CN113656911A - High-speed bearing lubrication temperature rise state analysis method - Google Patents

High-speed bearing lubrication temperature rise state analysis method Download PDF

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CN113656911A
CN113656911A CN202110918038.7A CN202110918038A CN113656911A CN 113656911 A CN113656911 A CN 113656911A CN 202110918038 A CN202110918038 A CN 202110918038A CN 113656911 A CN113656911 A CN 113656911A
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钱东升
邓松
华林
赵贵强
王丰
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Wuhan University of Technology WUT
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Abstract

The invention relates to a method for analyzing the lubrication temperature rise state of a high-speed bearing, which comprises the following steps: 1) obtaining structural parameters, working condition parameters and initial value conditions of the bearing; 2) calculating the stress balance of the steel ball and the stress balance of the inner ring; 3) solving the stress balance of the steel ball and the stress balance of the inner ring; 4) determining the rough friction coefficient of the steel ball and the raceway by a sliding-rolling ratio of the steel ball and a rough friction coefficient calculation equation; 5) establishing a bearing computational fluid dynamics model, then defining the boundary condition of the bearing computational fluid dynamics model according to the motion state of the steel ball and the bearing power loss which are calculated by the bearing nonlinear dynamics model, and further calculating the lubrication and temperature rise states of the steel ball in the bearing cavity; the bearing structure is optimized by the computational data of the bearing nonlinear dynamics model and the computational fluid dynamics model. The invention can accurately calculate the motion conditions and power loss of the bearing steel ball, the inner ring, the outer ring and the retainer under the working conditions of high speed, low speed and light and heavy load, and simulate and analyze the lubricating and temperature rising state structure in the bearing cavity.

Description

High-speed bearing lubrication temperature rise state analysis method
Technical Field
The invention relates to the field of high-speed bearings, in particular to a method for analyzing a lubrication temperature rise state of a high-speed bearing.
Background
The high-speed bearing is widely applied to important high-speed equipment such as an aircraft engine, a high-speed motor of a new energy automobile, a high-speed machine tool and the like, the rotating speed of the high-speed bearing is more than or equal to 10000r/min, and the lubricating and temperature rising states of the high-speed bearing have the rotating precision of the whole mechanical system. The temperature rise of the bearing induces the thermal deformation to aggravate the internal pressure of the bearing and reduce the reliability, the service life and other performances of the bearing. At present, sensors are mostly adopted to collect the flowing state of the lubricating fluid of the bearing cavity and the temperature data of the bearing ring, the method has high experimental cost and long period, and the temperature rise state of the bearing lubrication under the working condition of high speed and light load is difficult to accurately monitor. Therefore, a high-rotating-speed bearing nonlinear dynamics model and a computational fluid dynamics model are established, the influence of the bearing motion state, the power loss and the bearing structure on the bearing lubrication and the temperature rise is quantitatively analyzed, and the method is low in cost, short in time and effective and reliable in result.
As can be seen from the existing literature, the high rotational speed bearing nonlinear dynamics model and the computational fluid dynamics model have been widely focused by researchers at home and abroad (Han Q, Chu F. nonlinear dynamics model for mounting noise of regular contact ball bearings. Journal of Sound and Vibration,2015,354: 219-235; Wu W, Hu C, Hu J, et al. jet mutual dynamics for ball bearings using the VOF multiple model. national Journal of Thermal Sciences,2017,116: 150-158). However, the influence of friction traction and lubrication traction on the movement of the steel ball is generally ignored by the bearing dynamics models, the lubricating viscosity and the traction force caused by macroscopic sliding of the steel ball are obviously enhanced during high-speed light load, and the friction traction and the lubrication traction must be considered during the analysis of the mechanical balance of the steel ball. In addition, the real-time change of the sliding-rolling ratio of the steel ball causes the real-time change of the rough friction coefficient of the steel ball and the raceway, so that the related friction force and friction torque change in real time. More importantly, the high-speed bearing lubrication and temperature rise state analysis can obtain accurate and reliable bearing lubrication temperature rise data only by setting the boundary conditions of a computational fluid dynamics model according to the motion states and power losses of the bearing steel ball and the inner and outer rings.
Disclosure of Invention
The invention aims to solve the technical problem of providing a high-speed bearing lubrication temperature rise state analysis method, which can more accurately calculate the motion conditions and power loss of a bearing steel ball, an inner ring, an outer ring and a retainer under the working conditions of high speed, low speed and light and heavy load, simulate and analyze the lubrication and temperature rise states in a bearing cavity and optimize the bearing structure based on the data.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for analyzing the lubrication temperature rise state of a high-speed bearing is constructed, and comprises the following steps:
1) obtaining structural parameters, working condition parameters and initial value conditions of the bearing; the structural parameters comprise bearing parameters, material parameters and oil-gas lubrication parameters;
2) applying the rotating speed and the load to a bearing, and respectively calculating the stress balance of the steel ball and the stress balance of the inner ring according to the principles of moment balance and force balance;
3) calculating friction traction and lubrication traction, the sliding speed, the spinning speed and the rolling speed of the steel ball relative to the inner and outer raceways, and the thickness of an oil film between the steel ball and the inner and outer raceways, and solving the stress balance of the steel ball and the stress balance of the inner ring;
4) determining the rough friction coefficient of the steel ball and the raceway by a sliding-rolling ratio of the steel ball and a rough friction coefficient calculation equation; in order to accurately calculate the friction traction of the steel ball, the friction traction and the lubrication traction are calculated by determining the lubrication state of the steel ball;
5) establishing a bearing computational fluid dynamics model by adopting an RNG k-epsilon model, a fluid flow mode and multiphase flow monitoring, then defining the boundary condition of the bearing computational fluid dynamics model according to the steel ball motion state and the bearing power loss calculated by the bearing nonlinear dynamics model, and further calculating the steel ball lubrication and temperature rise state in a bearing cavity; the bearing structure is optimized by the computational data of the bearing nonlinear dynamics model and the computational fluid dynamics model.
In the scheme, the structural parameters comprise bearing parameters, material parameters and oil-gas lubrication parameters; the working condition parameters comprise rotating speed and radial and axial loads; the initial conditions include a bearing nonlinear dynamics model and a solution initial value of a computational fluid dynamics model.
In the scheme, the bearing nonlinear dynamic model is established by considering steel ball friction traction and lubrication traction aiming at steel ball stress analysis and based on a bearing coordinate system in the establishment process of the bearing nonlinear dynamic model.
In the above scheme, the bearing nonlinear dynamical model includes:
the steel ball being subjected to surface traction FfInner and outer raceway contact pressure QiAnd QoCentrifugal force FcOil gas dragging force FvRetainer collision force FcageAnd gyro moment Mg，FfFor friction traction FfaWith lubricated traction FfhThe resulting mechanical equilibrium equation is shown as:
Qocosαo-Fx″osinαo-Qicosαi+Fx″isinαi-Fc＝0 (1)
Qosinαo+Fx″ocosαo-Qisinαi-Fx″icosαi＝0 (2)
Fy′i-Fy′o+Fv+Fcage＝0 (3)
0.5D(γoFx″o+γiFx″i)＝Mgy′ (4)
0.5D(γoFy′osinαo+γiFy′isinαi)＝Mgz′ (5)
0.5D(γoFy′ocosαo+γiFy′icosαi)＝Mgx′ (6)
Figure BDA0003206385160000031
in which the indices i and o denote the inner and outer tracks, alpha denotes the contact angle, Fy′Is FfComponent in the coordinate system (o-x ' y ' z '), Fx″Is FfComponent in the coordinate system (o-x "y" z "), ζ ═ 2fi/o/(2fi/o+ 1); d is the steel ball diameter, a is the contact ellipse length;
steel ball traction force F caused by significant increase of friction traction and lubrication traction in high-speed light loadfThe calculation formula is as follows:
Figure BDA0003206385160000032
Figure BDA0003206385160000033
Figure BDA0003206385160000041
in the formula, mucIs the coefficient of friction of roughness, a and b are the length and width of the contact ellipse, x "and y" are the major and minor axes of the ellipse, LaAsperity load ratio, p (x ", y") is contact pressure, η (p (x ", y"), T) is lubricating viscosity, Δ u (x ", y") relative sliding velocity, h (x ", y") is oil film thickness, and lubrication condition parameter Λ ═ h ″t/(σr+σb)0.5，htIs the thickness of the central oil film, σrAnd σbIs the roughness of the raceway and the steel ball, Λ<0.01 denotes dry friction, 0.01. ltoreq. -)<3 represents mixed lubrication, and Λ is more than or equal to 3 represents full lubrication; frictional traction F obviously influenced by differential sliding and self-rotating motion of steel ballsfaAnd lubricating the traction FfhThe sliding speed calculation equation of the steel ball is as follows:
for the outer circle ellipse contact point (x ″)o,y″o)
Δvy″o＝-(ωx′cosαo+ωz′sinαo+ωc cosαo)
Figure BDA0003206385160000042
Figure BDA0003206385160000043
In the formula (d)mIs the bearing pitch diameter, RoIs the curvature radius of the deformed surface of the outer ring;
for the inner circle elliptical contact point (x ″)i,y″i)
Δvy″i＝-(ωx′cosαi+ωz′sinαi-(ωi-ωc)cosαi)
Figure BDA0003206385160000044
Figure BDA0003206385160000045
In the formula, ωiIs the revolution speed of the inner ring, RiIs the radius of curvature of the deformed surface of the inner ring; the spin speeds of the inner and outer raceways are:
ωso＝ωcsinαo+ωx′sinαo-ωz′cosαo (15)
ωsi＝(ωi-ωc)sinαi-ωx′sinαi+ωz′cosαi (16)
steel ball at contact point (x ″)o,y″o) And (x ″)i,y″i) Rolling speed VoAnd ViThe calculation formula is as follows:
Vo＝0.5(ωx′cosαo+ωz′sinαo-ωccosαo)
Figure BDA0003206385160000051
Vi＝0.5(ωx′cosαi+ωz′sinαi+(ωi-ωc)cosαi)
Figure BDA0003206385160000052
thus, the relative sliding velocity Δ u (x ', y') can be obtained
Figure BDA0003206385160000053
Aiming at the calculation of the time-varying friction coefficient of the steel ball, the rough friction coefficient of the steel ball and the raceway changes in real time in a high-speed light-load state, which is closely related to the sliding-rolling ratio s of the steel ball, and the rough friction coefficient calculation equation is as follows:
μc＝(-0.1+22.28s)e-181.46s+0.1 (20)
the steel ball sliding-rolling ratio calculation equation is as follows:
Figure BDA0003206385160000054
in the formula, VoAnd ViIs an elliptical contact point (x ″)o,y″o) And (x ″)i,y″i) Average scrolling speed of;
aiming at the elastic fluid dynamic lubrication condition, the steel ball lubricating oil film thickness calculation equation is as follows:
Figure BDA0003206385160000055
in the formula, h0Is the minimum oil film thickness, Rx"and Ry"is the ratio of curvature in the x" and y "directions, E is the elastic modulus, Γ is the continuous fluid domain, xeAnd yeIs a continuous fluid domain boundary.
Aiming at the stress balance of the bearing, under the action of radial and axial loads, the stress balance equation of the inner ring is as follows:
Figure BDA0003206385160000061
Figure BDA0003206385160000062
Figure BDA0003206385160000063
Figure BDA0003206385160000064
Figure BDA0003206385160000065
aiming at the calculation of the power loss of the steel ball, the power loss of the high-speed ball bearing is closely related to the differential sliding and the spinning sliding of the steel ball, the shearing force of an oil film, the elastic hysteresis deformation of a raceway, the collision force of the steel ball and a retainer and the lubricating viscosity, the power loss caused by the six factors is determined by the relationship between the friction torque and the rotating speed, and the calculation formula is as follows:
shearing friction moment M caused by oil film shearing actionL
Figure BDA0003206385160000066
In the formula, nbThe number of the steel balls;
lubricating viscosity friction torque Mv
Mv＝nbFvdm/2 (29)
Differential slip friction torque Md
Figure BDA0003206385160000071
Spin friction torque Ms
Figure BDA0003206385160000072
Elastic hysteresis friction moment Me
Figure BDA0003206385160000073
In the formula, the epsilon elastic hysteresis loss coefficient, Q is the contact force of the steel ball and the raceway, and delta is the contact deformation of the steel ball and the raceway;
collision friction moment Mc
Figure BDA0003206385160000074
In the formula eta0Is the dynamic viscosity of lubrication, WcIs the width of the guide surface of the holder, CnIs taking the coefficient 1, dcageIs the diameter of the cage guide surface, omegacageIs the rotational speed of the cage, d1Is the small diameter of the cage and inner ring guide surface, d2The diameter of the retainer and the outer ring guide surface is large;
power loss PLComprises the following steps:
PL＝(ML+Md+Me+Ms+Mv+Mc)ωi (34)。
the method for analyzing the lubrication temperature rise state of the high-speed bearing has the following beneficial effects:
1. the method considers the friction traction and the lubrication traction of the steel ball, and the steel ball is mainly acted by contact force because the friction traction and the lubrication traction of the steel ball are very small in low-speed heavy load; the steel ball contact force is significantly reduced at high speed and light load, but the friction drag and lubrication drag caused by high rotational speed are significantly increased so that their effect on the steel ball movement cannot be ignored. Due to the comprehensive consideration of the conditions, the model can more accurately simulate the real-time running condition of the bearing under the working conditions of high and low speed, light and heavy load.
2. The method provided by the invention considers that the real-time change of the rough friction coefficient and the lubrication shearing action caused by the real-time change of the lubrication state and the sliding-rolling ratio of the steel ball under high-speed light load, and reasonably considers the real-time change of the rough friction coefficient and the lubrication shearing action to accurately calculate the traction force and the friction torque of the steel ball, so that the model can accurately analyze the dynamic behaviors such as differential sliding, spinning sliding, gyroscopic sliding, time-varying friction force, time-varying friction torque and the like between the steel ball and the raceway, and further accurately calculate the power loss of the bearing. The method provides a theoretical basis for accurately defining the boundary conditions of the bearing computational fluid dynamics model and provides an efficient and reliable engineering technical means for correctly analyzing the lubrication and temperature rise in the bearing cavity. On the basis, the bearing structure is optimized to improve the lubricating effect and reduce the temperature rise. The method is efficient and reliable and has low cost.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a schematic diagram of a bearing dynamics model coordinate system definition;
FIG. 2 is a schematic view of a force balance of a steel ball;
FIG. 3 is a flow chart of a high speed bearing non-linear dynamics model and a computational fluid dynamics model;
FIG. 4 is a schematic diagram of the variation curve of three angular velocities of the steel ball along with the variation of the axial force;
FIG. 5 is a schematic diagram of revolution speed and power loss of a steel ball;
FIG. 6a is a schematic diagram of CFD model meshing;
FIG. 6b is a schematic view of a bearing cavity, steel balls, and cage grid;
FIG. 7 is a schematic diagram of the distribution of oil volume fraction at different axial forces, wherein (a)50N, (b)100N, (c)300N, (d) 1000N;
FIG. 8 is a schematic view showing the distribution of oil gas flow around the steel ball, wherein (a) is Fa50N, angular velocity ωx′When (b) is Fa1000N, angular velocity ωx′And ωy′The function of (1);
FIG. 9 is a schematic diagram showing the formation of periodic lubricant films of steel balls, wherein (a)50N and (b) 1000N;
FIG. 10 is a schematic view showing the temperature distribution of the inner and outer raceways at high and low speeds under light and heavy loads, wherein (a) Fa100N inner raceway, (b) Fa100N outer raceway (c) Fa1000N inner race, (d) Fa1000N is the outer raceway.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
Referring to fig. 3, the invention provides a method for analyzing a lubrication temperature rise state of a high-speed bearing, which comprises the following steps:
1) obtaining bearing structure parameters, working condition parameters, fluid heat transfer parameters and initial value conditions; the structural parameters comprise bearing parameters, material parameters and oil-gas lubrication parameters; the working condition parameters comprise rotating speed and radial and axial loads (high and low speed and light and heavy load); the lubricating heat transfer parameters comprise a VOF model, an RNG k-e turbulence model considering wall adhesion and an MRF model for zone rotation; the initial conditions include a bearing nonlinear dynamics model and an initial value for solving a computational fluid dynamics model.
2) And applying the rotating speed and the load to the bearing, and respectively calculating the stress balance of the steel ball and the stress balance of the inner ring according to the principles of moment balance and force balance.
3) In order to solve the stress balance of the steel ball and the stress balance of the inner ring, friction traction force and lubrication traction force need to be calculated, the sliding speed, the spinning speed and the rolling speed of the steel ball relative to the inner raceway and the outer raceway, and the thickness of an oil film between the steel ball and the inner raceway and the thickness of the oil film between the steel ball and the inner raceway and the outer raceway. The nonlinear dynamic model of the bearing considering the importance of the friction traction force of the steel ball under high-speed light load is represented by the following formula:
aiming at the stress analysis of the steel ball, the established bearing nonlinear dynamic model considers the friction traction and the lubrication traction of the steel ball, and the steel ball is mainly acted by contact force because the friction traction and the lubrication traction of the steel ball are very small in the low-speed heavy load process; the steel ball contact force is significantly reduced at high speed and light load, but the friction drag and lubrication drag caused by high rotational speed are significantly increased so that their effect on the steel ball movement cannot be ignored. The steel ball being subjected to surface traction Ff(Friction traction F)faWith lubricated traction FfhAnd), inner and outer raceway contact pressure QiAnd QoCentrifugal force FcOil gas dragging force FvRetainer collision force FcageAnd gyro moment MgThe resulting mechanical equilibrium is shown in fig. 1. The mechanical equilibrium equation obtained is as follows:
Qocosαo-Fx″osinαo-Qicosαi+Fx″isinαi-Fc＝0 (1)
Qosinαo+Fx″ocosαo-Qisinαi-Fx″icosαi＝0 (2)
Fy′i-Fy′o+Fv+Fcage＝0 (3)
0.5D(γoFx″o+γiFx″i)＝Mgy′ (4)
0.5D(γoFy′osinαo+γiFy′isinαi)＝Mgz′ (5)
0.5D(γoFy′ocosαo+γiFy′icosαi)＝Mgx′ (6)
Figure BDA0003206385160000101
in which the indices i and o represent the inner and outer raceways,alpha represents the contact angle, Fy′Is FfComponent in the coordinate system (o-x ' y ' z '), Fx″Is FfComponent in the coordinate system (o-x "y" z "), ζ ═ 2fi/o/(2fi/o+1). D is the steel ball diameter and a is the contact ellipse length.
The sliding speed calculation equation of the steel ball is as follows:
for the outer circle ellipse contact point (x ″)o,y″o)
Δvy″o＝-(ωx′cosαo+ωz′sinαo+ωc cosαo)
Figure BDA0003206385160000102
Figure BDA0003206385160000103
In the formula (d)mIs the bearing pitch diameter, RoIs the curvature radius of the deformed surface of the outer ring. Likewise, for the inner circle elliptical contact point (x ″)i,y″i)：
Δvy″i＝-(ωx′cosαi+ωz′sinαi-(ωi-ωc)cosαi)
Figure BDA0003206385160000104
Figure BDA0003206385160000111
In the formula, ωiIs the revolution speed of the inner ring, RiIs the radius of curvature of the deformed surface of the inner ring. The inner and outer raceway spin speeds are as follows:
ωso＝ωcsinαo+ωx′sinαo-ωz′cosαo (12)
ωsi＝(ωi-ωc)sinαi-ωx′sinαi+ωz′cosαi (13)
steel ball at contact point (x ″)o,y″o) And (x ″)i,y″i) Rolling speed VoAnd ViThe calculation formula is as follows:
Vo＝0.5(ωx′cosαo+ωz′sinαo-ωc cosαo)
Figure BDA0003206385160000112
Vi＝0.5(ωx′cosαi+ωz′sinαi+(ωi-ωc)cosαi)
Figure BDA0003206385160000113
then, the relative sliding speed Δ u (x ", y ″) can be obtained:
Figure BDA0003206385160000114
the steel ball lubricating oil film thickness calculation equation is as follows:
Figure BDA0003206385160000115
in the formula, h0Is the minimum oil film thickness, Rx″And Ry″Is the ratio of curvature in the x 'and y' directions, E is the modulus of elasticity, Γ is the continuous fluid domain, xeAnd yeIs a continuous fluid domain boundary.
4) In order to calculate the rough friction coefficient of the steel ball and the raceway which changes in real time under high-speed light load, the rough friction coefficient of the steel ball and the raceway is determined through a sliding-rolling ratio of the steel ball and a rough friction coefficient calculation equation; in order to accurately calculate the friction traction force of the steel ball, the friction traction force and the lubrication traction force are calculated by determining the lubrication state of the steel ball.
Aiming at the calculation of the time-varying friction coefficient of the steel ball, the rough friction coefficient of the steel ball and the raceway changes in real time in a high-speed light-load state, which is closely related to the sliding-rolling ratio s of the steel ball, and the rough friction coefficient calculation equation is as follows:
μc＝(-0.1+22.28s)e-181.46s+0.1 (18)
the steel ball slip ratio calculation equation is as follows
Figure BDA0003206385160000121
In the formula, VoAnd ViIs an elliptical contact point (x ″)o,y″o) And (x ″)i,y″i) Average scrolling speed of (1).
Aiming at the calculation of the time-varying traction force of the steel ball, under the radial and axial loads, the real-time changes of the lubrication state and the sliding-rolling ratio of the steel ball cause the real-time changes of the rough friction coefficient and the lubrication shearing action, and the real-time changes of the rough friction coefficient and the lubrication shearing action need to be reasonably considered to accurately calculate the traction force of the steel ball. Steel ball traction force F caused by significant increase of friction traction and lubrication traction in high-speed light loadfThe calculation formula is as follows:
Figure BDA0003206385160000122
Figure BDA0003206385160000123
Figure BDA0003206385160000124
in the formula, mucIs the coefficient of friction of roughness, and a and b are the contact ellipse lengthAnd width, x "and y" being the major and minor axes of the ellipse, LaAsperity load ratio, p (x ", y") is contact pressure, η (p (x ", y"), T) is lubricating viscosity, Δ u (x ", y") relative sliding velocity, h (x ", y") is oil film thickness, and lubrication condition parameter Λ ═ h ″t/(σr+σb)0.5，htIs the thickness of the central oil film, σrAnd σbIs the roughness of the raceway and the steel ball, Λ<0.01 denotes dry friction, 0.01. ltoreq. -)<3 represents mixed lubrication, and Λ ≧ 3 represents full lubrication.
Based on the above-mentioned solving of the steel ball stress balance, according to the action relation of the steel ball to the bearing inner ring, the solving of the inner ring stress balance equation is as follows:
Figure BDA0003206385160000131
Figure BDA0003206385160000132
Figure BDA0003206385160000133
Figure BDA0003206385160000134
Figure BDA0003206385160000135
5) the method comprises the steps of establishing a bearing computational fluid dynamics model by adopting a VOF model, considering an RNG k-e turbulence model with wall adhesion and an MRF model with zone rotation, a fluid flow mode, multiphase flow monitoring and other technologies, then defining the boundary conditions of the bearing computational fluid dynamics model according to the steel ball motion state and the bearing power loss calculated by the bearing nonlinear dynamics model, and further calculating the steel ball lubrication and temperature rise state in a bearing cavity. The bearing structure is optimized by the computational data of the bearing nonlinear dynamics model and the computational fluid dynamics model.
Aiming at the calculation of bearing power loss, the power loss of a high-speed ball bearing is closely related to the differential sliding and spinning sliding of a steel ball, the shearing force of an oil film, the elastic hysteresis deformation of a raceway, the collision force of the steel ball and a retainer and the lubricating viscosity, the power loss caused by the six factors is determined by the relationship between friction torque and rotating speed, and the calculation formulas are as follows:
shearing friction moment M caused by oil film shearing actionL
Figure BDA0003206385160000141
In the formula, nbThe number of the steel balls.
Lubricating viscosity friction torque Mv
Mv＝nbFvdm/2 (29)
Differential slip friction torque Md
Figure BDA0003206385160000142
Spin friction torque Ms
Figure BDA0003206385160000143
Elastic hysteresis friction moment Me
Figure BDA0003206385160000144
In the formula, the epsilon elastic hysteresis loss coefficient, Q is the contact force of the steel ball and the raceway, and delta is the contact deformation of the steel ball and the raceway.
Collision friction moment Mc
Figure BDA0003206385160000145
In the formula eta0Is the dynamic viscosity of lubrication, WcIs the width of the guide surface of the holder, CnIs taking the coefficient 1, dcageIs the diameter of the cage guide surface, omegacageIs the rotational speed of the cage, d1Is the small diameter of the cage and inner ring guide surface, d2The diameter of the retainer and the outer ring guide surface is large.
Thus, the power loss PLComprises the following steps:
PL＝(ML+Md+Me+Ms+Mv+Mc)ωi (34)
the method for analyzing the temperature rise state of lubrication of a high speed bearing according to the present invention will be described in further detail with reference to an example, which is not intended to limit the present invention. The method comprises the following steps:
1) the bearing structure parameters and lubrication conditions as shown in fig. 1 were obtained as shown in table 1:
TABLE 17008C angular contact bearing construction and lubrication parameters
Figure BDA0003206385160000151
2) Calculating the sliding speed, the spinning speed and the rolling speed of the steel ball relative to the inner and outer raceways and the thickness of an oil film between the steel ball and the inner and outer raceways according to the parameters in the step 1) and a bearing kinetic equation, and further calculating the rough friction coefficient and the lubricating state parameters of the steel ball to predict the friction traction force and the lubricating traction force.
3) Solving a force balance equation of the steel ball and the inner ring according to the calculation result in the step 2), and calculating the motion state of the steel ball and the power loss of the bearing, as shown in figures 4 and 5.
4) A VOF model, an RNG k-e turbulence model considering wall adhesion, an MRF model for zone rotation, a fluid flow mode, multiphase flow monitoring and other technologies are used to build a bearing computational fluid dynamics model, as shown in fig. 6. According to the angular velocity ω of the steel ball around the x ', y ' and z ' axes in FIGS. 4 and 5x′、ωy′And ωz′Defining the motion boundary of the steel ball and the revolution speed omega of the steel ballcA fluid domain motion boundary is defined. The power loss is distributed to the inner ring, the outer ring and the steel ball according to the ratio of 1:1:2 in figure 5. The inner ring, the outer ring, the steel ball and the interaction surface of the retainer and the fluid domain are defined as a heat flow wall to simulate the temperature distribution in the bearing cavity. The nozzle diameter was 1.5mm, and Mil-L-23699 lubricant was sprayed with a spray volume of 1L/min.
Fig. 4 and 5 show the change curves of three angular velocities of the steel ball, the revolution velocity of the steel ball and the power loss under the condition of light and heavy loads at 10000r/min, the boundary conditions of the computational fluid dynamics model of the bearing can be defined according to the data, the special load conditions are determined according to the data, and the lubrication and temperature rise conditions in the bearing cavity at 50N,100N,300N and 1000N are analyzed. Similarly, the bearing dynamic model provided by the patent is adopted to calculate the change curves of three angular velocities of the steel ball, the revolution velocity of the steel ball and the power loss at high and low speeds (such as 5000, 10000, 15000 and 20000r/min) and light and heavy loads (such as 100N and 1000N of axial force), and further analyze the lubrication and temperature rise conditions in the bearing cavity.
FIG. 7 shows the volume distribution of the lubricating oil, FIG. 8 shows the oil-gas flow in the bearing cavity, and FIG. 9 shows the oil-gas distribution around the steel ball, which reveals the formation of the lubricating oil film on the steel ball. Fig. 10 depicts the temperature distribution of the inner and outer raceways of the high and low speed light and heavy load bearing. The bearing temperature rise prediction method not only can change the motion state of the bearing and reduce power loss by improving the bearing structure according to the lubricating temperature rise condition in the bearing cavity, but also can be used for optimizing a sealing structure, an oil injection structure and the oil injection speed, and can predict the lubricating temperature rise condition of the bearing according to the actual engineering.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (4)

1. A method for analyzing the lubrication temperature rise state of a high-speed bearing is characterized by comprising the following steps:
1) obtaining structural parameters, working condition parameters and initial value conditions of the bearing; the structural parameters comprise bearing parameters, material parameters and oil-gas lubrication parameters;
2) applying the rotating speed and the load to a bearing, and respectively calculating the stress balance of the steel ball and the stress balance of the inner ring according to the principles of moment balance and force balance;
3) calculating friction traction and lubrication traction, the sliding speed, the spinning speed and the rolling speed of the steel ball relative to the inner and outer raceways, and the thickness of an oil film between the steel ball and the inner and outer raceways, and solving the stress balance of the steel ball and the stress balance of the inner ring;
4) determining the rough friction coefficient of the steel ball and the raceway by a sliding-rolling ratio of the steel ball and a rough friction coefficient calculation equation; in order to accurately calculate the friction traction of the steel ball, the friction traction and the lubrication traction are calculated by determining the lubrication state of the steel ball;
5) establishing a bearing computational fluid dynamics model by adopting an RNG k-epsilon model, a fluid flow mode and multiphase flow monitoring, then defining the boundary condition of the bearing computational fluid dynamics model according to the steel ball motion state and the bearing power loss calculated by the bearing nonlinear dynamics model, and further calculating the steel ball lubrication and temperature rise state in a bearing cavity; the bearing structure is optimized by the computational data of the bearing nonlinear dynamics model and the computational fluid dynamics model.
2. The method for analyzing the lubrication temperature rise state of the high-speed bearing according to claim 1, wherein the structural parameters comprise bearing parameters, material parameters and oil-gas lubrication parameters; the working condition parameters comprise rotating speed and radial and axial loads; the initial conditions include a bearing nonlinear dynamics model and a solution initial value of a computational fluid dynamics model.
3. The method for analyzing the lubrication temperature rise state of the high-speed bearing according to claim 2, wherein the established bearing nonlinear dynamical model considers steel ball friction traction and lubrication traction in the bearing nonlinear dynamical model establishing process aiming at steel ball stress analysis and based on a bearing coordinate system.
4. The method of claim 3, wherein the bearing nonlinear dynamical model comprises:
the steel ball being subjected to surface traction FfInner and outer raceway contact pressure QiAnd QoCentrifugal force FcOil gas dragging force FvRetainer collision force FcageAnd gyro moment Mg，FfFor friction traction FfaWith lubricated traction FfhThe resulting mechanical equilibrium equation is shown as:
Qocosαo-Fx″osinαo-Qicosαi+Fx″isinαi-Fc＝0 (1)
Qosinαo+Fx″ocosαo-Qisinαi-Fx″icosαi＝0 (2)
Fy′i-Fy′o+Fv+Fcage＝0 (3)
0.5D(γoFx″o+γiFx″i)＝Mgy′ (4)
0.5D(γoFy′osinαo+γiFy′isinαi)＝Mgz′ (5)
0.5D(γoFy′ocosαo+γiFy′icosαi)＝Mgx′ (6)
Figure FDA0003206385150000021
in the formula, subscripti and o represent inner and outer raceways, alpha represents the contact angle, Fy′Is FfComponent in the coordinate system (o-x ' y ' z '), Fx″Is FfComponent in the coordinate system (o-x "y" z "), ζ ═ 2fi/o/(2fi/o+ 1); d is the steel ball diameter, a is the contact ellipse length;
steel ball traction force F caused by significant increase of friction traction and lubrication traction in high-speed light loadfThe calculation formula is as follows:
Figure FDA0003206385150000022
Figure FDA0003206385150000023
Figure FDA0003206385150000024
in the formula, mucIs the coefficient of friction of roughness, a and b are the length and width of the contact ellipse, x "and y" are the major and minor axes of the ellipse, LaAsperity load ratio, p (x ", y") is contact pressure, η (p (x ", y"), T) is lubricating viscosity, Δ u (x ", y") relative sliding velocity, h (x ", y") is oil film thickness, and lubrication condition parameter Λ ═ h ″t/(σr+σb)0.5，htIs the thickness of the central oil film, σrAnd σbIs the roughness of the raceway and the steel ball, Λ<0.01 denotes dry friction, 0.01. ltoreq. -)<3 represents mixed lubrication, and Λ is more than or equal to 3 represents full lubrication; frictional traction F obviously influenced by differential sliding and self-rotating motion of steel ballsfaAnd lubricating the traction FfhThe sliding speed calculation equation of the steel ball is as follows:
for the outer circle ellipse contact point (x ″)o,y″o)
Figure FDA0003206385150000031
Figure FDA0003206385150000032
In the formula (d)mIs the bearing pitch diameter, RoIs the curvature radius of the deformed surface of the outer ring;
for the inner circle elliptical contact point (x ″)i,y″i)
Figure FDA0003206385150000033
Figure FDA0003206385150000034
In the formula, ωiIs the revolution speed of the inner ring, RiIs the radius of curvature of the deformed surface of the inner ring; the spin speeds of the inner and outer raceways are:
ωso＝ωcsinαo+ωx′sinαo-ωz′cosαo (15)
ωsi＝(ωi-ωc)sinαi-ωx′sinαi+ωz′cosαi (16)
steel ball at contact point (x ″)o,y″o) And (x ″)i,y″i) Rolling speed VoAnd ViThe calculation formula is as follows:
Figure FDA0003206385150000041
Figure FDA0003206385150000042
thus, the relative sliding velocity Δ u (x ', y') can be obtained
Figure FDA0003206385150000043
Aiming at the calculation of the time-varying friction coefficient of the steel ball, the rough friction coefficient of the steel ball and the raceway changes in real time in a high-speed light-load state, which is closely related to the sliding-rolling ratio s of the steel ball, and the rough friction coefficient calculation equation is as follows:
μc＝(-0.1+22.28s)e-181.46s+0.1 (20)
the steel ball sliding-rolling ratio calculation equation is as follows:
Figure FDA0003206385150000044
in the formula, VoAnd ViIs an elliptical contact point (x ″)o,y″o) And (x ″)i,y″i) Average scrolling speed of;
aiming at the elastic fluid dynamic lubrication condition, the steel ball lubricating oil film thickness calculation equation is as follows:
Figure FDA0003206385150000045
in the formula, h0Is the minimum oil film thickness, Rx″And Ry″Is the ratio of curvature in the x 'and y' directions, E is the modulus of elasticity, Γ is the continuous fluid domain, xeAnd yeIs a continuous fluid domain boundary.
Aiming at the stress balance of the bearing, under the action of radial and axial loads, the stress balance equation of the inner ring is as follows:
Figure FDA0003206385150000051
Figure FDA0003206385150000052
Figure FDA0003206385150000053
Figure FDA0003206385150000054
Figure FDA0003206385150000055
aiming at the calculation of the power loss of the steel ball, the power loss of the high-speed ball bearing is closely related to the differential sliding and the spinning sliding of the steel ball, the shearing force of an oil film, the elastic hysteresis deformation of a raceway, the collision force of the steel ball and a retainer and the lubricating viscosity, the power loss caused by the six factors is determined by the relationship between the friction torque and the rotating speed, and the calculation formula is as follows:
shearing friction moment M caused by oil film shearing actionL
Figure FDA0003206385150000056
In the formula, nbThe number of the steel balls;
lubricating viscosity friction torque Mv
Mv＝nbFvdm/2 (29)
Differential slip friction torque Md
Figure FDA0003206385150000061
Spin friction torque Ms
Figure FDA0003206385150000062
Elastic hysteresis friction moment Me
Figure FDA0003206385150000063
In the formula, the epsilon elastic hysteresis loss coefficient, Q is the contact force of the steel ball and the raceway, and delta is the contact deformation of the steel ball and the raceway;
collision friction moment Mc
Figure FDA0003206385150000064
In the formula eta0Is the dynamic viscosity of lubrication, WcIs the width of the guide surface of the holder, CnIs taking the coefficient 1, dcageIs the diameter of the cage guide surface, omegacageIs the rotational speed of the cage, d1Is the small diameter of the cage and inner ring guide surface, d2The diameter of the retainer and the outer ring guide surface is large;
power loss PLComprises the following steps:
PL＝(ML+Md+Me+Ms+Mv+Mc)ωi (34)。
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