Method and system for determining the friction dynamics in a helicopter in heavy oil loss conditions

Abstract

The application discloses a method and system for determining the friction dynamics of a helicopter intermediate reduction gear under a severe oil loss state, and relates to the field of transmission system friction dynamics. The method comprises the following steps: combining a finite element node method with a lumped mass method to establish a nonlinear friction dynamics model; dividing the tooth surface according to the severe oil loss state; establishing a time-varying friction coefficient of the tooth surface in the oil loss process according to the division result; simulating and calculating the convective heat transfer coefficient inside the intermediate reduction gear by a CFD method; establishing a transient thermal model of the intermediate reduction gear according to the thermal nodes inside the intermediate reduction gear, the corresponding convective heat transfer coefficient and the heat transfer relationship of the thermal nodes inside the intermediate reduction gear, and then constructing a thermal balance equation; coupling the nonlinear friction dynamics model, the time-varying friction coefficient of the tooth surface in the oil loss process and the thermal balance equation to determine the friction dynamics coupling characteristics of the intermediate reduction gear. The application can accurately obtain the friction dynamics coupling characteristics of the intermediate reduction gear under the oil loss state.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of transmission system tribology, in particular to a method and system for determining the tribology of a helicopter intermediate gearbox under heavy oil loss condition. BACKGROUND

[0002] When the helicopter intermediate gearbox (intermediate gearbox) enters the oil loss state due to failure or attack, the oil gradually decreases until there is no oil, but the liquid film between the contact interface is still mainly elastohydrodynamic lubrication. This stage is called light oil loss state. As the film thickness continues to thin out until it breaks, the tooth surface temperature rises significantly, the friction and wear and vibration intensify, and the load between the contact interfaces is borne by the adsorbed film lubrication and rough peaks. At this time, it is called heavy oil loss state. The specific oil loss evolution process is shown in Figure 1

[0003] Considering the great difference in the tribology evolution mechanism of the helicopter intermediate gearbox between light oil loss and heavy oil loss, research on them needs to be carried out respectively.

[0004] However, the existing technology has research on the tribology of gear transmission system under full lubrication, but lacks research on the tribology of the complex object of intermediate gearbox under extreme working conditions of oil loss.

[0005] Therefore, there is an urgent need for a method or system for determining the tribology of a helicopter intermediate gearbox under heavy oil loss condition to solve the above problems. SUMMARY

[0006] The purpose of the present application is to provide a method and system for determining the tribology of a helicopter intermediate gearbox under heavy oil loss condition, which can accurately obtain the tribology coupling characteristics of the intermediate gearbox under oil loss condition.

[0007] To achieve the above purpose, the present application provides the following solutions:

[0008] A method for determining the tribology of a helicopter intermediate gearbox under heavy oil loss condition, comprising:

[0009] Combining the finite element node method with the lumped mass method to establish a nonlinear tribology model of the intermediate gearbox; the intermediate gearbox comprises: spiral bevel gears, tail horizontal shafts, tail inclined shafts, bearings and a casing;

[0010] Dividing the tooth surface according to the heavy oil loss condition; establishing the time-varying friction coefficient of the tooth surface in the oil loss process according to the division result; the division result includes: adsorbed film lubrication area and dry friction area between the tooth surfaces;

[0011] Simulating and calculating the convective heat transfer coefficient inside the intermediate gearbox by CFD method;

[0012] ​According to the thermal nodes inside the intermediate reducer, corresponding convective heat transfer coefficients and heat transfer relationships of the thermal nodes inside the intermediate reducer, a transient thermal model of the intermediate reducer is established, and then a thermal balance equation is constructed;

[0013] The nonlinear friction dynamics model, the time-varying friction coefficient of the tooth surface in the oil loss process and the thermal balance equation are coupled to determine the intermediate reduction heat friction dynamics coupling characteristics; the intermediate reduction heat friction dynamics coupling characteristics include: tooth surface temperature rise, gear heat source, bearing heat source, friction coefficient and area distribution coefficient, adsorption lubrication and dry friction coefficient and dynamics characteristics.

[0014] Optionally, the finite element node method is combined with the lumped mass method to establish a nonlinear friction dynamics model of the intermediate reducer, and specifically includes:

[0015] The nonlinear friction dynamics model of the intermediate reducer is determined by using the formula

[0016] Wherein, M is the system mass matrix, C is the system damping matrix, K is the system stiffness matrix, x(t) is the displacement column vector of all nodes, F is the force matrix, t is the time, is the derivative of x(t), is the second derivative of x(t).

[0017] Optionally, the nonlinear friction dynamics model of the intermediate reducer includes: a friction dynamics model of a gear meshing unit; the friction dynamics model of the gear meshing unit is:

[0018]

[0019] Wherein, m p , m g are the masses of the driving and driven wheels; c px , c py , c pz , c gx , c gy , c gz are the meshing dampings of the driving and driven wheels; k px , k py , k pz , k gx , k gy , k gz are the meshing stiffnesses of the driving and driven wheels; I px , I py , J p , I gx , I gy , J g are the moments of inertia of the driving and driven wheels in x, y and z directions; Ω p , Ω g ​The rotational speed of the driving and driven gears; λ px , λ py , λ pz , λ gx , λ gy , λ gz The lever arm at the meshing point of the driving and driven wheels; F n For dynamic meshing force, F f For friction; T ps T gs The resistance torque of the driving and driven wheels; θ p θ g Master-slave rotation angle; x p x g The displacement of the master and driven wheels in the x-direction; y p y g The displacement of the master and driven wheels in the y-direction; z-direction. p z g The displacement of the master and driven wheels in the z-direction.

[0020] Optionally, the step of dividing the tooth surface according to the severe oil loss state and establishing the time-varying friction coefficient of the tooth surface during the oil loss process based on the division results specifically includes:

[0021] Using the formula μ s =αf d +(1-α)f a Determine the time-varying friction coefficient of the tooth surface during the oil loss process;

[0022] Where, μ s f is the time-varying friction coefficient of the tooth surface during the oil loss process. d f is the coefficient of friction in the dry friction region. a α is the friction coefficient of the adsorption film region, and α is the area ratio of the dry friction region.

[0023] Optionally, the step of establishing a transient thermal model of the intermediate reducer based on the internal hot nodes, the corresponding convective heat transfer coefficients, and the heat transfer relationships of the internal hot nodes, and then constructing a heat balance equation, specifically includes:

[0024] Using formula Determine the transient thermal model of the intermediate reducer;

[0025] Where T is the node average temperature, R is the thermal resistance, Q is the heat flowing into the node, i, j, k, l are the node numbers, c and v represent conduction and convection heat transfer, respectively, and R icj Let C represent the thermal resistance for heat transfer from node i to node j, and R represent the thermal resistance for heat transfer. ivk Let be the thermal resistance of convective heat transfer from node i to node j.

[0026] A system for determining the heat-friction dynamics of a helicopter intermediate reduction gear in a heavy oil loss state, comprising:

[0027] A friction dynamics model establishing module for establishing a nonlinear friction dynamics model of the intermediate reduction gear by combining a finite element node method with a lumped mass method; the intermediate reduction gear comprises an arc tooth bevel gear, a tail horizontal shaft, a tail inclined shaft, a bearing and a casing;

[0028] A time-varying friction coefficient establishing module for dividing the tooth surface according to the heavy oil loss state; and establishing the time-varying friction coefficient of the tooth surface in the oil loss process according to the division result; the division result comprises an adsorbed film lubrication region and a dry friction region between the tooth surfaces;

[0029] A convection heat transfer coefficient determining module for simulating and calculating the convection heat transfer coefficient inside the intermediate reduction gear by a CFD method;

[0030] A heat balance equation constructing module for establishing a transient heat model of the intermediate reduction gear according to the heat nodes inside the intermediate reduction gear, the corresponding convection heat transfer coefficient and the heat transfer relationship of the heat nodes inside the intermediate reduction gear, and then constructing a heat balance equation;

[0031] A reduction gear heat-friction dynamics coupling characteristic determining module for coupling the nonlinear friction dynamics model, the time-varying friction coefficient of the tooth surface in the oil loss process and the heat balance equation to determine the reduction gear heat-friction dynamics coupling characteristic; the reduction gear heat-friction dynamics coupling characteristic comprises a tooth surface temperature rise, a gear heat source, a bearing heat source, a friction coefficient and an area distribution coefficient, an adsorbed lubrication and dry friction coefficient and a dynamic characteristic.

[0032] A system for determining the heat-friction dynamics of a helicopter intermediate reduction gear in a heavy oil loss state, comprising: at least one processor, at least one memory and computer program instructions stored in the memory, which, when executed by the processor, implement the method.

[0033] A storage medium having computer program instructions stored thereon, which, when executed by a processor, implement the method.

[0034] According to the specific embodiments of the present application, the following technical effects are provided:

[0035] The application provides a method and system for determining the heat-friction dynamics of a helicopter intermediate reduction gear in a severe oil loss state, the tooth surface is divided according to the severe oil loss state; the time-varying friction coefficient of the tooth surface in the oil loss process is established according to the division result; the transient thermal model of the intermediate reduction gear is established according to the thermal nodes inside the intermediate reduction gear, the corresponding convective heat transfer coefficient and the heat transfer relationship of the thermal nodes inside the intermediate reduction gear, and then the heat balance equation is constructed; the nonlinear friction dynamics model, the time-varying friction coefficient of the tooth surface in the oil loss process and the heat balance equation are coupled; the application provides a combination method of the adsorbed film lubrication friction coefficient and the dry friction area friction coefficient in the severe oil loss lubrication condition, and the combination with the nonlinear friction dynamics model, so as to obtain the intermediate reduction coupling thermal characteristics and dynamic characteristics in the severe oil loss state. BRIEF DESCRIPTION OF DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0037] Figure 1 It is a schematic diagram of the oil loss state evolution process of the helicopter intermediate reduction gear.

[0038] Figure 2 It is a flowchart of the method for determining the heat-friction dynamics of the helicopter intermediate reduction gear in the severe oil loss state.

[0039] Figure 3 It is a schematic diagram of the overall process of the present application.

[0040] Figure 4 It is a schematic diagram of the finite element node model of the intermediate reduction gear.

[0041] Figure 5 It is a schematic diagram of the adsorbed film lubrication area and the dry friction area in the oil loss state.

[0042] Figure 6 It is a schematic diagram of the rough peak simulation.

[0043] Figure 7 It is a schematic diagram of the intermediate reduction CFD calculation model.

[0044] Figure 8 It is a schematic diagram of the temperature distribution inside the casing of the CFD simulation calculation.

[0045] Figure 9 It is a schematic diagram of the air flow line inside the casing.

[0046] Figure 10 It is a schematic diagram of the convective heat transfer coefficient.

[0047] Figure 11 Schematic diagram for medium heat reduction node arrangement;

[0048] Figure 12 Schematic diagram for medium heat reduction network;

[0049] Figure 13 Schematic diagram for node temperature rise;

[0050] Figure 14 Schematic diagram for tooth surface temperature rise;

[0051] Figure 15 Schematic diagram for gear heat source;

[0052] Figure 16 Schematic diagram for bearing heat source;

[0053] Figure 17 Schematic diagram for friction coefficient and area distribution coefficient;

[0054] Figure 18 Schematic diagram for adsorbed lubrication and dry friction coefficient;

[0055] Figure 19 Schematic diagram for X-direction displacement and speed;

[0056] Figure 20 Schematic diagram for shaft center trajectory change. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0058] The present application aims to provide a method and system for determining helicopter medium heat reduction friction dynamics under heavy oil loss state, which can accurately obtain the medium heat reduction friction dynamics coupling characteristics under oil loss state.

[0059] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0060] As shown in Figure 2 and Figure 3 The present application provides a method for determining helicopter medium heat reduction friction dynamics under heavy oil loss state, which comprises:

[0061] S101, a finite element node method is combined with a lumped mass method to establish a nonlinear friction dynamics model of the intermediate reducer; the intermediate reducer comprises: an arc tooth bevel gear, a tail horizontal shaft, a tail inclined shaft, a bearing and a casing;

[0062] The transmission shaft adopts the finite element node method, the arc tooth bevel gear adopts the lumped mass method, and the nonlinear friction dynamics model of the intermediate reducer is established, and the distribution of the finite element nodes is as shown in Figure 4 .

[0063] S101 specifically comprises:

[0064] The nonlinear friction dynamics model of the intermediate reducer is determined by using the formula .

[0065] Wherein, M is a system mass matrix, C is a system damping matrix, K is a system stiffness matrix, x(t) is a displacement column vector of all nodes, F is a force matrix, t is time, is a derivative of x(t), is a second derivative of x(t).

[0066] The generalized displacement vector of the two nodes of the shaft segment unit is q s ={x1,y1,z1,θ x1 ,θ y1 ,θ z1 ,x2,y2,z2,θ x2 ,θ y2 ,θ z2} and the unit stiffness matrix K s is as follows:

[0067]

[0068] The mass matrix Ms of the shaft segment unit is as follows:

[0069]

[0070] In the formula, ρ is the material density, kg / m 3 ; A is the unit cross-sectional area, m 2 ; and l is the unit length, m.

[0071] The friction dynamics model of the gear meshing unit is as follows:

[0072]

[0073] Wherein, m p , m g are the masses of the driving wheel and the driven wheel; c px , c py , c pz , c gx , cgy , c gz is the meshing damping of the driving and driven wheels; k px , k py , k pz , k gx , k gy , k gz is the meshing stiffness of the driving and driven wheels; I px , I py , J p , I gx , I gy , J g is the moment of inertia of the driving and driven wheels in the x, y, z directions; Ω p , Ω g is the rotational speed of the driving and driven wheels; λ px , λ py , λ pz , λ gx , λ gy , λ gz is the force arm at the meshing point of the driving and driven wheels; F n is the dynamic meshing force, F f is the friction force; T ps , T gs is the resistance torque of the driving and driven wheels; θ p , θ g is the rotational angle of the driving and driven wheels; x p , x g is the displacement of the driving and driven wheels in the x direction; y p , y g is the displacement of the driving and driven wheels in the y direction; z p , z g is the displacement of the driving and driven wheels in the z direction.

[0074] S102, according to the heavy oil loss state, the tooth surface is divided; the time-varying friction coefficient of the tooth surface in the oil loss process is established according to the division result; the division result includes: the adsorbed film lubrication area and the dry friction area between the tooth surfaces;

[0075] S102 is aimed at the heavy oil loss lubrication situation, the area ratio calculation method of the adsorbed film lubrication area and the dry friction area between the tooth surfaces is researched, and the tooth surface friction coefficient in the oil loss process is established.

[0076] S102 specifically includes:

[0077] The time-varying friction coefficient of the tooth surface in the oil loss process is determined by the formula μ s = αf d + (1-α)f a ;

[0078] Wherein, μ s is the time-varying friction coefficient of the tooth surface in the oil loss process, fd f is the coefficient of friction in the dry friction region. a α is the friction coefficient of the adsorption film region, and α is the area ratio of the dry friction region.

[0079] like Figure 5 As shown, under good boundary lubrication conditions, the proportion of the dry friction region is typically below 0.01. However, as oil loss intensifies, the intermediate reducer relies solely on residual lubricating oil on the tooth surface for lubrication, at which point the area of ​​the dry friction region A increases. a Gradually increase, A b The area of ​​the adsorption film lubrication region is α = A, which is the ratio of the area of ​​the dry friction region to the oil film loss. α / (A α +A b ).

[0080] The area percentage of the adsorption membrane region is:

[0081]

[0082] In the formula: t x For the friction surface to slide at a speed U s The time t is determined by the contact length x. x =x / U s ;t r The average time that adsorbed molecules occupy the contact surface:

[0083]

[0084] In the formula: t0 is the period of thermal vibration of polar molecules perpendicular to the surface, s; ε is the heat of adsorption, cal / mol; R is the gas constant, 0.0292 J / (g·K); θ s Let K be the surface contact temperature.

[0085]

[0086] x = 1.46 × 10 -8 V 1 / 3 ;

[0087] In the formula: M0 is the molar mass, g / mol; V is the molar volume, cm³. 3 / mol; θ m The melting point of the base lubricant is K.

[0088] The critical temperature is calculated as follows:

[0089]

[0090] When the surface contact temperature exceeds the critical temperature, the adsorption film is broken, the friction coefficient increases rapidly, but it can still maintain a certain lubrication effect, and this temperature is called the first critical temperature; when the surface temperature continues to rise, the boundary film completely fails, and the friction pair appears sharp wear, and this temperature is called the second critical temperature.

[0091] Assuming that the surface of the friction pair of the gear transmission is separated by the adsorption film in the boundary lubrication state, and the adsorption film is a solid condensed monolayer film, then the friction coefficient f of the adsorption film lubrication area is a The calculation method is:

[0092]

[0093] In the formula: τ s is the shear strength of the adsorption film, S is the contact area of the adsorption film, and W is the load.

[0094] The shear strength of the adsorption film is:

[0095]

[0096] In the formula: P is the contact stress, MPa, f0=0.05, and ψ=0.00005.

[0097] The friction coefficient f of the adsorption film is a :

[0098]

[0099] Assuming that the roughness peaks of the solid contact area of the gear surface are normally distributed:

[0100]

[0101] Generally, the test uses a gear with a 5-level precision: the ten-point height of micro-irregularities R z =3.2um, the profile arithmetic average deviation R a =0.4um, and the average spacing S of the profile micro-irregularities m =0.3mm. According to the size of the deformation degree, it can be judged that the contact is elastic, elastoplastic or plastic contact.

[0102] The judgment standard of elastic deformation is that the deformation is less than ω e :

[0103]

[0104] In the formula: H c is the roughness, E p is the equivalent elastic modulus, and β is the equivalent curvature radius of the convex body.

[0105] For example Figure 6As shown, the surface morphology of the contact area and the structure of one of the rough peaks are simulated using a tooth surface standard with a precision of level 5.

[0106] The load applied to the convex body during the simulation causes it to deflect. Figure 5 δ s The deflection of a cantilever beam is expressed as:

[0107] F T =K T ·δ s ;

[0108] In the formula: parameter k s It is obtained from the ratio of the actual contact area to the nominal contact area; b s d is the end diameter of each cantilever. s Let be the height of the rough peak; E be the elastic modulus; when the two surfaces move relative to each other, the relationship between the deflection displacement of the rough peak end and time can be obtained as follows:

[0109]

[0110] Where: V rel F is the relative velocity between two objects. t0 It is static friction.

[0111] like Figure 6 As shown, f d The value obtained from simulation in Matlab is related to F. T K T K b δ s b s Related to ds.

[0112] S103, the convective heat transfer coefficient inside the intermediate reducer was calculated by CFD simulation.

[0113] After the helicopter's intermediate reduction gear enters a loss-of-oil state, all the lubricating oil in the casing flows out within approximately 3 minutes, but an oil film still remains between the gear teeth. Therefore, in cases of severe loss-of-oil, the casing is essentially oil-free, and heat exchange within the casing primarily occurs through convective heat transfer with the air and heat conduction and convection from the outer casing walls. The MRF model was used to simulate and calculate the internal temperature distribution and convective heat transfer coefficient of the intermediate reduction gear during the loss-of-oil process. The calculation model is as follows: Figure 7 As shown.

[0114] Figure 8 The internal temperature distribution of the casing, calculated by CFD simulation, shows that the highest temperature occurs at the gear meshing surface, at approximately 63°C. Figure 9For the air flow chart in the gearbox, the gas near the tooth surface is affected by the high-speed rotation of the gear, and the gas flow from the driven wheel end surface carries away the heat of the tooth surface, and contacts the outside air at the air outlet hole to realize heat dissipation. The convective heat transfer coefficient between the surface of each structure and the air at different temperatures is shown in the table. Figure 10

[0115] S104, according to the thermal nodes inside the intermediate reducer and the corresponding convective heat transfer coefficient and the heat transfer relationship of the thermal nodes inside the intermediate reducer, a transient thermal model of the intermediate reducer is established, and then a thermal balance equation is constructed;

[0116] S104 specifically includes:

[0117] In the intermediate reduction of the helicopter, the heat generated by the friction of the gear and the bearing will not only be convective heat transfer, but also be thermal conduction between the transmission shaft and the gearbox wall. Generally, the thermal resistance of heat conduction is divided into plane heat conduction and cylindrical heat conduction, wherein the thermal resistance of plane heat conduction is:

[0118]

[0119] In the formula: L t is the length in the direction of heat transfer, m; λ is the thermal conductivity, W / (m·K); A t is the heat conduction area, m 2 .

[0120] The thermal resistance of cylindrical heat conduction is:

[0121]

[0122] In the formula: r1, r2 are the diameters of the inner and outer walls of the cylinder, m; L s is the axial length perpendicular to the direction of heat flow, m; λ is the thermal conductivity, W / (m·K).

[0123] The thermal resistance of cylindrical heat conduction is:

[0124]

[0125] Where: d is the diameter of the cylinder, m; α is the convective heat transfer coefficient, W / (m 2 ·K).

[0126] The temperature field changes sharply with time under the condition of heavy oil loss, so a transient thermal analysis model of the intermediate reduction is needed to analyze the thermal friction dynamics during oil loss. The basic equation of the transient thermal model is:

[0127]

[0128] In the formula: q i , ρ i , C i , V​i and T i represent the net heat flow, material density, specific heat, volume and temperature at node i, respectively; t is time; dT i / dt represents the temperature rise rate at node i.

[0129] For the solution of transient temperature field, the equation of transient thermal model is obtained according to the law of conservation of energy:

[0130]

[0131] where T is the average temperature of the node, R is the thermal resistance, Q is the heat flowing into the node, i, j, k, l are the numbers of the nodes, c, v represent the heat conduction and heat exchange, R icj is the thermal resistance of heat conduction and heat exchange from node i to node j, C represents heat conduction, R ivk is the thermal resistance of convective heat exchange from node i to node j.

[0132] The thermal node model of the helicopter reduction is established, as shown in Figure 11 The thermal node numbers are numbered in the order from the input shaft to the output shaft, Figure 12 The connection relationship between the nodes is established according to the heat transfer relationship in the system, wherein the flanges of the input shaft and the output shaft, the gear box and the external air are in convective heat exchange, the thin-walled input shaft, the output shaft, the web plate of the spiral bevel gear and the tooth surface of the spiral bevel gear are in convective heat exchange with air; at the same time, heat is generated due to gear meshing, and the gear also transmits heat to the transmission shaft and the bearing through the web plate, and the positions and symbols of the internal thermal nodes of the reduction are determined according to Table 1, and the names of the heat sources are determined according to Table 2.

[0133] Table 1

[0134]

[0135]

[0136] Table 2

[0137]

[0138]

[0139] According to Figure 12 The thermal balance equation set of the reduction is listed as:

[0140] T1:

[0141] T2:

[0142] T3:

[0143] T4:

[0144] T5:

[0145] T6:

[0146] T7:

[0147] T8:

[0148] T9:

[0149] T10:

[0150] T11:

[0151] T12:

[0152] T13:

[0153] T14:

[0154] T15:

[0155] T16:

[0156] T17:

[0157] T18:

[0158] T19:

[0159] T20:

[0160] T21:

[0161] T22:

[0162] T23:

[0163] Ta:

[0164] S105, coupling the nonlinear friction dynamics model, the time-varying friction coefficient of the gear surface in the oil loss process and the heat balance equation to determine the intermediate reduction heat friction dynamics coupling characteristics; the intermediate reduction heat friction dynamics coupling characteristics include: gear surface temperature rise, gear heat source, bearing heat source, friction coefficient and area distribution coefficient, adsorbed lubrication and dry friction coefficient and dynamics characteristics.

[0165] When the helicopter intermediate reducer is in splash lubrication, the gear surface of each structure is fully lubricated, and the temperature is about 90℃. During the several minutes from the beginning of the loss of lubricating oil in the gear box to the complete loss, the gear surface is still mainly lubricated in the form of liquid film lubrication; after the oil is completely consumed, the temperature of each node is calculated by the heavy oil loss lubrication coefficient calculation method proposed in the patent. Assuming that the helicopter intermediate reducer can still run for 30 minutes up and down, the temperature of each thermal node of the helicopter intermediate reducer in the heavy oil loss lubrication state is rapidly rising, as shown in Figure 13 and Figure 14 However, due to the large temperature difference between the gas in the gear box and the gear surface, the heat dissipation is accelerated, resulting in a slower temperature rise.

[0166] The transient heat production of the gear surface heat source calculated by the coupling model changes all the time due to the influence of the vibration and impact of the transmission system, so in order to reduce the calculation cost, different time scales are used to calculate the dynamics model and the transient heat model. The time step of the dynamics model in the simulation program is 2.4x10 -5 s, and the time step of the transient heat model is 0.01s. Figure 15 and Figure 16 The gear and bearing heat source in the dynamics model and the transient heat model. Due to the many nonlinear factors in the system, the heat production in the coupling model is greatly affected by the system vibration, so the average value of the heat production is taken to observe the trend of the heat production. The gear and bearing heat production in the system increases obviously, and rises with the increase of the friction coefficient and other factors.

[0167] Due to the complexity of the spiral bevel gear transmission system and the difficulty and limitations of the analytical method, numerical methods are usually used to analyze the spiral bevel gear transmission system. Figure 17 The change trend of the friction coefficient and the area distribution coefficient in the entire oil loss process, the friction coefficient fluctuates between 0.1 and 0.6, and the proportion of heavy oil loss lubrication area gradually increases with the deepening of the oil loss lubrication degree. Figure 18 The change of the adsorbed film lubrication friction coefficient and the heavy oil loss lubrication coefficient in a certain period of time, wherein the adsorbed film lubrication friction coefficient decreases with the increase of the gear surface load, because the number of adsorbed film layers composed of polar molecules decreases with the increase of the load, and the friction coefficient of the heavy oil loss lubrication area increases with the increase of the load, which leads to the increase of the number of rough peak contacts.

[0168] Figure 19 For the vibration displacement and speed change of the driving wheel in the x-axis direction, in the nonlinear dynamics model, the calculation result of the vibration displacement is relatively high in accuracy under a small time step; Figure 20 For the change of the shaft center trajectory with the deepening of the lubrication loss, since the friction coefficient gradually increases with the temperature rise, the friction force generated by the gear contact surface is excited to be larger, and the degree of the shaft center trajectory deviation is larger.

[0169] The application establishes a dynamic heat source calculation method for gears and bearings; a time-varying convection heat transfer coefficient in a heavy oil loss process is calculated by using a multi-reference frame method, a transient thermal network model is established, and a thermal calculation model is provided for the thermal, friction and dynamics coupling research of the heavy oil loss.

[0170] The application provides a combination method of the adsorption film lubrication friction coefficient and the dry friction area friction coefficient under the heavy oil loss lubrication condition, and is combined with a nonlinear friction dynamics model to obtain the thermal and dynamics characteristics of the heavy oil loss state, and it is found that although the convection heat transfer of the air in the gearbox is intensified, it still maintains an increasing trend.

[0171] As another specific embodiment, the helicopter intermediate reduction heat friction dynamics determination system under the heavy oil loss state provided by the application comprises:

[0172] The friction dynamics model establishment module is used for combining the finite element node method with the lumped mass method to establish a nonlinear friction dynamics model of the intermediate reduction gear; the intermediate reduction gear comprises an arc tooth bevel gear, a tail horizontal shaft, a tail inclined shaft, a bearing and a casing;

[0173] The tooth surface time-varying friction coefficient establishment module is used for dividing the tooth surface according to the heavy oil loss state; the tooth surface time-varying friction coefficient in the oil loss process is established according to the division result; the division result comprises an adsorption film lubrication area and a dry friction area between the tooth surfaces;

[0174] The convection heat transfer coefficient determination module is used for simulating and calculating the convection heat transfer coefficient inside the intermediate reduction gear by using the CFD method;

[0175] The thermal balance equation construction module is used for establishing a transient thermal model of the intermediate reduction gear according to the thermal nodes inside the intermediate reduction gear, the corresponding convection heat transfer coefficient and the heat transfer relationship of the thermal nodes inside the intermediate reduction gear, and further constructing the thermal balance equation;

[0176] The intermediate and reduced heat friction dynamics coupling characteristic determination module is configured to couple a non-linear friction dynamics model, a time-varying friction coefficient of a gear surface in an oil loss process and a heat balance equation to determine intermediate and reduced heat friction dynamics coupling characteristics; the intermediate and reduced heat friction dynamics coupling characteristics include gear surface temperature rise, gear heat source, bearing heat source, friction coefficient and area distribution coefficient, adsorbed lubrication and dry friction coefficient and dynamics characteristics.

[0177] In order to perform the method corresponding to the above-mentioned embodiment one, to realize the corresponding function and technical effect, the application also provides a helicopter intermediate and reduced heat friction dynamics determination system under severe oil loss state, comprising: at least one processor, at least one memory and computer program instructions stored in the memory, when the computer program instructions are executed by the processor, the method is realized.

[0178] Based on the above description, the technical scheme of the application or the part of the prior art that contributes essentially or the part of the technical scheme can be embodied in the form of a software product, which is stored in a storage medium and includes instructions to make a computer device (which can be a personal computer, a server or a network device, etc.) execute all or part of the steps of the method of each embodiment of the application. The aforementioned computer storage medium includes: U disk, mobile hard disk, read-only memory, random access memory, magnetic disk or optical disk and various program code storage media.

[0179] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method part.

[0180] The principles and implementation modes of the application are described by using specific examples in this paper, and the above embodiment description is only used to help understand the method of the application and its core idea; at the same time, for those skilled in the art, according to the idea of the application, the specific implementation mode and application range will be changed. In view of the above, the content of the specification should not be understood as a limitation of the application.

Claims

1. A method for determining the heat-reducing friction dynamics of a helicopter under severe oil loss conditions, characterized in that, include: A nonlinear frictional dynamics model of the intermediate reducer is established by combining the finite element nodal method with the lumped mass method. The intermediate reducer includes: an arc bevel gear, a tail horizontal shaft, a tail helical shaft, bearings, and a housing; The tooth surface is divided according to the severe oil loss state; the time-varying friction coefficient of the tooth surface during the oil loss process is established based on the division results; the division results include: the adsorption film lubrication region and the dry friction region between the tooth surfaces; The convective heat transfer coefficient inside the intermediate reducer was calculated using CFD simulation. Based on the hot nodes inside the intermediate reducer, the corresponding convective heat transfer coefficients, and the heat transfer relationship of the hot nodes inside the intermediate reducer, a transient thermal model of the intermediate reducer is established, and then a heat balance equation is constructed. The nonlinear tribodynamic model, the time-varying friction coefficient of the tooth surface during the oil loss process, and the thermal balance equation are coupled to determine the intermediate-heat-reducing tribodynamic coupling characteristics. The intermediate-heat-reducing tribodynamic coupling characteristics include: tooth surface temperature rise, gear heat source, bearing heat source, friction coefficient and area distribution coefficient, adsorption lubrication and dry friction coefficient, and dynamic characteristics. The process of dividing the tooth surface according to the severe oil loss state and establishing the time-varying friction coefficient of the tooth surface during the oil loss process based on the division results specifically includes: Using formula μ s = α f d + (1- α ) f a Determine the time-varying friction coefficient of the tooth surface during the oil loss process; in, μ s The time-varying friction coefficient of the tooth surface during the oil loss process. f d The coefficient of friction in the dry friction region; f a The friction coefficient of the adsorption film region is . α This represents the area ratio of the dry friction region.

2. The method for determining the heat-reducing friction dynamics of a helicopter under severe oil loss conditions according to claim 1, characterized in that, The method of combining the finite element nodal method with the lumped mass method to establish a nonlinear frictional dynamics model for the intermediate reducer specifically includes: Using formula Determine the nonlinear friction dynamics model of the intermediate reducer; in, M The system quality matrix, C Here is the system damping matrix. K Here is the system stiffness matrix. x ( t ) represents the column vector of all nodal displacements. F The force matrix, t For time, for x ( t The derivative of ) for x ( t The second derivative of ).

3. The method for determining the heat-reducing friction dynamics of a helicopter under severe oil loss conditions according to claim 2, characterized in that, The nonlinear tribodynamic model of the intermediate reducer includes: a tribodynamic model of the gear meshing unit; the tribodynamic model of the gear meshing unit is: ； in, m p , m g The mass of the driving and driven wheels; c px , c py , c pz , c gx , c gy , c gz Damping of the meshing between the master and driven wheels; k px , k py , k pz , k gx , k gy , k gz The meshing stiffness of the driving and driven gears; I px , I py , J p , I gx , I gy , J g master and slave wheels x , y , z Moment of inertia in the direction; Ω p Ω g The rotational speed of the master and driven wheels; λ px , λ py , λ pz , λ gx , λ gy , λ gz The lever arm at the meshing point of the driving and driven wheels; F n For dynamic meshing force, F f Friction; T ps , T gs The resistance torque of the driving and driven wheels; θ p , θ g Rotation angle of the master and driven wheels; x p , x g master and slave wheels x Displacement in direction; y p , y g master and slave wheels y Displacement in direction; z p , z g master and slave wheels z Displacement in direction.

4. The method for determining the heat-reducing friction dynamics of a helicopter under severe oil loss conditions according to claim 1, characterized in that, The transient thermal model of the intermediate reducer is established based on the hot nodes inside the intermediate reducer, the corresponding convective heat transfer coefficients, and the heat transfer relationships of the hot nodes inside the intermediate reducer. This is followed by the construction of a heat balance equation, specifically including: Using formula Determine the transient thermal model of the intermediate reducer; in, T The node average temperature R For thermal resistance, Q For the heat flowing into the node, i , j , k For the node number, c , v This indicates heat conduction and heat transfer, and convection. Let be the thermal resistance for heat transfer from node i to node j. Let be the thermal resistance of convective heat transfer from node i to node j.

5. A system for determining the thermal friction dynamics of a helicopter under severe fuel loss conditions, used to implement the method for determining the thermal friction dynamics of a helicopter under severe fuel loss conditions as described in any one of claims 1-4, characterized in that, include: The friction dynamics model building module is used to combine the finite element nodal method with the lumped mass method to build a nonlinear friction dynamics model of the intermediate reducer. The intermediate reducer includes: an arc bevel gear, a tail horizontal shaft, a tail helical shaft, bearings, and a housing; A tooth surface time-varying friction coefficient establishment module is used to divide the tooth surface according to the severe oil loss state; and to establish the tooth surface time-varying friction coefficient during the oil loss process based on the division results; the division results include: the tooth surface adsorption film lubrication region and the dry friction region; The convective heat transfer coefficient determination module is used to simulate and calculate the convective heat transfer coefficient inside the intermediate reducer using CFD methods. The heat balance equation construction module is used to establish a transient thermal model of the intermediate reducer based on the hot nodes inside the intermediate reducer, the corresponding convective heat transfer coefficients, and the heat transfer relationship of the hot nodes inside the intermediate reducer, and then construct the heat balance equation. The intermediate-heat-reducing friction dynamics coupling characteristic determination module is used to couple the nonlinear friction dynamics model, the time-varying friction coefficient of the tooth surface during the oil loss process, and the thermal balance equation to determine the intermediate-heat-reducing friction dynamics coupling characteristics. The intermediate-heat-reducing friction dynamics coupling characteristics include: tooth surface temperature rise, gear heat source, bearing heat source, friction coefficient and area distribution coefficient, adsorption lubrication and dry friction coefficient, and dynamic characteristics.

6. A system for determining the heat-reducing friction dynamics of a helicopter under severe oil loss conditions, characterized in that, include: The system comprises at least one processor, at least one memory, and computer program instructions stored in the memory, which, when executed by the processor, implement a method for determining the thermal friction dynamics of a helicopter under severe oil loss conditions as described in any one of claims 1-4.

7. A storage medium storing computer program instructions thereon, characterized in that, When the computer program instructions are executed by the processor, a method for determining the heat-reducing friction dynamics of a helicopter under severe oil loss conditions as described in any one of claims 1-4 is implemented.

Images