A similarity method for obtaining gas film characteristics of dynamic pressure motor of three-float gyroscope

Abstract

The application discloses a similarity method for obtaining gas film characteristics of a three-float gyroscope dynamic pressure motor, and takes an internal dynamic pressure motor of a certain gyroscope as an example. Firstly, the shape characteristics and internal structure features of the motor are analyzed, the distribution area of gas is determined according to the structure features, then the similarity model of gas flow in the semi-spherical dynamic pressure motor across scales and small gaps is established by combining the computational dynamics method and the similarity theory, and the aerodynamic characteristics such as the gas pressure and flow in the bearing gap of the dynamic pressure motor are obtained by model calculation. The application can accurately obtain the gas film characteristic parameters of the dynamic pressure motor by solving the gas film flow similarity model without complex measurement and calculation. The method is characterized by combining the computational fluid dynamics method and the similarity theory and used for the gas film characteristic analysis of the three-float gyroscope dynamic pressure motor, and provides a theoretical basis for the optimized design and fault analysis of the dynamic pressure motor.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of precision characteristic analysis of aviation navigation instruments, and particularly relates to a similarity method for obtaining gas film characteristics of a three-floating gyro dynamic pressure motor. BACKGROUND

[0002] The hemispherical dynamic pressure motor has the advantages of equal rigidity, low noise, long service life and high precision, and is an ideal choice for generating gyro effect for the electro-mechanical gyro instrument. Figure 2 As shown in the general structure of the hemispherical dynamic pressure motor,

[0003] In the design process of the hemispherical dynamic pressure motor, the gap size, spiral groove type, groove depth, groove number and other parameters need to be designed according to the load capacity, gas film stiffness and other performances to be obtained; meanwhile, in the use process of the motor, the gas flow state, heat generation, heat dissipation and other performances in the gap are expected to be known for comprehensive evaluation of the motor performance. For this purpose, on the one hand, the performances can be measured through tests, but the tests have the disadvantages of high cost, insufficient comprehensive data and many external interference factors, and therefore a desired method is to achieve through numerical calculation or simulation. In order to obtain good lubrication performance and load capacity, the gas film gap and spiral groove depth of the hemispherical dynamic pressure motor are generally in the micron level, and the spherical surface size is generally in the 10mm level. In order to achieve effective numerical simulation of fluid flow in such a cross-scale model, the discrete grid needs to be at least in the 10 9 level, and such calculation in the 10 SUMMARY

[0004] The technical problem to be solved by the application is to solve the problem of difficulty in analyzing the gas film characteristics in the gap of the three-floating gyro dynamic pressure motor in the prior art, and to provide a similarity method for obtaining the gas film characteristics of the three-floating gyro dynamic pressure motor. The method has the advantage that the model equivalence is performed on the fluid flow model calculation of the cross-scale model of the dynamic pressure motor by using the similarity criterion, and the gas film characteristic parameters of the dynamic pressure motor can be accurately obtained by solving the gas film flow similarity model without complex measurement and calculation, thereby providing a theoretical basis for the optimal design and fault analysis of the dynamic pressure motor.

[0005] The technical scheme adopted by the application is a similarity method for obtaining the gas film characteristics of a three-floating gyro dynamic pressure motor, and the implementation steps are as follows:

[0006] Step one, preparation: analyze the working conditions, shape characteristics and internal structure characteristics of the dynamic pressure motor of the three-float gyroscope, and obtain the structural size parameters of the dynamic pressure motor;

[0007] Step two, establish the Reynolds equation of the original model and the similar model fluid: establish the Reynolds equation of the original system model describing the internal gas flow of the dynamic pressure motor and the Reynolds equation of the similar system model, so as to determine the similarity criterion of the two systems and the similarity ratio of each physical quantity;

[0008] Step three, calculate the similarity criterion and the similarity ratio of the physical quantity: according to the equation established in step two, for the general flow of fluid, the similarity of the two systems also needs to meet other general similarity criteria, including Reynolds number Re, Euler number Eu, Mach number Ma, Weber number We, Froude number Fr and Strouhal number Sr. According to these similarity criteria, the numerical proportional relationship of fluid density, fluid viscosity, fluid velocity, fluid pressure and lubrication gap before and after similarity is determined;

[0009] Step four, calculate the structural parameters of the similar model: according to the working conditions and structure of the three-float gyroscope dynamic pressure motor obtained in step one, determine the structural size parameter ratio of the dynamic pressure motor similar model that needs to be enlarged;

[0010] Step five, establish the simulation model after similarity: according to the similarity ratio numerical relationship of fluid density, fluid viscosity, fluid velocity, fluid pressure and lubrication gap obtained in step three and the structural size parameters after enlargement, determine the specific numerical value of each physical quantity of the dynamic pressure motor similar model.

[0011] Step six, solution calculation: according to the similar model determined in step four, use the CFX module in ANSYS / WB to carry out numerical calculation simulation, so as to obtain the dynamic characteristics of the gas in the gap of the dynamic pressure motor.

[0012] Further, in step two, the similarity criterion is used to establish the Reynolds equation of the similar model according to the Reynolds equation of the original dynamic pressure motor system model; the Reynolds equation of the gas flow of the original dynamic pressure motor system is

[0013]

[0014] The Reynolds equation of the gas flow of the similar system is

[0015]

[0016] Wherein,

[0017]

[0018] In the formula, λ is the similarity ratio of each physical quantity in the two systems, ρ is the fluid density, μ is the fluid viscosity, u is the fluid velocity, h is the lubrication gap, and p is the fluid pressure. , respectively, are the partial derivatives of the terms in parentheses with respect to the independent variables x and y.

[0019] Furthermore, in step three, for the hydrodynamic lubrication problem of the hemispherical motor, since there is no surface tension of the two-phase fluid, We can be ignored; since it is a steady flow, Sr can be ignored; since the influence of gravity is ignored, Fr can be ignored; the boundary condition λu=1, Ma is self-satisfied; the gas inlet and outlet are open pressure boundaries, Eu is self-satisfied; therefore, only the Re similarity criterion still needs to be satisfied:

[0020]

[0021] This determines the similarity ratio of each physical quantity:

[0022] λ p =1; λ u =1;

[0023] Furthermore, in step four, the lubrication clearance needs to be enlarged according to the operating conditions and structural characteristics of the dynamic pressure motor, and the enlargement ratio of the lubrication clearance is set to λ. h .

[0024] Furthermore, in step five, the amplification ratio λ of the lubrication gap is set. h And from the similarity ratio of each quantity, the values ​​of each physical quantity of the similar model of the dynamic pressure motor can be obtained as follows:

[0025] h'=λ h h; p' = p; u' = u;

[0026] Furthermore, in step six, the similarized 3D model is imported into ANSYS / WB software. The CFX module is used to set the rotor surface rotational speed ω', the gas inlet and outlet are set as open boundaries, and the remaining surfaces are set as non-slip walls. Simultaneously, the fluid viscosity μ' and density ρ' are given according to their respective similarity ratios. The simulation model is calculated, and the convergence criterion is set to RMS < 1E-5. The calculation results are obtained, and the velocity field distribution of the gas within the gap of the dynamic pressure motor and the forces and moments generated by the airflow on the wall are acquired using the CFX-POST module.

[0027] The advantages of this invention compared to the prior art are:

[0028] Firstly, the application does not need expensive experimental equipment and professional experimenters, effectively reducing the cost of obtaining the gas film characteristics of the three-floating gyro dynamic pressure motor; secondly, the current calculation method of the gas film characteristics of the dynamic pressure motor needs to simulate calculation according to the real model size parameters, and has very high requirements for computer operation capacity, and the application can greatly reduce the requirements for computer operation capacity. Finally, since the application uses the similarity method, the gas film characteristics of the three-floating gyro dynamic pressure motor of any different size can be obtained. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 The flow chart of the method of the application is shown in the figure;

[0030] Figure 2 The schematic diagram of the hemispherical dynamic pressure motor in the application is shown in the figure;

[0031] Figure 3 The similar dynamic pressure motor gap gas domain model in the application is shown in the figure;

[0032] Figure 4 The similar dynamic pressure motor gap gas domain grid discrete model in the application is shown in the figure;

[0033] Figure 5 The calculation result of the similar dynamic pressure motor gap gas domain in the application is shown in the figure. DETAILED DESCRIPTION

[0034] The following will take a gyro internal dynamic pressure motor as an example to make a detailed description of the implementation of the method of the application in combination with the drawings, but the protection scope of the application is not limited to the following examples:

[0035] As shown in the figure, the specific implementation process of the three-floating gyro dynamic pressure motor gas film characteristic analysis method of the application is as follows: Figure 1

[0036] Step one, preparation. Determine the working condition of the three-floating gyro dynamic pressure motor, including the dynamic pressure motor rotor speed and working temperature, the dynamic pressure motor size parameters, including the motor stator hemisphere radius, the hemisphere and bowl gap and the spiral groove depth, to provide necessary parameter support for the establishment of the fluid flow Reynolds equation.

[0037] Step two, establish the original model and the similar model fluid Reynolds equation. According to fluid mechanics, the Reynolds equation of the three-floating gyro dynamic pressure motor gap fluid dynamic pressure lubrication is established:

[0038]

[0039] In the formula, p is the fluid density, μ is the fluid viscosity, u is the fluid velocity, h is the lubrication gap, and p is the fluid pressure.

[0040] ​If there is another model similar to the original dynamic pressure motor, it also satisfies the Reynolds equation:

[0041]

[0042] Wherein:

[0043]

[0044] In the formula, λ is the similarity ratio of each physical quantity in the two systems.

[0045] Therefore, the similar model Reynolds equation is expressed as:

[0046]

[0047] If the similar system and the original system describe the same fluid carrying capacity and flow state, the following conditions need to be met:

[0048]

[0049] Thus, the similarity boundary conditions of the established similar model can be determined:

[0050] λ p = 1; λ u = 1

[0051] Therefore:

[0052] λ μ = λ h 2

[0053] Step three, calculate the similarity criterion and the similarity ratio of the physical quantity. For general fluid flow, the similar system Reynolds equation and the original system also need to meet several other general similarity criteria. The general similarity criteria of fluid flow mainly include Reynolds number Re (representing viscous force), Euler number Eu (representing pressure), Mach number Ma (compressibility measure), Weber number We (representing surface tension), Froude number Fr (representing gravity), Strouhal number Sr (time correlation), etc.

[0054] For the dynamic pressure lubrication problem of the hemispherical motor discussed in the present application, there is no surface tension of two-phase fluid, We can not be considered; for steady flow, Sr can not be considered; the influence of gravity can be ignored, Fr can not be considered; the boundary condition λu = 1, Ma is satisfied automatically; the gas outlet and inlet are open pressure boundary, Eu is satisfied automatically. Therefore, only the Re similarity criterion needs to be met:

[0055]

[0056] Therefore:

[0057]

[0058] Accordingly, the similar ratio of each physical quantity in the two systems can be obtained:

[0059] λ p = 1; λ u = 1;

[0060] Step four, calculating the similar model structure parameters. According to the working condition and structure of the three-float gyroscope obtained in step one, the structure size parameter ratio of the dynamic pressure motor similar model needs to be enlarged; according to the working condition and structure characteristics of the dynamic pressure motor, the size of the lubrication gap needs to be enlarged, and the lubrication gap is set to be enlarged by λ h .

[0061] Step five, establishing the simulation model after similarity. The gap h' of the dynamic pressure motor similar model is determined, and other physical quantity specific values are obtained, including gas density, viscosity, pressure, and gas flow rate. The specific calculation method is as follows:

[0062] h' = λ h h; p' = p; u' = u;

[0063] The ball bowl radius r b ' and the spiral groove depth d' of the dynamic pressure motor similar model are respectively:

[0064] r w ' = r b + λ h h

[0065] d' = λ h d

[0066] Wherein: r b is the stator hemisphere radius of the original dynamic pressure motor model, m; d is the spiral groove depth, m.

[0067] At the same time, in order to meet the similar condition u' = u, there is:

[0068]

[0069] Wherein: ω' and ω are the rotor speeds of the similar model and the original model respectively, rad / s.

[0070] Step six, solving calculation. According to the similar model determined in step four, the CFX module in ANSY / WB is used to carry out numerical calculation simulation, so as to obtain the dynamic characteristics of the gas in the gap of the dynamic pressure motor.

[0071] The similar three-dimensional model is imported into ANSYS / WB software, CFX module is used to set the surface rotating speed ω' of the rotor, the gas inlet and outlet are set as open boundary, the rest surfaces are set as no-slip wall, and the fluid viscosity μ' and density ρ' are set according to the respective similarity ratio. The gas calculation domain model of the dynamic pressure motor gap is shown in Figure 3 , which is obtained by Boolean operation in AYSYS / WB software. The mesh unit size is set by meshing the gas calculation domain model, and the network discrete model of the gas calculation domain of the dynamic pressure motor gap is shown in Figure 4 . The simulation model is calculated, the convergence criterion RMS < 1E-5 is set, the calculation results are obtained, the velocity field distribution of the gas in the dynamic pressure motor gap and the force and torque generated by the gas flow on the wall are obtained in CFX-POST module, the calculation is run to convergence, and the flow state of the gas flow in the gap is shown in Figure 5 . It can be found that the gas flow rate at the groove is large.

[0072] The calculation results of λ h = 100 and λ h = 50 are extracted respectively, as shown in Table 1.

[0073] Table 1 Calculation results of different similarity ratios

[0074]

[0075] It can be seen that the maximum deviation of the calculation results of λ h = 100 and λ h = 50 is 6%, and the calculation results are basically not affected by the value of the similarity ratio, which shows that the established similarity model can better restore the original system, and the obtained gas flow characteristics can truly reflect the dynamic characteristics of the gas in the actual motor gap.

[0076] The above-described embodiments are only used to describe the preferred embodiments of the present application, and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements of the technical solutions of the present application made by those skilled in the art shall fall within the protection scope of the claims of the present application.

Claims

1. A similarity method for obtaining gas film characteristics of a dynamic pressure motor of a three-float gyroscope, characterized by The implementation steps are as follows: Step one, preparation: analyze the working condition, shape characteristics and internal structure characteristics of the dynamic pressure motor of the three-float gyroscope, and obtain the structure size parameters of the dynamic pressure motor; Step two, establish the original model and the similar model fluid Reynolds equation: establish the Reynolds equation of the original system model describing the internal gas flow of the dynamic pressure motor and the Reynolds equation of the similar system model, so as to determine the similarity criteria of the two systems and the similarity ratio of each physical quantity; Step three, calculate the similarity criterion and the similarity ratio of the physical quantity: according to the equation established in step two, for the general flow of fluid, the similarity of the two systems also needs to meet other general similarity criteria, including Reynolds number Re, Euler number Eu, Mach number Ma, Weber number We, Froude number Fr and Strouhal number Sr, according to these similarity criteria, the numerical proportional relationship of fluid density, fluid viscosity, fluid velocity, fluid pressure and lubrication gap before and after similarity is determined; Step four, calculate the structure parameters of the similar model: according to the working condition and structure of the three-float gyroscope dynamic pressure motor obtained in step one, determine the structure size parameter ratio of the dynamic pressure motor similar model that needs to be enlarged; Step five, establish the simulation model after similarity: according to the similarity ratio numerical relationship of fluid density, fluid viscosity, fluid velocity, fluid pressure and lubrication gap obtained in step three and the structure size parameter after enlargement, the specific numerical value of each physical quantity of the dynamic pressure motor similar model is determined; Step six, solve the calculation: according to the similar model determined in step four, the CFX module in ANSYS / WB is used to carry out numerical calculation simulation, so as to obtain the dynamic characteristics of the gas in the dynamic pressure motor gap; In step three, for the dynamic pressure lubrication problem of the hemispherical motor, there is no surface tension of two-phase fluid, We can not be considered; for steady flow, Sr can not be considered; ignoring the influence of gravity, Fr can not be considered; the boundary condition λu=1, Ma is satisfied automatically; the gas outlet and inlet are open pressure boundary, Eu is satisfied automatically; therefore, only Re similarity criterion needs to be met: From which the similarity ratio of each physical quantity is determined: In step two, according to the similarity criterion, the Reynolds equation of the similar model is established according to the Reynolds equation of the original dynamic pressure motor system model; the Reynolds equation of the gas flow of the original dynamic pressure motor system is The Reynolds equation of the gas flow of the similar system is Wherein, where λ is the similarity ratio of each physical quantity in the two systems, p is the fluid density, μ is the fluid viscosity, u is the fluid velocity, h is the lubrication gap, p is the fluid pressure, are the partial derivatives of each term in the brackets with respect to the independent variables x and y, respectively.

2. The similarity method for obtaining gas film characteristics of a dynamic pressure motor of a three-float gyroscope according to claim 1, characterized in that: In the fourth step, the lubrication gap is enlarged in size according to the working condition and structural characteristics of the dynamic pressure motor, and the enlargement ratio of the lubrication gap is λ h .

3. The similarity method for obtaining gas film characteristics of a dynamic pressure motor of a three-floated gyroscope according to claim 1, characterized in that: In step five, the magnification ratio λ of the lubrication gap is set h And the similar ratio of each dimension can get the value of each physical quantity of the similar model of the hydrodynamic motor:

4. The similarity method for obtaining gas film characteristics of a dynamic pressure motor of a three-floated gyroscope according to claim 3, characterized in that: In step six, the similar three-dimensional model is imported into ANSYS / WB software, the CFX module is used to set the rotor surface speed ω', the gas inlet and outlet are set as open boundary, the remaining surfaces are set as no-slip wall, and the fluid viscosity μ' and density ρ' are given according to the respective similarity ratio, the simulation model is calculated, the convergence criterion is set as RMS<1E-5, the calculation result is obtained, and the velocity field distribution of the gas in the dynamic pressure motor gap and the force and torque generated by the gas flow on the wall are obtained in CFX-POST module.

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