CN106777467B - Static pressure sliding seat static balance calculation method considering fluid-solid coupling - Google Patents
Static pressure sliding seat static balance calculation method considering fluid-solid coupling Download PDFInfo
- Publication number
- CN106777467B CN106777467B CN201611001393.3A CN201611001393A CN106777467B CN 106777467 B CN106777467 B CN 106777467B CN 201611001393 A CN201611001393 A CN 201611001393A CN 106777467 B CN106777467 B CN 106777467B
- Authority
- CN
- China
- Prior art keywords
- oil film
- deformation
- oil
- sliding seat
- film thickness
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
Abstract
The invention discloses a quick calculation method for a rectangular static pressure oil pad considering fluid-solid coupling, and particularly relates to a quick calculation method for rectangular bearing capacity considering mutual influence of static pressure oil pad guide rail surface deformation and oil pad pressure distribution. The method comprises the steps of firstly carrying out grid division, calculating and storing standard deformation of a guide surface, then mutually iterating and solving oil film pressure distribution according to a Reynolds equation and a deformation equation, and finally integrating and solving oil film bearing capacity. The method is characterized in that the influence of fluid-solid coupling on the bearing capacity is fully considered in the process of calculating the bearing capacity of the hydrostatic oil film. And a rapid calculation method for the deformation of the guide rail surface is provided, so that a double integral does not need to be calculated every time the deformation of the guide rail surface is calculated, and the design efficiency is greatly improved.
Description
Technical Field
The invention belongs to the field of design and analysis of a static pressure system of a heavy numerical control machine tool, and designs a static balance calculation method of a static pressure sliding seat in consideration of fluid-solid coupling, in particular to a static balance calculation method in consideration of the fluid-solid coupling characteristic between a static pressure oil pad at the static pressure sliding seat and the deformation of a guide rail surface.
Background
The static pressure slide carriage is widely applied to a gantry movable type heavy numerical control machine tool and is arranged between a machine tool body and a gantry frame, the gantry frame is fixed on the static pressure slide carriage, and the static pressure slide carriage is connected with the machine tool body through two rows of static pressure guide rails. The static pressure slide carriage plays a supporting role for the gantry frame, and the static characteristic of the static pressure slide carriage plays a crucial role in influencing the machining precision of the machine tool.
The static pressure slide carriage is under the gravity action of the gantry frame and the supporting force of the static pressure oil pad. The weight of the gantry frame is about hundreds of tons, and according to the static balance principle, the static pressure oil pad needs to provide a supporting force equal to the gravity of the gantry frame. The sliding seat can be inevitably deformed under the action of the two components. The thickness of a static pressure oil pad oil film at the static pressure guide rail is changed due to the deformation of the static pressure sliding seat, and the supporting force is further influenced. And (3) the deformation of the sliding seat correspondingly changes due to the change of the supporting force of the oil pad, so that the thickness of the oil film changes again, and the process is circulated until the static pressure sliding seat reaches a static equilibrium state. The static pressure slide seat reaches the equilibrium state, and the vertical direction displacement and the whole inclination angle of the static pressure slide seat can change. According to the basic principle of hydrostatic bearing, the change of the oil film thickness and the change of the bearing capacity of the oil pad are in a cubic relation, and the bearing capacity of the hydrostatic bearing system can be greatly influenced by one-point change of the oil film thickness. Therefore, the mutual influence of fluid-solid coupling, namely the oil film pressure distribution on the deformation of the guide surface, must be considered in the design analysis process of the hydrostatic bearing system. The research provides a static balance calculation method of the static pressure sliding seat considering fluid-solid coupling, and the vertical displacement and inclination angle values of the static pressure sliding seat can be obtained through calculation, so that a theoretical basis is provided for the optimal design of the static pressure sliding seat.
Disclosure of Invention
The invention aims to provide a static balance calculation method of a static pressure sliding seat in consideration of fluid-solid coupling. The method is mainly characterized in that on the basis of considering fluid-solid coupling, according to static balance conditions, the connection between a Reynolds equation and a deformation equation is established by using the oil film thickness, and the values of the vertical displacement and the inclination angle of the static pressure sliding seat are finally obtained through iterative calculation. The calculation method takes the fluid-solid coupling characteristic between the static pressure oil pad and the guide rail surface at the static pressure slide seat into consideration. The calculation result is closer to the actual working condition.
The invention is realized by adopting the following technical means:
and S1, meshing the sliding seat, and setting the initial oil film thickness and the inclination angle.
And S2, regarding the sliding seat as a rigid body, and calculating the pressure distribution condition of each oil pad by using a Reynolds equation. And checking the initial oil film thickness and the inclination angle according to a force balance equation and a moment balance equation to obtain the actual oil film thickness and the actual inclination angle. And then calculating the actual pressure distribution of each oil pad by using the Reynolds equation again.
And S3, the sliding seat is regarded as an elastic body, and the deformation condition of the sliding seat under the simultaneous action of the external load and each oil pad is calculated according to a deformation equation. And obtaining a deformation curve at the slide guide rail, namely an oil film thickness curve.
And S4, recalculating the pressure distribution condition of each oil pad by using the oil film thickness curve, and checking the oil film thickness and the inclination angle according to a force balance moment balance equation. And when the difference between the calculated deformation amount of the guide surface and the deformation amount of the guide surface calculated last time is in an error allowable range, jumping out of the cycle. And obtaining the actual oil film thickness, the actual pressure distribution condition and the actual inclination angle of the sliding seat of each oil pad in a balanced state.
Drawings
FIG. 1 is a schematic view of a hydrostatic slider
FIG. 2 is a schematic view of the static pressure slide bearing
Detailed Description
The invention is described in further detail below with reference to figures 1 and 2.
Step (1) dividing the grid
And (4) carrying out grid division on the static pressure sliding seat according to the calculation precision requirement to obtain i x j calculation nodes. Wherein i is the number of the divided nodes in the x direction of the static pressure sliding seat, and j is the number of the divided nodes in the y direction of the static pressure sliding seat. And preliminarily setting the initial oil film thickness and the sliding seat inclination angle.
And (2) checking the oil film thickness and the sliding seat, and calculating the actual oil film thickness and the sliding seat inclination angle.
And calculating the pressure distribution of the oil pad according to the initial slide inclination angle and the oil film thickness. The static pressure oil film conforms to the film lubrication theory, and the basic assumption is that according to the Reynolds equation: the fluid does not slide on the interface, namely the flow velocity of the fluid attached to the surface is the same as the surface velocity; the variation of pressure in the thickness direction of the lubricating film is not counted; neglecting the influence of oil film curvature, and replacing the rotation speed with translation speed; the lubricant is a newtonian fluid; the flow is laminar flow, and eddy and turbulent flow do not exist in the oil film; compared to viscous forces, the effect of inertial forces can be neglected; the viscosity value is constant along the thickness direction of the lubricating film. The Reynolds equation is:
carrying out non-dimensionalization on the equation, solving the Reynolds equation by a finite difference method, and carrying out non-dimensionalization on the equation:
in the formula: p is the pressure intensity; p is a radical of0The pressure in the oil pocket, the Ux the moving speed of the guide rail in the X direction, the h the oil film thickness and η the oil viscosity.
Is a dimensionless pressure;
is a dimensionless length;
is a dimensionless width;
is of dimensionless thickness
The moving speed of the dimensionless guide rail is adopted;
is the thickness of the dimensionless oil film. The oil film thickness h is a matrix h (i, j) and correspondingly represents the oil film thickness at each node. With the initial oil film thickness h known, the pressure distribution P (x, y) is solved using the finite difference method. And integrating in the whole oil pad range to obtain the oil film bearing capacity value.
F＝∫∫p(x,y)dxdy
The equilibrium equation in the vertical direction of a single carriage is:
in the formula FiThere are two rows of 16 pads for each bearing pad load capacity. MiThe support moment of each oil pad. And checking the bearing capacity value of each oil pad according to the actual total bearing capacity G and the actual moment M, and checking the initial oil film thickness and the sliding seat inclination angle. And obtaining the actual oil film thickness and the slide seat inclination angle. And calculating the actual bearing condition of each oil pad by using the Reynolds equation again.
And (4) regarding the seat in the step (3) as an elastic body, and calculating the deformation condition of the sliding seat under the simultaneous action of the external load and each oil pad according to a deformation equation. And obtaining a deformation curve at the slide guide rail, namely an oil film thickness curve.
According to the basic principle of elasticity mechanics, a deformation expression of the guide surface under the action of unit concentration force W is solved by using a Navier (Navier) solution of the rectangular sheet with the four sides doubling as a whole. The coordinates of the action point of the concentration force W are (m, n), the length of the side of the guide surface in the X direction is a, the length of the side of the guide surface in the Y direction is b, and the corresponding coordinates are X and Y respectively. The deformation ω at the guide surface (x, y) when subjected to the unit force W at the coordinates (m, n) is calculated by the formula:
in the formula, j and k are iterative calculation times, the higher the iterative precision, on the premise of ensuring the precision, the calculation times are reduced as much as possible, and the value of j and k is selected to be 50. Wherein D is the bending rigidity of the thin plate, and the calculation formula is as follows:
wherein E is the elastic modulus of the sliding seat, and mu is the Poisson's ratio h of the sliding seat material and the thickness of the sliding seat. Calculating the deformation of each node through cyclic calculationAnd respectively calculating the deformation condition of the guide surface when the unit force W acts at each node, and storing for later use. Finally, i x j deformation matrixes are obtained, and each matrix B0And (i, j) comprises i x j data, and corresponds to the nodes one by one. Correspondingly multiplying the pressure value at each node of the pressure distribution p (x, y) by the deformation matrix when the unit force is applied to the node and the stress of the other nodes is 0, and superposing all the nodes to obtain the total deformation matrix A of the guide surface1(i,j)。
And obtaining the oil film thickness condition of each oil pad of the hydrostatic sliding seat guide rail according to the total deformation matrix.
And (4) recalculating the pressure distribution condition of each oil pad by using the oil film thickness curve, and checking the oil film thickness and the inclination angle according to a force balance moment balance equation. And when the difference between the calculated deformation amount of the guide surface and the deformation amount of the guide surface calculated last time is in an error allowable range, jumping out of the cycle. And obtaining the actual oil film thickness, the actual pressure distribution condition and the actual inclination angle of the sliding seat of each oil pad in a balanced state.
Claims (1)
1. A static balance calculation method of a static pressure sliding seat considering fluid-solid coupling is mainly characterized in that on the basis of considering fluid-solid coupling, a relation between a Reynolds equation and a deformation equation is established by using oil film thickness according to static balance conditions, and the vertical displacement and inclination angle values of the static pressure sliding seat are finally obtained through iterative calculation; the calculation method considers the fluid-solid coupling characteristic between the static pressure oil pad and the guide rail surface at the static pressure slide seat; the calculation result is closer to the actual working condition;
the method is characterized in that: the method is realized by adopting the following technical means,
s1, carrying out grid division on the sliding seat, and giving an initial oil film thickness and an inclination angle;
s2, regarding the sliding seat as a rigid body, and calculating the pressure distribution condition of each oil pad by using a Reynolds equation; checking the initial oil film thickness and the inclination angle according to a force balance equation and a moment balance equation to obtain the actual oil film thickness and the actual inclination angle; then, calculating the actual pressure distribution condition of each oil pad by using the Reynolds equation again;
s3, the sliding seat is used as an elastic body, and the deformation condition of the sliding seat under the simultaneous action of the external load and each oil pad is calculated according to a deformation equation; obtaining a deformation curve at the slide guide rail, namely an oil film thickness curve;
s4, recalculating the pressure distribution condition of each oil pad by using the oil film thickness curve, and checking the oil film thickness and the inclination angle according to a force balance moment balance equation; when the difference between the calculated deformation of the guide surface and the deformation of the guide surface calculated last time is within an error allowable range, the actual oil film thickness, the actual pressure distribution condition and the actual inclination angle of the sliding seat of each oil pad in a balanced state are obtained;
the dividing grid of S1 is implemented as follows:
according to the calculation precision requirement, grid division is carried out on the static pressure sliding seat to obtain i x j calculation nodes; wherein i is the number of divided nodes in the x direction of the static pressure sliding seat, and j is the number of divided nodes in the y direction of the static pressure sliding seat; preliminarily setting the initial oil film thickness and the slide seat inclination angle;
the oil film thickness and the sliding seat are checked in the S2, and the actual oil film thickness and the sliding seat inclination angle are calculated as follows:
calculating the pressure distribution of the oil pad according to the initial slide seat inclination angle and the oil film thickness; the static pressure oil film conforms to the film lubrication theory, and the basic assumption is that according to the Reynolds equation: the fluid does not slide on the interface, namely the flow velocity of the fluid attached to the surface is the same as the surface velocity; the variation of pressure in the thickness direction of the lubricating film is not counted; neglecting the influence of oil film curvature, and replacing the rotation speed with translation speed; the lubricant is a newtonian fluid; the flow is laminar flow, and eddy and turbulent flow do not exist in the oil film; compared to viscous forces, the effect of inertial forces can be neglected; the viscosity value is unchanged along the thickness direction of the lubricating film; the Reynolds equation is:
carrying out non-dimensionalization on the equation, solving the Reynolds equation by a finite difference method, and carrying out non-dimensionalization on the equation:
in the formula: p is the pressure intensity; p is a radical of0The pressure intensity in the oil pocket, Ux the moving speed of the guide rail in the X direction, h the oil film thickness and η the oil viscosity;
is a dimensionless pressure;
is a dimensionless length;
is a dimensionless width;
is of dimensionless thickness
The moving speed of the dimensionless guide rail is adopted;
is the thickness of the dimensionless oil film; the oil film thickness h is a matrix h (i, j) and correspondingly represents the oil film thickness at each node; under the condition that the initial oil film thickness h is known, solving the pressure distribution P (x, y) by using a finite difference method; integrating in the whole oil pad range to obtain an oil film bearing capacity value;
F＝∫∫p(x,y)dxdy
the equilibrium equation in the vertical direction of a single carriage is:
in the formula FiTwo rows of 16 oil pads are used for supporting the bearing capacity of each oil pad; miThe supporting moment of each oil pad; checking the bearing capacity value of each oil pad according to the actual total bearing capacity G and the actual moment M, and checking the initial oil film thickness and the sliding seat inclination angle; obtaining the actual oil film thickness and the slide seat inclination angle; calculating the actual bearing condition of each oil pad by using the Reynolds equation again;
s3, the sliding seat is taken as an elastic body, and the deformation condition of the sliding seat under the simultaneous action of external load and each oil pad is calculated according to a deformation equation; obtaining a deformation curve at the slide guide rail, namely an oil film thickness curve;
according to the basic principle of elasticity mechanics, solving a deformation expression of the guide rail surface under the action of unit concentration force W by using a Navier (Navier) solution of a rectangular sheet with four sides doubling as a whole; the coordinate of an acting point of the concentration force W is (m, n), the length of the side of the guide surface in the X direction is a, the length of the side of the guide surface in the Y direction is b, and the corresponding coordinates are X and Y respectively; the deformation ω at the guide surface (x, y) when subjected to the unit force W at the coordinates (m, n) is calculated by the formula:
in the formula, j and k are iterative calculation times, the higher the iterative precision, on the premise of ensuring the precision, the calculation times are reduced as much as possible, and the value of j and k is selected to be 50; wherein D is the bending rigidity of the thin plate, and the calculation formula is as follows:
wherein E is the elastic modulus of the sliding seat, mu is the Poisson's ratio h of the sliding seat material and is the thickness of the sliding seat; calculating the deformation of each node through cyclic calculation, and then respectively calculatingCalculating the deformation condition of the guide surface when the unit force W acts at each node, and storing for later use; finally, i x j deformation matrixes are obtained, and each matrix B0(i, j) contains i x j data, corresponding to nodes one by one; correspondingly multiplying the pressure value at each node of the pressure distribution p (x, y) by the deformation matrix when the unit force is applied to the node and the stress of the other nodes is 0, and superposing all the nodes to obtain the total deformation matrix A of the guide surface1(i,j)；
The oil film thickness condition of each oil pad of the hydrostatic sliding seat guide rail can be obtained according to the total deformation matrix;
s4, recalculating the pressure distribution condition of each oil pad by using the oil film thickness curve, and checking the oil film thickness and the inclination angle according to a force balance moment balance equation; when the difference between the calculated deformation of the guide surface and the deformation of the guide surface calculated last time is within the error allowable range, jumping out of the cycle; and obtaining the actual oil film thickness, the actual pressure distribution condition and the actual inclination angle of the sliding seat of each oil pad in a balanced state.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611001393.3A CN106777467B (en) | 2016-11-09 | 2016-11-09 | Static pressure sliding seat static balance calculation method considering fluid-solid coupling |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611001393.3A CN106777467B (en) | 2016-11-09 | 2016-11-09 | Static pressure sliding seat static balance calculation method considering fluid-solid coupling |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106777467A CN106777467A (en) | 2017-05-31 |
| CN106777467B true CN106777467B (en) | 2020-05-22 |
Family
ID=58968048
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611001393.3A Active CN106777467B (en) | 2016-11-09 | 2016-11-09 | Static pressure sliding seat static balance calculation method considering fluid-solid coupling |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106777467B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN110298106B (en) * | 2019-06-26 | 2022-11-18 | 哈尔滨理工大学 | Optimal positioning and mounting method for displacement sensor of static pressure rotary table under unbalanced load working condition |
| CN112231853B (en) * | 2020-09-10 | 2023-12-12 | 东南大学 | Calculation method and system for static characteristics of hydrostatic guideway considering elastic deformation |
| 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 |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103823940A (en) * | 2014-03-07 | 2014-05-28 | 北京工业大学 | Static-pressure turntable dynamic response computing method based on overall dynamical model |
| CN104091021A (en) * | 2014-07-11 | 2014-10-08 | 北京工业大学 | Method for calculating bearing capacity of oil pad when oil pad inclines |
| CN104680018A (en) * | 2015-03-09 | 2015-06-03 | 北京工业大学 | Analyzing and optimizing method for hydrostatic guideway to inhibit inertia force impact |
-
2016
- 2016-11-09 CN CN201611001393.3A patent/CN106777467B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103823940A (en) * | 2014-03-07 | 2014-05-28 | 北京工业大学 | Static-pressure turntable dynamic response computing method based on overall dynamical model |
| CN104091021A (en) * | 2014-07-11 | 2014-10-08 | 北京工业大学 | Method for calculating bearing capacity of oil pad when oil pad inclines |
| CN104680018A (en) * | 2015-03-09 | 2015-06-03 | 北京工业大学 | Analyzing and optimizing method for hydrostatic guideway to inhibit inertia force impact |
Non-Patent Citations (2)
| Title |
|---|
| Loading Capacity Analysis of Hydrostatic Oil Pad Based on Fluid-structure Coupling;Yongsheng Zhao 等;《Proceedings of the 2016 International Conference on Mechatronics Engineering and Information Technology》;20160831;327-334 * |
| 流固耦合对油静压导轨动静特性的影响;王智伟 等;《机械工程学报》;20140505;第50卷(第9期);148-152 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106777467A (en) | 2017-05-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106777467B (en) | Static pressure sliding seat static balance calculation method considering fluid-solid coupling | |
| CN107169158B (en) | Static pressure sliding seat working performance calculation method based on fluid-solid coupling effect | |
| Liu et al. | Analytical modeling for thermal errors of motorized spindle unit | |
| CN103823940B (en) | Static-pressure turntable dynamic response computing method based on overall dynamical model | |
| CN104772653B (en) | The Oil Film Thickness for Hydrostatic Slide control system and method compensated based on oil temperature | |
| CN104091021B (en) | Method for calculating bearing capacity of oil pad when oil pad inclines | |
| CN104462752B (en) | A kind of hydrostatic slideway load-bearing capacity analysis method for considering guide rail facial disfigurement | |
| Boyko et al. | Flow rate-pressure drop relation for deformable channels via fluidic and elastic reciprocal theorems | |
| CN104537189A (en) | Hydrostatic rotary table kinematic error modeling and computing method | |
| CN106503391B (en) | A kind of quick calculation method of Rectangular Hydrostatic lubricating pad considering fluid structurecoupling | |
| Qi et al. | Investigation on the influence of structural rigidity on the stiffness of aerostatic guideway considering fluid-structure interaction | |
| Felderhof | Effect of fluid inertia on the motion of a collinear swimmer | |
| Chen et al. | Dynamic responses of planar multilink mechanism considering mixed clearances | |
| Dong et al. | Deformation analysis of hydrostatic guideways based on the cantilever plate bending calculation method | |
| CN104680018A (en) | Analyzing and optimizing method for hydrostatic guideway to inhibit inertia force impact | |
| Zhang et al. | Influence of pressure-equalizing groove on static load performance of aerostatic guideway | |
| CN108971528B (en) | Method and device for automatically centering machine tool spindle by using sliding bearing | |
| Li et al. | Blow-up analysis of hydrodynamic forces exerted on two adjacent $ M $-convex particles | |
| Lancmanová et al. | Steady incompressible flow through a branched channel | |
| Hui et al. | Application and research of the Clip Type Manipulator | |
| CN209804271U (en) | Triaxial removes micro-adjustment platform | |
| Schwendeman et al. | A homogenization analysis of the compressible flow between a slider and a moving patterned rough surface | |
| CN204902667U (en) | People's rifle interact force measuring device of system | |
| Stach et al. | Analytical Solution of Hydrostatic Pocket Tilting | |
| Sharma et al. | A study of misaligned micropolar lubricated membrane compensated hybrid journal bearing system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |