Hydrostatic guide rail bearing performance calculation method for realizing fluid-structure interaction based on thick plate theory

Abstract

The invention discloses a static pressure guide rail bearing performance calculation method for realizing fluid-structure interaction based on a thick plate theory, which comprises the following steps of: 1, calculating the deflection of a cantilever thick plate under the action of concentrated force based on a work interoperability theorem, establishing a deflection surface equation and a stress formula of the cantilever thick plate, solving unknown parameters through a Gaussian iteration method, and calculating the deflection of the cantilever thick plate under the action of concentrated force; and the deformation condition of the thick plate under the action of concentrated force is obtained. And 2, discretizing the Reynolds equation by using a finite difference method, establishing an iterative equation of oil film pressure distribution, and solving the pressure distribution of the rectangular oil pad under set boundary conditions by using a Gaussian-Seidel iterative method. And step 3, comprehensively considering the influence of the pressure plate deformation on the oil film thickness and the pressure distribution through iterative coupling calculation, repeatedly iterating until the tolerance requirement is met, and finally obtaining the pressure plate deformation and the oil film pressure distribution under the consideration of the fluid-solid coupling effect. According to the calculation method, the bearing capacity of the hydrostatic guideway under the actual working condition can be evaluated more accurately.

Description

Technical Field

[0001] The invention relates to the field of hydrostatic guide rails, and in particular to a method for calculating the bearing performance of hydrostatic guide rails by realizing fluid-solid coupling based on thick plate theory. Background Art

[0002] During the operation of the hydrostatic guide rail, the hydrostatic effect causes the upper and lower oil films to generate bearing force and act on the guide rail base. At this time, the pressure plate part is in contact with the upper oil chamber, and the pressure plate structure is a cantilever plate with three free sides and one fixed side. In order to reduce the influence of the pressure plate deformation on the hydrostatic oil film, the pressure plate of the guide rail is usually made of thicker material. However, since the pressure plate is a cantilever plate, its deformation still needs to be considered. As the thickness of the pressure plate increases, the interlayer shear deformation gradually becomes non-negligible, and it is no longer reasonable to continue to use the thin plate theory at this time. Therefore, the present invention adopts the Reissner theory and proposes a method for calculating the bearing performance of a hydrostatic guide rail based on the thick plate theory to realize fluid-solid coupling. Summary of the invention

[0003] The technical solution adopted by the present invention is a method for calculating the load-bearing performance of a hydrostatic guide rail, in particular, a method for calculating the load-bearing performance of a hydrostatic guide rail based on thick plate theory to realize fluid-solid coupling. By combining the thick plate theory with the Reynolds equation, the method systematically considers the mutual influence between the deformation of the pressure plate under the action of the oil film pressure and the oil film pressure distribution, thereby realizing the accurate calculation of the load-bearing performance of the hydrostatic guide rail.

[0004] Step 1: Based on the reciprocity theorem of work, calculate the deflection of the cantilever thick plate under the concentrated force, establish the deflection surface equation and stress formula of the cantilever thick plate, and solve the unknown parameters through the Gaussian iteration method to obtain the deformation of the thick plate under the concentrated force.

[0005] Step 2: The Reynolds equation is discretized using the finite difference method, the iterative equation for the oil film pressure distribution is established, and the Gauss-Seidel iteration method is used to solve the pressure distribution of the rectangular oil pad under the set boundary conditions.

[0006] Step 3: Through iterative coupling calculation, comprehensively consider the influence of pressure plate deformation on oil film thickness and pressure distribution, repeatedly iterate until the tolerance requirements are met, and finally obtain the pressure plate deformation and oil film pressure distribution under fluid-solid coupling.

[0007] Compared with the existing technology, this calculation method overcomes the limitations of traditional thin plate theory in thick plate deformation analysis, and can solve the problems of difficult and long calculation time of bidirectional fluid-solid coupling finite element calculation. It can more accurately evaluate the bearing capacity of hydrostatic guide rails under actual working conditions. It has the advantages of high calculation accuracy and wide application range, and provides strong theoretical support for the design and optimization of hydrostatic guide rails. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 Force and constraint diagram of cantilever thick plate.

[0009] Figure 2 Rectangular oil pad pressure distribution diagram.

[0010] Figure 3 Fluid-structure interaction solution flow chart. DETAILED DESCRIPTION

[0011] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0012] The first step is to calculate the deflection of the cantilever thick plate under the concentrated force based on the reciprocity theorem of work;

[0013] The length of the plate is a, the width is b, the magnitude of the concentrated force is P, and the action coordinates are (x1, y1), such as Figure 1 As shown, through the reciprocal theorem of work, the flexure surface equation of the suspended thick plate coordinates (ξ,η) is assumed:

[0014]

[0015] The larger the n and m are, the more accurate the results are. Generally, 80 is used, and the results can meet the accuracy requirements. is the bending stiffness of the plate; v is Poisson’s ratio; b n ,c m ,d m ,k2,k3,f n ,g m ,h m ,A n is an unknown parameter.

[0016] At the same time, assume the stress formula:

[0017]

[0018] For this system, three sides are free and one side is fixed. Substituting the above deflection and stress boundary conditions into the torque angle and deflection boundary conditions of the corresponding sides, it should meet the following conditions:

[0019] ω ξ0 =0,

[0020] Q ξa =0,

[0021] Q η0 =0,

[0022] Q ηb =0,

[0023] M ξηηb =0,

[0024] M ξηη0 =0,

[0025] M ξηξa =0,

[0026] M ξηξan0 =0,

[0027] M ξηη0m0 =0,

[0028] M ξηηbm0 =0,

[0029] And corner static conditions.

[0030] This example contains six sets of unknown parameters, which are arranged in order into b n ,c m ,d m ,k2,k3,f n ,g m ,h m ,A n , where m = 1, 2, 3, ...; n = 1, 2, 3, ..., the coefficient matrix is ​​also arranged in the corresponding order, and the unknown parameters are solved by the Gauss iteration method, thereby obtaining the unknown parameters in the deflection surface equation. The deformation of the cantilever thick plate under multiple concentrated forces can be solved by the superposition theorem.

[0031] The second step is to solve the pressure distribution of the oil film and establish the Reynolds equation in the rectangular coordinate system:

[0032]

[0033] Where, p is the pressure (Pa); h is the oil film thickness (m); η is the oil viscosity (Pa·s); U is the relative moving speed of the two bearing surfaces in the x direction (m / s); V is the relative moving speed of the two bearing surfaces in the y direction (m / s); is the film thickness change rate (m / s).

[0034] Using the finite difference method for discretization, we get the iterative equation of the dimensionless pressure of the Reynolds equation:

[0035]

[0036] Where i and j are the microelement counts of the two dimensions respectively; is the dimensionless discrete step length in the x direction; is the dimensionless discrete step length in the y direction; L is the length of the oil pad; B is the width of the oil pad.

[0037] The boundary condition for the iterative equation calculation is that the dimensionless pressure is 1 inside the oil chamber and 0 outside the oil seal edge. The public expression is:

[0038]

[0039] Where l is the length of the oil chamber part; b is the width of the oil chamber part.

[0040] The termination condition of Gauss-Seidel iteration is:

[0041]

[0042] Where n is the iteration count; tol is the calculation setting accuracy, which is generally taken as 1×10 -7 .

[0043] Finally, the pressure distribution of the rectangular oil pad is obtained, such as Figure 2 shown.

[0044] The third step is to use thick plate theory and Reynolds equation to comprehensively calculate the bearing capacity of the hydrostatic guide rail considering fluid-solid coupling. The calculation flow chart is as follows: Figure 3 As shown, the calculation order is as follows:

[0045] S3.1 Define the platen structure and basic parameters, and solve the deformation matrix of the cantilever thick plate under unit force at any position;

[0046] S3.2 defines the oil film parameters and calculates the oil film pressure distribution under the original parameters;

[0047] S3.3 Apply the supporting force of each point of the oil film to the pressure plate, and solve the deformation of the pressure plate structure under the action of the oil film pressure;

[0048] S3.4 Consider the influence of pressure plate deformation on oil film thickness, recalculate the thickness of oil film at each position, and recalculate the oil film pressure distribution;

[0049] S3.5 Check whether the platen deformation meets the tolerance, otherwise iterate steps 3.3-3.4 again;

[0050] S3.6 The calculation is completed, and the pressure plate deformation and oil film pressure distribution under the effect of fluid-solid coupling are obtained.

Claims

1. A method for calculating the load-bearing performance of a hydrostatic guide rail based on thick plate theory to realize fluid-solid coupling, characterized in that: The method comprises the following steps: Step 1: Based on the reciprocal theorem of work, calculate the deflection of the cantilever thick plate under the concentrated force, establish the deflection surface equation and stress formula of the cantilever thick plate, and solve the unknown parameters through the Gaussian iteration method to obtain the deformation of the thick plate under the concentrated force; Step 2: Discretize the Reynolds equation using the finite difference method, establish the iterative equation for the oil film pressure distribution, and use the Gauss-Seidel iteration method to solve the pressure distribution of the rectangular oil pad under the set boundary conditions; Step 3: Through iterative coupling calculation, comprehensively consider the influence of pressure plate deformation on oil film thickness and pressure distribution, repeatedly iterate until the tolerance requirements are met, and finally obtain the pressure plate deformation and oil film pressure distribution under fluid-solid coupling.

2. The method for calculating the load-bearing performance of a hydrostatic guide rail based on thick plate theory and fluid-solid coupling according to claim 1 is characterized in that: Calculate the deflection of cantilever thick plate under concentrated force based on the reciprocity theorem of work; The length of the plate is a, the width is b, the magnitude of the concentrated force is P, and the action coordinates are (x1, y1). By the reciprocal theorem of work, the deflection surface equation of the suspended thick plate coordinates (ξ, η) is assumed: 0≤ξ≤x1 x1≤ξ≤a Among them, n and m are 80; is the bending stiffness of the plate; v is Poisson’s ratio; b n ,c m ,d m ,k2,k3,f n ,g m ,h m ,A n is an unknown parameter; At the same time, assume the stress formula: With three sides free and one side fixed, the deflection and stress boundary conditions are substituted into the torque angle and deflection boundary conditions of the corresponding sides to satisfy: oh x0 =0, Q xa ＝0, Q h0 ＝0, Q hb ＝0, M xhhb ＝0, M xhh0 ＝0, M xhxa ＝0, M xhxan0 ＝0, M xhh0m0 ＝0, M xhhbm0 ＝0, and corner static conditions; The six sets of unknown parameters are arranged in order into b n ,c m ,d m ,k2,k3,f n ,g m ,h m ,A n , where m = 1, 2, 3, ...; n = 1, 2, 3, ..., the coefficient matrix is ​​also arranged in the corresponding order, and the unknown parameters are solved by the Gauss iteration method, thereby obtaining the unknown parameters in the deflection surface equation; the deformation of the cantilever thick plate under multiple concentrated forces is solved by the superposition theorem.

3. The method for calculating the load-bearing performance of a hydrostatic guide rail based on thick plate theory and fluid-solid coupling according to claim 1 is characterized in that: In order to solve the pressure distribution of the oil film, the Reynolds equation in the rectangular coordinate system is established: Where, p is the pressure (Pa); h is the oil film thickness (m); η is the oil viscosity (Pa·s); U is the relative moving speed of the two bearing surfaces in the x direction; V is the relative moving speed of the two bearing surfaces in the y direction; is the film thickness change rate; Using the finite difference method for discretization, we get the iterative equation of the dimensionless pressure of the Reynolds equation: Where i and j are the microelement counts of the two dimensions respectively; is the dimensionless discrete step length in the x direction; is the dimensionless discrete step length in the y direction; L is the length of the oil pad; B is the width of the oil pad; The boundary condition for the iterative equation calculation is that the dimensionless pressure is 1 inside the oil chamber and 0 outside the oil seal edge. The public expression is: Where l is the length of the oil chamber; b is the width of the oil chamber; The termination condition of Gauss-Seidel iteration is: Where n is the iteration loop count; tol is the calculation setting accuracy with a value of 1×10 -7， Finally, the pressure distribution of the rectangular oil pad is obtained.

4. The method for calculating the load-bearing performance of a hydrostatic guide rail based on thick plate theory and fluid-solid coupling according to claim 1 is characterized in that: The comprehensive calculation of the load-bearing capacity of the hydrostatic guide considering fluid-solid coupling is carried out by using thick plate theory and Reynolds equation. The sequence is as follows: S3.1 Define the platen structure and basic parameters, and solve the deformation matrix of the cantilever thick plate under unit force at any position; S3.2 defines the oil film parameters and calculates the oil film pressure distribution under the original parameters; S3.3 Apply the supporting force of each point of the oil film to the pressure plate, and solve the deformation of the pressure plate structure under the action of the oil film pressure; S3.4 Consider the influence of pressure plate deformation on oil film thickness, recalculate the thickness of oil film at each position, and recalculate the oil film pressure distribution; S3.5 checks whether the platen deformation meets the tolerance, otherwise iterates S3.3-S3.4 again; S3.6 The calculation is completed, and the pressure plate deformation and oil film pressure distribution under the effect of fluid-solid coupling are obtained.

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