A rapid calculation method for the optimal air film thickness and stiffness of a aerostatic guideway

Abstract

A rapid calculation method for the optimal air film thickness and stiffness of a gas static pressure guide rail, which relates to the technical field of gas static pressure guide rails. To solve the problem of low calculation efficiency of the existing fluid-structure interaction calculation method for gas static pressure guide rails. First, a CFD analysis model of the air film flow field is established, function fitting is carried out according to the calculation data, and then considering the static balance of the gas static pressure guide rail, the optimal actual thickness of each air film and the corresponding air film force and air film stiffness are obtained through optimization calculation; a transient analysis model of the structural field is established, and combined with the air film force and air film stiffness obtained previously, the deformation of the solid structure under the action of the air film force is obtained, and finally the optimal initial air film thickness of each air film, that is, the optimal design parameter of the gas static pressure guide rail, is calculated; then through the virtual load loading method, the actual optimal stiffness of the gas static pressure guide rail is calculated on the transient analysis model of the structural field; this algorithm improves the calculation efficiency while ensuring the calculation accuracy. The present invention is applicable to the parameter design of gas static pressure guide rails.

Description

Technical Field

[0001] The present invention relates to the technical field of aerostatic guides, and particularly relates to a rapid calculation method for the optimal air film thickness and stiffness of an aerostatic guide. Background Art

[0002] Aerostatic guides are widely used in ultra-precision machining and testing equipment due to their excellent characteristics such as high supporting accuracy, low friction coefficient, and low heat generation rate. Aerostatic guides are non-standard parts and need to be designed according to the usage scenarios and design specifications in actual applications. Therefore, the accuracy of the calculation method for the optimal air film thickness and its corresponding optimal stiffness of an aerostatic guide will directly affect the quality of the final design scheme. Currently, the performance calculation of aerostatic guides is mainly achieved through numerical calculation methods such as the finite element method and the finite volume method for the air film flow field. However, in the pure numerical calculation (CFD calculation) of the air film flow field, the influence of the structural deformation caused by gas pressure on its performance is ignored. The large bearing capacity of the air film flow field will cause micron-level deformation of the guide rail slider, significantly changing the air film thickness; in the design of high-stiffness aerostatic bearings, large calculation errors will occur, resulting in the actual stiffness of the guide rail being lower than the design expectation. Currently, the commonly used calculation method for the performance of aerostatic guides considering fluid-structure interaction mainly achieves balance through establishing a data interface between the fluid field and the solid field and performing transient fluid-structure interaction analysis through repeated iterations. Generally, the calculation of the optimal air film thickness and its optimal stiffness of an aerostatic guide takes hundreds of hours or even thousands of hours.

[0003] In summary, the existing fluid-structure interaction calculation method for aerostatic guides has the problem of low calculation efficiency. Summary of the Invention

[0004] In order to solve the problem of low calculation efficiency existing in the existing fluid-structure interaction calculation method for aerostatic guides and on the premise of ensuring calculation accuracy, the present invention proposes a rapid calculation method for the optimal air film thickness and stiffness of an aerostatic guide.

[0005] The rapid calculation method for the optimal air film thickness and stiffness of an aerostatic guide of the present invention is specifically as follows:

[0006] Step 1: Perform CFD flow field calculations on the upper, side, and lower air films of the aerostatic guide respectively to obtain the calculation data of the air film force and air film stiffness varying with the air film thickness;

[0007] Step 2: Perform function fitting on the upper and lower air film data obtained in Step 1 based on the least squares method to establish a static equilibrium equation in the vertical direction;

[0008]

[0009] In the formula, F UThe upper air film air film force, F I The lower air film air film force, W1 is the constant load of the aerostatic guideway, W 2m is the maximum variable load of the aerostatic guideway;

[0010] Step 3: For the upper air film with any thickness, obtain its corresponding lower air film thickness and the overall vertical stiffness of the aerostatic guideway through Step 2. On this basis, find the actual air film thicknesses h Ua 、h Ia of the upper and lower air films corresponding to the optimal stiffness of the aerostatic guideway through optimization calculation, as well as the air film force F U ,F I and the air film stiffness K U ,K I at this time;

[0011] Step 4: Establish a transient analysis model of the structure field of the slide plate of the aerostatic guideway. This model is simplified by using symmetric constraints. Obtain the change in the air film thickness under the action of the optimal actual air film thickness through this model. Combine the optimal actual air film thickness obtained in Step 1 and Step 3 to calculate the optimal initial air film thickness;

[0012] Step 5: Combine the transient analysis model of the structure field in Step 4. Through the virtual load loading method in the conventional fluid-structure coupling calculation method of the aerostatic guideway, perform virtual load loading in the proposed transient analysis model to obtain the actual optimal stiffness of the aerostatic guideway;

[0013] Furthermore, in the calculation data of the air film force and air film stiffness varying with the air film thickness obtained in Step 1, for the side air film, due to its symmetric force situation and structural characteristics, the ideal optimal thickness at this time corresponds to the optimal actual air film thickness h La-op of the side air film, and the air film force F L corresponding to the side air film at this time can be obtained;

[0014] Furthermore, the specific calculation method for establishing the transient analysis model of the structure field of the slide plate of the aerostatic guideway in Step 4 is as follows:

[0015] Step 4-1: Load the air film force F L corresponding to the side air film in Step 1 on the side air film surface of the slide plate;

[0016] Step 4-2: Load the air film forces F U ,F I of the upper and lower air films in Step 3 on the upper and lower air film surfaces. At the same time, in order to perform constraints in the vertical direction to avoid non-convergence of the model, elastic constraints are loaded on the upper and lower air film surfaces, and their stiffness values are the ideal stiffnesses K U ,K I corresponding to the upper and lower air films in Step 3;

[0017] Step Four Three: Through this model, the structural deformation of each air film surface under the air film force corresponding to the actual air film thickness can be obtained, and this value is the change in air film thickness Δh under the air film force. U-op , Δh I-op , Δh L-op ; Δh U-op is the change value of the upper air film thickness, Δh I-op is the change value of the lower air film thickness, Δh L-op is the change value of the side air film thickness;

[0018] Step Four Four: After calculating by combining the actual air film thicknesses of each air film in Steps One, Two, and Three, the optimal initial air film thickness h of this aerostatic guide can be obtained. U0-op , h I0-op、 h L0-op ; h U0-op is the optimal initial upper air film thickness; h I0-op is the optimal initial lower air film thickness; h L0-op is the optimal initial side air film thickness, that is, the optimal design parameter of this aerostatic guide;

[0019] Furthermore, the formula for the optimal initial upper air film thickness h in Step Four Four is; U0-op

[0020] h U0-op = h Ua-op - Δh U-op (2)

[0021] In the formula, h Ua-op is the optimal actual air film thickness of the upper air film;

[0022] Furthermore, the formula for the optimal initial lower air film thickness h in Step Four Four is; I0-op

[0023] h I0-op = h Ia-op - Δh I-op (3)

[0024] In the formula, h Ia-op is the optimal actual air film thickness of the lower air film;

[0025] Furthermore, the formula for the optimal initial side air film thickness h in Step Four Four is; L0-op

[0026] h L0-op = h La-op - Δh L-op (4)

[0027] In the formula, h La-op ​​​is the actual air film thickness with the optimal side air film.

[0028] The present invention has the following beneficial effects compared with the prior art:

[0029] The present invention overcomes the shortcomings of the prior art, greatly improves the calculation efficiency on the premise of ensuring the calculation accuracy, and the present invention is realized based on computational fluid dynamics, numerical calculation methods, numerical fitting methods, and structural dynamics; this calculation method can accurately and quickly calculate the optimal air film thickness and optimal stiffness of the aerostatic guideway, the modeling process is simple and general, the calculation process is clear, the calculation efficiency is high, and it is of great significance for the accurate prediction of the optimal design parameters and static performance of the aerostatic guideway. First, a flow field analysis model of the aerostatic guideway is established to obtain the CFD calculation data of the air film flow field. Through function fitting of the calculation data, and then considering the static balance of the aerostatic guideway, the optimal actual thickness, corresponding air film force and air film stiffness of each air film are obtained through optimization calculation; a transient analysis model of the structural field is established, combined with the air film force and air film stiffness obtained before, the deformation of the solid structure under the action of the air film force, that is, the change value of the air film thickness, is obtained. Combining the obtained actual optimal air film thickness and structural deformation, the optimal initial air film thickness of the aerostatic guideway is calculated, which is also the optimal design parameter of the aerostatic guideway; then through the virtual load loading method, the actual optimal stiffness of the aerostatic guideway is calculated on the transient analysis model of the structural field; this algorithm improves the calculation efficiency while ensuring the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a schematic diagram of the fluid-structure interaction deformation of the aerostatic guideway

[0031] Figure 2 is a schematic diagram of a rapid calculation method for the optimal air film thickness of an aerostatic guideway considering fluid-structure interaction;

[0032] Figure 3 is the CFD calculation grid division and boundary conditions of the air film flow field;

[0033] Figure 4 Schematic diagram of the proposed transient analysis model of the structural field. DETAILED DESCRIPTION OF THE INVENTION

[0034] DETAILED DESCRIPTION OF THE INVENTION 1: Combining Figures 1 to 3 This embodiment is described, and a rapid calculation method for the optimal air film thickness and stiffness of an aerostatic guideway described in this embodiment is as follows:

[0035] Step 1: Perform CFD flow field calculations on the upper, side, and lower air films of the aerostatic guideway respectively to obtain the calculation data of the air film force and air film stiffness varying with the air film thickness;

[0036] Step 2: Based on the least squares method, perform function fitting on the upper and lower air film data obtained in Step 1 to establish a static equilibrium equation in the vertical direction;

[0037]

[0038] In the formula, F U is the air film force of the upper air film, F I is the air film force of the lower air film, W1 is the constant load of the aerostatic guide rail, and W 2m is the maximum variable load of the aerostatic guide rail;

[0039] Step 3: For the upper air film with any thickness, obtain the corresponding lower air film thickness and the overall vertical stiffness of the aerostatic guide rail through Step 2. On this basis, through optimization calculation, find the actual air film thicknesses h Ua and h Ia of the upper and lower air films corresponding to the optimal stiffness of the aerostatic guide rail, as well as the air film force F U and F I and the air film stiffness K U and K I at this time;

[0040] Step 4: Establish a transient analysis model of the structural field of the slide plate of the aerostatic guide rail. This model is simplified by using symmetric constraints. Through this model, obtain the change in the air film thickness under the action of the optimal actual air film thickness, and combine the optimal actual air film thickness obtained in Step 1 and Step 3 to calculate the optimal initial air film thickness;

[0041] Step 5: Combine the transient analysis model of the structural field in Step 4, and through the virtual load loading method in the conventional fluid-structure interaction calculation method of the aerostatic guide rail, perform virtual load loading in the proposed transient analysis model to obtain the actual optimal stiffness of the aerostatic guide rail;

[0042] In this specific embodiment, taking the lower guide rail of the aerostatic guide rail with a cross distribution shown in Figure 4 as an example, the optimal clearance (the sum of the initial air film thicknesses of the upper and lower air films) calculated by the present invention is 23.32 μm, while the optimal clearance calculated by the conventional fluid-structure interaction calculation method is 23 μm, and the error is only 1.39%; the optimal stiffness calculated by the present invention is 1010.101 N / μm, while the optimal stiffness calculated by the conventional fluid-structure interaction calculation method is 1081.081 N / μm, and the error is only 6.57%. And the calculation time is shortened from 1740 hours of the conventional fluid-structure interaction calculation method to 2.75 hours of the fast calculation method of the present invention, and the calculation efficiency is increased by about 633 times.

[0043] Specific Embodiment 2: Combine Figures 1 to 3To describe this embodiment, this embodiment is a further limitation on the calculation method described in the first specific embodiment. For the rapid calculation method of the optimal air film thickness and stiffness of a gas static pressure guide rail described in this embodiment, among the calculation data of the air film force and air film stiffness varying with the air film thickness obtained in Step 1, for the side air film, due to its symmetric force-bearing situation and structural characteristics, the ideal optimal thickness at this time corresponds to the optimal actual air film thickness h of the side air film La-op , and the air film force F corresponding to the side air film at this time can be obtained L .

[0044] Specific Embodiment 3: In combination with Figures 1 to 3 To describe this embodiment, this embodiment is a further limitation on the calculation method described in the first specific embodiment. For the rapid calculation method of the optimal air film thickness and stiffness of a gas static pressure guide rail described in this embodiment, the specific calculation method for establishing the transient analysis model of the structural field of the slide plate of the gas static pressure guide rail in Step 4 is as follows:

[0045] Step 4-1: Load the air film force F corresponding to the side air film in Step 1 L onto the side air film surface of the slide plate;

[0046] Step 4-2: Load the air film forces F U , F I of the upper and lower air films in Step 3 onto the upper and lower air film surfaces. At the same time, in order to perform constraints in the vertical direction to avoid non-convergence of the model, elastic constraints are loaded on the upper and lower air film surfaces, and their stiffness values are the ideal stiffnesses K U , K I corresponding to the upper and lower air films in Step 3;

[0047] Step 4-3: Through this model, the structural deformation of each air film surface under the action of the air film force corresponding to the actual air film thickness can be obtained, and this value is the change in air film thickness Δh U-op , Δh I-op , Δh L-op ; Δh U-op is the change value of the upper air film thickness, Δh I-op is the change value of the lower air film thickness, and Δh L-op is the change value of the side air film thickness;

[0048] Step 4-4: After calculating in combination with the actual air film thicknesses of each air film in Steps 1, 2, and 3, the optimal initial air film thickness h U0-op , h I0-op , h L0-op of this gas static pressure guide rail can be obtained; h U0-op is the optimal initial upper air film thickness; h I0-op is the optimal initial lower air film thickness; h L0-opis the optimal initial side air film thickness, that is, the optimal design parameter of this aerostatic guideway.

[0049] Specific Embodiment 4: Combining Figures 1 to 3 to illustrate this embodiment, this embodiment is a further limitation on the calculation method described in Specific Embodiment 3. For a rapid calculation method of the optimal air film thickness and stiffness of an aerostatic guideway described in this embodiment, the formula for the optimal initial upper air film thickness h U0-op in Step 4 is as follows;

[0050] h U0-op = h Ua-op - Δh U-op (2)

[0051] where h Ua-op is the actual air film thickness of the optimal upper air film.

[0052] Specific Embodiment 5: Combining Figures 1 to 3 to illustrate this embodiment, this embodiment is a further limitation on the calculation method described in Specific Embodiment 3. For a rapid calculation method of the optimal air film thickness and stiffness of an aerostatic guideway described in this embodiment, the formula for the optimal initial lower air film thickness h I0-op in Step 4 is as follows;

[0053] h I0-op = h Ia-op - Δh I-op (3)

[0054] where h Ia-op is the actual air film thickness of the optimal lower air film.

[0055] Specific Embodiment 6: Combining Figures 1 to 3 to illustrate this embodiment, this embodiment is a further limitation on the calculation method described in Specific Embodiment 3. For a rapid calculation method of the optimal air film thickness and stiffness of an aerostatic guideway described in this embodiment, the formula for the optimal initial side air film thickness h L0-op in Step 4 is as follows;

[0056] h L0-op = h La-op - Δh L-op (4)

[0057] where h La-op is the actual air film thickness of the optimal side air film.

Claims

1. A rapid calculation method for the optimal air film thickness and stiffness of a gas static pressure guide rail, characterized in that: The specific calculation method is as follows: Step 1: Conduct CFD flow field calculations on the upper, side, and lower air films of the aerostatic guide rail respectively to obtain the calculation data of the air film force and air film stiffness varying with the air film thickness; Step 2: Based on the least squares method, perform function fitting on the upper and lower air film data obtained in Step 1 to establish the static equilibrium equation in the vertical direction; where F U is the upper air film force, F I is the lower air film force, W1 is the constant load of the aerostatic guideway, and W 2m is the maximum variable load of the aerostatic guideway; Step 3. For the upper air film with any thickness, obtain its corresponding lower air film thickness and the overall vertical stiffness of the aerostatic guide through Step 2. On this basis, find the actual air film thicknesses h Ua 、h Ia of the upper and lower air films corresponding to the optimal stiffness of the aerostatic guide through optimization calculation, as well as the air film force F U ,F I and the air film stiffness K U ,K I at this time; Step 4: Establish a transient analysis model of the structural field of the slider of the aerostatic guide rail. This model is simplified by using symmetric constraints. Through this model, obtain the change in the air film thickness under the action of the optimal actual air film thickness. Combining the optimal actual air film thickness obtained in Step 1 and Step 3, the optimal initial air film thickness can be calculated; Step 5: Combining the transient analysis model of the structural field in Step 4, through the virtual load loading method in the conventional fluid-structure interaction calculation method of the aerostatic guide rail, perform virtual load loading in the proposed transient analysis model to obtain the actual optimal stiffness of this aerostatic guide rail.

2. The rapid calculation method for the optimal air film thickness and stiffness of a gas static pressure guide rail according to claim 1, characterized in that: Among the calculation data of the aerostatic force and stiffness varying with the air film thickness obtained in the first step, for the side air film, due to its symmetric force condition and structural characteristics, the ideal optimal thickness at this time corresponds to the optimal actual air film thickness h of the side air film La-op , and the aerostatic force F corresponding to the side air film at this time can be obtained L .

3. The rapid calculation method for the optimal air film thickness and stiffness of a gas static pressure guide rail according to claim 1, characterized in that: The specific calculation method for establishing the transient analysis model of the structural field of the slider of the aerostatic guide rail in Step 4 is as follows: Step 4.1: Apply the air film force F corresponding to the side air film in Step 1 L to the side air film surface of the skateboard; Step 42: Apply the aerodynamic forces F U , F I on the upper and lower aerodynamic film surfaces. At the same time, in order to impose constraints in the vertical direction to avoid non - convergence of the model, elastic constraints are applied on the upper and lower aerodynamic film surfaces, and the stiffness value is the ideal stiffness K U , K I ; Step 43: Through this model, the structural deformation of each gas film surface under the gas film force corresponding to the actual gas film thickness can be obtained, and this value is the change in gas film thickness Δh under the gas film force. U-op , Δh I-op , Δh L-op ; Δh U-op is the change value of the upper gas film thickness, Δh I-op is the change value of the lower gas film thickness, Δh L-op is the change value of the side gas film thickness; Step Four: After calculating by combining the actual air film thicknesses of each air film in Steps One, Two, and Three, the optimal initial air film thickness h of this aerostatic guideway can be obtained. U0-op , h I0-op , h L0-op ; h U0-op is the optimal initial upper air film thickness; h I0-op is the optimal initial lower air film thickness; h L0-op is the optimal initial side air film thickness, which is also the optimal design parameter of this aerostatic guideway.

4. A rapid calculation method for the optimal air film thickness and stiffness of a gas static pressure guide rail according to claim 3, characterized in that: The optimal initial upper gas film thickness h in Step 44 U0-op has the formula as follows; h U0-op = h Ua-op - Δh U-op (2) where h Ua-op is the actual film thickness of the optimal upper air film.

5. A rapid calculation method for the optimal air film thickness and stiffness of a gas static pressure guide rail according to claim 3, characterized in that: The optimal initial thickness h of the lower air film in Step 44 I0-op is given by the formula; h I0-op = h Ia-op - Δh I-op (3) where h Ia-op is the actual gas film thickness optimal for the lower gas film.

6. The rapid calculation method for the optimal air film thickness and stiffness of a gas static pressure guide rail according to claim 3, characterized in that: The optimal initial side air film thickness h in Step 44 L0-op has the formula of; h L0-op = h La-op - Δh L-op (4) where h La-op is the actual air film thickness of the optimal side air film.

Images