CN107169158B - Static pressure sliding seat working performance calculation method based on fluid-solid coupling effect - Google Patents
Static pressure sliding seat working performance calculation method based on fluid-solid coupling effect Download PDFInfo
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Abstract
The invention discloses a fluid-solid coupling based working performance calculation method of a static pressure sliding seat, which comprises the following steps: (1) analyzing the stress condition of the static pressure sliding seat according to the actual working condition, and establishing a sliding seat stress analysis schematic diagram; (2) simplifying the sliding seat into a thin plate model and an oil pad model according to the thin plate deformation theory and the basic structure size of the static pressure sliding seat; (3) calculating the pressure distribution of a static pressure sliding seat oil pad model and the change of the oil film thickness, and establishing an equation; (4) calculating the deformation condition of the static pressure sliding seat thin plate model under the action of external force, and obtaining the deflection function of the static pressure sliding seat thin plate model; (5) establishing a slide seat-oil pad fluid-solid coupling model through a mutual coupling relation between slide seat deformation and oil film thickness change, and establishing a dynamic balance equation of the slide seat-oil pad fluid-solid coupling model; (6) and (3) dynamically analyzing the working performance of the static pressure sliding seat under the actual working condition by utilizing matlab software, and finally obtaining the evaluation of the working performance of the static pressure sliding seat based on the fluid-solid coupling effect under the actual working condition.
Description
Technical Field
The invention discloses a calculation method of the working performance of a static pressure sliding seat based on the fluid-solid coupling effect between the sliding seat and an oil pad, belonging to the field of mechanical design and manufacturing.
Background
The static pressure slide carriage is a key part of a precise ultra-precise heavy high-grade numerical control machine tool, plays a role in supporting the heavy machine tool and drives the whole gantry frame to move linearly. Because the static pressure slide seat has the advantages of low friction, high bearing capacity, high motion precision and the like, the static pressure slide seat is widely applied to the manufacturing industry of various heavy machinery parts. The static pressure slide seat is earlier researched abroad, products cover all parts, and mature manufacturing technologies and products are available. Although the domestic research is slightly late, under the trend of reform and opening, foreign technologies are greatly introduced, advanced experience is learned, and scientific researchers have great development under the continuous effort of national support. Various types of static pressure supports are designed in heavy machine tool manufacturing in a plurality of large machine manufacturing enterprises such as a north machine tool factory, a second machine tool factory of the ziqi hall, a heavy machine tool factory of the wuhan, and the like, and a static pressure slide seat is one of the static pressure supports.
With the development of national defense industry, the wide application of heavy machine tools and the deep research of static pressure technology, the requirement on the processing quality of workpieces is higher and higher, and the research on the working performance of the workpieces is also more and more important. In recent years, considerable research has been done by many experts on hydrostatic slides. However, the slide carriage is subject to not only the gravity of the upright post, the cross beam, the slide carriage, the ram and various components during the movement process, but also the overturning moment of the upper structural member during the movement process, so the slide carriage can also deform. In the prior design calculation, the sliding seat is simplified into a rigid body, and the influence of the mutual coupling action between the self deformation of the sliding seat and the change of the oil film thickness on the working performance of the sliding seat is ignored. Therefore, extensive research must be carried out on the coupling effect to improve the design of the hydrostatic slider, improve its working performance and life. Therefore, the invention discloses a method for calculating the working performance of the static pressure sliding seat based on the fluid-solid coupling effect, which can provide a better design method for the design and manufacture of the static pressure sliding seat, so that the static pressure sliding seat has better working performance.
Disclosure of Invention
The invention mainly aims at the working performance of a static pressure sliding seat and designs a calculation method of the working performance of the static pressure sliding seat based on the fluid-solid coupling effect between the sliding seat and an oil pad. The method is mainly characterized in that the mutual coupling effect between the self deformation of the sliding seat and the thickness change of an oil film is considered in the calculation process of the working performance of the static pressure sliding seat, the pressure distribution of each oil cavity on the sliding seat is calculated, and the working performance of the sliding seat is compared with that under the condition that the sliding seat is regarded as a rigid body.
The technical problem to be solved by the invention is realized by the following scheme:
a static pressure slide carriage working performance calculation method based on fluid-solid coupling is characterized by comprising the following steps: the calculation method comprises the following steps:
(1) analyzing the stress condition of the static pressure sliding seat according to the actual working condition, and establishing a sliding seat stress analysis schematic diagram;
(2) carrying out meshing on the sliding seat by using a finite element method, and simplifying the sliding seat into a thin plate model and an oil pad model according to a thin plate deformation theory and the basic structure size of the static pressure sliding seat;
(3) calculating the pressure distribution of the static pressure sliding seat oil pad and the change of the oil film thickness, and establishing a deformation equation of the static pressure sliding seat oil pad;
(4) calculating the deformation condition of the static pressure sliding seat thin plate model under the action of external force, and obtaining the deflection function of the static pressure sliding seat thin plate model;
(5) establishing a slide seat-oil pad fluid-solid coupling model and a dynamic balance equation thereof according to a mutual coupling relation between slide seat deformation and oil film thickness change, the oil film thickness deformation equation established in the step (3) and the deflection function of sheet deformation established in the step (4);
(6) and (3) dynamically analyzing the working performance of the static pressure sliding seat under the actual working condition by utilizing matlab software, and finally obtaining the evaluation of the working performance of the static pressure sliding seat based on the fluid-solid coupling effect under the actual working condition.
In the step (1), the upper surface of the static pressure sliding seat is subjected to the gravity action of the upright posts, the cross beam and the slide carriage assembled on the cross beam, and the lower surface of the static pressure sliding seat is subjected to the pressure action of two rows of fourteen static pressure oil pads.
And (2) accurately positioning the position of the static pressure oil pad by using grid nodes divided by the finite element grids.
And (2) analyzing basic conditions of a static pressure sliding seat actual structure size thin plate deformation theory, judging whether the sliding seat structure size meets the basic conditions of the thin plate deformation theory, and calculating sliding seat deformation according to the deformation theory.
Compared with the prior art, the invention has the following advantages:
by analyzing the stress analysis and the working mechanism of the static pressure sliding seat of the heavy static pressure machine tool, the pressure distribution of the oil cushion is calculated based on the Reynolds equation according to the boundary condition of the single oil cushion, the actual deformation of the thin plate is calculated according to the simplified thin plate model and the thin plate deformation theory, and an oil cushion-sliding seat fluid-solid coupling analysis model is established according to the thin plate model and the oil cushion model. The method comprehensively considers the influence of the self-deformation of the sliding seat on the oil film thickness and the self-deformation of the sliding seat caused by the change of the oil film thickness, the method is most consistent with the actual working condition, the obtained result is most accurate, and the defect of the working performance of the static-pressure sliding seat without considering the self-deformation of the sliding seat when the sliding seat is regarded as a rigid body is overcome.
Drawings
FIG. 1 is a flow chart of fluid-solid coupling calculation design of a static pressure slide carriage of a heavy gantry machine tool according to the present invention;
FIG. 2 is a schematic view of the force analysis of the hydrostatic slider according to the present invention;
FIG. 3 is a simplified process diagram of the hydrostatic slider of the present invention;
FIG. 4 is a schematic structural view of a rectangular static pressure oil pad according to the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in fig. 1, a method for calculating a static pressure slide of a heavy gantry machine tool based on fluid-solid coupling analysis includes the following steps:
1. and (3) carrying out stress analysis on the static pressure sliding seat according to the actual stress condition of the static pressure sliding seat to obtain a stress analysis diagram (as shown in figure 2) of the static pressure sliding seat.
2. And (2) carrying out grid division on the sliding seat according to a grid division method of finite element analysis, wherein the side length of the sliding seat in the X direction is a, the side length of the sliding seat in the Y direction is b, and corresponding coordinates are X and Y respectively. And determining grid nodes of the sliding seat according to the actual position of the oil pad on the sliding seat. The sliding seat is simplified into a thin plate structure and a multi-oil-pad structure.
3. And deducing a Reynolds equation according to the multi-oil-pad model, and solving the Reynolds equation by finite difference to obtain the pressure distribution of the oil cavity.
The calculation and the solution of the fluid lubrication theoretical model are solved by using a special form Reynolds equation of a Navier-Stokes equation. The Reynolds equation is a second-order partial differential equation, is derived from a motion equation and a continuity equation, and is the most basic equation of the fluid lubrication theory. The derivation of the Reynolds equation is based on the following basic assumptions:
(1) neglecting the influence of the gravity action, the magnetic action and the like.
(2) The fluid does not slide on the interface at the interface, and the speed of the fluid contacting the surface is the same as the speed of the surface.
(3) In the oil film thickness direction, oil film pressure changes are not counted.
(4) Compared with the oil film thickness, the curvature radius of the guide rail surface is large, the influence of the curvature radius is ignored, and the rotation speed is replaced by the translation speed.
(5) Static pressure oil is regarded as Newtonian fluid.
(6) Because the guide rail does not move at a high speed, the oil flow is considered to be laminar.
(7) For simple calculation, the viscosity value in the thickness direction of the oil film is regarded as a constant value
(8) Neglecting the force of fluid acceleration and the centrifugal force of oil film bending, the inertial force is negligible compared to the viscous force of oil.
And deducing a Reynolds equation by using a infinitesimal balance and a continuity equation. The basic flow is as follows: and solving the oil liquid velocity distribution in the oil film thickness z direction according to the infinitesimal stress balance condition. And integrating the oil liquid velocity distribution in the oil film thickness direction, and solving the oil liquid flow. And finally, obtaining a Reynolds equation derivation form according to the continuity equation.
Therefore, the continuity equation and the N-S equation of the rectangular oil pad are simplified as follows:
u is the speed of the lubricating oil along the x direction, v is the speed of the lubricating oil along the y direction, the viscous shearing force p is the oil cavity pressure, and eta is the oil viscosity. Since the oil film thickness Z is much smaller than the oil film length X and width B, the removal velocity gradientAndin addition, other velocity gradient factors having values that are too small may have negligible effect. Therefore, when force is applied in the X direction, the dxdz surface has no viscous shear force effect, and the method is simplified
The basic assumption (5) and the basic assumption (6) are derived from the Reynolds equation, and Newton's law of viscosity is simplified:
substituting the equation to obtain:
the same can be said in the Y direction:
from the basic assumption (3) it is possible to obtain in the Z direction:
because the pressure P is not a function of z and the viscosity eta is not a function of z, twice integrating z, and simultaneously, according to the Reynolds equation, basically assuming that (2) the fluid speed of surface contact is the same as the surface speed, determining the boundary condition, and the speed of the two solid surfaces in the X direction is UhAnd U0Velocity V in Y directionhAnd V0. When the oil film thickness z is equal to 0, namely, when the oil film is close to the lower guide rail surface U is equal to U0When the oil film thickness z is equal to h, namely, the oil film is close to the upper guide surface U is equal to Uh. The velocity in the X direction after integration is:
similarly, the speed in the Y direction is:
according to the continuity equation:
the x-direction speed and the Y-direction speed are substituted into a continuity equation and the oil film thickness is integrated:
neglecting the change of the oil density with time, the general form of the Reynolds equation is obtained:
wherein: u is equal to Uh-U0,V=Vh-V0。
The Reynolds equation is then solved for finite difference. And (3) carrying out finite difference solution, firstly, carrying out grid division, defining the number of nodes, defining m nodes in the X direction and n nodes in the Y direction. And then the partial differential equation is dimensionless, thereby reducing the number of independent variables and dependent variables and enabling the solution of the equation to have universality. Carrying out non-dimensionalization on variables in the Reynolds equation:
wherein p is pressure;
-pressure in the oil pocket;
Ux-the speed of movement of the guide rail in the X direction;
h is oil film thickness;
eta-oil viscosity;
-dimensionless pressure;
-a dimensionless length;
-a dimensionless width;
-a dimensionless thickness;
-the dimensionless guide movement speed;
-dimensionless oil film thickness.
The oil film thickness h is a matrix h (i, j) and correspondingly represents the oil film thickness at each node. And solving the pressure distribution condition in the oil film area, wherein the pressure value in the oil cavity can be considered to be constant, and the pressure distribution at the oil sealing edge is solved by utilizing a Reynolds equation. The distribution of the pressure p in the oil seal area can be represented by the pressure value of each node, and according to the differential principle, the first and second derivatives of any node p (i, j) are represented by the variable values of the surrounding nodes, as shown in the figure, wherein L and B represent the length and width of the oil pad, and represent the step size in the X direction and the Y direction. In the land area, the pressure at the node may be expressed as:
the pressure distribution is integrated in the node area, and the pressure distribution q (x, y) at each node is obtained.
5. And carrying out deformation analysis according to the simplified thin plate model of the sliding seat and a thin plate deformation theory.
In elastic mechanics, an object enclosed by two parallel cylindrical surfaces or prismatic surfaces is called a plate, two planes with larger area are called plate surfaces, the planes with smaller area, such as the cylindrical surfaces or the prismatic surfaces, are called plate edges, and the planes with equal distance to the upper plate surface and the lower plate surface are the middle surfaces of the plate. The plates can be divided into thick plates, thin plates and thin films according to the different ratio of the plate thickness h to the side length b of the plate short. Plates with a ratio of plate thickness h to shorter side B greater than 0.2 are called thick plates, plates with a ratio between 0.0125 and 0.2 are called thin plates, and plates with a ratio less than 0.0125 are called thin films. The ratio of the shortest side length of the hydrostatic slide to the thickness of the hydrostatic slide, which is generally between 0.0125 and 0.2, falls within the range of thin plates. According to the theory of sheet deformation, the deformation ω at the slide (x, y) is calculated as:
ω=ω(x,y) (14)
because the oil film thickness needs to be given in the initial condition when the derivation of the Reynolds equation and the finite difference solution are carried out, the boundary condition is set to be a four-side simple support when the deformation equation of the sliding seat guide surface is derived. The side lengths are a and b respectively and are acted by a distributed load q. The mathematical expression of the boundary condition is as follows:
when the thin plate surface benefits the multiple purposes of concentrated force load q, the coordinate of the action point is (m, n), namely the stress at the point (m, n) is q, and the stress at the rest positions is zero. The expression of the deflection ω at any node (x, y) of the carriage is now obtained as:
and substituting the calculated oil chamber pressure q (x, y) into a formula (16), and calculating the deformation of the sliding seat when the fluid-solid coupling is considered according to a balance equation in the z direction.
F is the acting force of the oil pad on the sliding seat, G is the self weight of the sliding seat, and M is the action of the eccentric action of the gravity center of the machine tool on the bending moment of the sliding seat.
Claims (6)
1. A static pressure slide carriage working performance calculation method based on fluid-solid coupling is characterized by comprising the following steps: the calculation method comprises the following steps:
(1) analyzing the stress condition of the static pressure sliding seat according to the actual working condition, and establishing a sliding seat stress analysis schematic diagram;
(2) carrying out meshing on the sliding seat by using a finite element method, and simplifying the sliding seat into a thin plate model and an oil pad model according to a thin plate deformation theory and the basic structure size of the static pressure sliding seat;
(3) calculating the pressure distribution of the static pressure sliding seat oil pad and the change of the oil film thickness, and establishing a deformation equation of the static pressure sliding seat oil pad;
(4) calculating the deformation condition of the static pressure sliding seat thin plate model under the action of external force, and obtaining the deflection function of the static pressure sliding seat thin plate model;
(5) establishing a slide seat-oil pad fluid-solid coupling model and a dynamic balance equation thereof according to a mutual coupling relation between slide seat deformation and oil film thickness change, the oil film thickness deformation equation established in the step (3) and the deflection function of sheet deformation established in the step (4);
(6) utilizing matlab software to carry out dynamic analysis on the working performance of the static pressure sliding seat under the actual working condition, and finally obtaining the working performance evaluation of the static pressure sliding seat based on the fluid-solid coupling action under the actual working condition;
in the step (3), the pressure distribution of the oil pad is calculated by the following formula:
the calculation and solution of the fluid lubrication theoretical model are solved by using a special form Reynolds equation of a Navier-Stokes equation; the Reynolds equation is a second-order partial differential equation, is derived from a motion equation and a continuity equation, and is the most basic equation of the fluid lubrication theory; the derivation of the Reynolds equation is based on the following basic assumptions:
(1) neglecting the influence of gravity action and magnetic force action volume force;
(2) the fluid does not slide on the interface at the joint, and the speed of the fluid contacting the surface is the same as the surface speed;
(3) in the thickness direction of the oil film, the change of the oil film pressure is not counted;
(4) compared with the oil film thickness, the curvature radius of the guide rail surface is very large, the influence of the curvature radius is neglected, and the rotation speed is replaced by the translation speed;
(5) regarding the static pressure oil as Newtonian fluid;
(6) because the motion speed of the guide rail is not high, the oil flow is regarded as laminar flow;
(7) for simple calculation, the viscosity value in the thickness direction of the oil film is regarded as a constant value
(8) Neglecting the fluid acceleration force and the centrifugal force of oil film bending, and neglecting the inertia force compared with the viscous force of the oil liquid;
deducing a Reynolds equation by utilizing a infinitesimal balance and a continuity equation; the basic flow is as follows: solving the oil liquid velocity distribution in the oil film thickness direction according to the infinitesimal stress balance condition; integrating the oil liquid velocity distribution in the oil film thickness direction, and solving the oil liquid flow; finally, obtaining a Reynolds equation derivation form according to the continuity equation; therefore, the continuity equation and the N-S equation of the rectangular oil pad are simplified as follows:
u is the speed of the lubricating oil along the X direction, v is the speed of the lubricating oil along the Y direction, and tau is the viscous shearing force p is the pressure of the oil cavity; since the oil film thickness z is much smaller than the oil film length X and width B, the velocity gradient is removedAndbesides, other velocity gradients have too small values to ignore their effect; therefore, when the stress in the X direction is analyzed, the dxdz surface has no viscous shear force; is simple and easy to obtain
The basic assumption (5) and the basic assumption (6) are derived from the Reynolds equation, and Newton's law of viscosity is simplified:
substituting the equation to obtain:
in the same way, in the Y direction:
according to the basic assumption (3) that in the Z direction:
because the oil cavity pressure p is not a function of the oil film thickness z, and the viscosity eta is not a function of the oil film thickness z, the oil film thickness z is integrated twice, and simultaneously, the boundary condition is determined according to the basic assumption that the surface contact fluid speed of (2) is the same as the surface speed, and the surface speeds of two solids are UhAnd U0When the oil film thickness z is 0, i.e. when the oil film is close to the lower guide rail surface U is U0When the oil film thickness z is equal to h, namely, the oil film is close to the upper guide surface U is equal to Uh(ii) a The velocity in the X direction after integration is:
similarly, the speed in the Y direction is:
according to the continuity equation:
the X-direction speed and the Y-direction speed are substituted into a continuity equation and the oil film thickness is integrated:
neglecting the change of the oil density with time, the general form of the Reynolds equation is obtained:
wherein: u is equal to Uh-U0,V=Vh-V0;
Then, carrying out finite difference solution on the Reynolds equation; finite difference solution is carried out, firstly, grid division is carried out, the number of nodes is defined, m nodes are defined in the X direction, and n nodes are defined in the Y direction; then, the partial differential equation is dimensionless, so that the number of independent variables and dependent variables is reduced, and the solution of the equation has universality; carrying out non-dimensionalization on variables in the Reynolds equation:
wherein p is pressure;
p0-pressure in the oil pocket;
ux-moving speed of the guide rail in the X direction;
h is oil film thickness;
eta-oil viscosity;
the oil film thickness h is a matrix h (i, j) and correspondingly represents the oil film thickness at each node; solving the pressure distribution condition in the oil film area, considering the pressure value in the oil cavity as constant, and solving the pressure distribution at the oil sealing edge by utilizing a Reynolds equation; the distribution of the pressure p in the oil seal edge area is represented by the pressure value of each node, according to the difference principle, the first-order derivative and the second-order derivative of any node p (i, j) are represented by variable values of surrounding nodes, wherein deltax and deltay represent the step length in the X direction and the step length in the Y direction; in the land area, the pressure at the node is expressed as:
the pressure distribution is integrated in the node area, and the pressure distribution q (x, y) at each node is obtained.
2. The fluid-solid coupling based working performance calculation method of the static pressure sliding base according to claim 1, wherein in the step (1), the upper surface of the static pressure sliding base is subjected to the gravity of the upright post, the cross beam and the slide carriage assembled on the cross beam, and the lower surface of the static pressure sliding base is subjected to the pressure of two rows of fourteen static pressure oil pads.
3. The fluid-solid coupling based working performance calculation method of the static pressure sliding seat according to claim 1, wherein in the step (2), the positions of the static pressure oil pads are accurately positioned by using mesh nodes divided by a finite element mesh.
4. The method for calculating the working performance of the hydrostatic sliding seat based on the fluid-solid coupling as claimed in claim 1, wherein in the step (2), basic conditions of a thin plate deformation theory of an actual structural size of the hydrostatic sliding seat are analyzed, whether the structural size of the sliding seat meets the basic conditions of the thin plate deformation theory is judged, and sliding seat deformation is calculated according to the deformation theory.
5. The method for calculating the working performance of the hydrostatic slider based on fluid-solid coupling as claimed in claim 1, wherein in the step (4), the deformation of the thin plate is calculated by the following formula:
in the elastic mechanics, an object enclosed by cylindrical surfaces or prismatic surfaces of two parallel surfaces is called a plate, two planes with larger areas of the plate are called plate surfaces, the planes with smaller areas of the cylindrical surfaces or the prismatic surfaces are called plate edges, and the planes with equal distance with the upper plate surface and the lower plate surface are the middle surfaces of the plate; dividing the plate into a thick plate, a thin plate and a thin film according to different ratios of the plate thickness h to the side length b of the plate short; the plate with the ratio of the plate thickness h to the shorter side B larger than 0.2 is called a thick plate, the plate with the ratio between 0.0125 and 0.2 is called a thin plate, and the plate with the ratio smaller than 0.0125 is called a thin film; the ratio of the shortest side length of the static pressure slide to the thickness of the static pressure slide is usually between 0.0125 and 0.2, and belongs to the range of thin plates; according to the theory of sheet deformation, the deformation ω at the slide (x, y) is calculated as:
ω=ω(x,y) (14)
when the derivation of the Reynolds equation and the finite difference solution are carried out, the oil film thickness needs to be given in the initial condition, so that the deformation equation of the slide seat guide surface is derived, and the boundary condition is set as a four-side simple support; the side lengths of the two-dimensional array are a and b respectively and are acted by a distributed load q; the mathematical expression of the boundary condition is as follows:
when the thin plate surface benefits the multiple purposes of concentrated force load q, the coordinate of an action point is (m, n), namely the stress at the point (m, n) is q, and the stress at the other positions is zero; the expression of the deflection ω at any node (x, y) of the carriage is now obtained as:
6. the fluid-solid coupling based working performance calculation method of the static pressure sliding seat according to claim 5, wherein: substituting the calculated oil cavity pressure q (x, y) into a formula (16), and calculating to obtain the deformation of the sliding seat when fluid-solid coupling is considered according to a balance equation in the z direction;
f is the acting force of the oil pad on the sliding seat, G is the self weight of the sliding seat, M is the bending moment action of the eccentric action of the gravity center of the machine tool on the sliding seat, and the working performance of the static pressure sliding seat is analyzed.
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CN109815548B (en) * | 2018-12-27 | 2021-01-19 | 西安交通大学 | Fluid film pressure calculation method based on Garlerkin idea |
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 |
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 |
CN110399670B (en) * | 2019-07-18 | 2023-12-26 | 上海理工大学 | Method for establishing fluid dynamic and static ball bearing oil film pressure calculation model |
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