A high-end high-speed bearing transient temperature calculation method based on coupling of dynamics and CFD

Abstract

The application discloses a high-end high-speed bearing transient temperature calculation method based on coupling of dynamics and CFD. The method comprises the following steps: step 1: a bearing dynamics numerical solution model is established, and the relative sliding speed and tangential force between the rolling body and the inner and outer rings, the rolling body and the retainer and the retainer and the guide sleeve ring are obtained according to the bearing geometric parameters, material parameters and working condition parameters; the bearing dynamics model is established, and the internal flow and heat transfer analysis are combined, the uniform description of bearing internal friction heat generation, fluid heat transfer and structure response is realized, and the accuracy of the temperature field calculation is improved; meanwhile, the bearing system section is divided into dynamic temperature nodes, and a heat network model is constructed, the model complexity and the calculation cost are reduced under the premise of ensuring the calculation accuracy, and the reliability of the temperature prediction is improved by introducing the convective heat transfer coefficient and the oil stirring loss.

Description

Technical Field

[0001] This invention belongs to the field of thermal analysis and condition assessment technology of rotating machinery, specifically involving a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD. Background Technology

[0002] Bearings are key basic components in various rotating machinery and equipment. Their operating status directly affects the performance, stability and service life of the entire system. Under actual working conditions, a large amount of heat is generated inside the bearing due to contact friction, relative sliding and shearing of the lubricating medium, which causes the bearing temperature to rise and causes thermal expansion of components such as inner and outer rings, rolling elements and cages. This changes the internal clearance and load distribution of the bearing, further affecting the bearing's operating accuracy and service reliability. Therefore, accurate analysis of the temperature field during bearing operation is of great significance.

[0003] Existing methods for analyzing bearing temperature fields are mostly based on thermal network models, typically employing static temperature node partitioning, which fails to reflect the transient temperature changes during bearing rotation. In calculating frictional heat generation, empirical formulas or simplified models are often used, failing to adequately consider the relative sliding and contact state changes between contact pairs, resulting in insufficient accuracy in heat generation prediction. This is particularly problematic under high-speed oil-lubricated conditions, where churning losses increase significantly. Existing empirical formulas rely on parameters such as the oil-air ratio and are based on simplified assumptions, making it difficult to accurately describe the internal flow and heat transfer characteristics of the bearing, thus affecting the reliability of temperature calculation results. Furthermore, existing methods generally lack an effective coupling mechanism between dynamics and the temperature field, exhibiting poor adaptability under varying operating conditions and hindering the achievement of high-precision calculations of the bearing's transient temperature field. Summary of the Invention

[0004] Technical Problem: To overcome the shortcomings of the existing technology, this invention provides a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD. The technical problem solved by this invention is to address the problems in existing bearing temperature field analysis methods, such as the difficulty in dynamically calculating transient temperature, large errors in predicting frictional heat generation, inaccurate description of internal lubrication flow and heat transfer processes, and insufficient coupling between dynamics and temperature field. This allows for more accurate calculation of the internal temperature of the bearing and enables the calculation of the transient temperature field of the bearing system.

[0005] According to one aspect of this disclosure, a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD is provided, including the following steps: Step 1: Establish a numerical solution model for bearing dynamics. Solve the model based on the bearing's geometric parameters, material parameters, and operating parameters to obtain the relative sliding speeds and tangential forces between the rolling elements and the inner and outer rings, between the rolling elements and the cage, and between the cage and the guide ring. Step 2: Based on the relative sliding speed and tangential stress obtained in Step 1, calculate the frictional heat generated by each contact pair using the local heat generation method, and distribute the frictional heat generated to the inner ring, outer ring, rolling elements and cage based on the heat distribution relationship; Step 3: Establish a CFD simulation model of lubrication flow and heat transfer inside the bearing. The frictional heat generated in Step 2 is used as a heat source and loaded into the numerical model. The convective heat transfer coefficient distribution of the inner and outer rings, rolling elements and cage surfaces and the oil churning loss are calculated. Step 4: Divide the dynamic temperature nodes on the bearing system profile. Based on the frictional heat generation obtained in Step 2 and the convective heat transfer coefficient distribution and oil churning loss obtained in Step 3, construct the bearing temperature node network model and solve for the transient temperature of each node. Step 5: Based on the temperature results obtained in Step 4, calculate the thermal expansion of each component according to the material thermal expansion relationship; Step 6: Correct the bearing geometric parameters and contact characteristics based on the thermal expansion obtained in Step 5, and feed them back to the dynamic model in Step 1 for iterative calculation, thereby obtaining the temperature node distribution of the bearing system over time and generating a transient temperature field.

[0006] in, In step 1, the input parameters of the bearing dynamics numerical solution model include bearing operating conditions, spindle speed, bearing geometry, material parameters, and lubricant performance parameters; the bearing dynamics numerical solution model includes the interaction model between the rolling elements and the raceway, the interaction model between the rolling elements and the cage, the interaction model between the cage and the guide components, as well as the inner ring dynamics differential equation, the rolling element dynamics differential equation, and the cage dynamics differential equation.

[0007] In step 2, the frictional heat generated includes: frictional heat generated between the rolling element and the inner ring, frictional heat generated between the rolling element and the outer ring, frictional heat generated between the rolling element and the cage, and frictional heat generated between the cage and the guide ring.

[0008] In step 3, the CFD simulation model establishes a three-dimensional geometric model of the bearing and extracts the internal fluid domain. Combining the VOF two-phase flow model, the standard k-ε turbulence model, and the energy equation, it performs numerical calculations on the lubricating oil flow, frictional heat generation, and fluid-structure heat transfer process. The multiple reference frame method is used to describe the motion of the rotating component. The frictional heat generation calculated in step 2 is used as a heat source and input into the fluid domain. The fluid domain is numerically solved to obtain the internal flow field of the bearing, the distribution of the convective heat transfer coefficient, and the oil churning loss.

[0009] In step 4, the node temperature is calculated as follows: Step 4.1. Establish the thermal network equations for the bearing system profile. Based on the known ambient temperature and the transient heat generated by each friction pair, iteratively solve for the temperature nodes of each profile. The nodes in the thermal network are connected by thermal resistance. The thermal network equations for the bearing system profile are as follows: ; In the formula, R h1-ta , R h2-ta It is the thermal resistance of convection between the outer surface of the bearing housing and the air. The model considers the following heat dissipation sources: (a) heat generated by the rolling elements ( H b (b) Maintain heat generation ( H c (c) Heat generation in the inner ring ( H i (d) Heat generated in the outer ring ( H e (e) Stirring oil generates heat ( H d ).

[0010] Step 4.2. The thermal equilibrium equation between the oil-air lubricant and the surfaces of each component is as follows: ; In the formula, R is the thermal resistance; T is the temperature matrix to be solved; Q is the heat source; when solving the thermal balance equations, the temperature of the key node was obtained by the Newton-Raphson iteration method.

[0011] The numerical solution model for bearing dynamics characterizes the interaction of each contact pair through forces and moments, wherein the interaction forces and moments between the rolling elements and the raceway are: ; In the formula, F t Q0 is the tangential force in the contact area, and Q0 is the normal contact force between the rolling element and the raceway. T it This is the transformation matrix from the inertial coordinate system to the contact coordinate system of the bearing ring. T at The transformation matrix from the orientation coordinate system to the contact coordinate system between the rolling element and the raceway.

[0012] The interaction forces and torques between the rolling elements and the cage are: ; In the formula, F tc The tangential force in the contact area, Q c This is the normal contact force between the rolling element and the pocket.T if This is the transformation matrix from the inertial coordinate system to the contact coordinate system. T af The transformation matrix from the orientation coordinate system to the contact coordinate system between the rolling element and the raceway.

[0013] The interaction forces and moments between the cage and the guide ring are: ; In the formula, F tr The tangential force in the contact area, Q r To maintain the normal contact force between the frame and the guide edge, T iq This is the transformation matrix from the inertial coordinate system to the contact coordinate system.

[0014] The equations of motion of the center of mass of the rolling element and its angular momentum equation can be expressed as follows: ; In the formula, These are the mass and moment of inertia of the rolling element, respectively. angular velocity The amount, , Torque vector The amount.

[0015] The equations of motion for the center of mass and the equations of motion for the angular momentum of the cage are as follows: , ; In the formula, To maintain the quality of the rack, To maintain the rotational inertia of the frame, The resultant force acting on the cage The amount, To maintain the angular velocity of the cage The amount, The resultant torque acting on the cage The amount.

[0016] The forces and moments are transformed between different coordinate systems through a coordinate transformation matrix and substituted into the dynamic equations of the inner ring, rolling elements, and cage for solution using the Runge-Kutta method.

[0017] The heat generated by the rolling elements and raceway during frictional heat generation is calculated using the localized heat generation method as follows: ; The heat generated between the rolling elements and the cage is: ; Similarly, the heat generated by the cage and guide ring is: .

[0018] In step 6, the friction between the internal components and the slippage of the rolling elements generate a large amount of heat, which leads to an increase in bearing temperature and further causes thermal expansion and deformation of the parts. ; Where Γ represents the linear thermal expansion coefficient of the material, L represents the characteristic dimension, and t represents the part temperature. t a The ambient temperature.

[0019] The advantages of this disclosure compared to existing technologies are as follows: It provides a method for calculating the transient temperature of high-speed bearings based on the coupling of dynamics and CFD. By establishing a bearing dynamics model and combining it with internal flow and heat transfer analysis, a unified description of internal frictional heat generation, fluid heat transfer, and structural response of the bearing is achieved, thereby improving the accuracy of temperature field calculation. At the same time, dynamic temperature nodes are divided into sections of the bearing system profile and a thermal network model is constructed, which reduces model complexity and computational cost while ensuring calculation accuracy. Furthermore, by introducing convective heat transfer coefficients and churning losses, the reliability of temperature prediction is improved. Moreover, by feeding the temperature calculation results back to the dynamic model, a two-way coupling mechanism between dynamics and thermodynamics is established to realize the dynamic calculation of the bearing transient temperature field. Compared with traditional methods, this method can more accurately describe the temperature evolution law under varying operating conditions, thereby improving the calculation accuracy and applicability of the method.

[0020] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0021] The accompanying drawings are provided to better understand this solution and do not constitute a limitation of this disclosure. Wherein: Figure 1 This is a schematic diagram of the bearing thermal network node method according to an exemplary embodiment of this disclosure; Figure 2 This is a processing flow based on a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD provided in this disclosure; Figure 3 This is a flowchart of the bearing dynamics model calculation according to an exemplary embodiment of the present disclosure; Figure 4 This is a cloud map of the convective heat transfer coefficient of the bearing surface according to an exemplary embodiment of the present disclosure. Detailed Implementation

[0022] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0023] To more clearly illustrate the technical solutions of the embodiments in this specification, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples or embodiments of this specification. For those skilled in the art, these drawings can be applied to other similar scenarios without creative effort. Unless obvious from the context or otherwise specified, the same reference numerals in the drawings represent the same structures or operations.

[0024] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0025] Reference Figure 2 This invention provides a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD. The method includes the following steps: Step 1: Establish a numerical solution model for bearing dynamics. Solve the model based on the bearing's geometric parameters, material parameters, and operating parameters to obtain the relative sliding speeds and tangential forces between the rolling elements and the inner and outer rings, between the rolling elements and the cage, and between the cage and the guide ring. Step 2: Based on the relative sliding speed and tangential stress obtained in Step 1, calculate the frictional heat generated by each contact pair using the local heat generation method, and distribute the frictional heat generated to the inner ring, outer ring, rolling elements and cage based on the heat distribution relationship; Step 3: Establish a CFD simulation model of lubrication flow and heat transfer inside the bearing. The frictional heat generated in Step 2 is used as a heat source and loaded into the numerical model. The convective heat transfer coefficient distribution and churning loss of the inner and outer rings, rolling elements and cage surfaces are calculated. Step 4: Divide the dynamic temperature nodes on the bearing system profile. Based on the frictional heat generation obtained in Step 2 and the convective heat transfer coefficient distribution and oil churning loss obtained in Step 3, construct the bearing temperature node network model and solve for the transient temperature of each node. Step 5: Based on the temperature results obtained in Step 4, calculate the thermal expansion of each component according to the material thermal expansion relationship; Step 6: Correct the bearing geometric parameters and contact characteristics based on the thermal expansion obtained in Step 5, and feed them back to the dynamic model in Step 1 for iterative calculation, thereby obtaining the temperature node distribution of the bearing system over time and generating a transient temperature field.

[0026] This invention addresses the difficulty in accurately calculating the transient temperature of bearings by proposing a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD. It establishes a bearing dynamic model to obtain the frictional heat generation characteristics of each contact pair and combines this with internal flow and heat transfer analysis to obtain convective heat transfer parameters. A temperature node network is then constructed to solve for the transient temperature field of the bearing. Simultaneously, the bearing geometric parameters are corrected based on temperature changes and fed back to the dynamic model, forming a two-way coupled analysis mechanism of dynamics and thermodynamics. Compared with existing technologies, this invention, based on dynamics, achieves the coordinated calculation of the internal heat generation and heat transfer processes of the bearing, improving the accuracy and dynamic response capability of the transient temperature field calculation and overcoming the problem of insufficient accuracy in traditional static thermal network models.

[0027] The following provides a detailed example of this implementation plan: This invention proposes a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD. This example uses the instantaneous temperature field calculation of an angular contact ball bearing system as an example. The bearing geometry and material parameters are shown in Tables 1 and 2 below, and the lubricating oil type is 4106. The specific implementation can be carried out according to the following steps: Step 1: Establish a numerical solution model for bearing dynamics and determine the relative sliding velocity and tangential force of each component; Step 2: Calculate the frictional heat generated by each contact pair using the local heat generation method, and distribute the frictional heat generated to different components; Step 3: Establish a CFD simulation model of the bearing interior based on frictional heat to obtain the convective heat transfer coefficient distribution and oil churning loss on the surface of each component. Step 4: Based on the frictional heat generated in Step 2 and the convective heat transfer coefficient distribution and oil churning loss obtained in Step 3, construct a bearing temperature node network model and solve for the transient temperature of each node. Step 5: Calculate the thermal expansion of each component; Step 7: Correct the bearing geometry and contact characteristics, and feed them back to the dynamic model for iterative calculation to generate a transient temperature field.

[0028] Table 1 Bearing Geometric Parameters Inner diameter(mm) 46 Inner groove curvature coefficient 0.53 Outer diameter (mm) 73.7 External groove curvature coefficient 0.51 Pitch circle diameter (mm) 59.85 Cage inner diameter (mm) 55.4 Ball diameter (mm) 9.525 Cage outer diameter (mm) 65.8 Number of balls 15 Pocket clearance (mm) 0.175 Initial contact angle (°) 22 Guide gap (mm) 0.3 ; Table 2 Bearing Material Parameters Ball and ring <![CDATA[2.07×10 5 ]]> 0.3 7.85 <![CDATA[8.47×10 3 ]]> cage 5000 0.36 1.36 7.0 .

[0029] The specific process is as follows: (1) Solving the bearing dynamics model: Based on the basic parameters of the angular contact ball bearing and the bearing operating conditions, a numerical solution model for bearing dynamics is established. The specific process is as follows: Figure 3 As shown.

[0030] Based on the relative position and relative velocity relationship between the components of the bearing, the corresponding contact force and torque are calculated, referring to formulas (1), (2), and (3). Then, the motion differential equation of the system is established, referring to formulas (5), (6), (7), and (8). The Runge–Kutta numerical integration method is used to solve the equation, thereby obtaining the displacement, velocity, and force state of the bearing at any time, and realizing an accurate description of the transient dynamic characteristics of the bearing under different working conditions.

[0031] The interaction force and torque between the ball and the raceway of the angular contact ball bearing can be expressed by formula (1): ; In the formula, F t Q0 is the tangential force in the contact area, and Q0 is the normal contact force between the rolling element and the raceway. T it This is the transformation matrix from the inertial coordinate system to the contact coordinate system of the bearing ring. T at The transformation matrix from the orientation coordinate system to the contact coordinate system between the rolling element and the raceway.

[0032] The interaction force and torque between the ball and the cage in the angular contact ball bearing can be expressed as formula (2): ; In the formula, F tc The tangential force in the contact area, Q c This is the normal contact force between the rolling element and the pocket. T if This is the transformation matrix from the inertial coordinate system to the contact coordinate system. T af The transformation matrix from the orientation coordinate system to the contact coordinate system between the rolling element and the raceway.

[0033] The interaction force and torque between the cage and guide ring of the angular contact ball bearing can be expressed as formula (3): ; The equation of motion for the center of the angular contact ball bearing can be expressed as formula (4): ; The established equation for the angular momentum of the ball center of the angular contact ball bearing can be expressed as formula (5): ; In the formula, Let be the mass and moment of inertia of the ball, respectively. angular velocity The amount, , Torque vector The amount.

[0034] The equation of motion of the center of mass of the angular contact ball bearing cage can be expressed as formula (6): ; The established equation for the angular momentum of the angular contact ball bearing cage can be expressed as formula (7): ; In the formula, To maintain the quality of the rack, To maintain the rotational inertia of the frame, The resultant force acting on the cage The amount, To maintain the angular velocity of the cage The amount, The resultant torque acting on the cage The amount.

[0035] (2) Calculate frictional power consumption using the local heat generation method According to the sliding speed and tangential force in step (1), the frictional heat is calculated using the local heat generation method, including: ball and ring, ball and cage, cage and guide ring, as shown in formulas (8) to (10); The heat generated by friction between the ball and the ring is calculated using the local heat generation method, as shown in formula (8): ; The heat generated between the ball and the cage during frictional heat generation is calculated using the local heat generation method, as shown in formula (9): ; The heat generated by the cage and guide ring in frictional heat is calculated using the local heat generation method, as shown in formula (10): .

[0036] (3) Solving the CFD simulation model of lubrication flow and heat transfer inside the bearing A three-dimensional geometric model of the bearing is established and its internal fluid domain is extracted. Simultaneously, an external fluid domain connected to the bearing cavity is constructed. The fluid domain undergoes geometric repair and simplification, and key components are dimensionally optimized to improve the mesh quality of the minimum flow channel. Based on this, the fluid domain is meshed and its quality optimized to obtain a computational mesh that meets the computational requirements. Flow and heat transfer control equations are established based on a two-phase flow model, a turbulence model, and energy equations. A multiple reference frame method is used to describe the motion characteristics of the rotating components inside the bearing. The frictional heat generated by the bearing dynamics model is used as a heat source and input into the fluid domain. Numerical solutions are then performed on the fluid domain to obtain the internal flow field and convective heat transfer coefficient distribution of the bearing. Figure 4 ) and oil churning loss.

[0037] (4) Divide the bearing profile into temperature nodes and solve the heat network model based on the heat generation. The division of dynamic temperature nodes on the bearing system cross-section can be referenced. Figure 1 As shown, the nodes include the spindle, inner ring, inner raceway, rolling elements, cage, outer raceway, outer ring, bearing housing, and lubricant. The thermal resistance between the nodes is calculated based on the heat transfer mode between the nodes, and the bearing profile thermal balance equations are established by analogy with Kirchhoff's current law.

[0038] The bearing system profile thermal network equation set is established as shown in equation (11). Based on the known ambient temperature and the transient heat generation of each friction pair, the temperature nodes of each profile are iteratively solved; the nodes in the thermal network are connected by thermal resistance; where, R h1-ta , R h2-ta This refers to the thermal resistance of the bearing housing's outer surface to air during convection. This paper uses Meneghetti's experimental results. R h1-ta and R h2-ta The value is 15 W / m 2 K, the model considers the following heat dissipation sources: (a) heat generated by the sphere ( H b (b) Maintain heat generation ( H c (c) Heat generation in the inner ring ( H i (d) Heat generated in the outer ring ( H e (e) Stirring oil generates heat ( H d ).

[0039] The equation set of the thermal network of the bearing system profile is established as Equation (11): ; The thermal equilibrium equation between the oil-air lubricant and the surfaces of each part is given by formula (12): ; In the formula, R is the thermal resistance; T is the temperature matrix to be solved; Q is the heat source; when solving the thermal balance equations, the temperature of the key node was obtained by the Newton-Raphson iteration method.

[0040] (5) Calculate the thermal expansion of each component. Based on the temperature results obtained in (4), the thermal expansion of each component can be calculated using the material thermal expansion relationship and expressed as formula (13): ; Where Γ represents the linear thermal expansion coefficient of the material, L represents the characteristic dimension, and t represents the part temperature. t a The ambient temperature.

[0041] (6) Correct bearing geometry and contact characteristics Based on the thermal expansion obtained in (5), the bearing geometric parameters and contact characteristics are corrected and fed back to the dynamic model in (1) for iterative calculation, thereby obtaining the temperature node distribution of the bearing system over time and generating a transient temperature field. The temperature results of each node of the bearing after stabilization are shown in Table 3.

[0042] Table 3 Temperature at various nodes of angular contact ball bearings Bearing housing end face 111.7 outer diameter of bearing housing 120.1 Outer ring 122.2 Outer ring contact point 120.0 Rolling body 117.8 cage 104.5 Inner ring contact point 114.1 Inner circle 110.9 Shaft inner diameter 97.7 Shaft end face 84.1 Oil inlet 80.0 .

[0043] This invention discloses a method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD. By establishing a bearing dynamic model to obtain the frictional heat generation characteristics of each contact pair, and combining this with internal flow and heat transfer analysis to obtain convective heat transfer parameters, a unified description of frictional heat generation, fluid heat transfer, and structural response is achieved, thereby constructing the bearing transient temperature field and completing the temperature calculation. Simultaneously, dynamic temperature nodes are divided into sections of the bearing system profile, and a thermal network model is established to reduce model complexity while ensuring calculation accuracy. Furthermore, the reliability of temperature prediction is improved by introducing convective heat transfer coefficients and churning losses. Further, by feeding the temperature calculation results back to the dynamic model, a two-way coupling mechanism between dynamics and thermodynamics is established to achieve dynamic calculation of the bearing transient temperature field. This invention solves the problem of accurately calculating the transient temperature inside the bearing. Compared with existing technologies, it can achieve high-precision calculation of the bearing transient temperature field, thereby improving the safety and stability of bearing operation and reducing the risk of thermal failure.

[0044] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved. This embodiment does not impose any limitations on these steps.

[0045] It should be understood that the terms "system," "device," "unit," and / or "module" used in this embodiment are a method of distinguishing different components, elements, parts, sections, or assemblies at different levels. However, if other terms can achieve the same purpose, they can be replaced by other expressions.

[0046] This embodiment uses a flowchart to illustrate the operations performed by the system according to this embodiment. It should be understood that the preceding or following operations are not necessarily performed precisely in sequence. Instead, each step can be processed in reverse order or simultaneously. Furthermore, other operations can be added to these processes, or one or more steps can be removed from them.

[0047] As shown in this embodiment, unless the context explicitly indicates an exception, words such as "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate that explicitly identified steps and elements are included, and these steps and elements do not constitute an exclusive list; the method or apparatus may also include other steps or elements.

[0048] The definitions used in this embodiment, such as the terms "having," "may have," "comprising," or "may include," indicate the presence of corresponding functions, operations, elements, etc., in this embodiment, but do not limit the presence of one or more other functions, operations, elements, etc. Furthermore, it should be understood that the terms "comprising" or "having," as used herein, indicate the presence of features, numbers, steps, operations, elements, components, or combinations thereof described in the specification, without excluding the presence or addition of one or more other features, numbers, steps, operations, elements, components, or combinations thereof.

[0049] In this embodiment, the definitions of "A or B", "at least one of A and / or B" or "one or more of A and / or B" as used herein include any and all combinations of the words listed therewith. For example, "A or B", "at least one of A and / or B" or "one or more of A and / or B" means (1) including at least one A, (2) including at least one B, or (3) including both at least one A and at least one B.

[0050] The definitions of "first" and "second" in this embodiment, and the descriptions of "first" and "second" appearing in this embodiment, are only for illustration and to distinguish the objects being described. They do not indicate any order and do not represent a special limitation on the number of devices in this embodiment, nor do they constitute any limitation on this embodiment. For example, the first element can be referred to as the second element without departing from the scope of this disclosure, and similarly, the second element can be referred to as the first element.

[0051] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD, characterized in that, Includes the following steps: Step 1: Establish a numerical solution model for bearing dynamics. Solve the model based on the bearing's geometric parameters, material parameters, and operating parameters to obtain the relative sliding speeds and tangential forces between the rolling elements and the inner and outer rings, between the rolling elements and the cage, and between the cage and the guide ring. Step 2: Based on the relative sliding speed and tangential stress obtained in Step 1, calculate the frictional heat generated by each contact pair using the local heat generation method, and distribute the frictional heat generated to the inner ring, outer ring, rolling elements and cage based on the heat distribution relationship; Step 3: Establish a CFD simulation model of lubrication flow and heat transfer inside the bearing. The frictional heat generated in Step 2 is used as a heat source and loaded into the numerical model. The convective heat transfer coefficient distribution of the inner and outer rings, rolling elements and cage surfaces and the oil churning loss are calculated. Step 4: Divide the dynamic temperature nodes on the bearing system profile. Based on the frictional heat generation obtained in Step 2 and the convective heat transfer coefficient distribution and oil churning loss obtained in Step 3, construct the bearing temperature node network model and solve for the transient temperature of each node. Step 5: Based on the temperature results obtained in Step 4, calculate the thermal expansion of each component based on the material thermal expansion relationship; Step 6: Correct the bearing geometric parameters and contact characteristics based on the thermal expansion obtained in Step 5, and feed them back to the dynamic model in Step 1 for iterative calculation, thereby obtaining the temperature node distribution of the bearing system over time and generating a transient temperature field.

2. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 1, characterized in that, In step 1, the input parameters of the bearing dynamics numerical solution model include bearing operating conditions, spindle speed, bearing geometry, material parameters, and lubricant performance parameters.

3. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 1, characterized in that, In step 1, the numerical solution model for bearing dynamics includes the interaction model between the rolling elements and the raceway, the interaction model between the rolling elements and the cage, the interaction model between the cage and the guide components, and the dynamic differential equations of the raceway, rolling elements, and cage.

4. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 1, characterized in that, In step 2, the frictional heat generated includes: frictional heat generated between the rolling element and the inner ring, frictional heat generated between the rolling element and the outer ring, frictional heat generated between the rolling element and the cage, and frictional heat generated between the cage and the guide ring.

5. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 1, characterized in that, In step 3, the CFD simulation model establishes a three-dimensional geometric model of the bearing and extracts the internal fluid domain. Combining the VOF two-phase flow model, the standard k-ε turbulence model, and the energy equation, it performs numerical calculations on the lubricating oil flow, frictional heat generation, and fluid-structure heat transfer process. The multiple reference frame method is used to describe the motion of the rotating component. The frictional heat generation calculated in step 2 is used as a heat source and input into the fluid domain. The fluid domain is numerically solved to obtain the internal flow field of the bearing, the distribution of the convective heat transfer coefficient, and the oil churning loss.

6. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 1, characterized in that, In step 4, the node temperature is calculated as follows: Step 4.

1. Establish the thermal network equations for the bearing system profile. Based on the known ambient temperature and the transient heat generated by each friction pair, iteratively solve for the temperature nodes of each profile. The nodes in the thermal network are connected by thermal resistance. The thermal network equations for the bearing system profile are as follows: ； In the formula, R h1-ta , R h2-ta It is the thermal resistance of convection between the outer surface of the bearing housing and the air. The model considers the following heat dissipation sources: (a) heat generated by the rolling elements ( H b (b) Maintain heat generation ( H c (c) Heat generation in the inner ring ( H i (d) Heat generated in the outer ring ( H e (e) Stirring oil generates heat ( H d ); Step 4.

2. The thermal equilibrium equation between the oil-air lubricant and the surfaces of each component is as follows: ； In the formula, R is the thermal resistance; T is the temperature matrix to be solved; Q is the heat source; when solving the thermal balance equations, the temperature of the key node was obtained by the Newton-Raphson iteration method.

7. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 3, characterized in that, The numerical solution model for bearing dynamics characterizes the interaction of each contact pair through forces and moments, wherein the interaction forces and moments between the rolling elements and the raceway are: ； In the formula, F t Q0 is the tangential force in the contact area, and Q0 is the normal contact force between the rolling element and the raceway. T it This is the transformation matrix from the inertial coordinate system to the contact coordinate system of the bearing ring. T at Transformation matrix from the orientation coordinate system to the rolling element and ring contact coordinate system; The interaction forces and torques between the rolling elements and the cage are: ； In the formula, F tc The tangential force in the contact area, Q c This is the normal contact force between the rolling element and the pocket. T if This is the transformation matrix from the inertial coordinate system to the contact coordinate system. T af Transformation matrix from the orientation coordinate system to the rolling element and ring contact coordinate system; The interaction forces and moments between the cage and the guide ring are: ； In the formula, F tr The tangential force in the contact area, Q r To maintain the normal contact force between the frame and the guide edge, T iq This is the transformation matrix from the inertial coordinate system to the contact coordinate system; The equations of motion of the center of mass of the rolling element and its angular momentum equation can be expressed as follows: ； In the formula, These are the mass and moment of inertia of the rolling element, respectively. angular velocity The amount, , Torque vector The amount; The equations of motion for the center of mass and the equations of motion for the angular momentum of the cage are as follows: ， ； In the formula, To maintain the quality of the rack, To maintain the rotational inertia of the frame, The resultant force acting on the cage The amount, To maintain the angular velocity of the cage The amount, The resultant torque acting on the cage The amount; The forces and moments are transformed between different coordinate systems through a coordinate transformation matrix and substituted into the dynamic equations of the inner ring, rolling elements, and cage for solution using the Runge-Kutta method.

8. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 1, characterized in that, In step 2, the heat generated by the rolling elements and the raceway during frictional heat is calculated using the localized heat generation method: ； The heat generated between the rolling elements and the cage is: ； Similarly, the heat generated by the cage and guide ring is: 。 9. The method for calculating the transient temperature of high-end high-speed bearings based on the coupling of dynamics and CFD as described in claim 1, characterized in that, In step 5, the friction between the internal components and the slippage of the rolling elements generate a large amount of heat, which leads to an increase in bearing temperature and further causes thermal expansion and deformation of the parts. ； Where Γ represents the linear thermal expansion coefficient of the material, L represents the characteristic dimension, and t represents the part temperature. t a The ambient temperature.

Images