CN112287482A - Method and system for calculating convection heat transfer coefficient of ball bearing - Google Patents
Method and system for calculating convection heat transfer coefficient of ball bearing Download PDFInfo
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Abstract
The invention relates to a method and a system for calculating a convection heat transfer coefficient of a ball bearing.A physical property parameter is obtained through a simulation model of the ball bearing, the physical property parameter is fitted to obtain a fitting relational expression between the physical property parameters, and a first relational expression of a size parameter, the convection heat transfer coefficient and the physical property parameter of the ball bearing is established; establishing a second relational expression of the size parameter, the rotating speed and the physical property parameter of the ball bearing; obtaining a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relation, the first relation and the second relation; and calculating the convective heat transfer coefficient according to the calculation formula. The calculation formula of the convective heat transfer coefficient is determined according to the physical parameters obtained by simulation and the specific parameters of the ball bearing, and the convective heat transfer coefficient is obtained according to the calculation formula, so that the obtained convective heat transfer coefficient is more accurate.
Description
Technical Field
The invention relates to the technical field of ball bearings, in particular to a method and a system for calculating a convection heat exchange coefficient of a ball bearing.
Background
The high-speed ball bearing is used as an important part and widely applied to aeroengines, and the lubrication mode of the high-speed ball bearing mainly adopts under-ring lubrication. The oil supply under the ring is adopted, so that the flowing condition of lubricating oil in the bearing can be improved, and the inner ring is sufficiently cooled and lubricated. For the high-speed angular contact ball bearing lubricated under the ring, when a certain amount of gas enters, the lubricating medium integrally shows the characteristic of oil-gas two-phase flow in the high-speed rotating state of the bearing. The oil-gas two-phase fluid generates convection heat transfer when flowing through the solid surface of the bearing, and the heat dissipation mechanism of the bearing is greatly influenced by the convection heat transfer criterion. The convection heat transfer coefficient of the existing bearing is calculated by adopting an empirical formula, the obtained convection heat transfer coefficient is applied to the whole bearing as a boundary condition, and the convection heat transfer coefficient calculation aiming at the internal channel of the ball bearing in a two-phase flow state, including the inner and outer ring raceways and the rolling element, is lacked. The inner channel of the bearing refers to the area between the inner and outer races, including the rolling elements, the cage, and the fluid field.
Disclosure of Invention
Based on the above, the invention aims to provide a method and a system for calculating the convection heat transfer coefficient of the ball bearing, so that the accuracy of temperature calculation is improved.
In order to achieve the purpose, the invention provides the following scheme:
the invention discloses a method for calculating the convection heat transfer coefficient of a ball bearing, which comprises the following steps:
establishing a simulation model of the ball bearing;
setting different rotating speeds and different oil injection speeds for the ball bearings;
obtaining physical parameters of oil-gas two-phase flow of the ball bearing internal channel;
fitting the physical property parameters to obtain a fitting relational expression between the physical property parameters;
establishing a first relational expression of the dimensional parameters, the convective heat transfer coefficients and the physical parameters of the ball bearing;
establishing a second relational expression of the size parameter, the rotating speed and the physical property parameter of the ball bearing;
obtaining a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relation, the first relation and the second relation;
and calculating the convective heat transfer coefficient according to the calculation formula.
Optionally, before the fitting the property parameter, the method further comprises:
and carrying out dimensionless transformation on the physical property parameters.
Optionally, the performing dimensionless on the property parameter specifically includes performing dimensionless on the property parameter according to a basic principle of dimensional analysis.
Optionally, the physical property parameters include hydrodynamic viscosity, density, isobaric specific heat capacity, thermal conductivity, prandtl number, reynolds number, and knoevenagel number.
Optionally, the calculation formula is:
The invention also discloses a system for calculating the convection heat transfer coefficient of the ball bearing, which comprises the following components:
the simulation model establishing module is used for establishing a simulation model of the ball bearing;
the setting module is used for setting different rotating speeds and different oil injection speeds for the ball bearings;
the physical property parameter obtaining module is used for obtaining the physical property parameters of the oil-gas two-phase flow of the internal channel of the ball bearing;
a fitting relation obtaining module for fitting the physical property parameters to obtain a fitting relation between the physical property parameters;
the first relational expression establishing module is used for establishing a first relational expression of the dimensional parameters, the convective heat transfer coefficients and the physical parameters of the ball bearings;
the second relational expression establishing module is used for establishing a second relational expression of the size parameter, the rotating speed and the physical property parameter of the ball bearing;
the convective heat transfer coefficient calculation formula obtaining module is used for obtaining a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relational expression, the first relational expression and the second relational expression;
and the convective heat transfer coefficient calculation module is used for calculating the convective heat transfer coefficient according to the calculation formula.
Optionally, the system further comprises:
and the non-dimensionalization module is used for carrying out non-dimensionalization on the physical property parameters before fitting the physical property parameters.
Optionally, the non-dimensionalization module specifically includes:
and the dimensionless subunit is used for performing dimensionless transformation on the physical property parameters according to the basic principle of dimension analysis.
Optionally, the physical property parameters include hydrodynamic viscosity, density, isobaric specific heat capacity, thermal conductivity, prandtl number, reynolds number, and knoevenagel number.
Optionally, the calculation formula is:
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a method and a system for calculating the convection heat transfer coefficient of a ball bearing, which are characterized in that physical property parameters are obtained through a simulation model of the ball bearing, the physical property parameters are fitted to obtain a fitting relational expression between the physical property parameters, and a first relational expression of the size parameters, the convection heat transfer coefficient and the physical property parameters of the ball bearing is established; establishing a second relational expression of the size parameter, the rotating speed and the physical property parameter of the ball bearing; obtaining a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relation, the first relation and the second relation; and calculating the convective heat transfer coefficient according to the calculation formula. According to the invention, the physical property parameters obtained by simulation are determined, the calculation formula of the convective heat transfer coefficient is determined according to the specific parameters of the ball bearing, and the convective heat transfer coefficient is obtained according to the calculation formula, so that the obtained convective heat transfer coefficient is more accurate.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a schematic flow chart of a method for calculating a convective heat transfer coefficient of a ball bearing according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a system for calculating a convective heat transfer coefficient of a ball bearing according to an embodiment of the present invention;
fig. 3 is a schematic structural view of a ball bearing according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method and a system for calculating the convection heat exchange coefficient of a ball bearing, which improve the accuracy of temperature detection.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a schematic flow chart of a method for calculating a convection heat transfer coefficient of a ball bearing according to the present invention, and as shown in fig. 1, the method for calculating a convection heat transfer coefficient of a ball bearing includes the following steps:
step 101: and establishing a simulation model of the ball bearing.
In step 101, a design model module in ANSYS-Workbench (finite element analysis software) is adopted to establish a three-dimensional simulation model of the under-ring lubrication ball bearing comprising a bearing inner ring 4, an outer ring 1, a rolling body 3 and a retainer 2. The schematic structure of the under-ring lubrication ball bearing is shown in fig. 3.
Step 102: different rotation speeds and different oil injection speeds are set for the ball bearings.
Specifically, in step 102, a Fluent (fluid simulation) module in the ANSYS-Workbench sets different rotating speeds and different oil injection speeds for a simulation model of the under-ring lubrication ball bearing.
Step 103: and obtaining the physical parameters of the oil-gas two-phase flow of the internal channel of the ball bearing.
The physical property parameters include hydrodynamic viscosity, density, isobaric specific heat capacity, thermal conductivity, prandtl number, reynolds number, and knoop-sel number.
Step 104: and fitting the physical property parameters to obtain a fitting relational expression between the physical property parameters.
Before step 104, the method further includes: and carrying out non-dimensionalization on the physical property parameters according to the basic principle of dimensional analysis.
Step 104 specifically includes: fitting the physical parameters after dimensionless according to a convection heat exchange rule relational expression Nu ═ f (Re, Rr) to obtain a fitting relational expression Nu ═ a.Reb·PrcWhere Pr represents a prandtl number, Re represents a reynolds number, Nu represents a knoop number, a represents a first constant, b represents a second constant, and c represents a third constant.
Step 105: and establishing a first relational expression of the dimensional parameters, the convective heat transfer coefficients and the physical parameters of the ball bearing.
Wherein the first relation comprises:
wherein h represents the convective heat transfer coefficient and has a unit of W/m2K; l represents the size parameter of the under-ring lubrication ball bearing, the size parameter is represented as the characteristic length of the under-ring lubrication ball bearing, and the characteristic length of the internal flow is the pipe diameterRefers to the diameter of the corresponding raceway where the inner ring 4 or outer ring 1 contacts the ball 3, and the characteristic length of the ball in the fluid is taken to be the diameter of the ball 3, K represents the thermal conductivity in units of W/m · K.
Step 106: and establishing a second relational expression of the dimensional parameters, the rotating speed and the physical parameters of the ball bearing.
Wherein the second relation comprises:
where ρ represents the fluid density in kg/m3(ii) a V represents the average flow velocity in m/s; μ represents hydrodynamic viscosity in Pa · s; in this embodiment, the average flow velocity is taken as the linear velocity at the bearing pitch circle.
The second relation further includes
CpIt represents the isobaric specific heat capacity, and the unit is J/kg.K.
Inside the under-ring lubrication ball bearing, the inner and outer raceway values can be the raceway widths, the raceway width is taken as the characteristic length l, and for the sphere 3, the characteristic length is the 3 diameter D of the sphereb. The average flow velocity V is taken as the linear velocity at the bearing pitch circle.
The expression for the average flow velocity V is:
wherein ω represents the bearing angular velocity, rad/s; n isbRepresenting the rotation speed of the bearing fluid domain (unit is r/min); dmDenotes the pitch circle diameter in m, dm＝(din+dout)/2，dinDenotes the inner diameter of the lubricated ball bearing under the ring, doutIndicating the outer diameter of the under-ring lubrication ball bearing; n isiIndicates the inner ring rotation speed (unit is r/min), DbDenotes the diameter of the sphere 3 in m and α denotes the contact angle.
Step 107: and obtaining a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relation, the first relation and the second relation.
Wherein, step 107 specifically comprises: simultaneously fitting the relational expression, the first relational expression, the second relational expression and the expression of the average flow velocity V to obtain a dimensionless calculation formula of the convective heat transfer coefficients of the inner and outer raceways and the sphere:
step 108: and calculating the convective heat transfer coefficient according to the calculation formula.
In this embodiment, the under-ring lubrication ball bearing is simulated, and the simulation conditions of the under-ring lubrication ball bearing are shown in table 1:
TABLE 1 simulated behavior of lubricated ball bearings under the ring
Taking the inner raceway as an example, the obtained simulation parameters are shown in table 2:
TABLE 2 simulation results
Fitting a dimensionless convective heat transfer rule relation of an inner ring raceway by using an MATLAB tool box, wherein the relation is as follows: nu 0.04072. Re0.7765·Pr0.07432。
By the formula Nu-0.04072. Re0.7765·Pr0.07432It can be seen that, for the inner ring raceway, a is 0.04072, b is 0.7765, and c is 0.07432. Substituting the a, the b and the c into a dimensionless calculation formula of the convective heat transfer coefficient to obtain a dimensionless calculation formula of the convective heat transfer coefficient of the inner ring raceway:
taking the diameter of the lubricating oil hole under the ring as 2mm and the oil injection speed as 15m/s as an example, the errors of the calculation result and the simulation result under different rotating speeds are compared, as shown in table 3:
TABLE 3 error between calculation result and simulation result at different rotation speeds
Further, by using an MATLAB tool box, a dimensionless convection heat transfer rule relation between the ball 3 and the outer ring raceway can be obtained: nu 0.0239. Re0.8154·Pr0.3051，Nu＝0.895·Re0.5·Pr0.1054。
By the formula Nu-0.0239. Re0.8154·Pr0.3051And Nu ═ 0.895. Re0.5·Pr0.1054It can be seen that the values of a, b, c for the ball 3 and outer race raceway are 0.0239, 0.8154, 0.3051 and 0.895, 0.5, 0.1054 respectively.
Substituting the a, b and c values of the ball 3 and the outer ring raceway into a dimensionless convective heat transfer coefficient calculation formula respectively to obtain the dimensionless convective heat transfer coefficient calculation formula of the ball 3 and the outer ring raceway:
the method for calculating the convection heat transfer coefficient of the ball bearing has the following technical effects:
(1) a dimensionless calculation formula of the convective heat transfer coefficient is obtained through simulation and nonlinear fitting, the calculation formula overcomes the defects of a single empirical formula for calculating the convective heat transfer coefficient of the bearing, a calculation method for single-phase flow and no part distinguishing, and when a finite element method and a thermal network method are used for carrying out bearing temperature field analysis, different convective heat transfer coefficients can be calculated and applied according to the bearing parts and the lubricating characteristics in a more targeted manner, the accuracy of the temperature field analysis is improved, the error of a test is reduced, the design of the bearing is guided more effectively, and the service life of the bearing is prolonged.
(2) According to the method for calculating the convection heat transfer coefficient of the internal channel of the ball bearing, provided by the invention, a three-dimensional simulation model of the ball bearing is established and simulation calculation is carried out, a simulation numerical value is obtained, a dimensionless calculation formula of the convection heat transfer coefficients of the inner ring, the outer ring and the ball body is obtained through a pi theorem dimensionless after-convection heat transfer criterion relational expression and nonlinear fitting, a comparison result of a calculated value and a simulation value is obtained, and the method has better accuracy.
Fig. 2 is a schematic structural diagram of a system for calculating a convection heat transfer coefficient of a ball bearing according to the present invention, and as shown in fig. 2, the system for calculating a convection heat transfer coefficient of a ball bearing includes:
a simulation model establishing module 201, configured to establish a simulation model of a ball bearing;
the setting module 202 is used for setting different rotating speeds and different oil injection speeds for the ball bearings.
And the physical property parameter obtaining module 203 is used for obtaining the physical property parameters of the oil-gas two-phase flow of the internal channel of the ball bearing.
A fitting relation obtaining module 204, configured to fit the physical property parameters to obtain a fitting relation between the physical property parameters.
And the first relational expression establishing module 205 is used for establishing a first relational expression of the dimensional parameters, the convective heat transfer coefficients and the physical parameters of the ball bearings.
And a second relation establishing module 206, configured to establish a second relation among the dimensional parameter, the rotational speed, and the physical property parameter of the ball bearing.
And a convective heat transfer coefficient calculation formula obtaining module 207, configured to obtain a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relation, the first relation, and the second relation.
And the convective heat transfer coefficient calculating module 208 is configured to calculate the convective heat transfer coefficient according to the calculation formula.
The system further comprises:
and the non-dimensionalization module is used for carrying out non-dimensionalization on the physical property parameters before fitting the physical property parameters.
The dimensionless module specifically includes:
and the dimensionless subunit is used for performing dimensionless transformation on the physical property parameters according to the basic principle of dimension analysis.
The physical property parameters include hydrodynamic viscosity, density, isobaric specific heat capacity, thermal conductivity, prandtl number, reynolds number, and knoop-sel number.
The calculation formula is as follows:
Although the invention only carries out simulation calculation on the under-ring lubrication ball bearing, the application of the method and the system for calculating the convection heat exchange coefficient of the ball bearing is not limited to the under-ring lubrication ball bearing, and the method and the system are also suitable for other lubrication type ball bearings such as oil injection lubrication.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A method for calculating the convection heat transfer coefficient of a ball bearing is characterized by comprising the following steps:
establishing a simulation model of the ball bearing;
setting different rotating speeds and different oil injection speeds for the ball bearings;
obtaining physical parameters of oil-gas two-phase flow of the ball bearing internal channel;
fitting the physical property parameters to obtain a fitting relational expression between the physical property parameters;
establishing a first relational expression of the dimensional parameters, the convective heat transfer coefficients and the physical parameters of the ball bearing;
establishing a second relational expression of the size parameter, the rotating speed and the physical property parameter of the ball bearing;
obtaining a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relation, the first relation and the second relation;
and calculating the convective heat transfer coefficient according to the calculation formula.
2. The method for calculating the convective heat transfer coefficient of the ball bearing according to claim 1, wherein before the fitting the physical property parameter, the method further comprises:
and carrying out dimensionless transformation on the physical property parameters.
3. The method for calculating the convective heat transfer coefficient of the ball bearing according to claim 2, wherein the non-dimensionalizing the physical property parameter specifically comprises the non-dimensionalizing the physical property parameter according to a basic principle of dimensional analysis.
4. The method for calculating the convective heat transfer coefficient of the ball bearing according to claim 1, wherein the physical property parameters include hydrodynamic viscosity, density, isobaric specific heat capacity, thermal conductivity, prandtl number, reynolds number and knoop-sel number.
5. The method for calculating the convective heat transfer coefficient of the ball bearing according to claim 1, wherein the calculation formula is as follows:
wherein h represents a convective heat transfer coefficient, l represents a characteristic length of the ball bearing, k represents a thermal conductivity, ρ represents a fluid density, μ represents a hydrodynamic viscosity, and C representspDenotes the isobaric specific heat capacity, niIndicating the rotational speed of the inner race of the bearing, DbDenotes the diameter of the sphere, dmDenotes the pitch circle diameter, dm＝(din+dout)/2，dinDenotes the ball bearing inner diameter, doutThe outer diameter of the ball bearing is shown, and alpha is the contact angle.
6. A system for calculating convective heat transfer coefficient of a ball bearing, the system comprising:
the simulation model establishing module is used for establishing a simulation model of the ball bearing;
the setting module is used for setting different rotating speeds and different oil injection speeds for the ball bearings;
the physical property parameter obtaining module is used for obtaining the physical property parameters of the oil-gas two-phase flow of the internal channel of the ball bearing;
a fitting relation obtaining module for fitting the physical property parameters to obtain a fitting relation between the physical property parameters;
the first relational expression establishing module is used for establishing a first relational expression of the dimensional parameters, the convective heat transfer coefficients and the physical parameters of the ball bearings;
the second relational expression establishing module is used for establishing a second relational expression of the size parameter, the rotating speed and the physical property parameter of the ball bearing;
the convective heat transfer coefficient calculation formula obtaining module is used for obtaining a calculation formula for calculating the convective heat transfer coefficient of the ball bearing according to the fitting relational expression, the first relational expression and the second relational expression;
and the convective heat transfer coefficient calculation module is used for calculating the convective heat transfer coefficient according to the calculation formula.
7. The system for calculating the convective heat transfer coefficient of a ball bearing according to claim 6, further comprising:
and the non-dimensionalization module is used for carrying out non-dimensionalization on the physical property parameters before fitting the physical property parameters.
8. The system for calculating the convective heat transfer coefficient of the ball bearing according to claim 7, wherein the non-dimensionalization module specifically comprises:
and the dimensionless subunit is used for performing dimensionless transformation on the physical property parameters according to the basic principle of dimension analysis.
9. The system for calculating the convective heat transfer coefficient of a ball bearing of claim 6, wherein the physical property parameters comprise hydrodynamic viscosity, density, isobaric specific heat capacity, thermal conductivity, prandtl number, reynolds number, and knoop number.
10. The system for calculating the convective heat transfer coefficient of the ball bearing according to claim 6, wherein the calculation formula is as follows:
wherein h represents a convective heat transfer coefficient, l represents a characteristic length of the ball bearing, k represents a thermal conductivity, ρ represents a fluid density, μ represents a hydrodynamic viscosity, and C representspDenotes the isobaric specific heat capacity, niIndicating the rotational speed of the inner race of the bearing, DbDenotes the diameter of the sphere, dmDenotes the pitch circle diameter, dm＝(din+dout)/2，dinDenotes the ball bearing inner diameter, doutThe outer diameter of the ball bearing is shown, and alpha is the contact angle.
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|---|---|---|---|---|
| CN113343494A (en) * | 2021-07-01 | 2021-09-03 | 中国航发沈阳发动机研究所 | Aeroengine bearing cavity thermal performance simulation calculation model correction method |
| CN113343494B (en) * | 2021-07-01 | 2023-01-17 | 中国航发沈阳发动机研究所 | Aircraft engine bearing cavity thermal performance simulation calculation model correction method |
| CN115587505A (en) * | 2022-12-08 | 2023-01-10 | 中国核动力研究设计院 | Flow heat transfer model construction method and device based on dimensionless characteristic parameters |
| CN115587505B (en) * | 2022-12-08 | 2023-03-14 | 中国核动力研究设计院 | Flow heat transfer model construction method and device based on dimensionless characteristic parameters |
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