CN109002610A - A kind of stochastic model that rough surface bush(ing) bearing turbulent lubrication calculates - Google Patents
A kind of stochastic model that rough surface bush(ing) bearing turbulent lubrication calculates Download PDFInfo
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Abstract
The present invention relates to the stochastic models that a kind of rough surface bush(ing) bearing turbulent lubrication calculates.The random laminar flow lubrication theory of rough surface bush(ing) bearing based on Clayton Christensen (Christensen) and the smooth surface bush(ing) bearing turbulent lubrication of zero equation form are theoretical, the stochastic turbulence lubrication Theory Model proposed suitable for the analysis of rough surface bush(ing) bearing turbulent lubrication is derived, the stochastic turbulence lubrication Theory Model is as follows:It is able to achieve using the stochastic turbulence lubrication model and the turbulent lubrication performance of one-dimensional longitudinal rough surface bush(ing) bearing, one-dimensional lateral rough surface bush(ing) bearing and isotropism rough surface bush(ing) bearing is analyzed.
Description
Technical field
The invention belongs to turbulent lubrication technical fields, and in particular to a kind of rough surface bush(ing) bearing turbulent lubrication meter
The stochastic model of calculation.
Background technique
The practical bush(ing) bearing surface that machining is formed is rough surface, although surface roughness is sliding compared to radial
Dynamic bearing gap is smaller, but bush(ing) bearing generally all works compared under large eccentricity, at this time surface roughness and radial direction
Sliding bearing minimum oil film thickness is in the same order of magnitude, and surface roughness produces the turbulent lubrication state to bush(ing) bearing
Life significantly affects, and shaggy influence be can not ignore.So needing to examine in the design analysis of bush(ing) bearing turbulent lubrication
Consider shaggy influence.
Up to the present, the computation model both at home and abroad for the analysis of rough surface bush(ing) bearing turbulent lubrication is mainly adopted
With bridge sheet (Hashimoto) homogeneous isotropism rough surface turbulent lubrication theoretical model.1989, this grade of bridge was first based on turbulent flow
Logarithmic rate distribution law in boundary layer is derived the resistance of pressure current and shear flow under smooth surface and rough surface respectively
Law formula is derived homogeneous isotropism rough surface in conjunction with Hess (Hirs) the bulk flow theory proposed and radially slides
Bearing turbulent lubrication theoretical model.Although the model is capable of handling the turbulent lubrication of homogeneous isotropism rough surface, simultaneously
Other type rough surfaces present in practical application cannot be handled as relatively mostly used in practice by grinding axle journal appearance
The turbulent lubrication problem for longitudinal rough surface bush(ing) bearing that face and boring processing inner surface of bearing bush are constituted.
Summary of the invention
Isotropism rough surface diameter can only be handled to solve existing rough surface bush(ing) bearing turbulent lubrication model
The problem of to sliding bearing turbulent lubrication, the present invention provides a kind of rough surface bush(ing) bearing turbulent lubrication calculate with
Machine model, is applicable not only to the turbulent lubrication analysis of isotropism rough surface bush(ing) bearing, but also is suitable for longitudinal
The turbulent lubrication analysis of rough surface bush(ing) bearing and lateral rough surface bush(ing) bearing.
The random laminar flow lubrication theory of rough surface bush(ing) bearing and zero based on Clayton Christensen (Christensen)
The smooth surface bush(ing) bearing turbulent lubrication of equation form is theoretical, and derivation, which is proposed, radially slides axis suitable for rough surface
The stochastic turbulence lubrication Theory Model of turbulent lubrication analysis is held, the stochastic turbulence lubrication Theory Model is as follows:
H is the oil film thickness between nominal smooth surface in formula (1),For average oil film pressure, μ is lubricant dynamic viscosity,
Gx、GzFor stochastic turbulence lubrication Theory Model equation parameter, V is journal surface tangential velocity, and x coordinate direction is axle journal rotation side
To z coordinate direction is bearing width direction, and t is the time.
Corresponding to one-dimensional longitudinal rough surface bush(ing) bearing turbulent lubrication model
H is true oil film thickness, K in formula (2)x、KzFor new turbulent lubrication equation coefficient, E () is expectation operator, by following formula
Definition
In E (x) expression formula, f (x) is the probability density function of stochastic variable x.
Corresponding to one-dimensional lateral rough surface bush(ing) bearing turbulent lubrication model
Variable declaration in formula (3) is identical as the variable declaration in formula (2).
Corresponding to isotropism rough surface bush(ing) bearing turbulent lubrication model
Gx=E (H3)E(1/Kx), Gz=E (H3)E(1/Kz) (4)
Variable declaration in formula (4) is identical as the variable declaration in formula (2).
Characterization bush(ing) bearing performance bearing capacity (Unbalance) be in the component of x and z coordinate axis direction
Fx、FzIn expression formula, L is bearing width, and θ is the angle measured along bearing circumferencial direction, and R is bearing radius.
Then the bearing capacity of bearing is
It is realized using the stochastic model that the rough surface bush(ing) bearing turbulent lubrication calculates coarse to one-dimensional longitudinal direction
Surface bush(ing) bearing, one-dimensional lateral rough surface bush(ing) bearing and isotropism rough surface bush(ing) bearing
The analysis of turbulent lubrication performance.
Referring to Fig. 1, the stochastic model establishment process explanation of rough surface bush(ing) bearing turbulent lubrication calculating of the present invention
As follows: step (1) establishes the average Reynolds type turbulent lubrication equation of rough surface bush(ing) bearing:
1. establishing the turbulent lubrication equation of any local location of rough surface
Zero equation turbulent lubrication model of smooth surface bush(ing) bearing is
In formula (5), p is oil film pressure, and oil film thickness of the h between smooth surface, V is journal surface tangential velocity, and μ is profit
Lubrication prescription dynamic viscosity, x coordinate direction are axle journal rotation direction, and z coordinate direction is bearing width direction, and t is time, kxAnd kzFor
Turbulent lubrication equation coefficient.
In formula (6), (7), a1、a2、b1And b2For turbulent lubrication model determine parameter, such as Constantine Nei Siku
(Constantinescu) a in turbulent lubrication model1=0.0260, b1=0.8265, a2=0.0198, b2=0.7410 and Buddhist nun
A in Ge-Pan (Ng-Pan) turbulent lubrication model1=0.0136, b1=0.9000, a2=0.0043, b2=0.9600；Re=ρ
Vh/ μ is local Reynolds number, and wherein ρ is lubricant density.
The application range of turbulent lubrication equation (5) is Re >=1000.As Re < 1000, kx=12, kz=12, equation (5)
It is changed into laminar flow lubrication equation.
For the turbulent lubrication of rough surface bush(ing) bearing, should all expire in any local location of bearing rough surface
Sufficient turbulent lubrication equation (5).Referring to fig. 2, H is true oil film thickness, and h is the oil film thickness between nominal smooth surface.In this way, knot
Close the specific expression of rough surface bush(ing) bearing oil film thickness, the available any part of rough surface bush(ing) bearing
The turbulent lubrication equation of position is
In formula (8), Kx、KzFor new turbulent lubrication equation coefficient.
Kx、KzBy by kx、kzH in expression formula substitutes to obtain with H, is
True oil film thickness H can be expressed as
H=h (x, z, t)+hs(x,z,ξ)
In the expression formula of H, hsTo make true oil film thickness H deviate nominal oil film thickness h's due to shaggy influence
It is worth (referred to as oil film thickness component), assumes h under normal circumstancessDesired value along entire bearing lubrication surface is 0.
For any rough surface, hsIt is the function of coordinate x, z and stochastic variable ξ.It is assumed that stochastic variable ξ's is specific
Value is from largely having the similar of identical statistical property but select one in not exclusively the same Rough surface height distribution situation
Specific Rough surface height distribution situation.In this way, under given ξ value (i.e. one given roughness height distribution), hsIt is
One about coordinate amount x and z qualitative function really.So H can be treated as ergodic stationary random process.
Description of the equation (8) just for any local location turbulent lubrication situation of rough surface sliding bearing, Bu Nengzhi
The turbulent lubrication situation of describing roughness surface sliding bearing entirety is connect, therefore can not be in the turbulent lubrication of rough surface sliding bearing
It is directly applied in analysis.
2. the turbulent lubrication of rough surface bush(ing) bearing entirety describes
It is obtained above based on the turbulent lubrication model of smooth surface bush(ing) bearing in conjunction with the specific expression of rough surface
The bush(ing) bearing turbulent lubrication equation (8) suitable for any local location of rough surface is arrived.Below by appoint take it is micro-
First control volume establishes the average Reynolds type turbulent lubrication equation of describing roughness surface bush(ing) bearing unitary turbulence lubrication.
Referring to Fig. 3, a control volume being made of floor space Δ x Δ z and high H is arbitrarily chosen, size is much smaller than lubrication
Oil film overall dimension, but include enough dimpling peak and trench.
Based on intracorporal average flow rate balance is controlled, have
Or
In formula (11),
E () is expectation operator, is defined by the formula
In E (x) expression formula, f (x) is the probability density function of stochastic variable x.
In this way, formula (11) can be expressed as
Formula (12) is the average Reynolds type turbulent lubrication side of describing roughness surface bush(ing) bearing unitary turbulence lubrication
Journey.Step (2) provides assumed condition
The actual use of equation (12) needs to combine specific rough surface situation.Here based on the coarse of concrete form
Surface, which derives, can be directly applied for the one-dimensional longitudinal rough surface of bush(ing) bearing, one-dimensional lateral rough surface and isotropism
The average Reynolds type turbulent lubrication equation of rough surface.
If s1Expression is parallel to rough surface direction, s2It indicates perpendicular to rough surface direction.Rough surface radially slides axis
That holds turbulent lubrication model is built with following two basic assumption:
I oil film pressure gradientIt is the stochastic variable that a variance is 0.
Specific discharge q of the II perpendicular to rough surface directions2It is the stochastic variable that a variance is 0.
Step (3) determines bush(ing) bearing stochastic turbulence lubrication Theory Model formula
1. the average Reynolds type turbulent lubrication equation of one-dimensional longitudinal direction rough surface bush(ing) bearing
Referring to fig. 4, one-dimensional longitudinal rough surface assume the form of rough surface be elongated dimpling peak and trench all along
Axle journal rotation direction.In this way, oil film thickness expression formula is
H=h (x, z, t)+hs(z,ξ) (13)
By formula (13) it is found that the random variation of oil film thickness is mainly along axial direction, then from assuming ISide
Difference is 0, andH3And 1/KxMutually independent random variables can be regarded as, so
Specific discharge in the z-direction is
ThenBy assuming q known to IIzVariance be 0, so
Formula (14) and (17) are substituted into formula (11), obtained
Formula (18) is the average Reynolds type turbulent lubrication equation of one-dimensional longitudinal rough surface bush(ing) bearing.
2. the average Reynolds type turbulent lubrication equation of one-dimensional transverse direction rough surface bush(ing) bearing
Referring to Fig. 5, it is one-dimensional transverse direction rough surface assume rough surface form be elongated dimpling peak and trench all along
Bearing axis direction.In this way, oil film thickness expression formula is
H=h (x, z, t)+hs(x,ξ) (19)
Similar to the processing of one-dimensional longitudinal rough surface, by assuming that I can be obtainedVariance be 0, andH3With 1/
KzMutually independent random variables can be regarded as, so
Specific discharge in the x-direction is
ThenBy assuming q known to IIxVariance be 0, so
Formula (20) and (23) are substituted into formula (11), obtained
Formula (24) is the average Reynolds type turbulent lubrication equation of one-dimensional lateral rough surface bush(ing) bearing.
3. the average Reynolds type turbulent lubrication equation of isotropism rough surface bush(ing) bearing
Since isotropic rough surface does not have direction characteristic, from assuming I: along the circumferential direction,Side
Difference is 0,H3And 1/KxMutually independent random variables can be regarded as；In axial direction,Variance be 0,
H3And 1/KzMutually independent random variables can be regarded as.So
Formula (25) and (26) are substituted into formula (11), obtained
Formula (27) is the average Reynolds type turbulent lubrication equation of isotropism rough surface bush(ing) bearing.
The calculating of oil film thickness function and turbulent lubrication equation coefficient function in step (4) model formation
The solution of above-mentioned average Reynolds type turbulent lubrication equation (18), (24) and (27) is it needs to be determined that the oil film in equation is thick
Spend function and turbulent lubrication equation coefficient function.
Enable random quantity f (hs) it is oil film thickness component hsProbability density function.For Reynolds type rough surface, it is assumed that table
The roughness height distributed density curves in face meet Gaussian probability density distribution curve, then stochastic variable hsBe desired for 0, variance is
σ2, i.e.,
Therefore
I.e.
Due to hsIt is symmetrically, thenSo
Enable A1=a1Reb 1,Then
I.e.
If regions of lubrication regulation is in hydrodynamic lubrication field, i.e. two relative motion surfaces are without directly contacting, then | hs/h|
< 1.It is considered based on calculating with precision, by E (Kx) integrand part Taylor series expansion on the right of equation in integral and take
First three items, then
Then have
Similarly,
Correspondingly,
I.e.
I.e.
Oil film thickness function and turbulent lubrication equation coefficient function are calculated using formula (30)~(37) with can be convenient, thus
Carry out the solution of average Reynolds type turbulent lubrication equation (18), (24) and (27).
Above rough surface bush(ing) bearing turbulent lubrication model can be unified into following form
Corresponding to one-dimensional longitudinal rough surface bush(ing) bearing turbulent lubrication model
Corresponding to one-dimensional lateral rough surface bush(ing) bearing turbulent lubrication model
Corresponding to isotropism rough surface bush(ing) bearing turbulent lubrication model
Gx=E (H3)E(1/Kx), Gz=E (H3)E(1/Kz) (4)
Characterization bush(ing) bearing performance bearing capacity (Unbalance) be in the component of x and z coordinate axis direction
Fx、FzIn expression formula, L is bearing width, and θ is the angle measured along bearing circumferencial direction, and R is bearing radius；
Then the bearing capacity of bearing is
It has obtained that isotropism rough surface bush(ing) bearing turbulent flow can not only be handled from the establishment process of model above
The mathematical model of lubrication problem, and the turbulent lubrication of the rough surface bush(ing) bearing with direction characteristic can also be handled
The mathematical model of problem.
Compared with prior art, the present invention having following advantageous effects:
1. the stochastic model of rough surface turbulent lubrication proposed by the present invention can make up smooth surface turbulent lubrication model
Or rough surface laminar flow lubrication model can only individually consider turbulent flow effect or rough surface effect not in utilization
Foot, provides theories integration to carry out the research of turbulent flow effect and rough surface effect in a deep going way comprehensively.
2. the turbulent lubrication problem that the present invention not only can solve isotropism rough surface bush(ing) bearing, moreover it is possible to solve
With the rough surface bush(ing) bearing turbulent lubrication problem of direction characteristic caused by actual machine processing method, such as by grinding
Cut the turbulent lubrication for longitudinal rough surface bush(ing) bearing that processing journal outer surface and boring processing inner surface of bearing bush are constituted
Analysis, has a wide range of application, easy to spread.
3. compared with smooth surface turbulent lubrication theoretical model formula (5), rough surface stochastic turbulence proposed by the present invention
Lubrication Theory Model formula (18), formula (24) are identical with the citation form of formula (27), and main only difference is that increases characterization
The synthesis r.m.s. roughness parameter σ of rough surface situation, thus the numerical solution mistake of stochastic turbulence lubrication Theory Model equation
Journey and the numerical solution process of smooth surface turbulent lubrication theoretical model equation are also essentially identical, strong applicability, solve simple.
4. the parts with frication pair such as sliding block and thrust bearing and bush(ing) bearing are based on same lubrication principle, therefore this hair
One-dimensional longitudinal rough surface turbulent lubrication model equation of bright proposition, one-dimensional lateral rough surface turbulent lubrication model equation and each
The turbulent flow profit of the parts with frication pair such as sliding block and thrust bearing is applied equally to same sex rough surface turbulent lubrication model equation
Sliding analysis, application are extensive.
Detailed description of the invention
Fig. 1 is calculating step schematic diagram of the invention；
Fig. 2 is rough surface oil film thickness schematic diagram of the invention；
Fig. 3 is the control volume schematic diagram of average flowing of the invention；
Fig. 4 is the one-dimensional longitudinal rough surface structure schematic diagram of bush(ing) bearing of the invention；
Fig. 5 is the one-dimensional lateral rough surface structure schematic diagram of bush(ing) bearing of the invention；
Fig. 6 be Re*=3500 of the invention when Suo Mofeide number with eccentricity variation schematic diagram；
Fig. 7 is the variation schematic diagram of one-dimensional longitudinal rough surface bush(ing) bearing bearing capacity of the invention with eccentricity；
Fig. 8 is the variation schematic diagram of one-dimensional lateral rough surface bush(ing) bearing bearing capacity of the invention with eccentricity.
Specific embodiment
With reference to the accompanying drawing, by embodiment, the invention will be further described, but the present invention be not limited to down it is true
Apply example.
Embodiment 1
The use of isotropism rough surface bush(ing) bearing turbulent lubrication model
Rough surface bush(ing) bearing turbulent lubrication model is as follows:
H is the oil film thickness between nominal smooth surface in equation (1),For average oil film pressure, μ sticks for lubricant power
Degree, Gx、GzFor stochastic turbulence lubrication Theory Model equation parameter, V is journal surface tangential velocity, and x coordinate direction is axle journal rotation
Direction, z coordinate direction are bearing width direction, and t is the time.
Corresponding to isotropism rough surface bush(ing) bearing turbulent lubrication model
Gx=E (H3)E(1/Kx), Gz=E (H3)E(1/Kz) (4)
H is true oil film thickness, K in formula (4)x、KzFor new turbulent lubrication equation coefficient, E () is expectation operator, by following formula
Definition
In E (x) expression formula, f (x) is the probability density function of stochastic variable x.
For isotropism rough surface bush(ing) bearing, the I type bush(ing) bearing structural parameters that are used in calculating
For bearing diameter D=7.0 × 10-2M, bearing width L=7.0 × 10-2M is based on journal surface roughness trench bottom and bearing
Average radial clearance C=2.51 × 10 of internal surface of hole roughness trench bottom-4The uniform outer surface of m, bearing internal surface of hole are coarse
Height ksb=1.0 × 10-5M, the uniform outer surface roughness height k of journal surfacesj=0.04 × 10-6M is based on journal surface and axis
Synthesis r.m.s. roughness σ=5.0 × 10 of bearing bore inner surface-6m；II type bush(ing) bearing structural parameters are bearing diameter D
=7.0 × 10-2M, bearing width L=7.0 × 10-2M is thick based on journal surface roughness trench bottom and bearing internal surface of hole
Average radial clearance C=3.15 × 10 of rugosity trench bottom-4M, the uniform outer surface roughness height k of bearing internal surface of holesb=
7.1×10-5M, the uniform outer surface roughness height k of journal surfacesj=0.19 × 10-6M, based on table in journal surface and bearing hole
Synthesis r.m.s. roughness σ=3.55 × 10 in face-5m。
1997 bridge sheet (Hashimoto) bearing is used to the test result of above-mentioned I type, II type bush(ing) bearing
Energy parameter Suo Mofeide number S indicates that bearing lubricant flow regime uses Re*Characterization.
S and Re*Expression formula in, μ is the dynamic viscosity of water, and R is bearing radius, and W is load, and V is journal surface speed,
ρ is the density of water.
Using in this experimental study of bridge I type, II type bush(ing) bearing as research object, using it is proposed by the present invention respectively to
The same sex rough surface bush(ing) bearing turbulent lubrication model (1) convolution (4), (31), (36) and (37), using finite difference
The theoretical analysis and calculation of method solving model equation (1) progress bush(ing) bearing turbulent lubrication performance.
Theoretical analysis and calculation result is compared with corresponding test result referring to Fig. 6.Wherein, C model calculated value and NPE model
Calculated value is respectively to use Constantine Nei Siku (Constantinescu) turbulent lubrication model and Ni Ge-Pan (Ng-Pan) rapid
Stream lubrication model determines formula (36) and (37) parameter a1、a2、b1And b2Theoretical analysis and calculation value under value condition.
By the comparison of Fig. 6 as it can be seen that using isotropism rough surface bush(ing) bearing turbulent lubrication proposed by the present invention
The analytical calculation value and the consistency of the test value of bridge sheet of theoretical model are preferable, demonstrate rough surface turbulent flow proposed by the present invention
Lubricate the correctness of theory of stochastic model.
Embodiment 2
The use of one-dimensional longitudinal direction rough surface bush(ing) bearing turbulent lubrication model
Rough surface bush(ing) bearing turbulent lubrication model is as follows:
H is the oil film thickness between nominal smooth surface in above-mentioned equation,For average oil film pressure, μ sticks for lubricant power
Degree, Gx、GzFor stochastic turbulence lubrication Theory Model equation parameter, V is journal surface tangential velocity, and x coordinate direction is axle journal rotation
Direction, z coordinate direction are bearing width direction, and t is the time.
Corresponding to one-dimensional longitudinal rough surface bush(ing) bearing turbulent lubrication model
H is true oil film thickness, K in formula (2)x、KzFor new turbulent lubrication equation coefficient, E () is expectation operator, by following formula
Definition
In E (x) expression formula, f (x) is the probability density function of stochastic variable x.
Characterization bush(ing) bearing performance bearing capacity (Unbalance) be in the component of x and z coordinate axis direction
Fx、FzIn expression formula, L is bearing width, and θ is the angle measured along bearing circumferencial direction, and R is bearing radius；
Then the bearing capacity of bearing is
For one-dimensional longitudinal rough surface bush(ing) bearing that processing is formed, corresponding bush(ing) bearing structural parameters
For bearing radius gap c=0.065mm, bearing diameter D=32mm, bearing width L=38.6mm, bearing revolving speed n=8000r/
Min, bearings synthesis r.m.s. roughness σ=0.5 μm, lubricant density p=0.7018g/cm3, lubricant kinematic viscosity v=
0.51mm2/s。
Using above-mentioned one-dimensional longitudinal rough surface bush(ing) bearing as research object, using proposed by the present invention one-dimensional vertical
To rough surface bush(ing) bearing turbulent lubrication model (1) convolution (2), (31), (33), (35) and (36), application is limited
The analytical calculation of calculus of finite differences solving model equation (1) progress bush(ing) bearing turbulent lubrication performance.By taking bearing capacity as an example,
The one-dimensional longitudinal rough surface bush(ing) bearing turbulent lubrication lower bearing bearing capacity being calculated with eccentricity variation referring to
Fig. 7.Wherein, C model calculated value and NPE model calculation value are respectively to use Constantine Nei Siku (Constantinescu) rapid
Stream lubrication model and Ni Ge-Pan (Ng-Pan) turbulent lubrication model determine formula (33) and (36) parameter a1、a2、b1And b2Value feelings
Theoretical analysis and calculation value under condition.
The premise for guaranteeing bush(ing) bearing long-term stable operation in practical applications is the lubricant energy in bearing clearance
Enough bearing capacities are enough provided, so that bearing shell, two surface of axle journal are not directly contacted with i.e. bearing and are in perfect lubrication state.This model
One-dimensional longitudinal rough surface bush(ing) bearing bearing capacity under turbulent lubrication state can be more accurately calculated, has filled up one-dimensional vertical
The blank designed to rough surface bush(ing) bearing turbulent lubrication, so that the rapids of one-dimensional longitudinal direction rough surface bush(ing) bearing
Lubrication analysis is flowed closer to reality, and theory has been established in the turbulent lubrication design for the secondary components of friction with identical lubrication principle
Basis has stronger engineer application promotional value.
Embodiment 3
The use of one-dimensional transverse direction rough surface bush(ing) bearing turbulent lubrication model
Rough surface bush(ing) bearing turbulent lubrication model is as follows:
H is the oil film thickness between nominal smooth surface in equation (1),For average oil film pressure, μ sticks for lubricant power
Degree, Gx、GzFor stochastic turbulence lubrication Theory Model equation parameter, V is journal surface tangential velocity, and x coordinate direction is axle journal rotation
Direction, z coordinate direction are bearing width direction, and t is the time.
Corresponding to one-dimensional lateral rough surface bush(ing) bearing turbulent lubrication model
H is true oil film thickness, K in formula (3)x、KzFor new turbulent lubrication equation coefficient, E () is expectation operator, by following formula
Definition
In E (x) expression formula, f (x) is the probability density function of stochastic variable x.
Characterization bush(ing) bearing performance bearing capacity (Unbalance) be in the component of x and z coordinate axis direction
Fx、FzIn expression formula, L is bearing width, and θ is the angle measured along bearing circumferencial direction, and R is bearing radius；
Then the bearing capacity of bearing is
For the lateral rough surface bush(ing) bearing that processing is formed, the bearing structure parameter used in calculating is bearing
Radius clearance c=0.065mm, bearing diameter D=32mm, bearing width L=38.6mm, bearing revolving speed n=8000r/min, axis
Hold comprehensive r.m.s. roughness σ=0.5 μm, lubricant density p=0.7018g/cm3, lubricant kinematic viscosity v=0.51mm2/
s。
Using above-mentioned one-dimensional longitudinal rough surface bush(ing) bearing as research object, one-dimensional cross proposed by the present invention is utilized
To rough surface bush(ing) bearing turbulent lubrication model (1) convolution (3), (31), (32), (35) and (37), application is limited
The analytical calculation of calculus of finite differences solving model equation (20) progress bush(ing) bearing turbulent lubrication performance.It is with bearing capacity
Example, the one-dimensional lateral rough surface bush(ing) bearing turbulent lubrication lower bearing bearing capacity being calculated are joined with the variation of eccentricity
See Fig. 8.Wherein, C model calculated value and NPE model calculation value are respectively to use Constantine Nei Siku (Constantinescu)
Turbulent lubrication model and Ni Ge-Pan (Ng-Pan) turbulent lubrication model determine formula (32) and (37) parameter a1、a2、b1And b2Value
In the case of theoretical analysis and calculation value.
Lubricant in bush(ing) bearing gap provides enough bearing capacities just and can guarantee the long-term stable operation of bearing.
This model can more accurately calculate the one-dimensional lateral rough surface bush(ing) bearing bearing capacity under turbulent lubrication state, fill up
The blank of one-dimensional transverse direction rough surface bush(ing) bearing turbulent lubrication design, so that one-dimensional transverse direction rough surface radially slides axis
The turbulent lubrication analysis held is closer practical.
Claims (1)
1. the stochastic model that a kind of rough surface bush(ing) bearing turbulent lubrication calculates, it is characterised in that:
The random laminar flow lubrication theory of rough surface bush(ing) bearing and zero equation based on Clayton Christensen (Christensen)
The smooth surface bush(ing) bearing turbulent lubrication of form is theoretical, and derivation proposes rapid suitable for rough surface bush(ing) bearing
The stochastic turbulence lubrication Theory Model of lubrication analysis is flowed, the stochastic turbulence lubrication Theory Model is as follows:
H is the oil film thickness between nominal smooth surface in formula (1),For average oil film pressure, μ is lubricant dynamic viscosity, Gx、
GzFor stochastic turbulence lubrication Theory Model equation parameter, V is journal surface tangential velocity, and x coordinate direction is axle journal rotation direction,
Z coordinate direction is bearing width direction, and t is the time；
Corresponding to one-dimensional longitudinal rough surface bush(ing) bearing turbulent lubrication model
H is true oil film thickness, K in formula (2)x、KzFor new turbulent lubrication equation coefficient, E () is expectation operator, is defined by the formula
In E (x) expression formula, f (x) is the probability density function of stochastic variable x；
Corresponding to one-dimensional lateral rough surface bush(ing) bearing turbulent lubrication model
Variable declaration in formula (3) is identical as the variable declaration in formula (2)；
Corresponding to isotropism rough surface bush(ing) bearing turbulent lubrication model
Gx=E (H3)E(1/Kx), Gz=E (H3)E(1/Kz) (4)
Variable declaration in formula (4) is identical as the variable declaration in formula (2)；
Characterization bush(ing) bearing performance bearing capacity (Unbalance) be in the component of x and z coordinate axis direction
Fx、FzIn expression formula, L is bearing width, and θ is the angle measured along bearing circumferencial direction, and R is bearing radius；
Then the bearing capacity of bearing is
It realizes using the stochastic model that the rough surface bush(ing) bearing turbulent lubrication calculates to one-dimensional longitudinal rough surface
The turbulent flow of bush(ing) bearing, one-dimensional lateral rough surface bush(ing) bearing and isotropism rough surface bush(ing) bearing
The analysis of greasy property.
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| WO2023176601A1 (en) * | 2022-03-14 | 2023-09-21 | 日本精工株式会社 | Measurement method, observation device, and program |
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| CN106568371A (en) * | 2016-11-07 | 2017-04-19 | 北京航空航天大学 | Fractal-based axial plunger pump rotor-valve plate dynamic mixture lubrication modeling method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2023176601A1 (en) * | 2022-03-14 | 2023-09-21 | 日本精工株式会社 | Measurement method, observation device, and program |
| JP7367898B1 (en) | 2022-03-14 | 2023-10-24 | 日本精工株式会社 | Measuring method, measuring device, and program |
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| CN109002610B (en) | 2023-03-14 |
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