Bearing transient temperature field calculation method considering circulating flow of lubricating oil

Abstract

The invention discloses a bearing transient temperature field calculation method considering lubricating oil circulation flow, and relates to the field of bearing temperature field simulation. An original thermal grid model simplifies lubricating oil and a lubricating system, so that the model obviously underestimates the thermal inertia of a bearing system, and the accuracy of temperature field calculation is influenced. The method comprises the following steps of: 1, forming a bearing lubricating system by an oil tank, a bearing and an oil collecting device, marking each temperature node on the bearing lubricating system, and establishing a bearing transient thermal network equation set according to each temperature node and heat exchange generated by circulating flow of lubricating oil in the bearing lubricating system; and 2, solving the bearing transient thermal network equation set by using a fourth-order Runge-Kutta method, obtaining the temperature of each node, and generating a bearing transient temperature field. The method is used for obtaining the transient temperature field of the bearing.

Description

Technical Field

[0001] This invention relates to the field of bearing temperature field simulation. Background Technology

[0002] The thermal network model (thermal network equations) is a method that divides a complex structure into multiple nodes and establishes a temperature field calculation model by analyzing the heat transfer resistance and energy exchange between the nodes. This method can simplify a complex temperature field into a grid composed of nodes and thermal resistances, making it very suitable for systems such as bearings that consist of multiple components. However, the original model still has the following shortcomings:

[0003] 1. Unable to reflect dynamic changes in lubricating oil temperature.

[0004] Traditional thermal mesh models treat lubricating oil as a constant temperature boundary condition, existing only as a passive "cooling source." Regardless of operating conditions, the lubricating oil temperature remains constant, making it impossible to simulate the dynamic changes in lubricating oil temperature.

[0005] 2. Unable to accurately describe the heat dissipation capacity of the lubricating oil.

[0006] After heat exchange occurs between the lubricating oil and the bearing, the temperature difference between them decreases, and the heat dissipation capacity declines. Traditional models will always maintain an idealized maximum temperature difference, thus continuously overestimating the heat dissipation capacity of the lubricating oil.

[0007] 3. It cannot simulate the cooling effect of an external cooling system on the lubricating oil.

[0008] Traditional thermal mesh models neglect the circulation of lubricating oil in the bearing lubrication system, and the heat dissipation of the lubricating oil tank and oil pipeline is ignored, making it completely unable to simulate the influence of the external cooling system on the temperature field of the bearing system.

[0009] 4. Underestimation of the thermal inertia of the bearing system

[0010] The original model's heat capacity was concentrated only on the fixed parts of the bearing system (inner ring, outer ring, rolling elements, cage, spindle, bearing housing, etc.), neglecting the heat capacity of the lubricating oil. Under the same heat generation, the lack of lubricating oil heat capacity makes the bearing system more easily heated to higher temperatures. Therefore, the original thermal mesh model underestimated the thermal inertia of the bearing system, resulting in higher transient temperature rises for various bearing components and a shorter time required for the system to reach a stable temperature. It failed to simulate the actual situation of a "slow temperature rise due to the presence of a large amount of lubricating oil."

[0011] In summary, the simplification of lubricating oil and lubrication system in the original thermal mesh model leads to a significant underestimation of the thermal inertia of the bearing system and inaccurate calculation of the system's heat dissipation rate, thus affecting the accuracy of temperature field calculations. Summary of the Invention

[0012] The purpose of this invention is to address the problem that the simplification of lubricating oil and lubrication system in the original thermal mesh model leads to a significant underestimation of the thermal inertia of the bearing system, thereby affecting the accuracy of temperature field calculation. This invention proposes a method for calculating the transient temperature field of bearings that considers the circulating flow of lubricating oil.

[0013] A method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil, the method comprising the following:

[0014] Step 1: The bearing lubrication system consists of an oil tank, bearings, and an oil collection device. Each temperature node is marked on the bearing lubrication system. Based on each temperature node and the heat exchange generated by the circulation of lubricating oil in the bearing lubrication system, a set of transient heat network equations for the bearing is established.

[0015] Step 2: Solve the bearing transient thermal network equations using the fourth-order Runge-Kutta method to obtain the temperature of each node and generate the bearing transient temperature field.

[0016] Preferably, in step 1, the bearing transient thermal network equations are as follows:

[0017] ,

[0018] In the formula, For time, This refers to the temperature of the bearing outer ring. The oil inlet temperature, The temperature of the steel ball. This refers to the temperature of the bearing inner ring. The thermal resistance between the bearing outer ring and the lubricating oil. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. This refers to the thermal resistance between the bearing inner ring and the lubricating oil. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. For lubricating oil node density, The specific heat capacity of the lubricating oil node. This refers to the lubricating oil outlet temperature point. The total volume of lubricating oil entering the bearing cavity, The total thermal resistance for heat dissipation of the lubricating oil outside the bearing cavity. This refers to the volume of lubricating oil in the tank. For ambient temperature, The thermal resistance between the main shaft and the air. The thermal resistance between the bearing inner ring and the spindle. For bearing housing node density, The specific heat capacity of the bearing housing node. The effective volume of the bearing housing node. Main spindle temperature, This is the heat generated by the friction between the steel balls and the inner ring of the bearing. The thermal resistance of the rolling element is the thermal conductivity. This refers to the thermal resistance between the inner ring of the bearing and the steel balls. This refers to the thermal resistance between the bearing inner ring and the lubricating oil. This refers to the node density of the bearing outer ring. , For lubricating oil temperature, This refers to the specific heat capacity of the bearing outer ring. This represents the effective volume of the bearing outer ring. This is the heat generated by the friction between the steel balls and the outer ring of the bearing. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. The thermal resistance between the bearing outer ring and the steel balls. For the density of steel ball nodes, The specific heat capacity of the steel ball joint. For the effective volume of the steel ball node, The thermal resistance between the bearing housing and the air. The thermal resistance between the bearing outer ring and the bearing housing. This refers to the node density of the bearing inner ring. This refers to the specific heat capacity of the bearing inner ring joint. This represents the effective volume of the bearing inner ring node. Main axis node density, The specific heat capacity of the main axis node. The effective volume of the main axis node.

[0019] Preferably, the thermal conductivity and thermal resistance of the rolling element for:

[0020] ,

[0021] In the formula, λ b D is the thermal conductivity coefficient of the sphere; w The diameter of the rolling element.

[0022] Preferably, the thermal resistance between the bearing inner ring and the steel balls is... for:

[0023] ,

[0024] In the formula, The width of the inner circle. The diameter of the inner channel. The inner diameter of the bearing. The thermal conductivity coefficient of the inner ring;

[0025] Thermal resistance between the bearing outer ring and the steel balls for:

[0026] ,

[0027] In the formula, The outer diameter of the bearing. The diameter of the outer channel. The thermal conductivity coefficient of the outer ring is... This refers to the width of the outer ring.

[0028] Preferably, the thermal resistance between the bearing housing and the air is... for:

[0029] ,

[0030] In the formula, , , and All are intermediate variables. , , , , The radial thermal resistance of the bearing housing, The outer diameter of the bearing housing. The thermal conductivity coefficient of the bearing housing. The circumferential surface thermal resistance of the bearing housing is the thermal resistance for heat convection. This is the thermal convection coefficient between the bearing housing and the air. The characteristic length of axial heat conduction of the bearing housing. The axial thermal resistance of the bearing housing, The characteristic length of axial thermal conduction of the outer ring. The thermal resistance of the bearing housing end face for thermal convection.

[0031] Thermal resistance between the bearing outer ring and the bearing housing for:

[0032] .

[0033] Preferably, the thermal resistance between the spindle and the air is... for:

[0034] ,

[0035] In the formula, The thermal resistance of the main spindle axial thermal conduction. The thermal resistance of the spindle end face for heat convection. The thermal resistance between the bearing inner ring and the spindle. , , , The characteristic length of axial heat conduction of the main shaft. The thermal conductivity coefficient of the main shaft The inner diameter of the bearing. This refers to the width of the bearing inner ring. The thermal convection coefficient between the main shaft and the air. , This refers to the bearing speed.

[0036] Preferably, the thermal resistance between the bearing outer ring and the lubricating oil is... for:

[0037] ,

[0038] In the formula, The combined convective heat transfer coefficient for two-phase flow. The diameter of the outer channel. , and This is the volume correction factor. The gas-to-air reciprocating heat transfer coefficient is... The oil relative heat transfer coefficient is... , This refers to the kinematic viscosity of the lubricating oil. The bearing pitch circle diameter, The thermal conductivity of the lubricating oil. The Prandtl number of the lubricating oil fluid. , The specific heat capacity of lubricating oil, The dynamic viscosity of the lubricating oil. The thermal conductivity of the lubricating oil. , , , , For the amount of lubricating oil supplied, The diameter of the rolling element;

[0039] Thermal resistance between the bearing inner ring and the lubricating oil for:

[0040] ,

[0041] In the formula, The diameter of the inner channel.

[0042] Thermal resistance between steel ball and lubricating oil for:

[0043] .

[0044] Preferably, the total thermal resistance of the lubricating oil outside the bearing cavity for heat dissipation is... for:

[0045] ,

[0046] In the formula, The total thermal resistance for heat dissipation in the fuel tank. The total thermal resistance of the oil pipeline for heat dissipation. , For radial thermal resistance of the pipe, The thermal resistance is due to the convective heat transfer between the lubricating oil and the inner wall of the pipe. The thermal resistance of the pipe's outer wall for convective heat transfer with air. , , , The outer diameter of the pipe. The inner diameter of the pipe. The thermal conductivity coefficient of the pipe, For the length of the pipe, The coefficient of heat transfer between the lubricating oil and the inner wall of the pipe is the convective heat transfer coefficient. The heat transfer coefficient between the outer wall of the pipe and the air during convection. , This refers to the surface area of ​​the fuel tank. The coefficient of heat transfer between the lubricating oil and the inner wall of the pipe is the convective heat transfer coefficient. The thermal conductivity coefficient of the lubricating oil, The heat transfer coefficient between the outer wall of the pipe and the air is convective.

[0047] The beneficial effects of this invention are:

[0048] This invention sets various temperature points, including the bearing outer ring temperature, oil inlet temperature, steel ball temperature, bearing inner ring temperature, lubricating oil outlet temperature, and ambient temperature. It establishes a transient thermal network equation set for the bearing, considering the heat exchange during the circulation of lubricating oil in the oil tank, oil pipe, and bearing cavity. Compared to existing thermal grid models, this invention can dynamically calculate the real-time changes in lubricating oil inlet and outlet temperatures, more accurately describing the heat dissipation capacity of the lubricating oil and achieving dynamic thermal coupling between the bearing system and the lubricating oil. It can also describe the heat exchange during the circulation of lubricating oil in the bearing lubrication system, simulating heat dissipation outside the bearing cavity or cooling by an external cooling system. For the first time, it incorporates the total amount of lubricating oil in the circulation system into the bearing system temperature field calculation. This more accurately describes the thermal inertia of the bearing system, improving the prediction accuracy and reliability of the model under transient conditions.

[0049] The heat dissipation of the entire bearing lubrication system in this invention is achieved through air, and the ambient temperature is the air temperature. All heat flowing to the ambient temperature is heat dissipation. Therefore, by setting multiple temperatures and calculating the bearing temperature field, the heat dissipation of the bearing can be accurately understood. Attached Figure Description

[0050] Figure 1 A flowchart of a method for calculating the transient temperature field of a bearing that takes into account the circulation of lubricating oil;

[0051] Figure 2 A schematic diagram showing the division of heat transfer nodes in a double-half inner ring ball bearing.

[0052] Figure 3 Transient thermal network diagram of a double-inner-ring ball bearing;

[0053] Figure 4 The graph shows the temperature changes of the bearing and lubricating oil over time (0~1000s).

[0054] Figure 5 The graph shows the temperature changes of the bearing and lubricating oil over time (0~6000s).

[0055] Figure 6 The curves showing the change of bearing outer ring temperature over time under different oil supply rates;

[0056] Figure 7 The graph shows the bearing temperature change over time for different total volumes of lubricating oil.

[0057] Figure 8 The graph shows the change of lubricating oil inlet temperature over time for different total volumes of lubricating oil.

[0058] Figure 9 This is a graph showing the change in lubricating oil outlet temperature over time for different total volumes of lubricating oil. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0061] Example:

[0062] A method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil, the method comprising the following:

[0063] Step 1: The bearing lubrication system consists of an oil tank, bearings, and an oil collection device. Each temperature node is marked on the bearing lubrication system. Based on each temperature node and the heat exchange generated by the circulation of lubricating oil in the bearing lubrication system, a set of transient heat network equations for the bearing is established.

[0064] Step 2: Solve the bearing transient thermal network equations using the fourth-order Runge-Kutta method to obtain the temperature of each node and generate the bearing transient temperature field.

[0065] Further specifying, in step 1, the bearing transient thermal network equations are:

[0066] ,

[0067] In the formula, For time, This refers to the temperature of the bearing outer ring. The oil inlet temperature, The temperature of the steel ball. This refers to the temperature of the bearing inner ring. The thermal resistance between the bearing outer ring and the lubricating oil. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. This refers to the thermal resistance between the bearing inner ring and the lubricating oil. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. For lubricating oil node density, The specific heat capacity of the lubricating oil node. This refers to the lubricating oil outlet temperature point. The total volume of lubricating oil entering the bearing cavity, The total thermal resistance for heat dissipation of the lubricating oil outside the bearing cavity. This refers to the volume of lubricating oil in the tank. For ambient temperature, The thermal resistance between the main shaft and the air. The thermal resistance between the bearing inner ring and the spindle. For bearing housing node density, The specific heat capacity of the bearing housing node. The effective volume of the bearing housing node. Main spindle temperature, This is the heat generated by the friction between the steel balls and the inner ring of the bearing. The thermal resistance of the rolling element is the thermal conductivity. This refers to the thermal resistance between the inner ring of the bearing and the steel balls. This refers to the thermal resistance between the bearing inner ring and the lubricating oil. This refers to the node density of the bearing outer ring. , For lubricating oil temperature, This refers to the specific heat capacity of the bearing outer ring. This represents the effective volume of the bearing outer ring. This is the heat generated by the friction between the steel balls and the outer ring of the bearing. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. The thermal resistance between the bearing outer ring and the steel balls. For the density of steel ball nodes, The specific heat capacity of the steel ball joint. For the effective volume of the steel ball node, The thermal resistance between the bearing housing and the air. The thermal resistance between the bearing outer ring and the bearing housing. This refers to the node density of the bearing inner ring. This refers to the specific heat capacity of the bearing inner ring joint. This represents the effective volume of the bearing inner ring node. Main axis node density, The specific heat capacity of the main axis node. The effective volume of the main axis node.

[0068] Specifically, the principle behind establishing the transient thermal network equations for bearings with circulating lubricating oil is as follows:

[0069] The core principle of the steady-state thermal grid method is that the heat flow through each node in the system is conserved, the heat entering and leaving each node is equal, and the temperature remains stable. To more accurately simulate the temperature rise during bearing operation, the internal energy variable of each bearing component is introduced, establishing the temperature field calculation equation for the transient thermal grid method. The heat entering and leaving each node of the bearing is not equal; excess heat is converted into the internal energy of that node, manifesting as a change in node temperature. The basic formula is shown below:

[0070] (1)

[0071] In the formula, φ is the heat flowing into the node; ρ is the node density; c is the specific heat capacity; V is the effective volume of the node; and dT / dt is the temperature rise rate at the node.

[0072] To improve analytical efficiency and simplify the analytical equations, the following assumptions are made:

[0073] (1) The frictional heat generated by the steel ball and the raceway is evenly distributed on the steel ball and the raceway;

[0074] (2) The temperature change of each component of the bearing is uniform, and the uneven temperature distribution due to structural differences is ignored. In this case, the temperature nodes of each component can be set at any position inside the component;

[0075] Based on the above assumptions, the heat transfer nodes of the double-half inner ring ball bearing are divided, as shown in the schematic diagram. Figure 1 As shown. When dividing the nodes, the circulation of lubricating oil throughout the entire lubrication system is considered, and the lubricating oil in the tank is included in the thermal mesh for calculation. In the figure, T0 is the ambient temperature, T... h T represents the bearing housing temperature. e T represents the outer ring temperature of the bearing. b T represents the temperature of the steel ball. i T represents the temperature of the bearing inner ring. zspindle temperature, T r0 T represents the oil inlet temperature. r1 For oil outlet temperature, O bi O be These are the contact points between the steel ball and the inner and outer rings, respectively.

[0076] Based on the schematic diagram of the heat transfer nodes of the double-half inner ring ball bearing, a transient heat network heat transfer model of the double-half inner ring ball bearing is established, such as... Figure 2 As shown in the figure. H i With H e This refers to the heat generated by the friction between the steel balls and the inner and outer rings of the bearing. (T) e T b T i Node to T r1 Nodal heat transfer can simulate the absorption of heat by lubricating oil from the inner and outer rings and steel balls of the bearing within the bearing cavity. r1 Node to T r0 Heat transfer at nodes can simulate the mixing of high-temperature lubricating oil in the oil collection device with low-temperature lubricating oil in the oil tank.

[0077] Lubricating oil continuously enters the bearing cavity from the outside, so the heat absorption temperature of the lubricating oil remains constant at the inlet temperature, and the volume of lubricating oil absorbing heat increases continuously over time. When calculating the change in the internal energy of the lubricating oil, it is necessary to integrate the volume of lubricating oil entering the bearing. Therefore, the basic formula for the change in the internal energy of the lubricating oil in the bearing cavity is transformed from equation (1) to:

[0078] (2)

[0079] In the formula, The heat absorbed by the lubricating oil; ρ r c represents the node density. r V is the specific heat capacity. r1 This refers to the total volume of lubricating oil entering the bearing cavity.

[0080] The temperature of the lubricating oil inside the oil tank is the inlet temperature. Since the continuous temperature change of the lubricating oil inside the bearing cavity is difficult to simulate, it is simplified as a transient process. The lubricating oil temperature is represented by the inlet temperature T. r0 When the material enters the bearing cavity and absorbs heat within it, it is assumed that the temperature is constant (T). r0 (It remains constant only within the bearing cavity). At the instant the lubricating oil flows out of the bearing cavity, its temperature suddenly changes to T. r1 That is, the lubricating oil in the bearing cavity always maintains a temperature T r0 The absorbed heat acts on the lubricating oil the instant it flows out of the bearing, causing its temperature to rise from T. r0 Transform into T r1 Oil outlet temperature T r1The equilibrium equation for the node is shown in equation (3). In this equation, the left side represents the heat absorbed by the lubricating oil from the various parts of the bearing, and the right side describes the change in the internal energy of the lubricating oil using the temperature rise of the lubricating oil.

[0081] (3)

[0082] In the formula, R br R is the thermal resistance between the steel ball and the lubricating oil. er R is the thermal resistance between the bearing outer ring and the lubricating oil. ir This refers to the thermal resistance between the bearing inner ring and the lubricating oil.

[0083] The lubricating oil flowing out of the bearing cavity at temperature T r1 Entering the fuel tank, the temperature inside the tank is T. r0 The mixing of lubricating oils caused the lubricating oil temperature T in the oil tank to rise. r0 The elevation increases. During this process, node T... r1 and T r0 Heat transfer between them is accomplished through the mixing of lubricating oils at different temperatures. The lubricating oil flowing out of the bearing cavity is at its outlet temperature T. r1 It enters the oil collection device and is heated to temperature T in the oil tank. r0 The mixing of the lubricating oil and the lubricating oil causes the temperature of the lubricating oil in the oil tank to rise. Part of the heat absorbed by the lubricating oil in the bearing cavity is dissipated into the air through the oil pipes and the oil tank, while the remainder is completely converted into the internal energy of the lubricating oil in the tank. Therefore, the temperature is T. r1 The lubricating oil only appears at the lubricating oil outlet, T r1 There is no thermal resistance between it and other nodes. Oil inlet temperature T r0 The nodal equilibrium equations are:

[0084] (4)

[0085] In the formula, V r0 R represents the volume of lubricating oil in the tank. r0 The total thermal resistance for heat dissipation of lubricating oil outside the bearing cavity.

[0086] The transient heat transfer equations for each node of the other components of the double-half inner ring ball bearing are shown in equations (5-9). Equations (3-9) are the transient thermal grid equations for the double-half inner ring ball bearing. The temperatures of each node in the thermal grid model can be obtained by solving the differential equations using the fourth-order Runge-Kutta method.

[0087] (5) (6)

[0088] (7)

[0089] (8)

[0090] (9)

[0091] In the formula, the ambient temperature T0 is a known constant, which serves as the initial condition for solving the equation; ρ, c, and V are the nodal density, nodal specific heat capacity, and nodal effective volume, respectively; and the subscripts z, i, b, e, and h represent the bearing housing, bearing outer ring, steel ball, bearing inner ring, and spindle, respectively.

[0092] Formulas (1) to (2) are the basic principles, and formulas (3) to (9) are the bearing transient thermal network equations.

[0093] The thermal resistance of the bearing system is calculated below:

[0094] (1) Thermal resistance of rolling elements:

[0095] Thermal conduction and thermal resistance of rolling elements for:

[0096] ,

[0097] In the formula, λ b D is the thermal conductivity coefficient of the sphere; w The diameter of the rolling element.

[0098] (2) Thermal resistance of inner and outer rings:

[0099] Thermal resistance between the bearing inner ring and the steel balls for:

[0100] ,

[0101] In the formula, The width of the inner circle. The diameter of the inner channel. The inner diameter of the bearing. The thermal conductivity coefficient of the inner ring;

[0102] Thermal resistance between the bearing outer ring and the steel balls for:

[0103] ,

[0104] In the formula, The outer diameter of the bearing. The diameter of the outer channel. The thermal conductivity coefficient of the outer ring is... This refers to the width of the outer ring.

[0105] (3) Thermal resistance of bearing housing

[0106] The heat conduction of the bearing housing consists of radial heat conduction, axial heat conduction, and heat convection at the bearing housing end face. The calculation formulas are as follows:

[0107] Thermal resistance between bearing housing and air for:

[0108] ,

[0109] In the formula, , , and All are intermediate variables. , , , , The radial thermal resistance of the bearing housing, The outer diameter of the bearing housing. The thermal conductivity coefficient of the bearing housing. The circumferential surface thermal resistance of the bearing housing is the thermal resistance for heat convection. The coefficient of thermal convection between the bearing housing and the air is given. For angular contact ball bearings, it can be taken as... =9.7; The characteristic length of axial heat conduction of the bearing housing. The axial thermal resistance of the bearing housing, The characteristic length of axial thermal conduction of the outer ring. The thermal resistance of the bearing housing end face for thermal convection.

[0110] Thermal resistance between the bearing outer ring and the bearing housing for:

[0111] .

[0112] (4) Thermal resistance of the spindle:

[0113] The main heat transfer methods of the spindle are: radial heat conduction, axial heat conduction, and heat convection between the spindle end face and the air. The calculations are as follows:

[0114] Thermal resistance between spindle and air for:

[0115] ,

[0116] In the formula, The thermal resistance of the main spindle axial thermal conduction. The thermal resistance of the spindle end face for heat convection. The radial thermal resistance of the main shaft is the thermal resistance for thermal conduction. , , , The characteristic length of axial heat conduction of the main shaft. The thermal conductivity coefficient of the main shaft The inner diameter of the bearing. This refers to the width of the bearing inner ring. The thermal convection coefficient between the main shaft and the air. , This refers to the bearing speed.

[0117] (5) Convection thermal resistance between the bearing and the oil-gas two-phase flow:

[0118] The convective thermal resistance between the bearing and the oil-gas two-phase flow is calculated based on the separated flow model theory. The oil-gas two-phase flow is regarded as the superposition of independent oil and gas flows, and the comprehensive convective heat transfer coefficient of the two-phase flow is calculated through a volume correction factor.

[0119] ,

[0120] In the formula, The combined convective heat transfer coefficient for two-phase flow. and This is the volume correction factor. The gas-to-air flow heat transfer coefficient is 9.7, because the oil supply pipe of the double-half inner ring ball bearing only supplies lubricating oil, resulting in poor gas flow. The oil relative heat transfer coefficient is...

[0121] The convective heat transfer between components by the lubricating oil in rolling contact bearings can be divided into natural convection and forced convection. In this model, the convective heat transfer between the two-phase flow and the components is all forced convection, and its average coefficient of forced convection can be approximated as:

[0122] , This refers to the kinematic viscosity of the lubricating oil. The bearing pitch circle diameter, The thermal conductivity of the lubricating oil. The Prandtl number of the lubricating oil fluid. , The specific heat capacity of lubricating oil, The dynamic viscosity of the lubricating oil. The thermal conductivity of the lubricating oil. , , Lubricating oil supply rate, L / min. The diameter of the rolling element;

[0123] Aviation lubricating oil is used, and the oil temperature is [temperature value missing]. The formulas for calculating its specific heat capacity, density, and thermal conductivity are as follows:

[0124] ,

[0125] ,

[0126] ,

[0127] Thermal resistance between bearing outer ring and lubricating oil for:

[0128] ,

[0129] In the formula, The diameter of the outer channel.

[0130] Thermal resistance between the bearing inner ring and the lubricating oil for:

[0131] ,

[0132] In the formula, The diameter of the inner channel.

[0133] Thermal resistance between steel ball and lubricating oil for:

[0134] .

[0135] (6) Thermal resistance of lubricating oil outside the bearing cavity for heat dissipation:

[0136] Lubricating oil in the oil tank enters the bearing through the inlet pipe and returns to the oil tank through the outlet pipe. The lubricating oil transfers heat to the inner walls of the oil tank and pipes via convection. The inner walls of the oil tank and pipes then transfer heat to the outer walls of the oil tank and pipes via heat conduction, and subsequently, the heat is transferred to the air via convection. The total thermal resistance of the lubricating oil outside the bearing cavity is calculated by combining the thermal resistance of the pipes and the thermal resistance of the oil tank in parallel, using the following formula:

[0137] Total thermal resistance of lubricating oil outside the bearing cavity for heat dissipation for:

[0138] ,

[0139] In the formula, The total thermal resistance for heat dissipation in the fuel tank. The total thermal resistance of the oil pipeline for heat dissipation. , For radial thermal resistance of the pipe, The thermal resistance is due to the convective heat transfer between the lubricating oil and the inner wall of the pipe. The thermal resistance of the pipe's outer wall for convective heat transfer with air. , , , The outer diameter of the pipe. The inner diameter of the pipe. The thermal conductivity coefficient, For the length of the pipe, The coefficient of heat transfer between the lubricating oil and the inner wall of the pipe is the convective heat transfer coefficient. The heat transfer coefficient between the outer wall of the pipe and the air during convection. , This refers to the surface area of ​​the fuel tank. The coefficient of heat transfer between the lubricating oil and the inner wall of the pipe is the convective heat transfer coefficient. The thermal conductivity coefficient of the lubricating oil, The heat transfer coefficient between the outer wall of the pipe and the air is convective.

[0140] To verify the calculation method for the transient temperature field of bearings considering the circulation of lubricating oil, a certain type of double-inner-ring ball bearing was used as the research object for temperature field calculation. Some of the calculation results are presented here. Bearing parameters are shown in Table 1. Lubricating oil parameters are shown in Table 2.

[0141] Table 1 Bearing Parameters

[0142]

[0143] Table 2 Lubricating Oil Performance Parameters

[0144]

[0145] 1. Transient temperature rise characteristics of bearings

[0146] Since the transient temperature rise characteristics of bearings under different operating conditions are similar, only the simulation results of the transient temperature rise of bearings under the following operating conditions are shown: radial load 2000N, axial load 15000N, bearing inner ring speed 14000r / min, ambient temperature 26℃, oil supply 9L / min, and total amount of lubricating oil in the oil tank 120L.

[0147] Figure 4 and Figure 5 The graph shows the temperature changes of the bearing and lubricating oil over time. As can be seen from the graph, at the very beginning of the simulation, the rates of change of the steel ball temperature, the inner and outer ring temperatures of the bearing, and the lubricating oil outlet temperature are extremely high, while the rate of change of the lubricating oil inlet temperature (i.e., the temperature of the lubricating oil in the oil tank) is the lowest. This is due to two factors: First, in the thermal mesh method, the heat source of the bearing is located at the contact point between the steel ball and the inner and outer rings. The steel ball is closer to the heat source, while the lubricating oil in the oil tank is farther away. Therefore, after the heat is generated, it first acts on the steel ball and the inner and outer rings, and then spreads outwards. Second, in the transient thermal mesh theory, when absorbing the same amount of heat, the larger the nodal heat capacity, the smaller the temperature rise. The total amount of lubricating oil in the oil tank is 120L, and its heat capacity is much greater than that of the individual bearing components, therefore its temperature change rate is the lowest.

[0148] The calculation results show that the proposed transient temperature field calculation method can successfully simulate the phenomenon that the temperature of lubricating oil entering and exiting the oil gradually increases over time and eventually reaches a steady state.

[0149] 2. The effect of oil supply on the transient temperature rise of the bearing

[0150] The following set of operating conditions is used to demonstrate the calculation results of the bearing outer ring temperature under different oil supply rates using the bearing temperature field calculation method in this paper: radial load 2000N, ambient temperature 26℃, axial load 15000N, bearing inner ring speed 14000r / min, oil supply rate 3~15L / min, and total amount of lubricating oil in the oil tank 120L.

[0151] Figure 6 The graph shows the temperature variation of the bearing outer ring over time under different oil supply rates. As can be seen from the graph, the bearing outer ring temperature initially decreases and then increases with increasing oil supply rate, reaching its lowest point at a supply rate of 9 L / min. The highest temperature is observed at a supply rate of 3 L / min, likely due to poor heat dissipation when the oil supply is too low. However, when the oil supply rate exceeds 9 L / min, the bearing outer ring temperature increases with increasing oil supply rate. This is because the increased oil supply rate intensifies the agitation of the lubricating oil, leading to increased heat generation in the bearing.

[0152] The calculation results show that the proposed transient temperature field calculation method can successfully simulate the influence of oil supply on the bearing temperature field.

[0153] 3. The effect of the total volume of lubricating oil in the oil tank on the transient temperature rise of the bearing.

[0154] The following set of operating conditions demonstrates the bearing temperature field calculation results of the bearing outer ring temperature under different total lubricating oil volumes using the bearing temperature field calculation method in this paper: radial load 2000N, axial load 15000N, bearing speed 14000r / min, ambient temperature 26℃, oil supply 9L / min, and lubricating oil volume in the oil tank 40~140L.

[0155] Figures 7 to 9 The graph shows the temperature changes of the bearing and lubricating oil over time under different total volumes of lubricating oil. It can be seen from the graph that the total volume of lubricating oil in the oil tank has a certain regulating effect on the transient temperature rise of the bearing, but has little effect on the steady-state temperature rise of the bearing. Therefore, when designing a bearing lubrication system, increasing the total amount of lubricating oil circulating in the lubrication system helps to reduce the transient temperature rise of the bearing.

[0156] The calculation results show that the proposed transient temperature field calculation method successfully simulates the influence of the total amount of lubricating oil in the oil tank on the bearing temperature field.

[0157] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil, characterized in that, The method includes the following: Step 1: The bearing lubrication system consists of an oil tank, bearings, and an oil collection device. Each temperature node is marked on the bearing lubrication system. Based on each temperature node and the heat exchange generated by the circulation of lubricating oil in the bearing lubrication system, a set of transient heat network equations for the bearing is established. Step 2: Solve the bearing transient thermal network equations using the fourth-order Runge-Kutta method to obtain the temperature of each node and generate the bearing transient temperature field.

2. The method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil according to claim 1, characterized in that, In step 1, the bearing transient thermal network equations are as follows: ， In the formula, For time, This refers to the temperature of the bearing outer ring. The oil inlet temperature, The temperature of the steel ball. This refers to the temperature of the bearing inner ring. The thermal resistance between the bearing outer ring and the lubricating oil. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. This refers to the thermal resistance between the bearing inner ring and the lubricating oil. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. For lubricating oil node density, The specific heat capacity of the lubricating oil node. This refers to the lubricating oil outlet temperature point. The total volume of lubricating oil entering the bearing cavity, The total thermal resistance for heat dissipation of the lubricating oil outside the bearing cavity. This refers to the volume of lubricating oil in the tank. For ambient temperature, The thermal resistance between the main shaft and the air. The thermal resistance between the bearing inner ring and the spindle. For bearing housing node density, The specific heat capacity of the bearing housing node. The effective volume of the bearing housing node. Main spindle temperature, This is the heat generated by the friction between the steel balls and the inner ring of the bearing. The thermal resistance of the rolling element is the thermal conductivity. This refers to the thermal resistance between the inner ring of the bearing and the steel balls. This refers to the thermal resistance between the bearing inner ring and the lubricating oil. This refers to the node density of the bearing outer ring. , For lubricating oil temperature, This refers to the specific heat capacity of the bearing outer ring. This represents the effective volume of the bearing outer ring. This is the heat generated by the friction between the steel balls and the outer ring of the bearing. The thermal resistance between the steel ball and the lubricating oil is the heat transfer resistance. The thermal resistance between the bearing outer ring and the steel balls. For the density of steel ball nodes, The specific heat capacity of the steel ball joint. For the effective volume of the steel ball node, The thermal resistance between the bearing housing and the air. The thermal resistance between the bearing outer ring and the bearing housing. This refers to the node density of the bearing inner ring. This refers to the specific heat capacity of the bearing inner ring joint. This represents the effective volume of the bearing inner ring node. Main axis node density, The specific heat capacity of the main axis node. The effective volume of the main axis node.

3. The method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil according to claim 2, characterized in that, Thermal conduction and thermal resistance of rolling elements for: ， In the formula, λ b D is the thermal conductivity coefficient of the sphere; w The diameter of the rolling element.

4. A method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil, as described in claim 2 or 3, characterized in that, Thermal resistance between the bearing inner ring and the steel balls for: ， In the formula, The width of the inner circle. The diameter of the inner channel. The inner diameter of the bearing. The thermal conductivity coefficient of the inner ring; Thermal resistance between the bearing outer ring and the steel balls for: ， In the formula, The outer diameter of the bearing. The diameter of the outer channel. The thermal conductivity coefficient of the outer ring is... This refers to the width of the outer ring.

5. The method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil according to claim 4, characterized in that, Thermal resistance between bearing housing and air for: ， In the formula, , , and All are intermediate variables. , , , , The radial thermal resistance of the bearing housing, The outer diameter of the bearing housing. The thermal conductivity coefficient of the bearing housing. The circumferential surface thermal resistance of the bearing housing is the thermal resistance for heat convection. This is the thermal convection coefficient between the bearing housing and the air. The characteristic length of axial heat conduction of the bearing housing. The axial thermal resistance of the bearing housing, The characteristic length of axial thermal conduction of the outer ring. The thermal resistance of the bearing housing end face for thermal convection. Thermal resistance between the bearing outer ring and the bearing housing for: 。 6. The method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil according to claim 5, characterized in that, Thermal resistance between spindle and air for: ， In the formula, The thermal resistance of the main spindle axial thermal conduction. The thermal resistance of the spindle end face for heat convection. The thermal resistance between the bearing inner ring and the spindle. , , , The characteristic length of axial heat conduction of the main shaft. The thermal conductivity coefficient of the main shaft The inner diameter of the bearing. This refers to the width of the bearing inner ring. The thermal convection coefficient between the main shaft and the air. , This refers to the bearing speed.

7. The method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil according to claim 6, characterized in that, Thermal resistance between bearing outer ring and lubricating oil for: ， In the formula, The combined convective heat transfer coefficient for two-phase flow. The diameter of the outer channel. , and This is the volume correction factor. The gas-to-air reciprocating heat transfer coefficient is... The oil relative heat transfer coefficient is... , This refers to the kinematic viscosity of the lubricating oil. The bearing pitch circle diameter, The thermal conductivity of the lubricating oil. The Prandtl number of the lubricating oil fluid. , The specific heat capacity of lubricating oil, The dynamic viscosity of the lubricating oil. The thermal conductivity of the lubricating oil. , , , , For the amount of lubricating oil supplied, The diameter of the rolling element; Thermal resistance between the bearing inner ring and the lubricating oil for: ， In the formula, The diameter of the inner channel. Thermal resistance between steel ball and lubricating oil for: 。 8. The method for calculating the transient temperature field of a bearing considering the circulation of lubricating oil according to claim 7, characterized in that, Total thermal resistance of lubricating oil outside the bearing cavity for heat dissipation for: ， In the formula, The total thermal resistance for heat dissipation in the fuel tank. The total thermal resistance of the oil pipeline for heat dissipation. , For radial thermal resistance of the pipe, The thermal resistance is due to the convective heat transfer between the lubricating oil and the inner wall of the pipe. The thermal resistance of the pipe's outer wall for convective heat transfer with air. , , , The outer diameter of the pipe. The inner diameter of the pipe. The thermal conductivity coefficient of the pipe, For the length of the pipe, The coefficient of heat transfer between the lubricating oil and the inner wall of the pipe is the convective heat transfer coefficient. The heat transfer coefficient between the outer wall of the pipe and the air during convection. , This refers to the surface area of ​​the fuel tank. The coefficient of heat transfer between the lubricating oil and the inner wall of the pipe is the convective heat transfer coefficient. The thermal conductivity coefficient of the lubricating oil, The heat transfer coefficient between the outer wall of the pipe and the air is convective.

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