Method and device for calculating mass flow coefficient of dynamic and static pressure air bearing

Abstract

The invention discloses a dynamic and static pressure air bearing mass flow coefficient calculation method and device, and the method comprises the steps: building a simulation model of a dynamic and static pressure air bearing based on a computational fluid dynamics method according to the structure parameters and rotating speed of the dynamic and static pressure air bearing, and obtaining the mass flow of each throttling hole; according to the structure parameters of the dynamic and static pressure air bearing, a throttling hole mass flow model with a mass flow coefficient is constructed, and the mass flow of each throttling hole in the throttling hole mass flow model is obtained; and the mass flow coefficient of the orifice mass flow model is adjusted according to the mass flow correction equation, so that the numerical relationship between the mass flow of each orifice in the simulation model and the mass flow of each orifice in the orifice mass flow model meets the convergence condition. According to the method, the flow coefficient of the orifice mass flow model is iterated by utilizing the mass flow correction equation, and the orifice mass flow coefficient can be calculated under any orifice, rotating speed and different gas film thickness gradients.

Description

Technical Field

[0001] The invention relates to the technical field of dynamic and static pressure air bearings, and in particular to a method and device for calculating a flow coefficient of a dynamic and static pressure air bearing. Background Art

[0002] As the manufacturing industry's requirements for processing efficiency and quality continue to increase, dynamic and static pressure air bearings, as core components of ultra-precision machine tools, are also further developing in the direction of lightweight, high load, high speed and low gas consumption. Establishing an accurate static performance calculation model for dynamic and static pressure air bearings at high speeds can provide theoretical guidance for the design of dynamic and static pressure air bearings.

[0003] The prior art discloses the influence of flow coefficient on the performance of hydrostatic air bearings and the influence of throttle-type restrictors in hydrostatic air bearings on mass flow. The research objects are all horizontal stationary bearings. In the calculation model, the mass flow of the restrictor is equivalent to the nozzle mass flow model, and the flow coefficient is introduced for correction. Then, a relatively accurate static model of the hydrostatic air bearing is established by numerically solving the Reynolds equation or the CFD method.

[0004] However, unlike horizontally stationary bearings, for radial bearings of dynamic and static pressure air bearings that work at high speeds and have uneven air film thickness, the mass flow coefficient fluctuates under different working conditions, and the change pattern is not clear. In addition, the difference in wind pressure downwind from different throttles is large, making it impossible to efficiently and accurately calculate and correct the mass flow coefficient of dynamic and static pressure air bearings. Summary of the invention

[0005] The purpose of the present invention is to provide a method and device for calculating the mass flow coefficient of a dynamic and static pressure air bearing, which can solve at least one of the technical problems mentioned above. The specific solution is as follows:

[0006] According to the specific embodiments disclosed in the present invention, the first aspect of the present invention provides a method for calculating the mass flow coefficient of a dynamic and static pressure air bearing, comprising:

[0007] According to the structural parameters and rotation speed of the dynamic and static pressure air bearing, a simulation model of the dynamic and static pressure air bearing based on the computational fluid dynamics method is established, and the mass flow rate of each throttle hole in the simulation model is calculated by the computational fluid dynamics method;

[0008] According to the structural parameters of the dynamic and static pressure air bearing, a throttle mass flow model with a mass flow coefficient is constructed, and the mass flow of each throttle in the throttle mass flow model is calculated by using a finite difference method;

[0009] Adjusting the mass flow coefficient of the throttle mass flow model according to the mass flow correction equation so that the numerical relationship between the mass flow of each throttle in the simulation model and the mass flow of each throttle in the throttle mass flow model satisfies a convergence condition;

[0010] The expression of the mass flow correction equation is:

[0011]

[0012] Among them, C d1 is the mass flow correction equation when the air film thickness increases along the speed direction of the dynamic and static pressure air bearing;

[0013] C d2 is the mass flow correction equation when the air film thickness decreases along the speed direction of the dynamic and static pressure air bearing;

[0014] Δh is the change in circumferential air film thickness, and h is the air film thickness;

[0015] δ is the depth of the pressure equalizing groove; d is the diameter of the throttle hole, and w is the angular velocity;

[0016] fac is a function related to the variation of the air film thickness in the circumferential direction of the dynamic and static pressure air bearing fitted by the fluid dynamics method and the finite difference method.

[0017] Preferably, the establishment of a simulation model of the dynamic and static pressure air bearing based on a computational fluid dynamics method, and the use of the computational fluid dynamics method to calculate the mass flow of each throttle hole in the simulation model, comprises: uniformly arranging a plurality of throttle holes along the circumference of the dynamic and static pressure air bearing, and solving the Navier-Stokes equations in three-dimensional space by using FLUENT software;

[0018] The method of solving the Navier-Stokes equations in three-dimensional space by using FLUENT software includes:

[0019] Select the standard k-ε turbulence model;

[0020] Set boundary conditions: The atmospheric pressure outside the bearing is 1×10 5 Pa, supply pressure is 6×10 5 Pa, the speed of the moving boundary is 0-150,000r / min;

[0021] Grid division: 300 grids are evenly divided along the circumference of the dynamic and static pressure air-floating axis, 120 grids are evenly divided along the axial direction, and 8 grids are evenly divided along the air film thickness direction;

[0022] The SIMPLE algorithm is selected for solution. The convergence condition of the SIMPLE algorithm is RNG<10 -6 .

[0023] Preferably, the expression of the throttle mass flow model with flow coefficient is:

[0024]

[0025] Among them, ψ s is the dimensionless coefficient, C d is the flow coefficient;

[0026] d is the diameter of the throttle hole, P s is the supply pressure, ρ a is the density of air at atmospheric pressure.

[0027] Preferably, the method of calculating the mass flow of each throttle hole in the throttle hole mass flow model by using the finite difference method includes:

[0028] The Reynolds equation is used to express the relationship between the thickness of the air film on the dynamic and static pressure air bearing and the gas pressure distribution;

[0029] Applying the weighted residual method to obtain a weak solution to the Reynolds equation;

[0030] Dividing the plane calculation flow domain formed by the deployment of the air film into a plurality of units and corresponding nodes, and using the finite element method to obtain a discrete equation for a weak solution of the Reynolds equation;

[0031] The discrete equation is solved to obtain the downwind pressure value of each throttle hole, and the mass flow of each throttle hole in the throttle hole mass flow model is obtained according to the downwind pressure value of each throttle hole.

[0032] Preferably, adjusting the mass flow coefficient of the throttle mass flow model according to the mass flow correction equation so that the mass flow of each throttle in the simulation model and the mass flow of each throttle in the throttle mass flow model meet the convergence condition includes:

[0033] According to the obtained mass flow of each throttle hole in the simulation model, an initial flow coefficient of the throttle hole mass flow model is set, and the mass flow of each throttle hole in the throttle hole mass flow model is calculated by using a finite difference method;

[0034] Determining whether a numerical relationship between the mass flow rate of each throttle hole in the simulation model and the mass flow rate of each throttle hole in the throttle hole mass flow model satisfies a convergence condition;

[0035] If the convergence condition is not met, iterating the initial mass flow coefficient of the orifice mass flow model according to the mass flow correction equation;

[0036] The mass flow coefficient when the convergence condition is met is the mass flow coefficient of the dynamic and static pressure air bearing.

[0037] Preferably, the expression of the convergence condition is:

[0038]

[0039] Among them, m CFD is the mass flow rate of each throttle hole in the simulation model;

[0040] m FEM is the mass flow rate of each throttle hole in the throttle hole mass flow model.

[0041] Preferably, the method of solving the Navier-Stokes equations in three-dimensional space by using FLUENT software further includes:

[0042] The enhanced wall equation is added to the standard k-ε turbulence model to improve the calculation accuracy.

[0043] Preferably, the expression of the discrete equation of the weak solution of the Reynolds equation is:

[0044]

[0045] Wherein, i=1, 2, ..., q;

[0046] Δ e represents the calculation boundary; e represents the node parameter; h represents the film thickness; N represents the node coefficient

[0047] Represents the horizontal normalization coefficient; Represents the normalization coefficient in the vertical direction;

[0048] represents dimensionless speed; c i represents the third finite element coefficient at the i-th node;

[0049] b i represents the second finite element coefficient at the i-th node;

[0050] c eT represents the transpose of the third finite element coefficient vector of the node;

[0051] b eT represents the transpose of the second finite element coefficient vector of the node;

[0052] h eT represents the transpose of the film thickness vector; N eT represents the transpose of the node pressure vector;

[0053] f represents the pressure square; k1 represents the quality coefficient; δ i Indicates the throttle position;

[0054] μ s Indicates the throttling ratio; m s represents the mass flow rate of the sth throttle hole; λ represents the number of bearings.

[0055] Preferably, the expressions of function fac1 and function fac2 are:

[0056]

[0057] Wherein, Δh is the change in circumferential air film thickness.

[0058] According to the specific implementation mode disclosed in the present invention, the second aspect of the present invention discloses a device for calculating the mass flow coefficient of a dynamic and static pressure air bearing, which is used to implement the above method, comprising:

[0059] A simulation model mass flow calculation unit is used to establish a simulation model of the dynamic and static pressure air bearing based on a computational fluid dynamics method according to the structural parameters and rotation speed of the dynamic and static pressure air bearing, and calculate the mass flow of each throttle hole in the simulation model using the computational fluid dynamics method;

[0060] A throttle mass flow calculation unit is used to construct a throttle mass flow model with a mass flow coefficient according to the structural parameters of the dynamic and static pressure air bearing, and calculate the mass flow of each throttle in the throttle mass flow model by using a finite difference method;

[0061] The correction unit adjusts the mass flow coefficient of the throttle mass flow calculation unit according to the mass flow correction equation so that the numerical relationship between the mass flow of each throttle in the simulation model and the mass flow of each throttle in the throttle mass flow model meets the convergence condition.

[0062] Compared with the prior art, the above solution disclosed in the present invention has at least the following beneficial effects:

[0063] The present invention establishes a simulation model of a dynamic and static pressure air bearing and a throttle mass flow model with a mass flow coefficient, compares the mass flow value of each throttle under the two models, and uses a mass flow correction equation to correct the mass flow coefficient of the throttle mass flow model. When the mass flow value of each throttle under the two models meets the convergence condition, the final mass flow coefficient is obtained. The mass flow correction equation is used to iterate the flow coefficient of the throttle mass flow model, and the calculation of the throttle mass flow coefficient under any throttle, rotation speed and different air film thickness gradient can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the disclosure of the present invention, and together with the specification, are used to explain the principles disclosed in the present invention. Obviously, the drawings described below are only some embodiments disclosed in the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0065] Figure 1 It is a flow chart of a method for calculating the mass flow coefficient of a dynamic and static pressure air bearing according to the first embodiment of the present invention;

[0066] Figure 2 is a schematic diagram of a simulation model of a first embodiment of the present invention;

[0067] Figure 3 A schematic diagram of a finite difference method calculation area according to a first embodiment of the present invention;

[0068] Figure 4 is a logic block diagram of calculating the mass flow coefficient according to the first embodiment of the present invention;

[0069] Figure 5 It is a schematic diagram of a device for calculating mass flow coefficient of a dynamic and static pressure air bearing according to a second embodiment of the present invention.

[0070] Reference numerals:

[0071] 1 the first throttle hole, 2 the second throttle hole, 3 the third throttle hole, 4 the fourth throttle hole, 5 the fifth throttle hole, 6 the sixth throttle hole, 7 the seventh throttle hole, 8 the eighth throttle hole, 9 the ninth throttle hole, 10 the tenth throttle hole;

[0072] 101 simulation model mass flow calculation unit, 102 throttle hole mass flow calculation unit, 103 correction unit. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical scheme and advantages disclosed in the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments disclosed in the present invention, rather than all the embodiments. Based on the embodiments disclosed in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection disclosed in the present invention.

[0074] The terms used in the embodiments disclosed in the present invention are only for the purpose of describing specific embodiments, and are not intended to limit the disclosure of the present invention. The singular forms "a", "said" and "the" used in the embodiments disclosed in the present invention and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings, and "multiple" generally includes at least two.

[0075] It should also be noted that the term "includes", "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, so that a commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprising a ..." do not exclude the existence of other identical elements in the commodity or device including the elements.

[0076] The optional embodiments disclosed in the present invention are described in detail below with reference to the accompanying drawings.

[0077] The dynamic and static pressure air bearing is a gas-lubricated bearing that combines the principles of dynamic pressure and static pressure. When the shaft rotates, the gas in the bearing is squeezed due to the dynamic pressure effect, forming a dynamic pressure gas film, which separates the shaft and the bearing sleeve to avoid direct contact. When compressed gas is provided by an external gas source, it enters the bearing through the throttle and forms a static pressure gas film, further increasing the bearing's load-bearing capacity. The throttle is provided with a throttle hole for controlling the flow rate and flow of the gas. When the air flow speed increases, the thickness of the gas film will decrease accordingly, which can enhance the bearing's support force. At the same time, the size and number of throttle holes will also affect the bearing's load-bearing capacity and rigidity.

[0078] When the mass flow of the throttle is equivalent to the nozzle mass flow model, the flow coefficient needs to be introduced to correct the flow coefficient model. The existing flow coefficient models are all based on the downwind pressure P d / Gas supply pressure P s function, and the downwind pressure P d Implicit in the numerical equations, and different restrictors P d There is a big gap.

[0079] On the other hand, for the radial bearings of the dynamic and static pressure air bearings working under high-speed conditions, the bearing speed and uneven air film thickness will cause the flow coefficient to fluctuate. Therefore, when correcting the flow coefficient, it is necessary to consider the influence of the dynamic and static pressure air bearing speed and the change of air film thickness.

[0080] Therefore, the first embodiment of the present invention provides a method for calculating the mass flow coefficient of a dynamic and static pressure air bearing, such as Figure 1 As shown, the following steps are included:

[0081] Step S1, establishing a simulation model of the dynamic and static pressure air bearing based on a computational fluid dynamics method according to the structural parameters and rotation speed of the dynamic and static pressure air bearing, and calculating the mass flow of each throttle hole in the simulation model using the computational fluid dynamics method.

[0082] Specifically, establish Figure 2In the simulation model shown, 10 throttle holes are evenly arranged along the circumference of the radial bearing of the dynamic and static pressure air bearing. In the air bearing, since there is relative movement between the two surfaces of the rotor and the stator and the gap between the two forms a wedge shape, when the bearing rotates in one direction, the two surfaces move relative to each other, and the gas with a certain viscosity is brought into the wedge gap due to its viscosity, and pressure is generated under the extrusion effect.

[0083] Therefore, the axial direction of the dynamic and static pressure air bearing is the Z axis, the vertical upward direction is the Y axis, and the horizontal right direction is the X axis. Figure 2 The coordinate system shown. Figure 2 The thickness of the wedge-shaped air film along the rotational speed direction of the second throttle hole 2 to the fifth throttle hole 5 shows an increasing trend, and the thickness of the wedge-shaped air film along the rotational speed direction of the seventh throttle hole 7 to the tenth throttle hole 10 shows a decreasing trend. The first throttle hole 1 and the sixth throttle hole 6 have nothing to do with the rotational speed of the bearing, and no subsequent correction is required.

[0084] The Navier-Stokes equations in three-dimensional space, namely the three-dimensional NS equations, are a basic tool in fluid mechanics and are used to simulate the flow of incompressible fluids.

[0085] In this embodiment, the Navier-Stokes equations in three-dimensional space are solved by FLUENT software, and the parameters are set as follows:

[0086] Since the bearing has a rotation effect, the airflow near the bearing wall will be subjected to rotational shear, so the influence of the movement of the bearing wall must be considered, so the standard k-ε turbulence model is selected;

[0087] Preferably, an enhanced wall equation is added to the standard k-ε turbulence model to improve the calculation accuracy.

[0088] Set boundary conditions: The atmospheric pressure outside the bearing is 1×10 5 Pa, supply pressure is 6×10 5 Pa, the speed of the moving boundary is 0-150,000r / min;

[0089] In order to obtain better convergence, the following grid division is performed: 300 grids are evenly divided along the circumference of the dynamic and static pressure air bearing axis, 120 grids are evenly divided along the axial direction, and 8 grids are evenly divided along the thickness direction of the air film;

[0090] The SIMPLE C algorithm is selected to solve the entire simulation model and boundary conditions. The convergence condition is RNG<10 -6 .

[0091] Finally, the mass flow rates m of the 10 throttle holes are calculated respectively. CFD. .

[0092] Step S2: construct a throttle mass flow model with a mass flow coefficient according to the structural parameters of the dynamic and static pressure air bearing, and calculate the mass flow of each throttle in the throttle mass flow model by using a finite difference method.

[0093] The method comprises: step S2-1, constructing a throttle mass flow model with a mass flow coefficient according to the structural parameters of the dynamic and static pressure air bearing, wherein the structural parameters of the dynamic and static pressure air bearing include: eccentricity, bearing diameter, throttle diameter, etc.

[0094] Specifically, based on the structural parameters of the dynamic and static pressure air bearings that are the same as those in step S1, the constructed throttle hole mass model is idealized into a nozzle model, and the pressure is increased from the supply pressure P s Down to the downwind pressure P d .

[0095] Therefore, the mass flow model of the throttle hole under ideal conditions can be expressed as:

[0096]

[0097] Among them, ψ s is the dimensionless coefficient;

[0098] d is the diameter of the throttle hole (mm), P s is the supply pressure (Pa);

[0099] ρ a is the density of air at atmospheric pressure (kg / m 3 );

[0100]

[0101] β κ =(2 / (κ+1)) (κ+1) / κ ;

[0102] Among them, β κ is the dimensionless coefficient; P d is the downwind pressure (Pa);

[0103] κ is the adiabatic index, and for air κ=1.4.

[0104] However, the actual mass flow rate is different from the mass flow rate in the theoretical nozzle, and a flow coefficient is needed to correct the mass flow rate. Therefore, the following expression exists:

[0105] m r =C d ×m t

[0106] Among them, m ris the actual mass flow rate, m t is the theoretical mass flow rate, C d is the flow coefficient.

[0107] The expression of the orifice mass flow model with flow coefficient is obtained as follows:

[0108]

[0109] Step S2-2, using the finite difference method to calculate the gas pressure distribution of the radial bearing of the dynamic and static pressure air bearing, and obtain the value of the downwind pressure, thereby calculating the mass flow rate m of each throttle hole in the throttle hole mass flow model. FEM .

[0110] Specifically, since the thickness of the air film is much smaller than the bearing diameter, the curvature of the air film can be ignored. Therefore, the dimensionless steady-state Reynolds equation for the air film to expand into a plane can be expressed as:

[0111]

[0112] The compression function is defined as:

[0113] The dimensionless steady-state Reynolds equation can be simplified to:

[0114]

[0115] Among them, x, y, z are coordinate values;

[0116] represents the dimensionless gas film thickness; represents the dimensionless mass flow parameter; represents the dimensionless rotation speed;

[0117] λ represents the number of bearings; ξ i Indicates the throttle position; represents dimensionless pressure;

[0118] h is the thickness of the air film; i is the number of the throttle hole; p is the air film pressure;

[0119] Λ x Indicates the bearing compressibility coefficient in the horizontal direction; Λ z Indicates the compressibility factor of the bearing in the vertical direction.

[0120] Applying the weighted residual method to equation (3), the weak solution of the equation can be expressed as:

[0121]

[0122] Among them, Ω represents the calculation area; δ represents the partial differential operator;

[0123] Represents the horizontal normalization coefficient; Represents the normalization coefficient in the vertical direction;

[0124] Further, such as Figure 3 As shown in the figure, the entire computational domain is divided into several units and their corresponding nodes, and the finite element method is used to solve the weak solution of the equation to obtain the following discrete equation:

[0125]

[0126] Wherein, i=1, 2, ..., q;

[0127] Δ e represents the symmetric boundary; e represents the node parameter; h represents the air film thickness; N represents the node coefficient;

[0128] Represents the horizontal normalization coefficient; Represents the normalization coefficient in the vertical direction;

[0129] represents dimensionless speed; c i represents the third finite element coefficient at the i-th node;

[0130] c eT represents the transpose of the third finite element coefficient vector of the node;

[0131] b i represents the second finite element coefficient at the i-th node;

[0132] b eT represents the transpose of the second finite element coefficient vector of the node;

[0133] h eT represents the transpose of the film thickness vector; N eT represents the transpose of the node pressure vector;

[0134] f represents the pressure square; k1 represents the quality coefficient; δ i Indicates the throttle position;

[0135] μ s Indicates the throttling ratio; m s represents the mass flow rate of the sth throttle hole; λ represents the number of bearings.

[0136] By solving the above discrete equations, the downwind pressure P of each throttle hole can be calculated: d , substitute into formula (2) in step S1 to calculate the mass flow rate m of each throttle hole in the orifice mass flow model FEM , and the mass flow rate m FEMThe size of is related to the bearing speed, air film thickness and throttle hole size.

[0137] Step S3, adjusting the mass flow coefficient of the throttle mass flow model according to the mass flow correction equation so that the numerical relationship between the mass flow of each throttle in the simulation model and the mass flow of each throttle in the throttle mass flow model meets the convergence condition.

[0138] Specifically, in order to obtain the mass flow correction equation, the present invention introduces a dimensionless quantity of air film change to characterize the change in the circumferential air film thickness Δh, which has the following expression:

[0139]

[0140] Where, h0 represents the average air film thickness; represents the dimensionless gas film thickness;

[0141] h(o P ) represents the air film thickness at the throttle hole.

[0142] The mass flow coefficient of the orifice with different speeds and eccentricities is calculated, and the flow coefficient curve is plotted with the mass flow coefficient as the ordinate and the speed as the abscissa. Furthermore, combined with the change in air film thickness Δh, the mass flow coefficient curve of the entire dynamic and static pressure air bearing in the circumferential direction is fitted to derive the growth / decline rate under different air film changes, thereby obtaining the mass flow correction equation C d , the expression is:

[0143]

[0144] Among them, C d1 is the mass flow correction equation when the air film thickness increases along the speed direction of the dynamic and static pressure air bearing;

[0145] C d2 is the mass flow correction equation when the air film thickness decreases along the speed direction of the dynamic and static pressure air bearing;

[0146] Δh is the change in the circumferential air film thickness, and h is the air film thickness;

[0147] δ is the depth of the pressure equalizing groove; d is the diameter of the throttle hole, and w is the angular velocity;

[0148] fac is a function related to the change of the air film thickness in the circumferential direction of the dynamic and static pressure air bearing fitted by the fluid dynamics method and the finite difference method.

[0149] by Figure 2Taking the throttling hole shown as an example, the mass flow coefficient of the second throttling hole 2, the third throttling hole 3, the fourth throttling hole 4 and the fifth throttling hole 5 is corrected using formula (1-1); the mass flow coefficient of the seventh throttling hole 7, the eighth throttling hole 8, the ninth throttling hole 9 and the tenth throttling hole 10 is corrected using formula (1-2), and there is no need to correct the first throttling hole 1 and the sixth throttling hole 6.

[0150] Furthermore, by fitting the bearing data calculated by computational fluid dynamics and the mass flow data calculated by finite difference method, we can obtain the approximate equations of function fac1 and function fac2 changing with the single coefficient Δh:

[0151]

[0152] Therefore, the mass flow correction equation can be expressed as:

[0153]

[0154] Figure 4 The flow chart of iterating the mass flow coefficient of the orifice mass flow model in step S3 of this embodiment to obtain the final mass flow coefficient is shown, including the following steps:

[0155] Step S31, calculating the mass flow of each throttle hole in the simulation model by computational fluid dynamics method; calculating the mass flow of each throttle hole in the throttle hole mass flow model by finite difference method.

[0156] Step S32, setting the rotation speed, eccentricity and initial mass flow coefficient of the throttle mass flow model according to the structural parameters of the dynamic and static pressure air bearing;

[0157] Step S33: Determine the mass flow rate m of each throttle hole in the simulation model CFD and the mass flow rate m of each orifice in the orifice mass flow model FEM Whether the numerical relationship of meets the convergence condition:

[0158]

[0159] If the convergence condition is not met, the initial mass flow coefficient of each throttle mass flow model is iterated according to the mass flow correction equation (1) until the convergence condition is met.

[0160] At this time, the mass flow coefficient of the throttle hole mass flow model is the final mass flow coefficient of the dynamic and static pressure air bearing.

[0161] In summary, the present invention provides a method for calculating the mass flow coefficient of a dynamic and static pressure air bearing, which can realize rapid calculation of the flow coefficient of a dynamic and static pressure air bearing under any structural throttle hole and rotation speed. It has the characteristics of high calculation accuracy, closer to the actual situation, and suitable for air bearings of different configurations. It realizes efficient and accurate calculation and correction of the flow coefficient of a dynamic and static pressure air bearing.

[0162] Example 2

[0163] The present invention also provides an apparatus embodiment that is consistent with the above embodiment, which is used to implement the method steps described in the above embodiment. The explanation based on the same name meaning is the same as the above embodiment, and has the same technical effect as the above embodiment, which will not be repeated here.

[0164] like Figure 5 As shown, the present invention discloses a device for calculating mass flow coefficient of a dynamic and static pressure air bearing, comprising:

[0165] The simulation model mass flow calculation unit 101 is used to establish a simulation model of the dynamic and static pressure air bearing based on the computational fluid dynamics method according to the structural parameters and rotation speed of the dynamic and static pressure air bearing, and calculate the mass flow of each throttle hole in the simulation model using the computational fluid dynamics method.

[0166] The throttle mass flow calculation unit 102 is used to construct a throttle mass flow model with a mass flow coefficient according to the structural parameters of the dynamic and static pressure air bearing, and calculate the mass flow of each throttle in the throttle mass flow model using a finite difference method.

[0167] The correction unit 103 adjusts the mass flow coefficient of the orifice mass flow calculation unit according to the mass flow correction equation so that the numerical relationship between the mass flow of each orifice in the simulation model and the mass flow of each orifice in the orifice mass flow model meets the convergence condition.

[0168] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to the various embodiments disclosed in the present invention. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some implementations as replacements, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0169] The units involved in the embodiments disclosed in the present invention may be implemented by software or hardware, wherein the name of a unit does not limit the unit itself in some cases.

Claims

1. A method for calculating the mass flow coefficient of a dynamic and static pressure air bearing, characterized in that: include: According to the structural parameters and rotation speed of the dynamic and static pressure air bearing, a simulation model of the dynamic and static pressure air bearing based on the computational fluid dynamics method is established, and the mass flow rate of each throttle hole in the simulation model is calculated by the computational fluid dynamics method; According to the structural parameters of the dynamic and static pressure air bearing, a throttle mass flow model with a mass flow coefficient is constructed, and the mass flow of each throttle in the throttle mass flow model is calculated by using a finite difference method; Adjusting the mass flow coefficient of the throttle mass flow model according to the mass flow correction equation so that the numerical relationship between the mass flow of each throttle in the simulation model and the mass flow of each throttle in the throttle mass flow model satisfies a convergence condition; The expression of the mass flow correction equation is: Among them, C d1 is the mass flow correction equation when the air film thickness increases along the speed direction of the dynamic and static pressure air bearing; C d2 is the mass flow correction equation when the air film thickness decreases along the speed direction of the dynamic and static pressure air bearing; Δh is the change in circumferential air film thickness, and h is the air film thickness; δ is the depth of the pressure equalizing groove; d is the diameter of the throttle hole, and w is the angular velocity; fac is a function related to the variation of the air film thickness in the circumferential direction of the dynamic and static pressure air bearing fitted by the fluid dynamics method and the finite difference method.

2. The method according to claim 1, characterized in that The method of establishing a simulation model of the dynamic and static pressure air bearing based on a computational fluid dynamics method and calculating the mass flow rate of each throttle hole in the simulation model by using the computational fluid dynamics method comprises: uniformly arranging a plurality of throttle holes along the circumference of the dynamic and static pressure air bearing and solving the Navier-Stokes equations in three-dimensional space by using FLUENT software; The method of solving the Navier-Stokes equations in three-dimensional space by using FLUENT software includes: Select the standard k-ε turbulence model; Set boundary conditions: The atmospheric pressure outside the bearing is 1×10 5 Pa, supply pressure is 6×10 5 Pa, the speed of the moving boundary is 0-150,000r / min; Grid division: 300 grids are evenly divided along the circumference of the dynamic and static pressure air-floating axis, 120 grids are evenly divided along the axial direction, and 8 grids are evenly divided along the air film thickness direction; The SIMPLE algorithm is selected for solution. The convergence condition of the SIMPLE algorithm is RNG<10 -6 .

3. The method according to claim 1, characterized in that The expression of the throttle mass flow model with flow coefficient is: Among them, ψ s is the dimensionless coefficient, C d is the flow coefficient; d is the diameter of the throttle hole, P s is the supply pressure, ρ a is the density of air at atmospheric pressure.

4. The method according to claim 1, characterized in that The method of calculating the mass flow of each throttle hole in the throttle hole mass flow model by using the finite difference method includes: The Reynolds equation is used to express the relationship between the thickness of the air film on the dynamic and static pressure air bearing and the gas pressure distribution; Applying the weighted residual method to obtain a weak solution to the Reynolds equation; Dividing the plane calculation flow domain formed by the deployment of the air film into a plurality of units and corresponding nodes, and using the finite element method to obtain a discrete equation for a weak solution of the Reynolds equation; The discrete equation is solved to obtain the downwind pressure value of each throttle hole, and the mass flow of each throttle hole in the throttle hole mass flow model is obtained according to the downwind pressure value of each throttle hole.

5. The method according to claim 1, characterized in that The step of adjusting the mass flow coefficient of the throttle mass flow model according to the mass flow correction equation so that the mass flow of each throttle in the simulation model and the mass flow of each throttle in the throttle mass flow model meet the convergence condition includes: According to the obtained mass flow of each throttle hole in the simulation model, an initial flow coefficient of the throttle hole mass flow model is set, and the mass flow of each throttle hole in the throttle hole mass flow model is calculated by using a finite difference method; Determining whether a numerical relationship between the mass flow rate of each throttle hole in the simulation model and the mass flow rate of each throttle hole in the throttle hole mass flow model satisfies a convergence condition; If the convergence condition is not met, iterating the initial mass flow coefficient of the orifice mass flow model according to the mass flow correction equation; The mass flow coefficient when the convergence condition is met is the mass flow coefficient of the dynamic and static pressure air bearing.

6. The method according to claim 5, characterized in that The expression of the convergence condition is: Among them, m CFD is the mass flow rate of each throttle hole in the simulation model; m FEM is the mass flow rate of each throttle hole in the throttle hole mass flow model.

7. The method according to claim 2, characterized in that The three Navier-Stokes equations in dimensional space, including: The enhanced wall equation is added to the standard k-ε turbulence model to improve the calculation accuracy.

8. The method according to claim 4, characterized in that The expression of the discrete equation of the weak solution of the Reynolds equation is: Wherein, i=1, 2, ..., q; Δ e represents the calculation boundary; e represents the node parameter; h represents the film thickness; N represents the node coefficient Represents the horizontal normalization coefficient; Represents the normalization coefficient in the vertical direction; represents dimensionless speed; c i represents the third finite element coefficient at the i-th node; b i represents the second finite element coefficient at the i-th node; c eT represents the transpose of the third finite element coefficient vector of the node; b eT represents the transpose of the second finite element coefficient vector of the node; h eT represents the transpose of the film thickness vector; N eT represents the transpose of the node pressure vector; f represents the pressure square; k1 represents the quality coefficient; δ i Indicates the throttle position; μ s Indicates the throttling ratio; m s represents the mass flow rate of the sth throttle hole; λ represents the number of bearings.

9. The method according to claim 1, characterized in that: The expressions of function fac1 and function fac2 are: Wherein, Δh is the change in circumferential air film thickness.

10. A device for calculating mass flow coefficient of dynamic and static pressure air bearing, characterized in that: Used to implement the method according to any one of claims 1 to 9, comprising: A simulation model mass flow calculation unit is used to establish a simulation model of the dynamic and static pressure air bearing based on a computational fluid dynamics method according to the structural parameters and rotation speed of the dynamic and static pressure air bearing, and calculate the mass flow of each throttle hole in the simulation model using the computational fluid dynamics method; A throttle mass flow calculation unit is used to construct a throttle mass flow model with a mass flow coefficient according to the structural parameters of the dynamic and static pressure air bearing, and calculate the mass flow of each throttle in the throttle mass flow model by using a finite difference method; The correction unit adjusts the mass flow coefficient of the throttle mass flow calculation unit according to the mass flow correction equation so that the numerical relationship between the mass flow of each throttle in the simulation model and the mass flow of each throttle in the throttle mass flow model meets the convergence condition.

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