Method and system for optimizing surface waviness of air bearing in air bearing-rotor system

Abstract

The invention discloses an air bearing surface waviness optimization method and system in an air bearing-rotor system, and the optimization method comprises the steps: calculating the rigidity and damping coefficient of an air bearing with waviness and the rigidity and damping matrix of a rotor based on the structure parameters and material attributes of the air bearing-rotor system and the waviness parameters of the bearing; timoshenko beam unit modeling is conducted on the air static pressure rotor, the air static pressure rotor is divided into a plurality of units, and the mass matrix, the rigidity matrix and the damping matrix of each unit are solved; coupling the rigidity and the damping coefficient of the air bearing with the waviness with the rigidity and the damping matrix of the rotor at corresponding nodes to obtain an air bearing-rotor model with the waviness; performing time-varying dynamic response solution on the air bearing-rotor model with waviness to obtain a bearing-rotor system dynamic response result corresponding to the bearing surface waviness parameter; according to the method, the influence of the surface topography parameters in the air bearing structure on the system dynamics response can be considered.

Description

Technical Field

[0001] The present invention belongs to the category of kinetic fine modeling, and specifically relates to a method and system for optimizing the surface waviness of an air bearing in an air bearing-rotor system. Background Technique

[0002] The aerostatic spindle is the core component of ultra-precision machining technology, which mainly consists of a high-precision rotor, an aerostatic bearing and its air supply circuit, a motor, a thrust plate, etc. Since the motor speed is as high as 100,000 r / min, the aerostatic spindle has no external motor, but chooses the direct motor connection method. When the spindle rotates at a high speed, it is supported by the air bearing. Therefore, the fine modeling of the rotor-bearing system plays a very important role in the fine solution of the spindle dynamics.

[0003] The theoretical modeling and solution of the static and dynamic characteristics of the aerostatic bearing became mature in the early 21st century. Its main idea focuses on the solution of the Reynolds equation, which is divided into the laminar flow assumption condition and the turbulent flow assumption condition. Since the rotation speed of the rotor cooperating with the air bearing is very high, the centrifugal force and rotational inertia should not be too large. During the manufacturing process of the spindle, very high precision (μm level) will be ensured, which makes the air flow conditions very stable during the service of the air bearing, except for drastic speed increase and decrease. Therefore, most scholars assume the air flow as the laminar flow condition when studying the aerostatic bearing. In the actual manufacturing process, due to the existence of machining errors, the roughness error of the inner race of the aerostatic radial bearing is inevitable. The high precision of the air bearing makes the inner race roughness quite small (less than one-fourth of the initial air film thickness). However, it can affect the air pressure distribution by affecting the air film thickness. Therefore, it is necessary to study the influence of different surface shapes of the aerostatic journal bearing on the static characteristics of the bearing. Most scholars only study the sine wave waviness shape (for example, Wang X, Xu Q, Wang B, et al. Effect of surface waviness on the static performance of aerostatic journal bearings [J]. Tribology International, 2016, 103: 394-405). Some study the waviness of the inner race of the bearing, and some study the waviness of the journal. The conclusion is that specific conditions of the waviness parameters can improve the load-carrying performance.

[0004] The finite element method is a very effective numerical calculation method for solving the dynamics of the main shaft. The Timoshenko beam element method is the most mature and effective one among them. It takes into account the shear deformation and rotational inertia of the beam, making each element have five independent degrees of freedom. When studying the dynamic behavior of the rotor-bearing system, a coupled model of the rotor and the air bearing must be established. Currently, the main methods for solving the dynamic equation are: the Newmark-β method and the fourth-order Runge-Kutta method. The former has a fast convergence speed, but it is prone to non-convergence when used in non-linear dynamic systems; the latter has a slow convergence speed, but it is easy to converge when used in non-linear dynamic systems. Therefore, there is an urgent need to propose a solution method that combines the convergence speed and convergence conditions, that is, the improved Newmark-β algorithm. Summary of the Invention

[0005] Aiming at the deficiencies of the above technologies, the present invention provides a time-varying dynamics modeling and calculation method for an air bearing-rotor system considering different surface waviness, focusing on the surface topography parameters in the actually processed air bearing structure, and being able to explore its influence on the dynamic response of the main shaft, so as to guide the structural design and actual production of the air bearing.

[0006] In order to achieve the above object, in the first aspect, the present invention provides an air bearing surface waviness optimization method for an air bearing-rotor system, including the following steps:

[0007] Based on the structural parameters, material properties of the air bearing-rotor system, and the waviness parameters of the bearing, calculate the stiffness, damping coefficient of the air bearing with waviness, and the stiffness and damping matrices of the rotor;

[0008] Perform Timoshenko beam element modeling on the aerostatic rotor, divide it into several elements, and solve the mass, stiffness, and damping matrices of each element; couple the stiffness, damping coefficient of the air bearing with waviness and the stiffness and damping matrices of the rotor at the corresponding nodes to obtain an air bearing-rotor model with waviness;

[0009] Use the improved Newmark-β algorithm to solve the time-varying dynamic response of the air bearing-rotor model with waviness, and obtain the dynamic response results of the bearing-rotor system corresponding to the bearing surface waviness parameters;

[0010] If the dynamic response results of the bearing-rotor system do not meet the requirements, re-initialize the bearing surface waviness parameters and execute the above steps; until the dynamic response results of the bearing-rotor system meet the requirements, the bearing surface waviness parameters are obtained.

[0011] Further, calculating the stiffness, damping coefficient of the air bearing with waviness and the stiffness and damping matrices of the rotor based on the structural parameters, material properties of the bearing and the rotor, and the waviness parameters of the bearing includes:

[0012] Calculate the air film thickness under the circumferential and axial fluctuation directions of the initial surface waviness, and consider the possible translational and rotational degrees of freedom at the rotor journal to obtain the air film thickness distribution of the aerostatic radial bearing considering the surface waviness of the inner ring of the bearing housing;

[0013] Based on the air film thickness distribution of the aerostatic radial bearing, use the finite difference method and the step-by-step iteration method to calculate the distribution of the air film pressure, and calculate the stiffness, damping coefficient of the air bearing with waviness and the stiffness and damping matrices of the rotor.

[0014] Furthermore, the expressions of different surface waviness of the aerostatic radial bearing in the circumferential and axial directions are:

[0015] Axial sine waviness:

[0016]

[0017] Circumferential sine waviness:

[0018]

[0019] Axial triangular waviness:

[0020]

[0021] Circumferential triangular waviness:

[0022]

[0023] Axial square wave waviness:

[0024]

[0025] Circumferential square wave waviness:

[0026]

[0027] Among them, A is the wave amplitude, λ is the wavelength, R is the rotor radius, θ is the circumferential angle, and z is the axial coordinate;

[0028] The expression of the air film thickness is as follows:

[0029] h = h0 + ecos(θ - φ) - δ (7)

[0030] Among them, h0 is the nominal clearance, e is the eccentricity, φ is the attitude angle.

[0031] Furthermore, based on the air film thickness distribution of the aerostatic radial bearing, the distribution of the air film pressure calculated by using the finite difference method and the step-by-step iteration method includes:

[0032] Solve the dimensionless steady-state Reynolds equation in the simplified cylindrical coordinate system that describes the air film pressure:

[0033]

[0034] where, η is the air viscosity coefficient, ω is the angular velocity of the rotor, and p a is the standard atmospheric pressure;

[0035] Discretize the Reynolds equation using the finite difference method:

[0036]

[0037] The dimensionless air film pressure is:

[0038]

[0039] In the formula:

[0040]

[0041] where, and are the dimensionless air film thickness and air film pressure at the discrete coordinate (i, j) point respectively, θ and are the widths of each grid in the circumferential and axial directions after dividing the air film grid.

[0042] Furthermore, based on the calculated air film pressure distribution, the steady-state performance parameters of the air bearing are calculated as follows:

[0043] Calculation of the bearing capacity:

[0044]

[0045] Calculation of the bearing moment:

[0046]

[0047] Stiffness calculation:

[0048]

[0049] Friction coefficient calculation:

[0050]

[0051] where, z m is the tilt center, ΔW is the change in the bearing capacity, Δe is the change in the eccentricity, f c is the circumferential friction coefficient, F c is the intermediate variable for solving the circumferential friction coefficient, W is the bearing capacity of the bearing, fa is the axial friction coefficient, F a is an intermediate variable for solving the axial friction coefficient, and f is the total friction coefficient.

[0052] Furthermore, when modeling the rotor with Timoshenko beam elements, the aerostatic spindle is divided into several Timoshenko beam elements, and its dynamic equation is:

[0053]

[0054] where: M = M b + M d , the superscripts b and d represent the beam element and the disk element respectively, M b and M d are the mass matrices, C = C B + C s - ω(G b + G d ), G b and G d are the gyro matrices, K b is the stiffness matrix, is the stiffness matrix caused by the axial force, is the mass matrix caused by the centrifugal force, C s is the structural damping of the spindle system, K B and C B are the stiffness and damping matrices of the air bearing respectively, F is the unbalanced mass force of the thrust disk, is the displacement vector of the rotor node.

[0055] Furthermore, the improved Newmark-β algorithm is specifically as follows:

[0056]

[0057] where and are the equivalent mass matrix and the equivalent load vector of the linear structure:

[0058]

[0059] α is the time integration parameter, α ∈ [0, 1 / 3], when α = 0 it is the Newmark-β method, and after obtaining the acceleration response i+1 at time t , the velocity response and the displacement response {q i+1} are obtained using the following formulas:

[0060]

[0061] where β = (1 + α) 2 / 4, γ = 1 / 2 + α, and a suitable parameter α is selected to achieve the rapid convergence of the equation.

[0062] In a second aspect, the present invention provides an air bearing surface waviness optimization system for an air bearing-rotor system, including a calculation module, a model construction module, a solution module, and a parameter determination module;

[0063] Based on the structural parameters, material properties of the bearing and the rotor, and the waviness parameters of the bearing, the calculation module calculates the stiffness, damping coefficient of the air bearing with waviness, and the stiffness and damping matrices of the rotor;

[0064] The model construction module is used to perform Timoshenko beam element modeling on the aerostatic rotor, divide it into several elements, and solve the mass, stiffness, and damping matrices of each element; couple the stiffness, damping coefficient of the air bearing with waviness and the stiffness and damping matrices of the rotor at the corresponding nodes to obtain an air bearing-rotor model with waviness;

[0065] The solution module uses the improved Newmark-β algorithm to solve the time-varying dynamic response of the air bearing-rotor model with waviness, and obtains the dynamic response results of the bearing-rotor system corresponding to the bearing surface waviness parameters;

[0066] The parameter determination module is used to determine whether to re-initialize the bearing surface waviness parameters and perform calculations and model solutions according to whether the dynamic response results of the bearing-rotor system meet the requirements; until the dynamic response results of the bearing-rotor system meet the requirements, the bearing surface waviness parameters are obtained.

[0067] In a third aspect, the present invention can also provide a computer device, including a processor and a memory, the memory is used to store computer executable programs, the processor reads the computer executable programs from the memory and executes them, and when the processor executes the calculation executable programs, it can implement the air bearing surface waviness optimization method for the air bearing-rotor system described in the present invention.

[0068] At the same time, a computer-readable storage medium is provided, in which a computer program is stored, and when the computer program is executed by a processor, it can implement the air bearing surface waviness optimization method for the air bearing-rotor system described in the present invention.

[0069] Compared with the prior art, the present invention has at least the following beneficial effects:

[0070] The present invention considers a total of four degrees of freedom including circumferential translation and rotation, and finally calculates a fine air film thickness distribution; in the process of solving the Reynolds equation, partial differential terms of the air film pressure and the air film thickness are involved. The analytical distribution of the air film thickness has been obtained, and the distribution of the air film pressure is finally solved by using the finite difference method and the step-by-step iteration method. Integrating the obtained air film pressure can obtain various steady-state performances of the air bearing; after coupling the rotor-bearing, an improved Newmark-β algorithm is proposed to improve the convergence speed of solving the nonlinear dynamic equation of the system. Compared with the traditional method, this method not only improves the efficiency but also improves the calculation accuracy; the present invention focuses on the surface topography parameters in the actually processed air bearing structure, can explore its influence on the dynamic response of the spindle, and thus in turn guides the structural design and actual production of the air bearing.

[0071] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments. Brief Description of the Drawings

[0072] Figure 1 It is a mathematical model diagram of the rotor-bearing with surface waviness in the present invention, where (a) has axial waviness and (b) has circumferential waviness;

[0073] Figure 2 It is a flow chart of the iterative Reynolds equation in the present invention;

[0074] Figure 3 It is a distribution diagram of the air film pressure with waviness after inputting the response bearing parameters in the present invention. (a) is under a certain triangular waviness, and (b) is under a certain square wave waviness;

[0075] Figure 4 It is a diagram showing the excellent performance of the bearing capacity of the bearing with square wave waviness in the present invention;

[0076] Figure 5 It is a coupling logic diagram of the rotor-bearing in the present invention;

[0077] Figure 6 It is a general flow chart of the present invention;

[0078] Figure 7 It is a comparison diagram of the displacement responses at the spindle end with and without square wave waviness in the present invention. Detailed Embodiment

[0079] Refer to Figures 1-7 , when the present invention considers the time-varying dynamic modeling and calculation method of the air bearing-rotor system with different surface waviness, it includes the following steps:

[0080] Step 1) Input the structural parameters and waviness parameters of the aerostatic radial bearing, including the parameters listed in Table 1;

[0081] Table 1 Bearing Parameters

[0082]

[0083] Step 2) Under the rotor-bearing model shown Figure 1 Separate the parameters of three waviness shapes, namely sine wave, triangular wave, and square wave, and each waviness shape is divided into axial waviness direction and circumferential waviness direction;

[0084] The expressions of three different surface waviness shapes of aerostatic radial bearings in the circumferential and axial directions are as follows:

[0085] Axial sine waviness:

[0086]

[0087] Circumferential sine waviness:

[0088]

[0089] Axial triangular waviness:

[0090]

[0091] Circumferential triangular waviness:

[0092]

[0093] Axial square wave waviness:

[0094]

[0095] Circumferential square wave waviness:

[0096]

[0097] Among them, A is the wave amplitude, λ is the wavelength, R is the rotor radius, and θ is the circumferential angle;

[0098] The expression of the air film thickness is as follows:

[0099] h = h0 + ecos(θ - φ) - δ (7)

[0100] Among them, h0 is the nominal clearance, e is the eccentricity, φ is the attitude angle.

[0101] Step 3) Given the four-degree-of-freedom parameter information of the rotor-bearing: eccentricity and attitude angle (two translational degrees of freedom), inclination angle of rotation about the x-axis and inclination angle of rotation about the y-axis Calculate the film thickness with waviness, and ensure that the value of the film thickness does not exceed the physical boundaries, i.e., the outer surface of the rotor and the inner surface of the bearing housing; solve the film pressure in the simplified dimensionless Reynolds equation by combining the partial derivative results of the film thickness.

[0102] At the inclination angle of rotation about the x-axis and the inclination angle of rotation about the y-axis , the change in the film thickness can be expressed as:

[0103]

[0104] Then consider the established surface waviness model, and the final film thickness expression is:

[0105]

[0106] where ε0 is the static eccentricity without inclination freedom, θ0 is the static eccentricity angle, and tanθ0 = y / x, is the dimensionless axial coordinate system, is the dimensionless axial tilt center, h0 is the nominal clearance, and are the tilt freedoms along the two circumferential coordinate axes.

[0107] Step 4) According to the Figure 2 iterative process of the Reynolds equation shown: First, input various initial bearing structure parameters and bearing waviness parameters, calculate the film thickness distribution under corresponding conditions, and assign the initial orifice outlet pressure. During the iteration process, the convergence of the mass flow rate and the film pressure should be satisfied. If the film pressure does not converge, reassign the orifice outlet pressure of the previous iteration.

[0108] Since the time for the gas to pass through the orifice is very short, the gas flow can be regarded as adiabatic flow. Introduce the dimensionless parameter of the gas flow rate:

[0109]

[0110] The inlet flow rate of the orifice is:

[0111]

[0112]

[0113] In the formula: A is the throttling area of the orifice, κ = 1.4 is the specific heat ratio, p s is the supply air pressure, ρ a is the density of the atmosphere, Φ = 0.8 is the throttling coefficient, p d is the orifice outlet air pressure, p a is the pressure of the atmosphere.

[0114] The circumferential and axial gas outlet flows of the small holes are respectively:

[0115]

[0116] In the formula: and are the dimensionless circumferential gas outlet flows, and are the dimensionless axial gas outlet flows, x1 and x2 are the circumferential boundaries of the gas calculation region, y1 and y2 are the axial boundaries of the gas calculation region, and ρ is the density of the ideal gas (ρ = ρ a ·p / p a ).

[0117] Calculating the distribution of the gas film pressure using the finite difference method and the step-by-step iteration method includes:

[0118] Solving the dimensionless steady-state Reynolds equation in the simplified cylindrical coordinate system for the gas film pressure:

[0119]

[0120] Among them, η is the air viscosity coefficient, ω is the angular velocity of the rotor, and p a is the standard atmospheric pressure;

[0121] Discretizing the Reynolds equation using the finite difference method:

[0122]

[0123] The dimensionless gas film pressure is:

[0124]

[0125] In the formula:

[0126]

[0127] Among them, and are respectively the dimensionless gas film thickness and gas film pressure at the discrete coordinate (i, j) point. Here, θ and are the widths of each grid in the circumferential and axial directions after dividing the gas film grid.

[0128] Based on the calculated gas film pressure distribution, the calculation formulas for the steady-state performance parameters of the air bearing are as follows:

[0129] Calculation of the bearing capacity:

[0130]

[0131] Calculation of bearing moment:

[0132]

[0133] Stiffness calculation:

[0134]

[0135] Coefficient of friction calculation:

[0136]

[0137] where z m is the tilt center, ΔW is the change in bearing capacity, and Δe is the change in eccentricity; after the calculation is completed, the static characteristic parameters of the bearing are output.

[0138] Step 5) Analyze the variation of the air bearing performance with the parameters and types of surface waviness. Figure 3 From the air film pressure distributions under different waviness shapes shown, it can be seen that the maximum and minimum pressure distributions at each row of small holes are irregularly distributed with different waviness types and waveform parameters. Specifically, mapped to the performance, such as Figure 4 the bearing capacity shown, it can be seen that the bearing capacity of the square wave with waviness is significantly better than that without waviness and changes regularly with the wavelength and amplitude. Such a law will be instructive for the design of the bearing structure parameters after quantitative research. The stiffness coefficient of the bearing is obtained through Equation (41), and the damping coefficient of the bearing is obtained through an empirical formula.

[0139] Refer to Figure 6 , Figure 6 which is the overall process flow diagram of the present invention. The specific steps are as follows:

[0140] (1) First, input the bearing and rotor structure parameters. Table 1 shows the bearing structure parameters, and Table 2 shows the rotor structure parameters.

[0141] Table 2 Rotor parameters

[0142]

[0143] (2) Through the above Steps 1)-Step 5), calculate the stiffness and damping coefficients of the front and rear air radial bearings distributed at different positions of the rotor.

[0144] (3) Through Figure 5 the distribution positions of the front / rear air static pressure radial bearings shown, couple the stiffness and damping coefficients of the front and rear air radial bearings distributed at different positions of the rotor into the dynamic equation of the entire system. The specific coupling equation is shown as follows. The M, C, and K matrices are those mentioned in Equation (15), and K B and C Bis the stiffness and damping coefficients of the front / rear radial bearings;

[0145]

[0146] The aerostatic spindle is divided into several Timoshenko beam elements, and its dynamic equation is:

[0147]

[0148] In the formula: M = M b + M d , the superscripts b and d represent the beam element and the disk element respectively, M b and M d are the mass matrices, C = C B + C s - ω(G b + G d ), G b and G d are the gyro matrices, K b is the stiffness matrix, is the stiffness matrix caused by the axial force, is the mass matrix caused by the centrifugal force, C s is the structural damping of the spindle system, K B and C B are the stiffness and damping matrices of the air bearing respectively, F is the unbalanced mass force of the thrust disk, is the displacement vector of the rotor node;

[0149] Input the structural parameters and material properties of the spindle, and calculate the stiffness matrix, damping matrix and mass matrix of each beam element;

[0150] is the mass matrix caused by the centrifugal force, and its specific expression is as follows:

[0151]

[0152] Among them, m1 = 156 + 294Φ + 140Φ 2 , m2 = (22 + 38.5Φ + 17.5Φ 2 )L, m3 = 54 + 126Φ + 70Φ 2 , m4 = -(13 + 31.5Φ + 17.5Φ 2 )L, m5 = (4 + 7Φ + 3.5Φ 2 )L 2 , m6 = -(3 + 7Φ + 3.5Φ 2 )L 2 .

[0153] The empirical calculation formula for the damping coefficient of the air bearing is as follows:

[0154] C s =CVμFv (25)

[0155] Wherein, CV is the volume of the bearing, μ is the viscosity coefficient, and Fv is the vibration force received by the bearing.

[0156] The stiffness and damping matrices of the air bearing-rotor coupling system are respectively expressed as:

[0157]

[0158] In the formula: and are respectively the stiffness and damping matrices of the rotor nodes i and j, is the stiffness and damping matrix of the front air radial bearing, is the stiffness and damping matrix of the rear air radial bearing.

[0159] (4) Based on the improved Newmark-β algorithm, initialize the time integration parameter α and the time step Δt, and perform the preliminary calculation of the dynamic motion equation. If the equation does not converge, readjust α and Δt, and then perform the Newmark-β algorithm calculation. If the equation converges, output the dynamic response at the end of the main shaft;

[0160] The specific improved Newmark-β algorithm is as follows:

[0161]

[0162] Wherein and are the equivalent mass matrix and equivalent load vector of the linear structure

[0163]

[0164] α is the time integration parameter, α ∈ [0, 1 / 3]. When α = 0, it is the Newmark-β method. Introducing this parameter can improve the convergence speed of the kinematic differential equation. After obtaining the acceleration response i+1 at time t the velocity response and displacement response {q i+1} are obtained by using the following formula:

[0165]

[0166] Where β = (1 + α) 2 / 4, γ = 1 / 2 + α. Select appropriate parameters α to achieve the rapid convergence of the equation.

[0167] (5) Figure 7 The vibration displacement responses at the spindle end with and without square-wave waviness are shown. The patterns presented include the rotor-bearing parameters selected in the present invention. From Figure 7 it can be seen that after introducing square-wave waviness, the stability of the rotor-bearing is higher, and the vibration displacement is suppressed by approximately 30%, with obvious effects. By using the method of the present invention, under the condition of given structural parameters of the air bearing and the rotor, the degree of vibration suppression of the spindle end by different surface waviness parameters can be quantitatively explored, thereby achieving the ultimate goal of accurately guiding the structural design and manufacturing of air bearings.

[0168] The present invention discloses a time-varying dynamics modeling and calculation method for an air bearing-rotor system considering different surface waviness, including: based on the rotor structural parameters, material properties, and the structural parameters and surface waviness parameters of the air bearing; calculating the stiffness and damping coefficients of the front / rear air radial bearings through the finite difference method and the step-by-step iteration method; dividing the rotor into several discrete Timoshenko beam elements, and regarding the thrust disk and the beam elements as rigid contacts; calculating the mass, stiffness, and damping matrices of the rotor-bearing system; using the improved Newmark-β algorithm to finally obtain the dynamic response of the rotor-bearing system and output the vibration displacement at the spindle end; by using the dynamic model of the rotor-bearing system established in the present invention, only by inputting the structural parameters of the rotor and the bearing, the influence of different surface waviness parameters of the inner ring of the air bearing on the vibration characteristics of the spindle end can be quantitatively explored, providing a solution for optimizing the bearing structural design and manufacturing.

[0169] The present invention provides an air bearing surface waviness optimization method in an air bearing-rotor system. Based on the modeling of the surface waviness of the inner ring of three complete air bearings in the circumferential and axial directions, considering a total of four degrees of freedom including circumferential translation and rotation, the fine air film thickness distribution is finally calculated; then, in the process of solving the Reynolds equation, partial differential terms of the air film pressure and the air film thickness are involved. Since the analytical distribution of the air film thickness has been obtained, the distribution of the air film pressure is finally solved by using the finite difference method and the step-by-step iteration method. Integrating the obtained air film pressure can obtain various steady-state performances of the air bearing; after coupling the rotor-bearing, an improved Newmark-β algorithm is proposed to solve the air bearing-rotor model, improving the convergence speed of solving the system's nonlinear dynamic equation. Compared with the traditional method, this method not only improves the efficiency but also improves the calculation accuracy; the present invention focuses on inputting the surface topography parameters of the actually processed air bearing structure, can explore its influence on the dynamic response of the spindle, and guides the structural design and actual production of the air bearing.

[0170] Embodiment 2. The present invention provides an air bearing surface waviness optimization system in an air bearing-rotor system, including a calculation module, a model construction module, a solution module, and a parameter determination module;

[0171] Based on the structural parameters, material properties of the bearing and the rotor, and the waviness parameters of the bearing, the calculation module calculates the stiffness, damping coefficient of the air bearing with waviness, and the stiffness and damping matrices of the rotor;

[0172] The model construction module is used to perform Timoshenko beam element modeling on the aerostatic rotor, divide it into several elements, and solve the mass, stiffness, and damping matrices of each element; couple the stiffness, damping coefficient of the air bearing with waviness and the stiffness and damping matrices of the rotor at the corresponding nodes to obtain an air bearing-rotor model with waviness;

[0173] The solution module uses the improved Newmark-β algorithm to solve the time-varying dynamic response of the air bearing-rotor model with waviness, and obtains the dynamic response results of the bearing-rotor system corresponding to the bearing surface waviness parameters;

[0174] The parameter determination module is used to determine whether to re-initialize the bearing surface waviness parameters and perform calculations and model solutions according to whether the dynamic response results of the bearing-rotor system meet the requirements; until the dynamic response results of the bearing-rotor system meet the requirements, the bearing surface waviness parameters are obtained.

[0175] On the other hand, the present invention provides a computer-readable storage medium. A computer program is stored in the computer-readable storage medium. When the computer program is executed by a processor, it can implement the air bearing surface waviness optimization method in the air bearing-rotor system of the present invention.

[0176] The present invention can also provide a computer device, including a processor and a memory. The memory is used to store computer-executable programs. The processor reads the computer-executable programs from the memory and executes them. When the processor executes the computer-executable programs, it can implement the air bearing surface waviness optimization method in the air bearing-rotor system of the present invention.

[0177] The computer device can be a laptop computer, a desktop computer, or a workstation.

[0178] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or a field-programmable gate array (FPGA).

[0179] For the memory of the present invention, it can be an internal storage unit of a laptop, a desktop computer or a workstation, such as a memory or a hard disk; or an external storage unit can be adopted, such as a mobile hard disk or a flash card.

[0180] A computer-readable storage medium may include a computer storage medium and a communication medium. The computer storage medium includes volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. The computer-readable storage medium may include: read-only memory (ROM, Read Only Memory), random access memory (RAM, Random Access Memory), solid state drives (SSD, Solid State Drives) or optical discs, etc. Among them, the random access memory may include resistive random access memory (ReRAM, Resistance Random Access Memory) and dynamic random access memory (DRAM, Dynamic Random Access Memory).

Claims

1. A method for optimizing the surface waviness of an air bearing in an air bearing-rotor system, characterized in that: The following steps are involved: Based on the structural parameters, material properties and bearing waviness parameters of the air bearing-rotor system, the stiffness and damping coefficient of the air bearing with waviness and the stiffness and damping matrix of the rotor are calculated; The aerostatic rotor is modeled by Timoshenko beam elements, divided into several units, and the mass, stiffness, and damping matrices of each unit are solved; The stiffness and damping coefficient of the air bearing with corrugation are coupled with the stiffness and damping matrix of the rotor at the corresponding nodes to obtain the air bearing-rotor model with corrugation; The improved Newmark-β algorithm is used to solve the time-varying dynamic response of the air bearing-rotor model with corrugation, and the dynamic response results of the bearing-rotor system corresponding to the bearing surface corrugation parameters are obtained; If the dynamic response result of the bearing-rotor system does not meet the requirements, the bearing surface waviness parameter is reinitialized and the above steps are performed; until the dynamic response result of the bearing-rotor system meets the requirements, the bearing surface waviness parameter is obtained.

2. The method for optimizing the surface waviness of an air bearing in an air bearing-rotor system according to claim 1, characterized in that: Based on the structural parameters, material properties of the bearing and rotor, and the waviness parameters of the bearing, the stiffness and damping coefficient of the air bearing with waviness and the stiffness and damping matrix of the rotor are calculated, including: The air film thickness of the initialized surface waviness in both the circumferential and axial directions is calculated, and the possible translational and rotational degrees of freedom at the rotor journal are considered to obtain the air film thickness distribution of the aerostatic radial bearing considering the surface waviness of the inner ring of the bearing seat. Based on the air film thickness distribution of the air static pressure radial bearing, the distribution of the air film pressure is calculated using the finite difference method and the stepwise iteration method. The stiffness and damping coefficient of the air bearing with corrugation and the stiffness and damping matrix of the rotor are calculated.

3. The method for optimizing the surface waviness of an air bearing in an air bearing-rotor system according to claim 2, characterized in that: The expressions for different surface waviness of aerostatic radial bearings in the circumferential and axial directions are: Axial sinusoidal corrugation: Circumferential sinusoidal corrugation: Axial triangular waviness: Circumferential triangular waviness: Axial square wave waviness: Circumferential square wave waviness: Among them, A is the amplitude, λ is the wavelength, R is the rotor radius, θ is the circumferential angle, and z is the axial coordinate; The expression of air film thickness is as follows: h=h0+ecos(θ-φ)-δ (7)where h0 is the nominal clearance, e is the eccentricity, φ is the attitude angle.

4. The method for optimizing the surface waviness of an air bearing in an air bearing-rotor system according to claim 2, characterized in that: Based on the air film thickness distribution of the air static pressure journal bearing, the distribution of the air film pressure is calculated using the finite difference method and the stepwise iteration method, including: Solve the dimensionless steady-state Reynolds equation in simplified cylindrical coordinates describing the film pressure: in, η is the air viscosity coefficient, ω is the angular velocity of the rotor, p a is the standard atmospheric pressure; The Reynolds equation is discretized using the finite difference method: Dimensionless film pressure for: Where: in, and are the dimensionless film thickness and film pressure at the corresponding discrete coordinate point (i, j), θ and It is the width of each grid in the circumferential and axial directions after the air film grid is divided.

5. The method for optimizing the surface waviness of an air bearing in an air bearing-rotor system according to claim 2, characterized in that: Based on the calculated air film pressure distribution, the steady-state performance parameters of the air bearing are calculated as follows: Calculation of bearing capacity: Calculation of bearing moment: Stiffness calculation: Calculation of friction coefficient: Among them, z m is the tilt center, ΔW is the change in bearing capacity, Δe is the change in eccentricity, and f c is the circumferential friction coefficient, F c To solve the intermediate variable of the circumferential friction coefficient, W is the bearing capacity, f a is the axial friction coefficient, F a To solve the intermediate variable of the axial friction coefficient, f is the total friction coefficient.

6. The method for optimizing the surface waviness of an air bearing in an air bearing-rotor system according to claim 1, characterized in that: When the rotor is modeled using Timoshenko beam elements, the air static pressure axis is divided into several Timoshenko beam elements, and the dynamic equation is: Where: M = M b +M d , the superscripts b and d represent beam elements and disk elements respectively, M b and M d is the mass matrix, C = C B +C s -ω(G b +G d ), G b and G d is the gyro matrix, K b is the stiffness matrix, is the stiffness matrix caused by the axial force, is the mass matrix caused by centrifugal force, C s is the structural damping of the spindle system, K B and C B are the stiffness and damping matrices of the air bearing, F is the unbalanced mass force of the thrust plate, is the displacement vector of the rotor node.

7. The method for optimizing the surface waviness of an air bearing in an air bearing-rotor system according to claim 6, characterized in that: The improved Newmark-β algorithm is as follows: in and are the equivalent mass matrix and equivalent load vector of the linear structure: α is the time integration parameter, α∈[0,1 / 3], when α=0, it is the Newmark-β method, and the solution is i+1 Acceleration response at each moment Then, the speed response is obtained using the following formula: and displacement response {q i+1 }: Where β=(1+α) 2 / 4, γ=1 / 2+α, and choose the appropriate parameter α to achieve rapid convergence of the equation.

8. A system for optimizing the surface waviness of an air bearing in an air bearing-rotor system, characterized in that: It includes a calculation module, a model building module, a solution module and a parameter determination module; The calculation module calculates the stiffness and damping coefficient of the air bearing with corrugation and the stiffness and damping matrix of the rotor based on the structural parameters, material properties and corrugation parameters of the bearing and the rotor; The model building module is used to model the air static pressure rotor with Timoshenko beam elements, divide it into several units, and solve the mass, stiffness, and damping matrix of each unit; the stiffness and damping coefficient of the air bearing with corrugation are coupled with the stiffness and damping matrix of the rotor at the corresponding nodes to obtain the air bearing-rotor model with corrugation; The solution module uses the improved Newmark-β algorithm to solve the time-varying dynamic response of the air bearing-rotor model with corrugation, and obtains the dynamic response results of the bearing-rotor system corresponding to the bearing surface corrugation parameters; The parameter determination module is used to determine whether to reinitialize the bearing surface waviness parameters and perform calculations and model solutions according to whether the dynamic response results of the bearing-rotor system meet the requirements; until the dynamic response results of the bearing-rotor system meet the requirements, the bearing surface waviness parameters are obtained.

9. A computer device, characterized in that: It includes a processor and a memory, the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and when the processor executes part or all of the computer executable program, it can implement the method for optimizing the surface waviness of an air bearing in an air bearing-rotor system as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: A computer program is stored in the computer-readable storage medium. When the computer program is executed by a processor, the method for optimizing the surface waviness of an air bearing in an air bearing-rotor system according to any one of claims 1 to 7 can be implemented.

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