CN113779826B - Mixed lubrication model modeling method for dynamic load sliding bearing transient state and time-lag deformation alternate coupling action - Google Patents
Mixed lubrication model modeling method for dynamic load sliding bearing transient state and time-lag deformation alternate coupling action Download PDFInfo
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Abstract
The invention relates to a modeling method of a hybrid lubrication model with alternating coupling action of transient state and time-lag deformation of a dynamic sliding bearing. The viscoelastic material of the sliding bearing has the characteristics that transient deformation and time-lapse deformation alternately occur under the action of time-varying load and mutually influence. Firstly, constructing a time sequence association deformation equation of a bearing bush based on a finite element method and a standard linear solid model to calculate time-lag deformation in unit time; then, calculating actual deformation at the current moment by using a Boltzmann superposition principle and accumulating transient deformation, so as to correct the calculation method of the oil film thickness; and finally, substituting the model into the existing mixed lubrication (MEHD) model to form a mixed lubrication model with the alternately coupling action of transient and time-lapse deformation. The invention has the capability of identifying the knocking and micro rough bumping and grinding characteristics of the dynamic load sliding bearing through comparison with the traditional modeling method.
Description
Technical Field
The invention relates to a modeling method of a dynamic load sliding bearing mixed lubrication state analysis model.
Background
Slide bearings are widely used in a variety of reciprocating and rotating machines. Typically it is subjected to heavy loads with small local clearances in a mixed lubrication regime with both microscopic asperity contact and oil film lubrication. The complete elastic assumption of the hybrid elastohydrodynamic lubrication (MEHD) model currently available for analyzing this lubrication state is that the bearing deformation is instantaneously completed, but the solid material has viscoelasticity, and a part of the deformation takes time to complete, i.e., the time-lapse deformation, in addition to the transient deformation generated at the loading moment. Thus, when the sliding shaft is subjected to a time-varying load, the bearing deformation always lags behind the load change, while the complete elasticity presumes that the deformation is matched synchronously with the load, and the "excessive" deformation will overcompensate the oil film thickness, thereby weakening or ignoring the knocking and micro-rough bump-and-wear characteristics of the bearing.
Therefore, aiming at the problems, the invention designs a dynamic sliding bearing mixed lubrication model modeling method aiming at the time lag characteristic of the dynamic sliding bearing viscoelasticity deformation. The method takes into account the characteristics of the interaction of the alternating occurrence of transients and time-lapse deformations of the viscoelastic solid material.
Disclosure of Invention
The invention aims to provide a modeling method for dynamic-load sliding bearing mixed lubrication state mechanism analysis. The invention establishes a time sequence-related deformation equation, thereby relating the alternating coupling influence of transient state and time-lag deformation on bearing lubrication, further correcting the calculation method of the oil film thickness, substituting the geometric boundary initial value into the equation for solving the average Reynolds equation, and calculating to obtain the mixed lubrication performance parameters of the bearing, such as the oil film pressure, the friction power consumption, the rough contact pressure and the like. The invention has the capability of accurately capturing the knocking and micro rough bumping and grinding characteristics of the dynamic sliding bearing.
The aim of the invention is achieved by the following technical scheme: firstly, constructing a time sequence association deformation equation of a bearing based on a finite element method and a standard linear solid model to calculate time-lag deformation in unit time; further, the actual deformation at the current moment is obtained by accumulating transient deformation through the Boltzmann superposition principle; then, correcting the oil film thickness calculation method; and finally substituting into a hybrid elastohydrodynamic lubrication (MEHD) model.
A dynamic load sliding bearing mixed lubrication model modeling method is characterized by comprising the following steps:
firstly, establishing a time sequence association deformation equation to calculate the actual deformation of the bearing at any moment.
(1) Integrating a motion equation of a standard linear solid model, establishing a time sequence correlation deformation equation, and calculating time-lag deformation of the sliding bearing in unit time under the action of time-varying load:
1) Standard linear solid model equation of motion integration:
wherein E is t And E is l Transient and time-lapse elastic moduli, E, of the bearing material respectively b ＝(1/E t +1/E l ) -1 ，E b Is the equivalent elastic modulus of the bearing. Eta is the viscosity of the material and epsilon t Sum epsilon l Transient and time-lapse strain normal to the bearing inner surface, respectively, τ=η/E l Let Δt=τ/10 empirically as the material relaxation time constant, Δt is the time step.
2) Multiplying the thickness of the bearing on the left side and the right side of the formula (2) according to strain definition to obtain a time sequence associated deformation equation about bearing deformation:
wherein delta l (x, z, t) is the accumulated time-lapse deformation of the bearing at the present moment, andfor the bearing at the current average oil film pressure +.>Corresponding time lag elastic modulus E under action l Is deformed with full time lag. i is a time step number (i=1, 2.,. Q-1), q is a total time point number, and can be freely selected according to requirements. />For the unit time-lag deformation in the ith time step, x and z are the circumferential direction and the axial direction of the bearing respectively, and t= (i-1) deltat is a time variable;
(2) Based on the Boltzmann principle, overlapping time-lag deformation in unit time and accumulating transient deformation, and calculating actual deformation of the bearing at the current moment:
wherein delta (x, z, t) is the actual deformation of the bearing at the current moment, delta t (x, z, t) is the current average oil film pressure of the bearingCorresponding transient elastic modulus E under action t The resulting transient deformation;
secondly, establishing a bearing overall rigidity matrix, solving a bearing finite element rigidity equation by adopting a Gausserdel iteration method, and calculating average oil film pressureTransient deformation delta generated by bearing under action t (x, z, t) and complete time-lapse deformation
Wherein d i，i Is an element in a displacement vector d of a node of the bearing finite element model, K i，j Is an element in the overall stiffness matrix K, F i，i Is an element in a node force vector (composed of oil film pressure sequences), m and n are axial and circumferential grid numbers respectively, and i and j are node numbers. Taking normal displacement of the node as bearing deformation;
thirdly, correcting the oil film thickness by using actual deformation, and further calculating the average oil film thickness by using a polynomial probability density function similar to Gaussian distribution, wherein the calculation mode is as follows:
wherein h (x, z, t) isThe thickness of the oil film corrected by the actual deformation,for average oil film thickness, R b The inner diameter of the bearing, c is the bearing clearance, epsilon is the eccentricity, sigma is the comprehensive surface roughness, g is the film thickness ratio coefficient, g=h/(3 sigma);
and fourthly, substituting the corrected oil film thickness into an average Reynolds equation and a rough contact model to calculate average oil film pressure and rough contact pressure, wherein the calculation equation is as follows:
(1) Equation of average Reynolds number
Wherein,is the average oil film pressure. U (U) 1 And U 2 Journal and bearing surface speeds, respectively, the bearing being fixed, thusOmega is the rotation speed of the journal and ∈>For the eccentricity speed>And θ is the circumferential angle of the bearing circumference. Mu is the viscosity of the lubricating oil, ">μ 0 Is the viscosity of the lubricating oil at normal pressure. Phi (phi) x And phi z Is the pressure flow factor, phi s For the shear flow factor, the formula is calculated:
wherein sigma j Is the standard deviation of the surface roughness of the journal;
(2) Greenwood and Tripp rough contact model
Wherein,for the average rough contact pressure, k is an empirical factor, 1.185×10 is taken -3 . E is the integrated elastic modulus, E= ((1-v) j 2 )/E j +(1-v b 2 )/E b ) Wherein E is b And E is j Elastic modulus, v, of bearing and journal, respectively b And v j Poisson's ratio for the bearing and journal, respectively.
Fifth, solving the model:
(1) Bearing motion parameter based on any momentCumulative time-lapse deformation delta l (x, z, t) and transient deformation delta t (x, z, t) =0, and calculating an initial oil film thickness value (h (x, z, t), +_using equation (6)>
(2) Substituting the initial value of the oil film thicknessSimultaneous iterative solution of average reynolds equation (8) and bearing finite element stiffness equation (5), transient deformation delta of iterative process change t (x, z, t) continuously updates the oil film thickness (h (x, z, t),obtaining average oil film pressure +.>
(3) Calculating an average rough contact pressure using a rough contact model (12) based on the oil film thickness h (x, z, t) corrected by the actual deformation delta (x, z, t)
(4) Calculating the unit time lag deformation delta in the ith time step by adopting a time sequence correlation deformation equation (3) l i (x, z, delta t) and obtaining the accumulated time-lapse deformation delta at the next moment by superposition of the Boltzmann principle l (x, z, t+Δt), and updating the bearing motion parameters
(5) Time step update (i=i+1, t=t+Δt), repeating the above steps until the total number of time steps (q-1) is reached.
Drawings
FIG. 1 solution flow chart of the invention
The motion law of the bearing of FIG. 2 is schematically represented
FIG. 3 Peak oil film pressure and cloud distribution
FIG. 4 bearing deformation and rough contact pressure
Detailed Description
For a better understanding of the technical solution of the present invention, the following detailed description of the specific embodiments of the present invention will be given with reference to the accompanying drawings.
The research object is a connecting rod big end bearing of a 3SFE four-cylinder petrol engine, which is a typical dynamic load sliding bearing, and the center of a shaft neck can generate periodical eccentric motion. The bearing geometry and material properties parameters are shown in table 1. Aiming at the eccentric motion rule of the dynamic load sliding bearing, the eccentric motion considering half-frequency whirling motion is set. Setting the eccentricity speed toSetting the total time q=120; setting the whirling speed to +.>Wherein ω is the rotation speed of the journal and the value is 315rad/s. The time step is set to Δt=1×10 -6 s. The variation rule of the eccentricity is +.>Initial eccentricity is set to epsilon 1 =1-3σ/c. There are two boundaries of the present invention: (1) Transient boundary,/->Only transient deformation exists, namely the existing mixed lubrication (MEHD) model; (2) Time-lag border->There is only a time-lapse deformation. To demonstrate the advantages of the present invention, the results of the calculations for both boundaries under the same conditions were compared. The solving flow chart of the invention is shown in fig. 1, and the motion rule diagram of the bearing is shown in fig. 2.
Table 1 bearing geometry and material parameters
| Bearing parameters | Numerical value | Bearing parameters | Numerical value |
| Bearing inner diameter (R) b ) | 0.024m | Standard deviation of journal surface roughness (sigma j ) | 0.8μm |
| Bearing gap (c) | 0.0001m | Integrated surface roughness (sigma) | 1.13μm |
| Bearing elastic modulus (E) b ) | 1.15×10 5 MPa | Ratio of elastic modulus (E t /E l ) | 1 |
| Journal elastic modulus (E) j ) | 2.2×10 5 MPa | Relaxation time of bearing material (tau) | 1.25×10 -5 s |
| Poisson ratio of bearing (v) b ) | 0.34 | Viscosity of lubricating oil (mu) 0 ) | 0.01Pa·s |
| Poisson ratio of journal (v) j ) | 0.3 |
The specific implementation steps of the invention are as follows:
in a first step, according to the viscoelastic characteristic parameters (E b ，E t /E l τ) determining a time sequence associated deformation equation (3), and further obtaining a calculation formula (4) of actual deformation of the bearing at any moment;
second, according to the elastic modulus E of the bearing material b And Poisson ratio v j Determining an overall stiffness matrix K and a stiffness equation (5) of the bearing finite element model;
third, according to the motion parameters of the bearingAnd the actual deformation delta of the bearing, the oil film thickness h is calculated by adopting a formula (6), and the oil film thickness h is further calculated based on the characteristic parameter (sigma) of the surface topography of the bearing j Sigma) and calculating the average oil film thickness using equation (7)
Fourthly, solving an average Reynolds equation (8) and a bearing finite element stiffness equation (5) through simultaneous iteration to obtain average oil film pressure at any momentThe actual deformation δ of the bearing and then the average rough contact pressure ++are calculated based on the actual deformation of the bearing using equation (12) and equation (13)>
Fifthly, calculating the average oil film pressure of the bearing in a set motion mode aiming at the actual dynamic load sliding bearing object by utilizing the established mixed lubrication modelActual deformation delta and rough contact pressure of bearing>As shown in fig. 3 and 4;
the calculation result aiming at the actual case shows that the deformation of the bearing calculated by the mixed lubrication model established by the invention is obviously lagged behind the result of the existing mixed lubrication (MEHD) model, so that the oil film thickness of the bearing is not effectively compensated in the initial stage of eccentric movement, and the average rough contact pressure and the average oil film pressure are increased. However, in the centripetal movement stage at the later stage of eccentric movement, the oil film pressure without extrusion effect is greatly reduced, and deformation cannot be unloaded and recovered in time, so that the rough contact pressure is smaller than the MEHD result. The mixed lubrication model established by the invention can be proved to be capable of capturing knocking (oil film pressure is rapidly increased) and microcosmic rough bumping and grinding characteristics of the eccentric motion process of the dynamic load sliding bearing more accurately.
Claims (1)
1. The modeling method of the dynamic load sliding bearing hybrid lubrication model is characterized by comprising the following steps of:
firstly, establishing a time sequence association deformation equation to calculate actual deformation of the bearing at any moment;
(1) Integrating a motion equation of a standard linear solid model, establishing a time sequence correlation deformation equation, and calculating time-lag deformation of the sliding bearing in unit time under the action of time-varying load:
1) Standard linear solid model equation of motion integration:
wherein E is t And E is l Transient and time-lapse elastic moduli, E, of the bearing material respectively b ＝(1/E t +1/E l ) -1 ，E b Is the equivalent elastic modulus of the bearing; eta is the viscosity of the material and epsilon t Sum epsilon l Transient and time-lapse strain normal to the bearing inner surface, respectively, τ=η/E l For the material relaxation time constant, Δt is the time step, Δt=τ/10;
2) Multiplying the thickness of the bearing on the left side and the right side of the formula (2) according to strain definition to obtain a time sequence associated deformation equation about bearing deformation:
wherein delta l (x, z, t) is the accumulated time-lapse deformation of the bearing at the present moment, andfor the bearing at the current average oil film pressure +.>Corresponding time lag elastic modulus E under action l Is completely time-lapse deformed; i is a time step number, i=1, 2, …, q-1, q is the total number of time points; delta l i (x, z, Δt) is the unit time-lag deformation in the ith time step, x and z are the bearing circumferential and axial directions, respectively, t= (i-1) Δt is the time variable;
(2) Based on the Boltzmann principle, overlapping time-lag deformation in unit time and accumulating transient deformation, and calculating actual deformation of the bearing at the current moment:
wherein delta (x, z, t) is the actual deformation of the bearing at the current moment, delta t (x, z, t) is the current average oil film pressure of the bearingCorresponding transient elastic modulus E under action t The resulting transient deformation;
secondly, establishing a bearing overall rigidity matrix, solving a bearing finite element rigidity equation by adopting a Gausserdel iteration method, and calculating average oil film pressureTransient deformation delta generated by bearing under action t (x, z, t) and complete time-lapse deformation +.>
Wherein d i,i Is an element in a displacement vector d of a node of the bearing finite element model, K i,j Is an element in the overall stiffness matrix K, F i,i The element in the node force vector F is formed by sequentially arranging oil film pressure; m and n are axial and circumferential grid numbers respectively, and i and j are node numbers; taking normal displacement of the node as bearing deformation;
thirdly, correcting the oil film thickness by using actual deformation, and further calculating the average oil film thickness by using a polynomial probability density function similar to Gaussian distribution, wherein the calculation mode is as follows:
wherein h (x, z, t) is the oil film thickness corrected by the actual deformation,for average oil film thickness, R b The inner diameter of the bearing, c is the bearing clearance, epsilon is the eccentricity, sigma is the comprehensive surface roughness, g is the film thickness ratio coefficient, g=h/(3 sigma);
and fourthly, substituting the corrected oil film thickness into an average Reynolds equation and a rough contact model to calculate average oil film pressure and rough contact pressure, wherein the calculation equation is as follows:
(1) Equation of average Reynolds number
Wherein,is the average oil film pressure; u (U) 1 And U 2 Journal and bearing surface speeds, respectively, the bearing being fixed, thusOmega is the rotation speed of the journal and ∈>For the eccentricity speed>The vortex speed is theta, and the circumferential angle of the bearing is theta; mu is the viscosity of the lubricating oil, ">μ 0 Is the viscosity of the lubricating oil under normal pressure; phi (phi) x And phi z Is the pressure flow factor, phi s For the shear flow factor, the formula is calculated:
wherein sigma j Is the standard deviation of the surface roughness of the journal;
(2) Greenwood and Tripp rough contact model
Wherein,for the average rough contact pressure, k is an empirical factor, 1.185×10 is taken -3 The method comprises the steps of carrying out a first treatment on the surface of the E is the integrated elastic modulus, E= ((1-v) j 2 )/E j +(1-v b 2 )/E b ) -1 Wherein E is b And E is j Elastic modulus, v, of bearing and journal, respectively b And v j Poisson's ratio for bearings and journals, respectively;
fifth, solving the model:
(1) Bearing motion parameter based on any momentCumulative time-lapse deformation delta l (x, z, t) and transient deformation delta t (x, z, t) =0, and calculating an initial value +.>
(2) Substituting the initial value of the oil film thicknessSimultaneous iterative solution of average reynolds equation (8) and bearing finite element stiffness equation (5), transient deformation delta of iterative process change t (x, z, t) continuously updates the oil film thickness (h (x, z, t),obtaining average oil film pressure +.>
(3) Calculating an average rough contact pressure using a rough contact model (12) based on the oil film thickness h (x, z, t) corrected by the actual deformation delta (x, z, t)
(4) Calculating the unit time lag deformation delta in the ith time step by adopting a time sequence correlation deformation equation (3) l i (x, z, delta t) and obtaining the accumulated time-lapse deformation delta at the next moment by superposition of the Boltzmann principle l (x, z, t+Δt), and updating the bearing motion parameters
(5) Time step update (i=i+1, t=t+Δt), repeating the above steps until the total number of time steps q-1 is reached.
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|---|---|---|---|---|
| GB877738A (en) * | 1959-03-05 | 1961-09-20 | Glacier Co Ltd | Lubrication of plain bearings in machinery subject to cyclic loading |
| CN108776430A (en) * | 2018-05-08 | 2018-11-09 | 苏州科技大学 | A kind of ball-screw feed drive system position loop gain optimization obtaining value method |
| CN108984933A (en) * | 2018-07-25 | 2018-12-11 | 太原科技大学 | The boundary element method of rolling bearing load and pressure is calculated under the conditions of elastohydrodynamic lubrication |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB877738A (en) * | 1959-03-05 | 1961-09-20 | Glacier Co Ltd | Lubrication of plain bearings in machinery subject to cyclic loading |
| CN108776430A (en) * | 2018-05-08 | 2018-11-09 | 苏州科技大学 | A kind of ball-screw feed drive system position loop gain optimization obtaining value method |
| CN108984933A (en) * | 2018-07-25 | 2018-12-11 | 太原科技大学 | The boundary element method of rolling bearing load and pressure is calculated under the conditions of elastohydrodynamic lubrication |
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| Title |
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| 织构化滑动轴承混合润滑与磨损耦合数值模型;金乐佳;杨建玺;李成功;;润滑与密封(第10期);全文 * |
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