Aerostatic guide rail motion error prediction method considering dynamic fluid-solid coupling

Abstract

The invention discloses a gas static pressure guide rail motion error prediction method considering dynamic fluid-solid coupling, relates to the technical field of mechanical design and manufacturing, and aims to solve the problem that the prior art cannot be suitable for real-time calculation of a dynamic irregular boundary gas film flow field considering machining errors. According to the method, the problem that the five-degree-of-freedom quasi-static motion error of the gas static pressure guide rail considering the dynamic fluid-solid coupling behavior cannot be predicted is solved, and real-time calculation of the irregular boundary gas film flow field considering the machining error is realized; therefore, the prediction of the five-degree-of-freedom quasi-static motion error of the gas static pressure guide rail considering the dynamic fluid-solid coupling behavior is realized. According to the method, the problems of complex modeling process and relatively poor calculation convergence of the traditional computational fluid mechanics for the irregular gas film thickness are solved.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical design and manufacturing, and in particular to a method for predicting motion errors of a gas hydrostatic guide rail taking dynamic fluid-solid coupling into consideration. Background Art

[0002] Gas hydrostatic guides with excellent properties such as low friction and high precision are widely used in key areas such as ultra-precision machine tools and measuring equipment. There is a significant fluid-structure interaction (FSI) behavior between the solid field of the structural components of the gas hydrostatic guide and the air film fluid field. The fluid-structure interaction behavior refers to the interaction between the air film flow field and the structural field of the gas hydrostatic guide system. The structural components will produce deformation and displacement under the action of the air film flow field load, and the change of the structural field will reversely cause the boundary conditions of the air film flow field to change, and finally reach a dynamic equilibrium state at the fluid-solid coupling surface between the two. The above-mentioned fluid-solid coupling behavior will lead to significant changes in the boundary conditions and pressure distribution of the air film flow field, and these effects will eventually be reflected in the key performance of the gas hydrostatic guide such as the motion accuracy. The motion error of the gas hydrostatic guide mainly comes from the machining error of the structural component, and the machining error of the structural component and the motion error of the slide assembly will also cause the boundary conditions of the air film flow field to change continuously during the movement of the slide assembly, causing the dynamic change of the above-mentioned fluid-solid coupling behavior, and then introducing a dynamic fluid-solid coupling effect during the movement. Due to limitations such as poor computational convergence and low computational efficiency, the current mainstream bidirectional transient fluid-solid coupling calculation method based on dynamic mesh technology and computational fluid dynamics three-dimensional air film flow field model cannot be applied to the real-time calculation of dynamic irregular boundary air film flow field considering processing errors. This leads to the problem of low accuracy in the prediction of the five-degree-of-freedom quasi-static motion error of the gas hydrostatic guide considering the dynamic fluid-solid coupling behavior. Summary of the invention

[0003] The purpose of the present invention is to propose a method for predicting the motion error of a gas hydrostatic guide rail considering dynamic fluid-solid coupling, in view of the fact that the existing technology is not suitable for real-time calculation of dynamic irregular boundary air film flow fields considering processing errors, which leads to the problem that the five-degree-of-freedom quasi-static motion error of a gas hydrostatic guide rail considering dynamic fluid-solid coupling behavior cannot be predicted.

[0004] The technical solution adopted by the present invention to solve the above technical problems is:

[0005] A method for predicting motion errors of a gas hydrostatic guideway considering dynamic fluid-solid coupling comprises the following steps:

[0006] Step 1: Obtain the machining errors of the gas hydrostatic guide system structural components and the gas hydrostatic guide system parameters, and calculate the change in air film thickness Δh caused by the ideal fluid-solid coupling effect through bidirectional transient fluid-solid coupling based on the gas hydrostatic guide system parameters. FSI-ideal ;

[0007] Step 2: Substitute the ideal air film thickness h0 and Δh in the gas static pressure guide system parameters FSI-ideal Import the two-dimensional air film flow field finite element model to obtain the initial air film force, then import the initial air film force into the finite element model of the skateboard component to obtain the initial deformation parameters of the air film and initialize the motion position i of the skateboard component;

[0008] Step 3: Based on the machining error of the gas hydrostatic guide rail system structure components, obtain the change in air film thickness Δh caused by the machining error of the guide rail component corresponding to the slide assembly at the motion position i man-err , the air film thickness at this time is expressed as:

[0009] h ij =h0+Δh FSI-ideal +Δh man-err ;

[0010] Step 4: Obtain the motion error of the skateboard component corresponding to the current air film thickness, and obtain the change in air film thickness Δh caused by the motion error of the skateboard component based on the motion error of the skateboard component mot-err , then construct the straightness error array E stp1 And the deflection angle error array E stp2 , set the current number of fluid-solid coupling cycles c = 0, and store the motion errors of the slide assembly corresponding to the current air film thickness into E stp1 (0) and E stp2 (0), the air film thickness at this time is expressed as:

[0011] h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err ;

[0012] Step 5: Import the current air film thickness into the two-dimensional air film flow field finite element model to obtain the actual air film force;

[0013] Step 6: Import the actual air film force into the finite element model of the skateboard component to obtain the actual deformation parameters of the air film;

[0014] Step 7: Subtract the actual deformation parameters of the air film from the initial deformation parameters of the air film to obtain the change in air film thickness Δh caused by the deformation component of the dynamic fluid-solid coupling effect during the motion process FSI-dyn , and update the dynamic fluid-solid coupling cycle number c=c+1. At this time, the air film thickness is expressed as:

[0015] h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err +Δh FSI-dyn ;

[0016] Step 8: Obtain the motion error of the skateboard component corresponding to the current air film thickness and store the motion error in E stp1 (c) with E stp2 (c) According to the motion error of the slide assembly corresponding to the current air film thickness, the change in air film thickness Δh caused by the motion error of the slide assembly is obtained. mot-err ', at this time the air film thickness is expressed as:

[0017] h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err '+Δh FSI-dyn ;

[0018] Step 9: According to the motion error of the slide assembly when the number of dynamic fluid-solid coupling cycles is c times and the motion error of the slide assembly when the number of dynamic fluid-solid coupling cycles is c-1 times, determine whether the dynamic fluid-solid coupling process reaches a steady state. If it reaches a steady state, directly execute step 10. If it does not reach a steady state, use the air film thickness at this time in step 8 as the current air film thickness in step 5, repeat steps 5 to 8 until a steady state is reached, and execute step 10;

[0019] Step 10: Record the motion error of the slide assembly corresponding to the motion position i, that is, E stp1 (c) with E stp2 (c) and store it in E total (i);

[0020] Step 11: Let the motion position of the slide assembly i=i+1, repeat steps 3 to 10 until the motion position reaches the extreme value, and derive all the recorded motion errors, that is, the full stroke motion error E total .

[0021] Furthermore, the steps of constructing the two-dimensional air film flow field finite element model are:

[0022] The six air membranes in the skateboard assembly are evenly divided into m×n regions, and the quasi-static equilibrium equation of the skateboard assembly is established in the direction of the five-degree-of-freedom motion error. The six air membranes are upper air membrane 1, upper air membrane 2, side air membrane 1, side air membrane 2, lower air membrane 1 and lower air membrane 2. The quasi-static equilibrium equation of the skateboard assembly is shown in formula (1):

[0023]

[0024] Among them, F U1-ij , F U2-ij is the local air film force of upper air film 1 and upper air film 2 in their respective ij regions, F L1-ij , F L2-ijis the local air film force of side air film 1 and side air film 2 in their respective ij regions, F I1-ij , F I2-ij is the local air film force of lower air film 1 and lower air film 2 in their respective ij regions, x U1-ij ,y U1-ij is the coordinate of the ij region of the upper air film 1 along the X and Y directions, x U2-ij ,y U2-ij is the coordinate of the ij region of the upper air membrane 2 along the X and Y directions, x I1-ij ,y I1-ij is the coordinate of the ij region of the lower air film 1 along the X and Y directions, x I2-ij ,y I2-ij is the coordinate of the ij region of the lower air film 2 along the X and Y directions, x L1-ij , x L2-ij is the coordinate of the ij region of the side air membrane 1 and the side air membrane 2 along the X direction, W load is the weight of the slide assembly and the external load, i = 1,2...m, j = 1,2...n;

[0025] Then the steady-state compressible equation of the air film flow field in any region is expressed in dimensionless form, specifically:

[0026]

[0027] in, is the dimensionless thickness of the regional air film, is the dimensionless coordinate of the region, is the dimensionless coordinate of the region, is the dimensionless pressure of the region, is the mass flow coefficient of the small hole throttling, δ i is the Kronecker symbol, which takes the value 1 in the calculation region where a throttle hole exists, and takes the value 0 otherwise. x is the dimensionless bearing number in the X direction, Λ y is the dimensionless bearing number in the Y direction;

[0028] Define the pressure square function As shown in formula (3), the square function Variables, according to formula (1) construct function Φ, as shown in formula (4):

[0029]

[0030]

[0031] Where, Ω is the calculation area of ​​the air film;

[0032] Solving the pressure square function using triangular finite element elements The interpolation function f divides the air film into 2 (q*k) triangular units, q is an integer multiple of n, k is an integer multiple of m, and the triangular finite element interpolation function is expressed as:

[0033] f=Ν eT f e (5)

[0034] f e =[f i f j f m ] T (6)

[0035] N e =[N i N j N m ] T (7)

[0036] Among them, f e is the square of the pressure at each node of triangular element e, N e is the shape function corresponding to the triangular element e, i, j, and m are the three nodes of any triangular finite element element;

[0037] Use the approximate interpolation function f to replace the pressure square function Substituting into equation (4) and applying it to the finite element of the entire calculation area Ω, we obtain equation (8);

[0038]

[0039] Take Φ(f) for f i The partial derivative of (8) is used to find the extreme value of (8), i = 1, 2, ... n, and the partial derivative is shown in (9):

[0040]

[0041] c e =[c i c j c m ] T (10)

[0042] b e =[b i b j b m ] T (11)

[0043] Among them, c e is the shape function coefficient of the triangular element, b e is the shape function coefficient of the triangular element, k1 is a constant coefficient, μ r is the proportional coefficient of the area of ​​the throttle hole r in the corresponding unit, is the mass flow rate out of the throttle orifice r, Δ i is the unit body with i as the node, c and b are the shape function coefficients of the triangular element at the node;

[0044] Let equation (9) equal to 0, and find the pressure function relationship at node i that makes Φ an extreme value. Expand it to the entire calculation area Ω and rewrite it into a matrix form, as shown in equation (12):

[0045] KF=T(12)

[0046] Among them, K is an n×n dimensional square matrix, F is an n×1 dimensional array of the square function of the node pressure to be calculated, and T is an n×1 dimensional array of the right-hand side of the equation, which has three elements, namely 0, as well as

[0047] in, and is the triangular unit function coefficient in different directions, Δ k is the area of ​​the kth triangle unit;

[0048] K is represented by:

[0049]

[0050] Among them, Δ i is the triangular element with node i, Δ j is a triangular element with node j, e is a element with both nodes i and j, Δ e is Δ i and Δ j The total area of ​​the intersection;

[0051] According to formula (12), the pressure of each node is obtained. Repeat formulas (4)-(13) for iteration. The node pressure containing the throttling hole is used as the convergence criterion. When the relative error between two adjacent iterations is less than the threshold, it is considered that convergence is achieved. The air film force in each area is calculated by integrating the node pressure.

[0052] The flow state of the throttle hole is simplified to compressible flow through an ideal throttle. When air flows through the throttle hole, the air pressure immediately decreases from the supply pressure P s Drop to the throttle end pressure P d , the ideal theoretical mass flow rate of a small orifice restrictor From formula (14), we can get:

[0053]

[0054] Where A is the cross-sectional area of ​​the throttle hole, ψ sis the flow function;

[0055] Introducing flow coefficient C d To correct the mass flow rate, as shown in formula (15):

[0056]

[0057] in, is the ideal theoretical mass flow rate of the corrected small-hole restrictor;

[0058] At this point, the construction of the two-dimensional air film flow field finite element model is completed.

[0059] Furthermore, the threshold is 10 -6 .

[0060] Furthermore, the flow coefficient C d =0.8.

[0061] Furthermore, the flow coefficient C d It is expressed as:

[0062]

[0063] Furthermore, the flow function ψ s It is expressed as:

[0064]

[0065] Among them, β k is the coefficient and k is the gas constant.

[0066] Furthermore, the specific steps of obtaining the motion error of the slide assembly corresponding to the current air film thickness are:

[0067] Step 1: Obtain the current air film thickness, initialize the motion error of the slide assembly, and calculate the air film force in each area through the two-dimensional air film flow field finite element model;

[0068] Step 2: For each of the five degrees of freedom, calculate the resultant force of the skateboard assembly in each direction. When the absolute value of the ratio of the resultant force in a certain direction to the reference value in that direction is not greater than the threshold, it is determined that the direction has reached a state of equilibrium. If it is greater than the threshold, the motion error value e in that direction is set to zero. i Adjust to e i +Δe i , Δe i Adjust the step resolution for the set error, Δe i The positive or negative value of is related to the direction of the resultant force, and the motion error value in this direction is used to update the current air film thickness in step 1, and then the resultant force in this direction is recalculated, and multiple iterations are performed until the direction reaches a balanced state, and the motion error in this direction is obtained;

[0069] Among them, e y The reference value for the direction is the total air film force F of the side air film 1 L1 , e z The reference value of the direction is the total air film force F of the upper air film 1 U1 , e α The reference value of the direction is the resultant moment M of the upper air film 1 in this direction. U1-α , e β The reference value of the direction is half of the resultant moment M of the upper air film 1 in this direction. U1-0.5-β , e γ The reference value of the direction is the resultant moment M of the air film 1 on the half side in this direction. L1-0.5-γ ;

[0070] Step 3: Calculate in sequence through the above process to obtain the five-degree-of-freedom motion error. After the five-degree-of-freedom motion error is calculated, verify the equilibrium state in the five directions. If the balance in any direction is destroyed, update the current air film thickness based on the current five-degree-of-freedom motion error and repeat the above calculation process until all five directions meet the equilibrium state to obtain the final five-degree-of-freedom motion error.

[0071] Furthermore, the threshold is 0.1%.

[0072] Further, the resultant force is expressed as:

[0073] F y =∑F L1-ij -∑F L2-ij

[0074] F z =∑F U1-ij +∑F U2-ij -∑F I1-ij -∑F I2-ij -W load

[0075] M α =∑F U1-ij y U1-ij +∑F U2-ij y U2-ij -∑F I1-ij y I1-ij -∑F I2-ij y I2-ij

[0076] M β =-∑F U1-ij x U1-ij -∑F U2-ij x U2-ij +∑F I1-ij x I1-ij +∑F I2-ij x I2-ij

[0077] M γ =∑F L1-ij x L1-ij -∑F L2-ij x L2-ij .

[0078] Furthermore, when the air film is the upper air film 1, the thickness change Δh of the air film caused by the motion error of the slide assembly is mot-err for e z +e α y U1-ij -e β x U1-ij ;

[0079] When the air film is the upper air film 2, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err for e z +e α y U2-ij -e β x U2-ij ;

[0080] When the air film is the side air film 1, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err -e y -e γ x L1-ij ;

[0081] When the air film is the side air film 2, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err for e y +e γ x L2-ij ;

[0082] When the air film is the lower air film 1, the change in air film thickness Δh caused by the motion error of the slide assembly mot-err -e z -e α y I1-ij +e β x I1-ij ;

[0083] When the air film is the lower air film 2, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err -e z -e α y I2-ij +e β x I2-ij .

[0084] The beneficial effects of the present invention are:

[0085] This application realizes the real-time calculation of irregular boundary air film flow field considering machining errors, and further realizes the prediction of five-degree-of-freedom quasi-static motion error of gas hydrostatic guide considering dynamic fluid-solid coupling behavior. This application overcomes the problems of complex modeling process and poor computational convergence for irregular air film thickness in traditional computational fluid dynamics. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 This is a schematic diagram of the five-degree-of-freedom motion error of the gas hydrostatic guide;

[0087] Figure 2 This is a schematic diagram of the air film area division;

[0088] Figure 3 It is a schematic diagram of the finite element model of the two-dimensional air film flow field;

[0089] Figure 4 This is the flow chart of motion error calculation without considering dynamic fluid-structure interaction;

[0090] Figure 5 Flow chart for calculating the overall motion error considering dynamic fluid-structure interaction;

[0091] Figure 6 Straightness error of 38CrMoAl slide assembly;

[0092] Figure 7 It is the deflection angle error of 38CrMoAl slide assembly;

[0093] Figure 8 It is the straightness error of the 7075 slide assembly;

[0094] Fig. 9 It is the deflection angle error of the 7075 slide assembly. DETAILED DESCRIPTION

[0095] It should be particularly noted that, in the absence of conflict, the various embodiments disclosed in this application can be combined with each other.

[0096] Specific implementation method 1: refer to Figure 1 Specifically describing this embodiment, a method for predicting motion errors of a gas hydrostatic guideway considering dynamic fluid-solid coupling described in this embodiment includes the following steps:

[0097] Step 1: Obtain the machining errors of the gas hydrostatic guide system structural components and the gas hydrostatic guide system parameters, and calculate the change in air film thickness Δh caused by the ideal fluid-solid coupling effect through bidirectional transient fluid-solid coupling based on the gas hydrostatic guide system parameters. FSI-ideal ;

[0098] Step 2: Substitute the ideal air film thickness h0 and Δh in the gas static pressure guide system parameters FSI-idealImport the two-dimensional air film flow field finite element model to obtain the initial air film force, then import the initial air film force into the finite element model of the skateboard component to obtain the initial deformation parameters of the air film and initialize the motion position i of the skateboard component;

[0099] Step 3: Based on the machining error of the gas hydrostatic guide rail system structure components, obtain the change in air film thickness Δh caused by the machining error of the guide rail component corresponding to the slide assembly at the motion position i man-err , the air film thickness at this time is expressed as:

[0100] h ij =h0+Δh FSI-ideal +Δh man-err ;

[0101] Step 4: Obtain the motion error of the skateboard component corresponding to the current air film thickness, and obtain the change in air film thickness Δh caused by the motion error of the skateboard component based on the motion error of the skateboard component mot-err , then construct the straightness error array E stp1 And the deflection angle error array E stp2 , set the current number of fluid-solid coupling cycles c = 0, and store the motion errors of the slide assembly corresponding to the current air film thickness into E stp1 (0) and E stp2 (0), the air film thickness at this time is expressed as:

[0102] h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err ;

[0103] Step 5: Import the current air film thickness into the two-dimensional air film flow field finite element model to obtain the actual air film force;

[0104] Step 6: Import the actual air film force into the finite element model of the skateboard component to obtain the actual deformation parameters of the air film;

[0105] Step 7: Subtract the actual deformation parameters of the air film from the initial deformation parameters of the air film to obtain the change in air film thickness Δh caused by the deformation component of the dynamic fluid-solid coupling effect during the motion process FSI-dyn , and update the dynamic fluid-solid coupling cycle number c=c+1. At this time, the air film thickness is expressed as:

[0106] h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err +Δh FSI-dyn ;

[0107] Step 8: Obtain the motion error of the skateboard component corresponding to the current air film thickness and store the motion error in E stp1(c) with E stp2 (c) According to the motion error of the slide assembly corresponding to the current air film thickness, the change in air film thickness Δh caused by the motion error of the slide assembly is obtained. mot-err ', at this time the air film thickness is expressed as:

[0108] h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err '+Δh FSI-dyn ;

[0109] Step 9: According to the motion error of the slide assembly when the number of dynamic fluid-solid coupling cycles is c times and the motion error of the slide assembly when the number of dynamic fluid-solid coupling cycles is c-1 times, determine whether the dynamic fluid-solid coupling process reaches a steady state. If it reaches a steady state, directly execute step 10. If it does not reach a steady state, use the air film thickness at this time in step 8 as the current air film thickness in step 5, repeat steps 5 to 8 until a steady state is reached, and execute step 10;

[0110] Step 10: Record the motion error of the slide assembly corresponding to the motion position i, that is, E stp1 (c) with E stp2 (c) and store it in E total (i);

[0111] Step 11: Let the motion position of the slide assembly i=i+1, repeat steps 3 to 10 until the motion position reaches the extreme value, and derive all the recorded motion errors, that is, the full stroke motion error E total .

[0112] This application regionalizes the dynamic air film during the motion process, solves the local air film force in each area by a local air film force calculation method based on the finite element method and the flow coefficient model, establishes the quasi-static equilibrium equation of the skateboard assembly, and performs data transmission and interactive calculation with the finite element model of the structural component on the basis of achieving static equilibrium. The final steady-state equilibrium is achieved through multiple iterations, thereby realizing the quasi-static motion error calculation of the gas hydrostatic guide system considering the dynamic fluid-solid coupling behavior.

[0113] The present application realizes the calculation of irregular dynamic air film flow field considering processing errors, overcomes the problems of complex modeling process and poor computational convergence for irregular air film thickness in traditional computational fluid dynamics, and lays the foundation for the calculation of actual air film regionalized air film force considering the processing errors of structural components. At the same time, the air film flow field is regionalized, and the air film thickness in each region is decomposed into components affected by five factors: initial air film thickness, ideal fluid-solid coupling, processing error, motion error, and dynamic fluid-solid coupling. The motion error is solved by the quasi-static equilibrium equation of the skateboard assembly, and then the dynamic fluid-solid coupling component is solved by interactive iterative calculation with the static model of the skateboard assembly based on the finite element method, thereby realizing the accurate prediction of the quasi-static motion error of the gas hydrostatic guide rail. Taking two sets of skateboard assemblies as an example, the five-degree-of-freedom motion error is calculated by the calculation method proposed in this application, and the results are as follows: Figure 6 to Figure 9 As shown in the figure, the two sets of slide assemblies have the same cross-sectional dimensions and share a set of guide rail assemblies. The two sets of slide assemblies only differ in material (38CrMoAl stainless steel and 7075 aluminum alloy, corresponding to the different structural rigidity of the slide assemblies) and slide length. γ Except for the fact that it is almost unaffected by the dynamic fluid-structure coupling effect, the other motion errors are all affected by the dynamic fluid-structure coupling behavior. For the 38CrMoAl stainless steel slide, the dynamic fluid-structure coupling effect causes the straightness error e in two directions. y 、e z The error peaks increased by about 18.3% and 10.6% respectively, and the pitch angle error e β The influence of dynamic fluid-solid coupling effect is moderate, and its maximum difference accounts for 12.3% of its maximum amplitude; the roll angle error e α The dynamic fluid-solid coupling effect has a significant impact on the straightness error in both directions, and the maximum difference accounts for 57.6% of the maximum amplitude. y 、e z The peak values ​​of the pitch angle error and the β The amplitude at the maximum deflection angle increases by about 20.2%, while the roll angle error e α The amplitude at the maximum deflection angle increases by about 81.0%.

[0114] The motion error of the gas hydrostatic guide slide assembly contains six degrees of freedom, such as Figure 1 As shown, the motion error along the X direction is x Usually referred to as positioning error, positioning error is mainly determined by the feedback unit and motion control algorithm, while the motion errors in the other five directions (including two translation errors e y 、e z , and three rotation errors e α、e β 、e γ ) is determined by the equilibrium state of the skateboard assembly at different positions, and the equilibrium state of the skateboard assembly is determined by the air film bearing capacity provided by the six air films on the inner side of the skateboard assembly and its external load. This application mainly calculates the five-degree-of-freedom quasi-static motion error caused by the difference in the static equilibrium position of the skateboard assembly. The processing errors of the guide rail assembly and the skateboard assembly, as well as the motion errors of the skateboard assembly itself, will cause the air film boundary conditions to change continuously during the movement, and then cause significant changes in the air film force. Therefore, the process of solving the five-degree-of-freedom quasi-static motion error can be equivalent to the process of solving the quasi-static equilibrium equation of the skateboard assembly at different positions.

[0115] Divide the six air films evenly into m×n regions (the finer the division area, the higher the calculation accuracy and the lower the calculation efficiency), such as Figure 2 As shown, the quasi-static equilibrium equation of the slide assembly established in the direction of the five-degree-of-freedom motion error is shown in formula (1).

[0116]

[0117] in,

[0118] F U1-ij ,F U2-ij ——Local air film forces of upper air film 1 and upper air film 2 in their respective ij regions;

[0119] F L1-ij ,F L2-ij ——Local air film force of side air film 1 and side air film 2 in their respective ij regions;

[0120] F I1-ij ,F I2-ij ——Local air film forces of lower air film 1 and lower air film 2 in their respective ij regions;

[0121] x U1-ij ,y U1-ij ——Coordinates of the ij area of ​​the upper air membrane 1 along the X and Y directions;

[0122] x U2-ij ,y U2-ij ——Coordinates of the ij area of ​​the upper air membrane 2 along the X and Y directions;

[0123] x I1-ij ,y I1-ij ——Coordinates of the ij area of ​​the lower air membrane 1 along the X and Y directions;

[0124] x I2-ij ,y I2-ij ——Coordinates of the ij area of ​​the lower air membrane 2 along the X and Y directions;

[0125] xL1-ij ,x L2-ij ——The coordinates of the ij area of ​​the side air membrane 1 and the side air membrane 2 along the X direction;

[0126] W load ——The weight of the skateboard assembly and external loads.

[0127] Taking into account the processing error, the shape of the air film along the thickness direction of the air film will be irregular, and as the position of the slide assembly changes, the shape and thickness of the air film will continue to change. Therefore, this application uses a two-dimensional air film flow field model based on the finite element method and the flow coefficient model to calculate the regionalized air film force considering the processing error, in which the air film thickness in different regions can be directly loaded to the corresponding nodes in the form of assignment, avoiding the limitation of re-gridding at different positions in the air film flow field calculation. The steady-state compressible equation of the air film flow field in any region is given in dimensionless form, as shown in formula (2).

[0128]

[0129] in,

[0130] ——dimensionless thickness of regional air film;

[0131] ——dimensionless coordinates of the region;

[0132] ——dimensionless coordinates of the region;

[0133] ——dimensionless pressure of the region;

[0134] ——Mass flow coefficient of small hole throttling;

[0135] δ i ——Kronecker sign, which takes the value 1 in the calculation region where a throttle hole exists, and takes the value 0 otherwise;

[0136] Λ x ——dimensionless bearing number in the X direction;

[0137] Λ y ——Dimensionless bearing number in Y direction.

[0138] Define the pressure square function As shown in formula (3), the square function Variables, according to formula (1), the function Φ can be constructed as shown in formula (4).

[0139]

[0140]

[0141] Where Ω is the calculation area of ​​the air film. It has been mathematically proved that under certain boundary conditions, the extreme value of formula (4) can only be obtained by a certain pressure square function The function is the solution of equation (1). In this application, a triangular finite element unit is used to solve the pressure square function The interpolation function f divides the air film into 2(q*k) triangular units, where q is an integer multiple of n and k is an integer multiple of m, where i, j, and m are the three nodes of any triangular finite element unit. The triangular finite element interpolation function can be defined by equations (5), (6), and (7).

[0142] f=Ν eT f e (5)

[0143] f e =[f i f j f m ] T (6)

[0144] N e =[N i N j N m ] T (7)

[0145] in,

[0146] f e ——The square of pressure at each node of triangular element e;

[0147] N e ——Shape function corresponding to the triangular element e.

[0148] Use the approximate interpolation function f to replace the pressure square function Substituting into equation (4) and applying it to the finite element of the entire calculation area, we can obtain equation (8).

[0149]

[0150] To find the extreme value of formula (8), take Φ(f) to f i (i=1,2,…n) partial derivatives, since it involves f i Therefore, the above partial derivative has a non-zero value only for the unit containing the i node, so the calculation area of ​​the partial derivative is reduced to Δ i , Δ i represents the unit cell with i as the node, and the final partial derivative is shown in formula (9).

[0151]

[0152] in,

[0153] c e ——triangular element shape function coefficient;

[0154] b e ——triangular element shape function coefficient;

[0155] k1——constant coefficient;

[0156] μ r ——The proportional coefficient of the area of ​​the throttle hole r in the corresponding unit;

[0157] ——Mass flow rate flowing out of the throttle hole r.

[0158] By setting equation (9) equal to 0, we can obtain the pressure function relationship at node i that makes Φ an extreme value. We can extend it to the entire calculation area Ω and rewrite it into a matrix form, as shown in equation (10).

[0159] KF=T(10)

[0160] in,

[0161] K is a square matrix of n×n dimensions, which can be calculated by formula (11);

[0162] F——n×1 dimensional array of square function of nodal pressure to be calculated;

[0163] T is an n×1 dimensional array on the right side of the equation, with three elements, namely 0, as well as

[0164]

[0165] in, and is the triangular unit function coefficient in different directions, c (k) and b (k) The difference between c and b is the coefficient of the triangle unit function in different directions, Δ k is the area of ​​the kth triangle unit.

[0166] After the above process is solved, the pressure of each node can be obtained. Repeat formula 4-11 for iteration, and use the node pressure containing the throttle hole as the convergence criterion for multiple iterations. When the relative error between two adjacent iterations is less than 10 -6 When the convergence is reached, the air film force in each calculation area can be obtained by integrating the node pressure. The finite element model of the air film of the gas static pressure guide is as follows: Figure 3As shown. The flow state of the throttle hole is generally simplified to compressible flow through an ideal throttle. When air flows through the throttle hole, the air pressure immediately changes from the supply pressure P s Down to P d , the ideal theoretical mass flow rate of a small orifice restrictor It can be calculated by formula (12).

[0167]

[0168] in,

[0169] A——Cross-sectional area of ​​throttle hole;

[0170] ψ s ——Flow function, which can be calculated by formula (13).

[0171]

[0172] in,

[0173] P d ——pressure at the end of the throttle hole;

[0174] β k --coefficient;

[0175] k——gas constant.

[0176] Taking into account the actual mass flow rate of the small orifice restrictor Theoretical mass flow rate The difference between the two introduces the flow coefficient C d To correct the mass flow rate, as shown in formula (14).

[0177]

[0178] In the modeling of hydrostatic guide rails, the value of the flow coefficient has an important influence on the calculation accuracy. In many studies, C is generally taken as d =0.8. However, the academic community generally believes that C d It is very sensitive to the geometric parameters (diameter of the throttling hole, thickness of the air film, etc.) and flow parameters (Reynolds number, etc.) of the small hole throttle. The machining error of the guide rail assembly and the fluid-solid coupling behavior will change the thickness of the air film, and then change the flow parameters of the air film, and finally change the flow coefficient. In order to accurately simulate the throttling effect of the small hole throttle, the above phenomenon and its influence on the flow coefficient should be considered in the finite element modeling. d is the pressure ratio P d / P s The function of is shown in formula (15), which is used to correct the mass flow rate of the gas film.

[0179]

[0180] The machining error of the gas hydrostatic guide system leads to different air film thicknesses in different areas. After obtaining the actual air film thickness of each area, the above-mentioned air film flow field finite element model is inserted, and the air film pressure of each area is integrated to solve the local air film force of each area. For any gas hydrostatic guide system with determined geometric parameters and working conditions, its parameters such as air supply pressure are known quantities. Therefore, for any air film in the gas hydrostatic guide system, when calculating its air film pressure distribution through the above-mentioned two-dimensional air film flow field finite element model, the only input variable is the actual air film thickness at each node. The actual air film thickness h in any area ij It is composed of and influenced by five factors, as shown in formula (16). ij Converted into a dimensionless quantity, it is the dimensionless real air film thickness of the corresponding unit in formula (2): Among the five parameters, h0 and Δh FSI-ideal It is independent of the position of the slide assembly and is a constant value during the entire motion process. FSI-ideal It can be obtained through conventional two-way transient fluid-structure coupling model calculation.

[0181] h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err +Δh FSI-dyn (16)

[0182] in,

[0183] h0——ideal thickness of air film, determined by design parameters;

[0184] Δh FSI -ideal——the change of air film thickness caused by the ideal fluid-solid coupling effect obtained by calculating the air film design parameters;

[0185] Δh man -err——the change of gas film thickness caused by the machining error of the structural components of the gas static pressure guide system;

[0186] Δh mot-err ——Changes in air film thickness caused by motion errors of the slide assembly;

[0187] Δh FSI -dyn——Change in film thickness caused by the deformation component of the dynamic fluid-structure interaction effect during motion.

[0188] The last three terms of air film thickness Δh man-err , Δh mot-err and Δh FSI-dyn It will change with the movement position of the skateboard assembly, and the third term Δh man-errIt can be obtained by measuring the actual machining error of the guide rail assembly and the slide assembly, and the fourth term Δh mot-err is the five-degree-of-freedom motion error e of the slide assembly during motion. y 、e z 、e α 、e β 、e γ The change in the thickness of each air film caused by the motion error of the slide assembly in the region ij can be calculated by equation (17). The five-degree-of-freedom motion error of the slide assembly can be obtained by iterative calculation of the quasi-static equilibrium equation of the slide assembly at different motion positions. The calculation flow chart of the motion error at any motion position is as follows: Figure 4 As shown. First, read the current air film thickness of each area and initialize the motion error. The local air film force of each area is calculated by the above two-dimensional air film flow field finite element model. For any degree of freedom, the resultant force of the slide assembly in that direction can be calculated by formula (1). When the absolute value of the ratio of the resultant force in that direction to the reference value in that direction is less than 0.1%, it is determined that the direction has reached a state of equilibrium. If the value is greater than 0.1%, the motion error value e in that direction needs to be adjusted. i To e i +Δe i , Δe i The positive or negative value of is related to the direction of the resultant force. After adjustment, the resultant force in that direction is recalculated and repeated multiple times until the direction reaches a state of equilibrium. The five-degree-of-freedom motion error is calculated in turn through the above process, where e y The reference value for the direction is the total air film force F of the side air film 1 L1 , e z The reference value of the direction is the total air film force F of the upper air film 1 U1 , e α The reference value of the direction is the resultant moment M of the upper air film 1 in this direction. U1-α , e β The reference value of the direction is half of the resultant moment M of the upper air film 1 in this direction. U1-0.5-β , e γ The reference value of the direction is the resultant moment M of the air film 1 on the half side in this direction. L1-0.5-γ It should be noted that there is a coupling phenomenon among the five degrees of freedom. The motion error of the subsequent calculation may cause the balance state of the previous motion error direction to be destroyed. Therefore, after the five-degree-of-freedom motion error calculation is completed, the balance state of the five directions needs to be verified. If the balance is destroyed, it is necessary to update the current air film thickness based on the current motion error and re-perform the above calculation process. Iterate multiple times until all directions reach a balance state and derive the five-degree-of-freedom motion error.

[0189]

[0190] The last term of the film thickness Δh FSI-dynThe change in film thickness is caused by the dynamic fluid-solid coupling effect caused by the change in the third and fourth parameters of the film thickness during the motion. It is worth noting that the dynamic fluid-solid coupling effect includes the displacement component and the deformation component, among which the displacement component is already included in the fourth parameter Δh mot-err Therefore, the fifth parameter Δh FSI-dyn It only includes the deformation component of the dynamic fluid-structure coupling effect, that is, the dynamic change of the deformation of the skateboard component structure caused by the dynamic change of the air film force during the movement. Since the computational resources required for dynamic fluid-structure coupling during the movement are too huge, it is almost impossible to calculate it using the existing two-way transient fluid-structure coupling model. However, due to the fifth term Δh FSI-dyn It only includes the deformation component in the dynamic fluid-solid coupling effect, so this item can be obtained through static finite element calculation with higher computational efficiency. First, a static finite element model of the skateboard assembly is established, and the air film force distribution corresponding to the air film thickness containing only the first two parameters is calculated through the previous two-dimensional air film flow field finite element model. The obtained air film force distribution is loaded onto the air film surface of the skateboard assembly finite element model, and its initial deformation parameters are obtained through the skateboard assembly finite element model calculation. Secondly, the air film force distribution corresponding to the air film thickness considering the first four parameters is calculated through the air film flow field finite element model, and loaded into the skateboard assembly finite element model to obtain its actual deformation parameters. The difference between the actual deformation parameters of each region and the initial deformation parameters is the change in air film thickness Δh caused by the dynamic deformation of the skateboard assembly. FSI-dyn , but it should be noted that Δh FSI-dyn It will also cause changes in the local air film force in each area, so it is necessary to calculate the motion error in the process ( Figure 3 The process) is iterated multiple times with the static finite element model of the skateboard component until the motion error between two adjacent iterative calculations reaches a stable state.

[0191] Taking the above five parameters into consideration, the comprehensive calculation process of the five-degree-of-freedom motion error of the gas hydrostatic guide system considering the dynamic fluid-solid coupling effect is as follows: Figure 5 As shown, the main steps of iterative calculation of motion error are as follows:

[0192] (a) Import the parameters of the gas static pressure guide rail system (including but not limited to the gas supply pressure, the structural dimensions of the slide plate assembly, and the geometric dimensions of the air film) and the machining error Δh between the slide plate assembly and the guide rail assembly obtained through measurement man-err , the ideal air film thickness of each region is obtained through bidirectional transient fluid-solid coupling calculation (including the first two parameters of formula (16));

[0193] (b) importing the ideal air film thickness into the two-dimensional air film flow field finite element model to calculate the ideal air film force in each region, importing the ideal air film force in each region into the finite element model of the slide assembly to calculate the initial deformation parameters of each air film, and initializing the motion position of the slide assembly;

[0194] (c) Read the current position processing error of the slide assembly and initialize the fourth item Δh mot-err (reset to zero), update the air film thickness of each region (including the first three parameters of formula (16));

[0195] (d) by Figure 4 The process calculates the motion error of the slide assembly at this position (without considering the dynamic fluid-solid coupling effect) and stores it in E stp1 (0) and E stp2 (0); Initialize the number of dynamic fluid-structure coupling cycles c and the fifth term Δh FSI-dyn , update the air film thickness of each region (including the first four parameters of formula (16));

[0196] (e) Import the air film thickness of each region into the two-dimensional air film flow field finite element model to calculate the actual air film force of each region, import the actual air film force of each region into the skateboard component finite element model to calculate the actual deformation parameter of each air film, and subtract it from the initial deformation parameter to obtain the fifth term Δh FSI-dyn , the number of dynamic fluid-solid coupling cycles c is updated to c+1, and the air film thickness in each region is updated (including the first five parameters of formula (16));

[0197] (f) By Figure 4 The process calculates the motion error of the slide assembly at this position (considering the dynamic fluid-solid coupling effect) and stores it in E stp1 (c) with E stp2 (c) Determine whether the dynamic fluid-structure coupling process has reached a steady state through the c-th and c-1-th motion errors. If it has not reached a steady state, return to (e) and iterate until the dynamic fluid-structure coupling reaches a steady state.

[0198] (g) Record the final motion error E at the current position total (i), the motion position i is changed to i+1, and the motion error is calculated by returning to step (c), and multiple iterations are performed until the motion position reaches the extreme value, and the full stroke motion error E is derived. total .

[0199] It should be noted that the specific implementation is only an explanation and description of the technical solution of the present invention, and cannot be used to limit the scope of protection of the rights. Any partial changes made according to the claims and description of the present invention should still fall within the scope of protection of the present invention.

Claims

1. A method for predicting the motion error of a gas hydrostatic guide considering dynamic fluid-solid coupling, characterized in that The following steps are involved: Step 1: Obtain the machining errors of the gas hydrostatic guide system structural components and the gas hydrostatic guide system parameters, and calculate the change in air film thickness Δh caused by the ideal fluid-solid coupling effect through bidirectional transient fluid-solid coupling based on the gas hydrostatic guide system parameters. FSI-ideal ; Step 2: Substitute the ideal air film thickness h0 and Δh in the gas static pressure guide system parameters FSI-ideal Import the two-dimensional air film flow field finite element model to obtain the initial air film force, then import the initial air film force into the finite element model of the skateboard component to obtain the initial deformation parameters of the air film and initialize the motion position i of the skateboard component; Step 3: Based on the machining error of the gas hydrostatic guide rail system structure components, obtain the change in air film thickness Δh caused by the machining error of the guide rail component corresponding to the slide assembly at the motion position i man-err , the air film thickness at this time is expressed as: h ij =h0+Δh FSI-ideal +Δh man-err ; Step 4: Obtain the motion error of the skateboard component corresponding to the current air film thickness, and obtain the change in air film thickness Δh caused by the motion error of the skateboard component based on the motion error of the skateboard component mot-err , then construct the straightness error array E stp1 And the deflection angle error array E stp2 , set the current number of fluid-solid coupling cycles c = 0, and store the motion errors of the slide assembly corresponding to the current air film thickness into E stp1 (0) and E stp2 (0), the air film thickness at this time is expressed as: h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err ; Step 5: Import the current air film thickness into the two-dimensional air film flow field finite element model to obtain the actual air film force; Step 6: Import the actual air film force into the finite element model of the skateboard component to obtain the actual deformation parameters of the air film; Step 7: Subtract the actual deformation parameters of the air film from the initial deformation parameters of the air film to obtain the change in air film thickness Δh caused by the deformation component of the dynamic fluid-solid coupling effect during the motion process FSI-dyn , and update the dynamic fluid-solid coupling cycle number c=c+1. At this time, the air film thickness is expressed as: h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err +Δh FSI-dyn ; Step 8: Obtain the motion error of the skateboard component corresponding to the current air film thickness and store the motion error in E stp1 (c) with E stp2 (c) According to the motion error of the slide assembly corresponding to the current air film thickness, the change in air film thickness Δh caused by the motion error of the slide assembly is obtained. mot-err ', at this time the air film thickness is expressed as: h ij =h0+Δh FSI-ideal +Δh man-err +Δh mot-err '+Δh FSI-dyn ; Step 9: According to the motion error of the slide assembly when the number of dynamic fluid-solid coupling cycles is c times and the motion error of the slide assembly when the number of dynamic fluid-solid coupling cycles is c-1 times, determine whether the dynamic fluid-solid coupling process reaches a steady state. If it reaches a steady state, directly execute step 10. If it does not reach a steady state, use the air film thickness at this time in step 8 as the current air film thickness in step 5, repeat steps 5 to 8 until a steady state is reached, and execute step 10; Step 10: Record the motion error of the slide assembly corresponding to the motion position i, that is, E stp1 (c) with E stp2 (c) and store it in E total (i); Step 11: Let the motion position of the slide assembly i=i+1, repeat steps 3 to 10 until the motion position reaches the extreme value, and derive all the recorded motion errors, that is, the full stroke motion error E total .

2. The method for predicting the motion error of a gas hydrostatic guide considering dynamic fluid-solid coupling according to claim 1 is characterized in that The steps for constructing the two-dimensional air film flow field finite element model are as follows: The six air membranes in the skateboard assembly are evenly divided into m×n regions, and the quasi-static equilibrium equation of the skateboard assembly is established in the direction of the five-degree-of-freedom motion error. The six air membranes are upper air membrane 1, upper air membrane 2, side air membrane 1, side air membrane 2, lower air membrane 1 and lower air membrane 2. The quasi-static equilibrium equation of the skateboard assembly is shown in formula (1): F y =∑F L1-ij -∑F L2-ij =0 F z =∑F U1-ij +∑F U2-ij -∑F I1-ij -∑F I2-ij -W load =0 M α =∑F U1-ij and U1-ij +∑F U2-ij and U2-ij -∑F I1-ij and I1-ij -∑F I2-ij and I2-ij =0 (1) M β =-∑F U1-ij x U1-ij -∑F U2-ij x U2-ij +∑F I1-ij x I1-ij +∑F I2-ij x I2-ij =0 M γ =∑F L1-ij x L1-ij -∑F L2-ij x L2-ij =0 Among them, F U1-ij , F U2-ij is the local air film force of upper air film 1 and upper air film 2 in their respective ij regions, F L1-ij , F L2-ij is the local air film force of side air film 1 and side air film 2 in their respective ij regions, F I1-ij , F I2-ij is the local air film force of lower air film 1 and lower air film 2 in their respective ij regions, x U1-ij ,y U1-ij is the coordinate of the ij region of the upper air film 1 along the X and Y directions, x U2-ij ,y U2-ij is the coordinate of the ij region of the upper air membrane 2 along the X and Y directions, x I1-ij ,y I1-ij is the coordinate of the ij region of the lower air film 1 along the X and Y directions, x I2-ij ,y I2-ij is the coordinate of the ij region of the lower air film 2 along the X and Y directions, x L1-ij , x L2-ij is the coordinate of the ij region of the side air membrane 1 and the side air membrane 2 along the X direction, W load is the weight of the slide assembly and the external load, i = 1,2...m, j = 1,2...n; Then the steady-state compressible equation of the air film flow field in any region is expressed in dimensionless form, specifically: in, is the dimensionless thickness of the regional air film, is the dimensionless coordinate of the region, is the dimensionless coordinate of the region, is the dimensionless pressure of the region, is the mass flow coefficient of the orifice throttling, δ i is the Kronecker symbol, which takes the value 1 in the calculation region where a throttle hole exists, and takes the value 0 otherwise. x is the dimensionless bearing number in the X direction, Λ y is the dimensionless bearing number in the Y direction; Define the pressure square function As shown in formula (3), the square function Variables, according to formula (1) construct function Φ, as shown in formula (4): Where, Ω is the calculation area of ​​the air film; The interpolation function f of the pressure square function f is solved by using triangular finite element units. The air film is divided into 2 (q*k) triangular units, q is an integer multiple of n, k is an integer multiple of m, and the triangular finite element interpolation function is expressed as: f=N eT f e (5) f e =[f i f j f m ] T (6) N e =[N i N j N m ] T (7) Among them, f e is the square of the pressure at each node of triangular element e, N e is the shape function corresponding to the triangular element e, i, j, and m are the three nodes of any triangular finite element element; Use the approximate interpolation function f to replace the pressure square function Substituting into equation (4) and applying it to the finite element of the entire calculation area Ω, we obtain equation (8); Take Φ(f) for f i The partial derivative of (8) is used to find the extreme value of (8), i = 1, 2, ... n, and the partial derivative is shown in (9): c e =[c i c j c m ] T (10) b e =[b i b j b m ] T (11) Among them, c e is the shape function coefficient of the triangular element, b e is the shape function coefficient of the triangular element, k1 is a constant coefficient, μ r is the proportional coefficient of the area of ​​the throttle hole r in the corresponding unit, is the mass flow rate out of the throttle orifice r, Δ i is the unit body with i as the node, c and b are the shape function coefficients of the triangular element at the node; Let equation (9) equal to 0, and find the pressure function relationship at node i that makes Φ an extreme value. Expand it to the entire calculation area Ω and rewrite it into a matrix form, as shown in equation (12): KF=T (12) Among them, K is an n×n dimensional square matrix, F is an n×1 dimensional array of the square function of the node pressure to be calculated, and T is an n×1 dimensional array of the right-hand side of the equation, which has three elements, namely 0, k1 μ r ,as well as in, and is the triangular unit function coefficient in different directions, Δ k is the area of ​​the kth triangle unit; K is represented by: Among them, Δ i is the triangular element with node i, Δ j is a triangular element with node j, e is a element with both nodes i and j, Δ e is Δ i and Δ j The total area of ​​the intersection; According to formula (12), the pressure of each node is obtained, and the node pressure is Repeat formulas (4)-(13) for iteration. The node pressure containing the throttling hole is used as the convergence criterion. When the relative error between two adjacent iterations is less than the threshold, it is considered that convergence is achieved. The air film force in each area is calculated by integrating the node pressure. The flow state of the throttle hole is simplified to compressible flow through an ideal throttle. When air flows through the throttle hole, the air pressure immediately decreases from the supply pressure P s Drop to the throttle end pressure P d , the ideal theoretical mass flow rate of a small orifice restrictor From formula (14), we can get: Where A is the cross-sectional area of ​​the throttle hole, ψ s is the flow function; Introduced flow coefficient C d To correct the mass flow rate, as shown in formula (15): in, is the ideal theoretical mass flow rate of the corrected small-hole restrictor; At this point, the construction of the two-dimensional air film flow field finite element model is completed.

3. The method for predicting the motion error of a gas hydrostatic guide considering dynamic fluid-solid coupling according to claim 2 is characterized in that The threshold is 10 -6 .

4. The method for predicting the motion error of a gas hydrostatic guide considering dynamic fluid-solid coupling according to claim 2 is characterized in that The flow coefficient C d =0.

8.

5. The method for predicting the motion error of a gas hydrostatic guide considering dynamic fluid-solid coupling according to claim 2 is characterized in that The flow coefficient C d It is expressed as:

6. The method for predicting the motion error of a gas hydrostatic guide considering dynamic fluid-solid coupling according to claim 2 is characterized in that The flow function ψ s It is expressed as: Among them, β k is the coefficient and k is the gas constant.

7. The method for predicting the motion error of a gas hydrostatic guideway considering dynamic fluid-solid coupling according to claim 1 is characterized in that The specific steps of obtaining the motion error of the slide assembly corresponding to the current air film thickness are: Step 1: Obtain the current air film thickness, initialize the motion error of the slide assembly, and calculate the air film force in each area through the two-dimensional air film flow field finite element model; Step 2: For each of the five degrees of freedom, calculate the resultant force of the skateboard assembly in each direction. When the absolute value of the ratio of the resultant force in a certain direction to the reference value in that direction is not greater than the threshold, it is determined that the direction has reached a state of equilibrium. If it is greater than the threshold, the motion error value e in that direction is set to zero. i Adjust to e i +Δe i , Δe i Adjust the step resolution for the set error, Δe i The positive or negative value of is related to the direction of the resultant force, and the motion error value in this direction is used to update the current air film thickness in step 1, and then the resultant force in this direction is recalculated, and multiple iterations are performed until the direction reaches a balanced state, and the motion error in this direction is obtained; Among them, e y The reference value for the direction is the total air film force F of the side air film 1 L1 , e z The reference value of the direction is the total air film force F of the upper air film 1 U1 , e α The reference value of the direction is the resultant moment M of the upper air film 1 in this direction. U1-α , e β The reference value of the direction is half of the resultant moment M of the upper air film 1 in this direction. U1-0.5-β , e γ The reference value of the direction is the resultant moment M of the air film 1 on the half side in this direction. L1-0.5-γ ; Step 3: Calculate in sequence through the above process to obtain the five-degree-of-freedom motion error. After the five-degree-of-freedom motion error is calculated, verify the equilibrium state in the five directions. If the balance in any direction is destroyed, update the current air film thickness based on the current five-degree-of-freedom motion error and repeat the above calculation process until all five directions meet the equilibrium state to obtain the final five-degree-of-freedom motion error.

8. The method for predicting the motion error of a gas hydrostatic guideway considering dynamic fluid-solid coupling according to claim 7 is characterized in that The threshold value is 0.1%.

9. The method for predicting motion error of a gas hydrostatic guideway considering dynamic fluid-solid coupling according to claim 7, characterized in that The resultant force is expressed as: F y =∑F L1-ij -∑F L2-ij F z =∑F U1-ij +∑F U2-ij -∑F I1-ij -∑F I2-ij -W load M α =∑F U1-ij and U1-ij +∑F U2-ij and U2-ij -∑F I1-ij and I1-ij -∑F I2-ij and I2-ij M β =-∑F U1-ij x U1-ij -∑F U2-ij x U2-ij +∑F I1-ij x I1-ij +∑F I2-ij x I2-ij M γ =∑F L1-ij x L1-ij -∑F L2-ij x L2-ij 。 10. The method for predicting motion error of a gas hydrostatic guideway considering dynamic fluid-solid coupling according to claim 7, characterized in that: When the air film is the upper air film 1, the change in air film thickness Δh caused by the motion error of the slide assembly mot-err for e z +e α y U1-ij -e β x U1-ij ; When the air film is the upper air film 2, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err for e z +e α y U2-ij -e β x U2-ij ; When the air film is the side air film 1, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err -e y -e γ x L1-ij ; When the air film is the side air film 2, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err for e y +e γ x L2-ij ; When the air film is the lower air film 1, the change in air film thickness Δh caused by the motion error of the slide assembly mot-err -e z -e α y I1-ij +e β x I1-ij ; When the air film is the lower air film 2, the thickness change of the air film caused by the motion error of the slide assembly is Δh mot-err -e z -e α y I2-ij +e β x I2-ij .

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