence The calculation formula is: (6)； in, It is the engagement angle; The lengths of the single-tooth meshing zone and the double-tooth meshing zone are obtained from the following two formulas: (7)； (8)； in, The length of the single-tooth meshing zone. This represents the length of the double-tooth meshing zone.

4. The method for predicting the contact temperature of the tooth surface of high-speed spiral bevel gears in aviation according to claim 3, characterized in that: In step three, the total tangential force With total normal force The calculation formula is as follows: (9)； (10)； The formation of the mechanical parameter dataset is as follows: For any meshing point C during the gear meshing process, the radii of the driving gear and the driven gear at that point are... , Its expression is as follows: (11)； (12)； The involute pressure angles of the tooth profiles of the driving and driven gears corresponding to the meshing point C are: (13)； Tangential slip velocity of the driving and driven gears at the meshing point C for: (14)； in, Let i be the angular velocities of the driving wheel and the driven wheel, i = 1, 2; Relative sliding velocity at engagement point C for: (15)； Based on the properties of involute curves, the radii of curvature of the tooth profiles of the driving and driven gears at the meshing point C are... for: (16)； According to Herz contact theory, the half-width of the contact band of the driving and driven gears at the meshing point C is obtained. The expression is: (17)； in, To calculate the coefficients, E is Poisson's ratio; i Let i be the elastic modulus, i = 1, 2; The relative sliding velocity, radius of curvature, and half-width of the contact zone corresponding to each meshing point on the meshing line are solved by iterative calculation, and the calculation results are integrated into a meshing mechanical parameter dataset.

5. The method for predicting the contact temperature of the tooth surface of high-speed spiral bevel gears in aviation according to claim 4, characterized in that: In step four, the frictional heat flux density The calculation formula is: （18）； Based on Blok's flash temperature theory, the instantaneous flash temperature of the tooth surface at each meshing point C is calculated. : (19)； in, For spiral bevel gears, the temperature rise coefficient is... ; The thermal conductivity of the two tooth surfaces; The material density of the two tooth surfaces; The contact band width is half. Specific heat capacity.

6. The method for predicting the contact temperature of the tooth surface of high-speed spiral bevel gears in aviation according to claim 5, characterized in that: The specific method for step five is as follows: Construct a two-dimensional structured mesh: M discrete sampling points are set at equal intervals along the meshing line to cover the complete meshing area of ​​the center of the drive wheel; N sampling points are evenly distributed along the tooth width to cover the full width range from 0 to tooth width B, forming an M×N structured two-dimensional planar mesh; Based on this mesh, a body temperature gradient model along the tooth width is constructed to simulate the temperature distribution characteristics of high temperature at the center and low temperature at both ends of the tooth; the specific formula is as follows: (21)； Where w represents the coordinates of the meshing point in the tooth width direction; For each discrete node within the grid, the body temperature at the corresponding tooth width position is superimposed with the instantaneous flash temperature at the corresponding point on the meshing line to obtain the total contact temperature data in two-dimensional space. For nodes in the non-meshing region, interpolation constrained by physical laws is used to complete the data, ensuring that the temperature field is continuous and conforms to the laws of heat conduction.

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