CN104462752B - A kind of hydrostatic slideway load-bearing capacity analysis method for considering guide rail facial disfigurement - Google Patents
A kind of hydrostatic slideway load-bearing capacity analysis method for considering guide rail facial disfigurement Download PDFInfo
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- 230000002706 hydrostatic effect Effects 0.000 title claims abstract description 47
- 238000004458 analytical method Methods 0.000 title claims abstract description 19
- 206010061619 Deformity Diseases 0.000 title claims abstract description 7
- 230000001815 facial effect Effects 0.000 title claims abstract description 7
- 230000001050 lubricating effect Effects 0.000 claims abstract description 32
- 229920001971 elastomer Polymers 0.000 claims abstract description 20
- 239000000806 elastomer Substances 0.000 claims abstract description 20
- 238000000034 method Methods 0.000 claims abstract description 17
- 239000012530 fluid Substances 0.000 claims abstract description 8
- 238000004364 calculation method Methods 0.000 claims abstract description 6
- 239000007788 liquid Substances 0.000 claims abstract description 4
- 239000000463 material Substances 0.000 claims description 12
- 238000010008 shearing Methods 0.000 claims description 7
- 230000009699 differential effect Effects 0.000 claims description 4
- 230000005483 Hooke's law Effects 0.000 claims description 2
- 230000000694 effects Effects 0.000 abstract description 2
- 230000003068 static effect Effects 0.000 description 7
- 238000007789 sealing Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 3
- 239000000446 fuel Substances 0.000 description 3
- 230000005540 biological transmission Effects 0.000 description 2
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000005461 lubrication Methods 0.000 description 1
- 238000003825 pressing Methods 0.000 description 1
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Abstract
A kind of hydrostatic slideway load-bearing capacity analysis method for considering guide rail facial disfigurement, belongs to support and lubricating area.It is deformed for load-bearing surface above and below hydrostatic slideway under oil liquid pressure effect, and then the bearing capacity problem for influenceing guide rail proposes a kind of analysis method.In method, based on Reynolds equation, pressure distribution in lubricating pad is solved after Reynolds equation is simplified, while introduces one-dimensional elastomer balance differential equation and solves guide rail deformation distribution.The differential equation is changed into difference equation using finite difference method in solution procedure, then accelerates to solve by Gauss-Saden that iteration and primary and secondary overrelaxation iteration.Reynolds equation is solved first, is drawn the pressure distribution of fluid, is substituted into elastomer balance differential equation using pressure as external force condition, ask lubricating pad lower guideway to deform.Reynolds equation is substituted into using deformation as oil film thickness change condition, draws more accurate pressure distribution.Loop iteration to result of calculation meets precision, changes according to this interpretation of result load-carrying properties.
Description
Technical field
The present invention is a kind of hydrostatic slideway load-bearing capacity analysis method for considering guide rail facial disfigurement, belongs to support and lubrication point
Analyse technical field.
Background technology
Hydrostatic support system has been widely used in the supporting and lubricating system of lathe at present, especially large-scale, heavily loaded
Played an important role in lathe.Static pressure support system provides pressure oil by outside oil supply system to the lubricating pad of carrying position,
Pressure oil flows between two supporting surfaces forms hydrostatic effects, and two load-bearing surfaces are separated, realize bearing capacity.Wherein lubricating pad can
It is roughly divided into oily pocket and sealing oil edge two parts.Pressure of the pressure oil in oily pocket is equal to the pressure that outside oil supply system provides.
At sealing oil edge, the viscous feature of fluid itself will hinder its flowing, so as to ensure that the pressure of oily pocket inner fluid, so pressure oil
Pressure distribution at sealing oil edge is the key that static pressure support system realizes bearing capacity.Hydrostatic slideway is static pressure support system
A kind of typical case, all kinds of heavy machine tools are widely used at present, be mainly used in the working condition of Linear transmission.Static pressure is led
In the work of rail, due to the demand of its Linear transmission, the lubricating pad of hydrostatic slideway generally use rectangular shape.Due to its bearing capacity
The characteristics of big, hydrostatic slideway are mainly used in large-scale, heavy machine tool.But in heavy duty machine tools, make in the pressure of supporting fluid
Under, upper and lower two load-bearing surface necessarily leads to certain deformation, and deforms and then influence the pressure distribution in lubricating pad, so as to right
Bearing capacity has an impact.
In the problem of pressure distribution in sealing oil edge in solving hydrostatic slideway, Reynolds equation is main analysis method.Thunder
The solution of promise equation is to analyze the basis of hydrostatic slideway load-carrying properties, but because its equation is partial differential equation of second order in itself,
Asking for for analytic solutions is relatively difficult, so in the current analysis method of static pressure support system again based on numerical method.Finite difference
Point method is a kind of very practical numerical method, and the differential equation can be changed into algebraic equation by finite difference method approximation,
Solved again by the method for value solving of algebraic equation, finally give the approximate solution that pressure is distributed in sealing oil edge.
The content of the invention
The present invention is with according to the characteristics of specific hydrostatic slideway model and condition of work, appropriate letter is carried out to Reynolds equation
Change, solve the pressure distribution of fluid in lubricating pad；One-dimensional elastomer balance differential equation is re-introduced into, solves the change of lubricating pad lower guideway
Shape.It is difference equation by Reynolds equation and elastomer balance differential equation Approximation Discrete, and then be changed into by finite difference calculus
Algebraic Equation set, reapplies Gauss-Saden that alternative manner afterwards and successive overrelaxation method accelerates to ask for numerical solution.
Reynolds equation is solved by the method first, draws the pressure distribution of lubricating pad inner fluid, then using this pressure as outer
Power condition substitutes into elastomer balance differential equation, and the deformation of lubricating pad lower guideway is obtained according to the above method.It is thick using deformation as oil film again
Spend change condition and substitute into Reynolds equation solution, draw more accurate pressure distribution.Loop iteration to result of calculation meets that precision will
Ask, draw the numerical solution of pressure distribution and guide rail deformation.The finally change according to this interpretation of result load-carrying properties.
The hydrostatic slideway load-bearing capacity analysis method provided by the invention for considering guide rail facial disfigurement comprises the following steps：
S1. the nondimensionalization of variable is carried out to the parameter in hydrostatic slideway first；
Wherein：P is fluid pressure；p0For pressure in hydrostatic slideway oil pocket；W is hydrostatic slideway bearing capacity；Q leads for static pressure
Rail fuel supply flow rate；Ux is hydrostatic slideway translational speed；H is oil film thickness；H0For initial oil film thickness；X is length to coordinate amount
Degree；Y is that width is measured to coordinate；Z measures for thickness coordinate；L is hydrostatic slideway lubricating pad length；B is hydrostatic slideway lubricating pad width；
dzFor deformation extent；η is oil viscosity；For dimensionless pressure；For non-dimensional length；For dimensionless width；To be immeasurable
Guiding principle bearing capacity；Flow is held for dimensionless；For dimensionless guide moving velocity；Dimensionless oil film thickness；Become for dimensionless
Shape degree.
S2. Reynolds equation and elastomer balance differential equation are simplified further according to model；Generally, static pressure is led
The translational speed of rail is less demanding, so heat problem and unobvious, that is, supports the viscosity B coefficent of liquid and variable density can be with
Ignore；Reynolds equation after simplification is：
Wherein：L is hydrostatic slideway lubricating pad length；B is hydrostatic slideway lubricating pad width；For dimensionless pressure；For dimensionless
Length；For dimensionless width；For dimensionless guide moving velocity；For dimensionless oil film thickness.
The deformation extent of lubricating pad lower guideway and actual conditions are closely related, and physical dimension, material, operating pressure will all influence
The deformation extent size of guide rail；But in the elastic range of material, the deformation side of the regularity of distribution of deformation necessarily satisfying for elastomer
Journey, i.e., meet boundary condition in boundary, remaining meets the regularity of distribution of distortional elastomer；It is micro- to introduce one-dimensional elastomer balance
Point equation is：
Wherein：X is that length is measured to coordinate；Y is that width is measured to coordinate；Z measures for thickness coordinate；σ is direct stress；τ
For shearing stress；F is body force.
S3. discrete with elastomer balance differential equation according to finite difference method Reynolds equation after is algebraic equation；Have
Calculus of finite differences is limited according to the property of differential, by partial differential equation Approximation Discrete, the Algebraic Equation set of limited rank is converted into, is passing through generation
Number solution of equations method is solved；Reynolds equation is changed into difference equation according to Differential Properties first, and arranges to obtain Reynolds
The iterative equation of equation：
Wherein：L is hydrostatic slideway lubricating pad length；B is hydrostatic slideway lubricating pad width；For dimensionless pressure；For x directions
Discrete steps；For y directions discrete steps；I counts for x directions infinitesimal；J counts for y directions infinitesimal；For dimensionless guide rail
Translational speed；For dimensionless oil film thickness
According to Hooke's law
Wherein：σ is direct stress；τ is shearing stress；E is guide material Young's modulus；G is guide material modulus of shearing；ε is
Linear strain；γ is shear strain.
Then one-dimensional elastomer balance differential equation-formula (2) is changed into difference equation according to Differential Properties, and arranges
The iterative equation of elastomer balance differential equation：
Wherein：E is guide material Young's modulus；G is guide material modulus of shearing；Xstep is x directions discrete steps；
Ystep is y directions discrete steps；Zstep is z directions discrete steps；K counts for z directions infinitesimal；dzFor deformation extent；F is body
Product power.
S4., algebraic equation is rewritten as to the iterative equation of solution, using Gauss-Saden, your alternative manner is solved,
And application successive overrelaxation method accelerates, and draws the numerical solution of pressure；The solution of pressureSubstituted into after obtaining as external applied load condition
The iterative formula of deformation solves, the solution of deformationThe iterative formula that rear oil film thickness condition brings pressure into is obtained to askSuch as
This circulation, until result of calculation meets that essence requires；
S5. the analysis of bearing capacity is carried out according to the above results.
Consider that the hydrostatic slideway load-bearing capacity analysis method of guide rail facial disfigurement has the following advantages that.
1st, for hydrostatic slideway the characteristics of and particular job situation simplify Reynolds equation and elastomer balance differential side
Journey, and drawn its corresponding iterative equation according to Finite-difference theory.
2nd, guide rail surface is introduced during analysis to deform under oil liquid pressure effect, can be drawn and more be met actual feelings
The result of condition.
3rd, the coupling solutions of pressure distribution and pressure distortion in lubricating pad have been obtained using numerical method analysis, and according to this number
Value solution carries out the analysis of bearing capacity change.
Brief description of the drawings
Fig. 1 is the load-bearing capacity analysis method flow diagram under pressure distortion based on the hydrostatic slideway of finite difference.
Fig. 2 a are the operating diagrams of hydrostatic slideway.
Fig. 2 b are the structural representations of hydrostatic slideway lubricating pad.
Fig. 3 is hydrostatic slideway surface pressing deformation schematic diagram.
Fig. 4 is the result of calculation of pressure distribution in lubricating pad.
Fig. 5 is the result of calculation of guide rail surface deformation distribution.
Fig. 6 a are that dimensionless bearing capacity obtains changing rule with deformation extent.
Fig. 6 b are that immeasurable flow obtains changing rule with deformation extent.
Fig. 7 is changing rule of the oil film thickness with guide rail deformation extent.
Embodiment
The specific size and actual condition of guide rail surface deformation are closely related, but the regularity of distribution deformed is basically identical, only
It is the deformation extent difference of maximum distortion position.With lower guideway deformation extentWhen exemplified by.As shown in Fig. 2 set lubricating pad length
L, wide B；The wide b of the oily long l of pocket；Design oil film thickness is H0；Lubricating pad lower guideway thickness T.
When solving pressure, Reynolds equation boundary condition is introduced：
When solving deformation distribution, the boundary condition of elastomer balance differential equation is introduced：
The flow chart according to Fig. 1, pressure distribution and guide rail surface deformation distribution in lubricating pad is calculated.According to this knot
Fruit is analyzed the load-carrying properties of hydrostatic slideway, Main Analysis bearing capacityAnd flowChange.WithFrom 0 increase
To 1, dimensionless bearing capacity adds about 16.2%, and dimensionless flow adds about 147%, and the increase degree of flow is more than carrying
The increase degree of power.Analyze influence of this change to actual bearer performance to also need to introduce specific fuel system, with quantitative
Exemplified by formula oil supply system, obtained according to nondimensionalization formula：
Wherein, W is actual carrying capacity, that is, load when working, when hydrostatic slideway steady operation, workload W change
Change very little, it can be considered that W is constant；Q is actual fuel supply flow rate, in quantitative oil supply system, the stream of oil pump offer
Amount is stable, it can be considered that q is constant；η is oil viscosity, and under hydrostatic slideway application environment, temperature change is little,
It can be considered that η is constant.The relation between dimensionless bearing capacity, dimensionless flow and oil film thickness can then be drawn：
I.e. the ratio between dimensionless bearing capacity and dimensionless flow are proportional to oil film thickness.It can thus be concluded that go out oil film thickness with guide rail
The changing rule of deformation extent.
Claims (1)
- A kind of 1. hydrostatic slideway load-bearing capacity analysis method for considering guide rail facial disfigurement, for analyzing hydrostatic slideway in heavy machine tool Change of the load-carrying properties under the influence of guide rail surface pressure distortion under application platform, it is characterised in that：The analysis method includes Following steps,S1. the nondimensionalization of variable is carried out to the parameter in hydrostatic slideway first；<mrow> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mi>p</mi> <msub> <mi>p</mi> <mn>0</mn> </msub> </mfrac> <mo>,</mo> <mover> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mi>x</mi> <mi>L</mi> </mfrac> <mo>,</mo> <mover> <mi>L</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mi>y</mi> <mi>B</mi> </mfrac> <mo>,</mo> <mover> <mi>B</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mi>h</mi> <msub> <mi>H</mi> <mn>0</mn> </msub> </mfrac> <mo>,</mo> </mrow><mrow> <msub> <mover> <mi>d</mi> <mo>&OverBar;</mo> </mover> <mi>z</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>d</mi> <mi>z</mi> </msub> <msub> <mi>H</mi> <mn>0</mn> </msub> </mfrac> <mo>,</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mover> <mi>U</mi> <mo>&OverBar;</mo> </mover> <mi>x</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>U</mi> <mi>x</mi> </msub> <mfrac> <mrow> <msubsup> <mi>H</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msub> <mi>p</mi> <mn>0</mn> </msub> </mrow> <mrow> <mi>L</mi> <mi>&eta;</mi> </mrow> </mfrac> </mfrac> <mo>,</mo> <mover> <mi>W</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mi>W</mi> <mrow> <msub> <mi>LBp</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>,</mo> <mover> <mi>q</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mi>q</mi> <mfrac> <mrow> <msubsup> <mi>H</mi> <mn>0</mn> <mn>3</mn> </msubsup> <msub> <mi>p</mi> <mn>0</mn> </msub> </mrow> <mi>&eta;</mi> </mfrac> </mfrac> </mrow>Wherein：P is fluid pressure；p0For pressure in hydrostatic slideway oil pocket；W is hydrostatic slideway bearing capacity；Q supplies for hydrostatic slideway Oil stream amount；UxFor hydrostatic slideway translational speed；H is oil film thickness；H0For initial oil film thickness；X is that length is measured to coordinate；Y is Width is measured to coordinate；Z measures for thickness coordinate；L is hydrostatic slideway lubricating pad length；B is hydrostatic slideway lubricating pad width；dzTo become Shape degree；η is oil viscosity；For dimensionless pressure；For non-dimensional length；For dimensionless width；Carried for dimensionless Power；Flow is held for dimensionless；For dimensionless guide moving velocity；For dimensionless oil film thickness；Journey is deformed for dimensionless Degree；S2. Reynolds equation and elastomer balance differential equation are simplified；The translational speed of hydrostatic slideway is less demanding, so Heat problem and unobvious, that is, the viscosity B coefficent of liquid is supported to ignore with variable density；Reynolds equation after simplification is：<mrow> <mfrac> <mo>&part;</mo> <mrow> <mo>&part;</mo> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>=</mo> <mrow> <mo>(</mo> <msup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mn>3</mn> </msup> <mo>&CenterDot;</mo> <mfrac> <mrow> <mo>&part;</mo> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> </mrow> <mrow> <mo>&part;</mo> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>L</mi> <mi>B</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mfrac> <mo>&part;</mo> <mrow> <mo>&part;</mo> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mrow> <mo>(</mo> <msup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mn>3</mn> </msup> <mo>&CenterDot;</mo> <mfrac> <mrow> <mo>&part;</mo> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> </mrow> <mrow> <mo>&part;</mo> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <mn>6</mn> <mfrac> <mo>&part;</mo> <mrow> <mo>&part;</mo> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mover> <mi>U</mi> <mo>&OverBar;</mo> </mover> <mi>x</mi> </msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>Wherein：L is hydrostatic slideway lubricating pad length；B is hydrostatic slideway lubricating pad width；For dimensionless pressure；For non-dimensional length；For dimensionless width；For dimensionless guide moving velocity；For dimensionless oil film thickness；The deformation extent of lubricating pad lower guideway and actual conditions are closely related, and physical dimension, material, operating pressure will all influence guide rail Deformation extent size；But in the elastic range of material, the regularity of distribution of deformation necessarily satisfying for elastomer deformation equation, i.e., Meet boundary condition in boundary, remaining meets the regularity of distribution of distortional elastomer；Introduce one-dimensional elastomer balance differential side Cheng Wei：<mrow> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>&tau;</mi> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>&tau;</mi> <mrow> <mi>y</mi> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>&sigma;</mi> <mrow> <mi>z</mi> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>z</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>f</mi> <mi>z</mi> </msub> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>Wherein：X is that length is measured to coordinate；Y is that width is measured to coordinate；Z measures for thickness coordinate；σ is direct stress；τ is to cut Stress；F is body force；S3. discrete with elastomer balance differential equation according to finite difference method Reynolds equation after is algebraic equation；Finite difference Point-score by partial differential equation Approximation Discrete, is converted into the Algebraic Equation set of limited rank, is passing through algebraically side according to the property of differential The solution of journey group is solved；Reynolds equation is changed into difference equation according to Differential Properties first, and arranges to obtain Reynolds equation Iterative equation：<mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <msub> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <msub> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>L</mi> <mi>B</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <msub> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>L</mi> <mi>B</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> <msub> <mover> <mi>p</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mn>6</mn> <mrow> <mo>(</mo> <mover> <mi>U</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <mover> <mi>U</mi> <mo>&OverBar;</mo> </mover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> </mrow> <mrow> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <mo>+</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>L</mi> <mi>B</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> <mn>3</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>L</mi> <mi>B</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mover> <mi>x</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> <mn>3</mn> </msubsup> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>Wherein：L is hydrostatic slideway lubricating pad length；B is hydrostatic slideway lubricating pad width；For dimensionless pressure；It is discrete for x directions Step-length；For y directions discrete steps；I counts for x directions infinitesimal；J counts for y directions infinitesimal；Moved for dimensionless guide rail Speed；For dimensionless oil film thicknessAccording to Hooke's law<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>&sigma;</mi> <mo>=</mo> <mi>E</mi> <mi>&epsiv;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&tau;</mi> <mo>=</mo> <mi>G</mi> <mi>&gamma;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>Wherein：σ is direct stress；τ is shearing stress；E is guide material Young's modulus；G is guide material modulus of shearing；ε is linear Strain；γ is shear strain；Then one-dimensional elastomer balance differential equation-formula (2) is changed into difference equation according to Differential Properties, and arranges elastic The iterative equation of body balance differential equation：<mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>Gy</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>z</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>dz</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>dz</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>Gx</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>z</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>dz</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>dz</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>dz</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>+</mo> <msubsup> <mi>Ex</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>y</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>dz</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>dz</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>fz</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> <msub> <mi>z</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msubsup> <mi>Gy</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>z</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>2</mn> <msubsup> <mi>Gx</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>z</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>2</mn> <msubsup> <mi>Ex</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> <msubsup> <mi>y</mi> <mrow> <mi>s</mi> <mi>t</mi> <mi>e</mi> <mi>p</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>Wherein：E is guide material Young's modulus；G is guide material modulus of shearing；xstepFor x directions discrete steps；ystepFor y side To discrete steps；zstepFor z directions discrete steps；K counts for z directions infinitesimal；dzFor deformation extent；F is body force；S4., algebraic equation is rewritten as to the iterative equation of solution, your alternative manner is solved using Gauss-Saden, and should Accelerated with successive overrelaxation method, draw the numerical solution of pressure；The solution of pressureAfter obtaining deformation is substituted into as external applied load condition Iterative formula solve, the solution of deformationThe iterative formula that rear oil film thickness condition brings pressure into is obtained to askSo follow Ring, until result of calculation meets that essence requires；S5. the analysis of bearing capacity is carried out according to the above results.
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