CN107169158A - A kind of static pressure slide service behaviour computational methods based on fluid structure interaction - Google Patents
A kind of static pressure slide service behaviour computational methods based on fluid structure interaction Download PDFInfo
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- CN107169158A CN107169158A CN201710226486.4A CN201710226486A CN107169158A CN 107169158 A CN107169158 A CN 107169158A CN 201710226486 A CN201710226486 A CN 201710226486A CN 107169158 A CN107169158 A CN 107169158A
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Abstract
The invention discloses a kind of static pressure slide service behaviour computational methods based on fluid structurecoupling, including：(1) static pressure slide stressing conditions are analyzed according to actual condition, sets up slide force analysis schematic diagram；(2) according to thin plate Deformation Theory and static pressure slide basic structure size, it is sheet model and lubricating pad model to simplify slide；(3) change of the pressure distribution of calculated static pressure slide lubricating pad model and oil film thickness, and set up equation；(4) deformation of calculated static pressure slide sheet model under external force, and obtain its deflection functions；(5) relation of intercoupling between oil film thickness change is deformed by slide and sets up slide lubricating pad fluid structure interaction mode, and set up its dynamic equilibrium equation；(6) enter Mobile state analysis to service behaviour of the static pressure slide under actual condition using matlab softwares, finally give the static pressure slide performance evaluation based on fluid structure interaction under actual condition.
Description
Technical field
The present invention is a kind of calculating side based on the static pressure slide service behaviour of fluid structure interaction between slide and lubricating pad
Method, belongs to machine design and manufacture field.
Background technology
Static pressure slide is the critical component of the heavy high-grade, digitally controlled machine tools of accurate ultra, and it plays support to heavy machine tool and made
With, and drive whole gantry frame to be moved along a straight line.Because static pressure slide has low friction, high bearing capacity and kinematic accuracy
High the advantages of, each heavy-duty machinery part manufacturing has been widely used in it.The external research for static pressure slide is more early, production
Product have covered each position, there has been the manufacturing technology and product of maturation.Although domestic research is slightly late, in reform and opening-up
Trend under, introduction of foreign technology energetically learns advanced experience, the support of country is added, under the unremitting effort of researcher
It there has also been larger development.A such as northern machine tool plant, Qiqihaer No.2 Machine Tool Factory, the multiple large scale computers in heavy machine tool plant in Wuhan
Tool manufacturing enterprise devises all kinds of static pressure supports in heavy machine tool manufacture, and static pressure slide is one of them.
With the development and the extensive use of heavy machine tool and the further investigation of static pressure technology to Defence business, to workpiece
Crudy requires more and more higher, and the research of its service behaviour is also just into the most important thing.In recent years, many experts learn
Person has done suitable research to static pressure slide.But because slide not only will be by column, crossbeam, slide carriage, cunning in motion process
The Action of Gravity Field of pillow and various parts, while tilting moment that also will be by slide in motion process superstructure part is made
With, therefore slide can also be deformed in itself.Slide is all reduced to rigid body to calculate in conventional design is calculated, cunning is have ignored
Influence of this effect of intercoupling to slide service behaviour between seat deformation itself and oil film thickness change.So having to
This coupling is furtherd investigate, to improve the design of static pressure slide, its service behaviour and life-span is improved.Therefore this is special
Profit has invented a kind of computational methods of the static pressure slide service behaviour based on fluid structure interaction, design that can be to static pressure slide
Manufacture provides more preferable design method, makes it have more preferable service behaviour.
The content of the invention
Devised present invention is generally directed to the invention of static pressure slide service behaviour a kind of based on the solid coupling of stream between slide and lubricating pad
The computational methods of the static pressure slide service behaviour of cooperation.This method is mainly characterized by the calculating in static pressure slide service behaviour
Considered in journey slide deform in itself oil film thickness change between this effect of intercoupling, and calculate on slide each
The pressure distribution of oil pocket is simultaneously contrasted with the service behaviour that slide is considered as rigid body situation lower slider.
Technical barrier to be solved by this invention is realized by following scheme：
A kind of static pressure slide service behaviour computational methods based on fluid structurecoupling, it is characterised in that：The computational methods include
It is as follows：
(1) static pressure slide stressing conditions are analyzed according to actual condition, sets up slide force analysis schematic diagram；
(2) mesh generation is carried out to slide using finite element method, tied substantially according to thin plate Deformation Theory and static pressure slide
Structure size, it is sheet model and lubricating pad model to simplify slide；
(3) change of the pressure distribution of calculated static pressure slide lubricating pad and oil film thickness, and set up its deformation equation；
(4) deformation of calculated static pressure slide sheet model under external force, and obtain its deflection functions；
(5) relation that intercouples between oil film thickness change is deformed by slide, and set up in the step (3)
Oil film thickness deformation equation and the step (4) in the deflection functions of thin plate deformation set up, set up the solid coupling of slide-lubricating pad stream
Matched moulds type, and set up its dynamic equilibrium equation；
(6) Mobile state analysis is entered to service behaviour of the static pressure slide under actual condition using matlab softwares, it is final to obtain
Static pressure slide performance evaluation based on fluid structure interaction under to actual condition.
In the step (1), static pressure slide upper surface is by column, crossbeam and the slide carriage being assembled on crossbeam
Action of Gravity Field, lower surface is acted on by the pressure of two rows, 14 static pressure oil pads.
In the step (2), using the grid node of FEM meshing, the position of static pressure oil pad is carried out accurately
Positioning.
In the step (2), the primary condition of static pressure slide practical structures size thin plate Deformation Theory is analyzed, judges to slide
Whether holder structure size meets thin plate Deformation Theory primary condition, and slide deformation is calculated according to Deformation Theory.
Compared with prior art, the present invention has advantages below：
By analyzing the force analysis and working mechanism of heavy static pressure machine tool static-pressure slide, according to the perimeter strip of single lubricating pad
Part calculates lubricating pad pressure distribution based on Reynolds equation, calculates thin according to the sheet model after simplification and thin plate Deformation Theory
The practical distortion of plate, lubricating pad-slide wind-structure interaction model is set up according to sheet model and lubricating pad model.This method is integrated
Consider slide self-deformation, this method caused by influence and oil film thickness change of the slide self-deformation to oil film thickness
Meet the most with actual condition, obtained result is the most accurate, compensate for not accounting for slide itself when slide is considered as rigid body
The deficiency of the static pressure slide service behaviour of deformation.
Brief description of the drawings
Fig. 1 is heavy gantry machine tool static pressure slide fluid and structural simulation design flow diagram of the present invention；
Fig. 2 is static pressure slide force analysis schematic diagram in the present invention；
Fig. 3 simplifies process schematic for static pressure slide in the present invention；
Fig. 4 is the structural representation of Rectangular Hydrostatic lubricating pad in the present invention.
Embodiment
The invention will be further described with reference to the accompanying drawings and examples：
As shown in figure 1, a kind of heavy gantry machine tool static pressure slide computational methods based on wind-structure interaction, it includes
Following steps：
1st, according to static pressure slide actual loading situation, force analysis is carried out to static pressure slide, the stress of static pressure slide is obtained
Analysis chart (such as Fig. 2).
2nd, mesh generation is carried out to slide according to the method for the grid division of finite element analysis, slide X-direction top is a length of
A, a length of b in Y-direction top, respective coordinates are respectively x, y.According to physical location of the lubricating pad on slide, the grid of slide is determined
Node.Slide is reduced to thin-slab structure and many oil pad structures.
3rd, according to many lubricating pad models, Reynolds equation is derived, and finite difference solution is carried out to Reynolds equation, oil pocket pressure is obtained
Power is distributed.
The calculating of theory of fluid lubrication model is with solving many special shape Reynolds equations using Navier-Stokes equations
Solved.Reynolds equation is partial differential equation of second order, is to be derived from by the equation of motion and continuity equation, is fluid lubrication
Theoretical most basic equation.The derivation of Reynolds equation is based on following basic assumption：
(1) influence of the isometric power of Action of Gravity Field, magneticaction is ignored.
(2) fluid is fricton-tight on the interface of joint, and the fluid velocity contacted with surface is identical with superficial velocity.
(3) in oil film thickness direction, oil film pressure change is disregarded.
(4) compared with oil film thickness, the radius of curvature of guide pass is very big, ignores the influence of radius of curvature, by velocity of rotation
Replaced with point-to-point speed.
(5) static pressure fluid is considered as Newtonian fluid.
(6) because guide rail movement velocity is not high, therefore fluid flowing is considered as laminar flow.
(7) it is easy calculating, the viscosity number in oil film thickness direction is considered as steady state value
(8) ignore the power of fluid acceleration and the centrifugal force of oil film bending, compared with the viscous force of fluid, inertia force can be neglected
Slightly.
Reynolds equation is derived using infinitesimal balance and continuity equation.Basic procedure is：According to infinitesimal stress balance condition,
Solve the fluid VELOCITY DISTRIBUTION on oil film thickness z directions.Fluid VELOCITY DISTRIBUTION is integrated on oil film thickness direction, asked
Solve fluid flow.Finally according to continuity equation, Reynolds equation resolvant is drawn.
Therefore the continuity equation of rectangle lubricating pad is with N-S equation simplifications：
U is the speed of lubricating oil in the x-direction, and v is the speed of lubricating oil in the y-direction, is that viscous shear p is oil pocket pressure
Power, η is oil viscosity.Because oil film thickness Z is much smaller compared to the long X and width B of oil film, therefore except velocity gradientWith
Outside, other velocity gradient factor values are too small to can be neglected its influence.Therefore when analyzing X-direction stress, dxdz surface tack frees
The effect of shearing force, abbreviation is obtained
Basic assumption (5) and basic assumption (6) are derived according to Reynolds equation, Newton's law of viscosity is carried out to simplify：
Equation is brought into obtain：
It can similarly obtain in the Y direction：
It can be obtained in z-direction according to basic assumption (3)：
Because pressure P is not z function, while viscosities il is nor z function, is integrated twice to z, while according to thunder
The fluid velocity of promise equation basic assumption (2) surface contact is identical with superficial velocity, determines boundary condition, two surface of solids X sides
Upward velocity is UhAnd U0, speed is V in Y-directionhAnd V0.As oil film thickness z=0, that is, u=U when pressing close to lower guideway face0, when
During oil film thickness z=h, that is, press close to upper rail face U=Uh.Speed in X-direction is obtained after integration is：
Similarly, speed is in Y-direction：
According to continuity equation：
Bring x directions speed and Y-direction speed into continuity equation and oil film thickness is integrated：
Ignore fluid density and change over time to obtain Reynolds equation general type：
Wherein：U=Uh-U0, V=Vh-V0。
Next finite difference solution is carried out to Reynolds equation.Finite difference solution is carried out, first has to carry out mesh generation,
Definition node number, definition X-direction, which has, n node in m node, Y-direction.Again by partial differential equation nondimensionalization, so that
The number of independent variable and dependent variable is reduced, makes non trivial solution that there is versatility.Nondimensionalization is carried out to variable in Reynolds equation：
P in formula --- pressure；
--- pressure in oily pocket；
Ux--- guide rail X-direction translational speed；
H --- oil film thickness；
η --- oil viscosity；
--- dimensionless pressure；
--- non-dimensional length；
--- dimensionless width；
--- dimensionless thickness；
--- dimensionless guide moving velocity；
--- dimensionless oil film thickness.
Wherein oil film thickness h is matrix h (i, j), and correspondence represents the oil film thickness at each node.Solve oil film region internal pressure
Power distribution situation, it is believed that oil pocket internal pressure value is constant, and pressure distribution at sealing oil edge is solved using Reynolds equation.In oil sealing
The distribution situation of pressure p in the domain of border area, can be represented with the pressure value of each node, according to differential principle, arbitrary node p (i,
J) single order and second dervative all represent with the variate-value of surroundings nodes, as illustrated, wherein with representing X-direction and Y-direction
Step-length, L and B are expressed as the length and width of lubricating pad.In sealing oil edge region, the pressure of node is represented by：
Pressure distribution is integrated in node region, pressure distribution q (x, y) at each node is tried to achieve.
5th, sheet model and thin plate Deformation Theory after being simplified according to slide carry out deformation analysis.
In Elasticity, the object referred to as plate that the cylinder or prismatic surface of two parallel surfaces are surrounded, two areas of plate
Larger plane is referred to as plate face, and cylinder or the less face of prismatic surface homalographic are called edges of boards, with the equidistant face in upper and lower plates face
For the middle face of plate.It is different from the ratio for the side length b that plate is short by thickness of slab h, plate can be divided into slab, thin plate and film.Thickness of slab h with compared with
The plate that short side B ratio is more than 0.2 is referred to as slab, and plate of the ratio between 0.0125 and 0.2 is referred to as thin plate, and ratio is less than
0.0125 plate is referred to as film.The most short side length of static pressure slide and the ratio of static pressure slide thickness, are usually located at 0.0125 to 0.2
Between, belong to thin plate scope.According to thin plate Deformation Theory, the deformation ω calculation formula at slide (x, y) place are：
ω=ω (x, y) (14)
When being solved because of the derivation of Reynolds equation with finite difference, needed in primary condition to fixed oil film thickness, therefore pushing away
Guide sliding base guide pass facial disfigurement equation, boundary condition is set as simply supported on four sides.Its length of side is respectively a and b, is made by distributed load q
With.The mathematic(al) representation of its boundary condition is：
When thin plate face is benefited concentrated force load q many used times, effect point coordinates is that (m, n) is in point (m, n) place stress
Q, is zero in remaining position stress.Now obtain be in the amount of deflection ω at slide arbitrary node (x, y) place expression formula：
Wherein D is the bending stiffness of thin plate,
The oil pocket pressure q (x, y) that calculating is obtained is brought into formula (16), and according to the equilibrium equation in z directions, calculating is obtained
The deformation of slide during consideration fluid structurecoupling.
F is active force of the lubricating pad to slide, and G conducts oneself with dignity for slide, and M makees for the wobbler action of lathe center of gravity to the moment of flexure of slide
With.
Claims (7)
1. a kind of static pressure slide service behaviour computational methods based on fluid structurecoupling, it is characterised in that：The computational methods are included such as
Under：
(1) static pressure slide stressing conditions are analyzed according to actual condition, sets up slide force analysis schematic diagram；
(2) mesh generation is carried out to slide using finite element method, according to thin plate Deformation Theory and static pressure slide basic structure chi
Very little, it is sheet model and lubricating pad model to simplify slide；
(3) change of the pressure distribution of calculated static pressure slide lubricating pad and oil film thickness, and set up its deformation equation；
(4) deformation of calculated static pressure slide sheet model under external force, and obtain its deflection functions；
(5) relation that intercouples between oil film thickness change, and the oil set up in the step (3) are deformed by slide
The deflection functions for the thin plate deformation set up in film thickness deformation equation and the step (4), set up slide-lubricating pad fluid structurecoupling mould
Type, and set up its dynamic equilibrium equation；
(6) enter Mobile state analysis to service behaviour of the static pressure slide under actual condition using matlab softwares, finally give reality
Static pressure slide performance evaluation based on fluid structure interaction under the operating mode of border.
2. a kind of static pressure slide service behaviour computational methods based on fluid structurecoupling according to claims 1, its feature
It is, in the step (1), static pressure slide upper surface is by column, crossbeam and the gravity for the slide carriage being assembled on crossbeam
Effect, lower surface is acted on by the pressure of two rows, 14 static pressure oil pads.
3. a kind of static pressure slide service behaviour computational methods based on fluid structurecoupling according to claims 1, its feature
It is, in the step (2), using the grid node of FEM meshing, the position of static pressure oil pad accurately determine
Position.
4. a kind of static pressure slide service behaviour computational methods based on fluid structurecoupling according to claims 1, its feature
It is, in the step (2), analyzes the primary condition of static pressure slide practical structures size thin plate Deformation Theory, judge slide
Whether physical dimension meets thin plate Deformation Theory primary condition, and slide deformation is calculated according to Deformation Theory.
5. a kind of static pressure slide service behaviour computational methods based on fluid structurecoupling according to claims 1, its feature
It is, in the step (3), the pressure distribution situation of lubricating pad is calculated by following equation：
The calculating of theory of fluid lubrication model is carried out with solving many special shape Reynolds equations using Navier-Stokes equations
Solve；Reynolds equation is partial differential equation of second order, is to be derived from by the equation of motion and continuity equation, is theory of fluid lubrication
Most basic equation；The derivation of Reynolds equation is based on following basic assumption：
(1) influence of the isometric power of Action of Gravity Field, magneticaction is ignored；
(2) fluid is fricton-tight on the interface of joint, and the fluid velocity contacted with surface is identical with superficial velocity；
(3) in oil film thickness direction, oil film pressure change is disregarded；
(4) compared with oil film thickness, the radius of curvature of guide pass is very big, ignores the influence of radius of curvature, and velocity of rotation is used into flat
Speed is moved to replace；
(5) static pressure fluid is considered as Newtonian fluid；
(6) because guide rail movement velocity is not high, therefore fluid flowing is considered as laminar flow；
(7) it is easy calculating, the viscosity number in oil film thickness direction is considered as steady state value
(8) ignore the power of fluid acceleration and the centrifugal force of oil film bending, compared with the viscous force of fluid, inertia force can be neglected；
Reynolds equation is derived using infinitesimal balance and continuity equation；Basic procedure is：According to infinitesimal stress balance condition, solve
Fluid VELOCITY DISTRIBUTION on oil film thickness direction；Fluid VELOCITY DISTRIBUTION is integrated on oil film thickness direction, oil is solved
Flow quantity；Finally according to continuity equation, Reynolds equation resolvant is drawn；Therefore the continuity equation and N-S of rectangle lubricating pad
Equation can be reduced to：
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In oil film thickness Z compared to oil film long X and width B it is much smaller, therefore except velocity gradient with addition to, other velocity gradient factor values
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Integrate twice, while the fluid velocity contacted according to Reynolds equation basic assumption (2) surface is identical with superficial velocity, determine border
Condition, two solid surface velocities are UhAnd U0, as oil film thickness z=0, that is, u=U when pressing close to lower guideway face0, as oil film thickness z
During=h, that is, press close to upper rail face U=Uh；Speed in X-direction is obtained after integration is：
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<mfrac>
<mrow>
<mo>&part;</mo>
<mrow>
<mo>(</mo>
<mi>&rho;</mi>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<mrow>
<mo>(</mo>
<mi>&rho;</mi>
<mi>w</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>z</mi>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
Bring x directions speed and Y-direction speed into continuity equation and oil film thickness is integrated：
<mrow>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&rho;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mi>d</mi>
<mi>z</mi>
</mrow>
<mo>+</mo>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mrow>
<mo>(</mo>
<mi>&rho;</mi>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mi>d</mi>
<mi>z</mi>
</mrow>
<mo>+</mo>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mrow>
<mo>(</mo>
<mi>&rho;</mi>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mi>d</mi>
<mi>z</mi>
</mrow>
<mo>+</mo>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mfrac>
<mrow>
<mo>&part;</mo>
<mrow>
<mo>(</mo>
<mi>&rho;</mi>
<mi>w</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>z</mi>
</mrow>
</mfrac>
<mi>d</mi>
<mi>z</mi>
<mo>&rsqb;</mo>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Reynolds equation general type can be obtained by ignoring fluid density and changing over time：
<mrow>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msup>
<mi>&rho;h</mi>
<mn>3</mn>
</msup>
</mrow>
<mi>&eta;</mi>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&rho;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msup>
<mi>&rho;h</mi>
<mn>3</mn>
</msup>
</mrow>
<mi>&eta;</mi>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&rho;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>6</mn>
<mo>&lsqb;</mo>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>U</mi>
<mi>&rho;</mi>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mo>&part;</mo>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>V</mi>
<mi>&rho;</mi>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein：U=Uh-U0, V=Vh-V0.
Next finite difference solution is carried out to Reynolds equation；Finite difference solution is carried out, first has to carry out mesh generation, definition
Interstitial content, definition X-direction, which has, n node in m node, Y-direction；Again by partial differential equation nondimensionalization, so as to reduce
The number of independent variable and dependent variable, makes non trivial solution have versatility；Nondimensionalization is carried out to variable in Reynolds equation：
<mrow>
<mtable>
<mtr>
<mtd>
<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>
<mi>p</mi>
<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>a</mi>
</mfrac>
<mo>,</mo>
<mover>
<mi>a</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>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<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>
<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>a</mi>
<mi>&eta;</mi>
</mrow>
</mfrac>
</mfrac>
<mo>,</mo>
<msub>
<mover>
<mi>u</mi>
<mo>&OverBar;</mo>
</mover>
<mi>y</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>U</mi>
<mi>y</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>a</mi>
<mi>&eta;</mi>
</mrow>
</mfrac>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
P in formula --- pressure；
--- pressure in oily pocket；
Ux --- guide rail X-direction translational speed；
H --- oil film thickness；
η --- oil viscosity；
--- dimensionless pressure；
--- non-dimensional length；
--- dimensionless width；
--- dimensionless thickness；
--- dimensionless guide moving velocity；
--- dimensionless oil film thickness；
Wherein oil film thickness h is matrix h (i, j), and correspondence represents the oil film thickness at each node；Solve oil film region internal pressure power point
Cloth situation, it is believed that oil pocket internal pressure value is constant, and pressure distribution at sealing oil edge is solved using Reynolds equation；In oil sealing border area
The distribution situation of pressure p in domain, can be represented with the pressure value of each node, according to differential principle, arbitrary node p's (i, j)
Single order and second dervative are all represented with the variate-value of surroundings nodes, wherein the step-length with representing X-direction and Y-direction；In sealing oil edge
In region, the pressure of node is represented by：
<mrow>
<msub>
<mover>
<mi>P</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>y</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>y</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>L</mi>
<mi>B</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<msub>
<mover>
<mrow>
<mi>U</mi>
<mi>x</mi>
</mrow>
<mo>&OverBar;</mo>
</mover>
<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>
<msub>
<mover>
<mrow>
<mi>U</mi>
<mi>x</mi>
</mrow>
<mo>&OverBar;</mo>
</mover>
<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>
<mi>&Delta;</mi>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>y</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mo>&lsqb;</mo>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>y</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>y</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<mi>&Delta;</mi>
<msup>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mn>2</mn>
</msup>
<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>
<mo>&rsqb;</mo>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
Pressure distribution is integrated in node region, pressure distribution q (x, y) at each node is tried to achieve.
6. the static pressure slide service behaviour computational methods based on fluid structurecoupling according to claims 1, it is characterised in that
In the step (4), the deformation of thin plate is calculated by following equation：
In Elasticity, the object referred to as plate that the cylinder or prismatic surface of two parallel surfaces are surrounded, two areas of plate are larger
Plane be referred to as plate face, cylinder or the less face of prismatic surface homalographic are called edges of boards, with the equidistant face in upper and lower plates face be plate
Middle face；It is different from the ratio for the side length b that plate is short by thickness of slab h, plate can be divided into slab, thin plate and film；Thickness of slab h and shorter edge
The plate that B ratio is more than 0.2 is referred to as slab, and plate of the ratio between 0.0125 and 0.2 is referred to as thin plate, and ratio is less than 0.0125
Plate is referred to as film；The most short side length of static pressure slide and the ratio of static pressure slide thickness, are usually located between 0.0125 to 0.2, belong to
In thin plate scope；According to thin plate Deformation Theory, the deformation ω calculation formula at slide (x, y) place are:
ω=ω (x, y) (14)
When being solved because of the derivation of Reynolds equation with finite difference, needed in primary condition to fixed oil film thickness, therefore slided deriving
Seat guide pass facial disfigurement equation, boundary condition is set as simply supported on four sides；Its length of side is respectively a and b, is acted on by distributed load q；Its
The mathematic(al) representation of boundary condition is：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mi>&omega;</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<mi>&omega;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>;</mo>
<mi>x</mi>
<mo>=</mo>
<mi>a</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<mi>&omega;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>y</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mi>&omega;</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<mi>&omega;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>;</mo>
<mi>y</mi>
<mo>=</mo>
<mi>a</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<mi>&omega;</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
When thin plate face is benefited concentrated force load q many used times, effect point coordinates is that (m, n) is q i.e. in point (m, n) place stress,
Remaining position stress is zero；Now obtain be in the amount of deflection ω at slide arbitrary node (x, y) place expression formula：
<mrow>
<mi>&omega;</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4</mn>
<mi>q</mi>
</mrow>
<mrow>
<msup>
<mi>&pi;</mi>
<mn>4</mn>
</msup>
<mi>a</mi>
<mi>b</mi>
<mi>D</mi>
</mrow>
</mfrac>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>&infin;</mi>
</munderover>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>&infin;</mi>
</munderover>
<mfrac>
<mrow>
<mi>sin</mi>
<mfrac>
<mrow>
<mi>m</mi>
<mi>&pi;</mi>
<mi>k</mi>
</mrow>
<mi>a</mi>
</mfrac>
<mi>sin</mi>
<mfrac>
<mrow>
<mi>n</mi>
<mi>&pi;</mi>
<mi>l</mi>
</mrow>
<mi>b</mi>
</mfrac>
</mrow>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msup>
<mi>m</mi>
<mn>2</mn>
</msup>
<msup>
<mi>a</mi>
<mn>2</mn>
</msup>
</mfrac>
<mo>+</mo>
<mfrac>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<msup>
<mi>b</mi>
<mn>2</mn>
</msup>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mfrac>
<mi>sin</mi>
<mfrac>
<mrow>
<mi>m</mi>
<mi>&pi;</mi>
<mi>k</mi>
</mrow>
<mi>a</mi>
</mfrac>
<mi>sin</mi>
<mfrac>
<mrow>
<mi>n</mi>
<mi>&pi;</mi>
<mi>y</mi>
</mrow>
<mi>b</mi>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein D is the bending stiffness of thin plate,
7. the static pressure slide service behaviour computational methods based on fluid structurecoupling according to claims 1, it is characterised in that：
The oil pocket pressure q (x, y) that calculating is obtained is brought into formula (16), according to the equilibrium equation in z directions, and calculating obtains considering that stream is solid
The deformation of slide during coupling；
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>16</mn>
</mrow>
</munderover>
<msub>
<mi>F</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>G</mi>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>16</mn>
</mrow>
</munderover>
<msub>
<mi>M</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mi>M</mi>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>18</mn>
<mo>)</mo>
</mrow>
</mrow>
F is active force of the lubricating pad to slide, and G conducts oneself with dignity for slide, and M is Moment of the wobbler action to slide of lathe center of gravity,
Analyze the service behaviour of static pressure slide.
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| CN109117522A (en) * | 2018-07-24 | 2019-01-01 | 北京工业大学 | A kind of calculation method of the static-pressure slide carriage fluid structurecoupling working performance based on MATLAB-ANSYS software |
| CN109815548A (en) * | 2018-12-27 | 2019-05-28 | 西安交通大学 | A kind of fluid film pressure calculation method based on Garlerkin thought |
| CN110287577A (en) * | 2019-06-20 | 2019-09-27 | 哈尔滨理工大学 | A kind of acquisition hydrostatic thrust bearing oil film three-dimensional pressure field method |
| CN110298106A (en) * | 2019-06-26 | 2019-10-01 | 哈尔滨理工大学 | Static pressure rotary worktable displacement sensor best orientation and installation method under a kind of unbalance loading operating condition |
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| CN109117522A (en) * | 2018-07-24 | 2019-01-01 | 北京工业大学 | A kind of calculation method of the static-pressure slide carriage fluid structurecoupling working performance based on MATLAB-ANSYS software |
| CN109117522B (en) * | 2018-07-24 | 2022-11-22 | 北京工业大学 | Method for calculating fluid-solid coupling working performance of static-pressure slide carriage based on MATLAB-ANSYS software |
| CN109815548A (en) * | 2018-12-27 | 2019-05-28 | 西安交通大学 | A kind of fluid film pressure calculation method based on Garlerkin thought |
| CN110287577A (en) * | 2019-06-20 | 2019-09-27 | 哈尔滨理工大学 | A kind of acquisition hydrostatic thrust bearing oil film three-dimensional pressure field method |
| CN110298106A (en) * | 2019-06-26 | 2019-10-01 | 哈尔滨理工大学 | Static pressure rotary worktable displacement sensor best orientation and installation method under a kind of unbalance loading operating condition |
| CN110399670A (en) * | 2019-07-18 | 2019-11-01 | 上海理工大学 | A kind of method for building up of liquid spheres bearing film calculation of pressure model |
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| CN113343462A (en) * | 2021-06-07 | 2021-09-03 | 西安交通大学 | High-order isogeometric multi-oil-cavity dynamic and static pressure sliding bearing oil film characteristic simulation method |
| CN113656917A (en) * | 2021-08-24 | 2021-11-16 | 中国航空发动机研究院 | Fluid-solid coupling calculation method for elastic ring type squeeze film damper |
| CN113656917B (en) * | 2021-08-24 | 2022-10-21 | 中国航空发动机研究院 | Fluid-solid coupling calculation method for elastic ring type squeeze film damper |
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