A method for designing a non-circular radial gas dynamic bearing stator inner profile

Abstract

The application provides a design method of a non-circular radial gas dynamic pressure bearing stator inner contour, belonging to the field of mechanical design, and setting a power or adding a correction coefficient to a cosine function of an eccentric angle theta in a lubricating gas film thickness equation based on a current circular radial gas dynamic pressure bearing, or setting a power and adding a correction coefficient to the cosine function of the eccentric angle theta, to obtain a design basis of a non-circular radial gas bearing stator inner contour, and the non-circular radial gas dynamic pressure bearing can be processed on a silicon-based material by using micro-nano etching technology, such as electron beam lithography or ion beam lithography, and then industrial application is realized. The application can improve bearing gas film pressure and carrying capacity.

Description

Technical Field

[0001] This invention belongs to the field of mechanical design, specifically relating to a design method for the inner contour of a non-circular radial gas hydrodynamic bearing stator. Background Technology

[0002] Gas bearings (also known as air-bearing bearings) are sliding bearings that use gas as lubricant. Air is the most commonly used lubricant, but depending on the specific circumstances, gases such as nitrogen, oxygen, hydrogen, helium, or carbon dioxide can also be used as lubricants in gas bearings. Gas hydrodynamic bearings do not require an external pressure source to generate a pressure film; the pressure film is generated during the high-speed relative motion between the two surfaces, thus providing load-bearing capacity. Currently, gas hydrodynamic bearings include rigid pneumatic bearings, foil gas hydrodynamic bearings, tilting pad gas hydrodynamic bearings, and multi-leaf cantilever gas hydrodynamic bearings, among others.

[0003] Regardless of the type of gas hydrodynamic bearing, they all follow the basic equations of gas lubrication, mainly including the Navier-Stokes equation or Reynolds equation, the equation of state of the lubricant (density and viscosity equations), the continuity equation, the energy equation, and the surface elastic deformation equation. Among these, the Reynolds equation and its variations under various conditions are the most widely used.

[0004] Assuming the miniature gas bearing has a large length-to-diameter ratio, the lubricating gas film pressure distribution can be simplified to a one-dimensional form, meaning that only the gas film pressure distribution along the bearing circumference needs to be solved. Therefore, the first-order modified Reynolds equation considering the rarefaction effect of the lubricating gas is:

[0005]

[0006] Where θ is the offset angle in rad; p is the film pressure in Pa; h is the lubricating film thickness in μm; λ is the mean free path of the gas in μm; μ is the gas dynamic viscosity coefficient in Pa·s; r is the rotor radius in μm; and ω is the rotor angular velocity in rad / s.

[0007] For traditional circular bearings, the schematic diagram of the bearing rotor and stator is as follows: Figure 1 As shown, the bearing clearance unfolded diagram is as follows: Figure 2 As shown, its lubricating film thickness equation is:

[0008] h=C0(1+εcosθ) (2)

[0009] Where C0 = Rr is the average radial clearance between the stator and rotor, R is the inner contour radius of the stator in μm; ε is the bearing eccentricity; h max Maximum atmospheric film thickness, h min It is the minimum air film thickness.

[0010] Film pressure and load capacity are key parameters for evaluating the static performance of bearings, and the shape of the stator's inner profile can significantly alter their magnitudes. Therefore, to improve the film pressure and load capacity of bearings, it is necessary to propose a new stator inner profile design method and verify the correctness and feasibility of this method. Summary of the Invention

[0011] To address the aforementioned technical problems, this invention proposes a design method for the inner contour of a non-circular radial gas bearing stator.

[0012] To achieve the above objectives, the present invention adopts the following technical solution:

[0013] A design method for the inner profile of a non-circular radial gas hydrodynamic bearing stator involves setting a power or adding a correction coefficient to the sine and cosine functions of the offset angle θ in the lubrication film thickness equation based on the current circular radial gas hydrodynamic bearing, or setting both a power and a correction coefficient, to obtain the lubrication film thickness equation based on the non-circular radial gas hydrodynamic bearing, thereby designing the inner profile of the non-circular radial gas bearing stator.

[0014] The equation for the lubricating film thickness upon which the current circular radial gas hydrodynamic bearing is based is:

[0015] h=C0(1+εcosθ) (2)

[0016] Where h is the thickness of the lubricating gas film in μm; C0 = Rr is the average radial clearance between the stator and rotor, R is the inner contour radius of the stator in μm, r is the radius of the rotor in μm; ε is the bearing eccentricity; θ is the offset angle in rad.

[0017] Furthermore, the equation for the lubricating film thickness upon which the non-circular radial gas hydrodynamic bearing is based is:

[0018] h=C0[1+ε(cosθ) m (3)

[0019] Where m is a power of cosθ, 1≤m≤5.

[0020] Furthermore, the equation for the lubricating film thickness upon which the non-circular radial gas hydrodynamic bearing is based is:

[0021] h=C0[1+εcosθ+a(|sinθ|) b (4)

[0022] Where a is (|sinθ|). b The coefficient of is 0 ≤ a ≤ 0.5; b is the power of |sinθ|, 2 ≤ b ≤ 4.

[0023] Beneficial effects:

[0024] This invention proposes a design method for the stator inner contour of a non-circular radial gas hydrodynamic bearing by setting a power power, adding a correction coefficient, or both, to the sine and cosine functions of the offset angle θ in the lubrication film thickness equation (Equation (2)) upon which the circular radial gas hydrodynamic bearing is based. Based on this design method, the non-circular radial gas hydrodynamic bearing is fabricated on a silicon-based material using micro / nano etching technology (electron beam lithography or ion beam lithography), thereby enabling industrial applications. Numerical calculations show that the film pressure and load-bearing capacity of the non-circular radial gas bearing are significantly higher than those of the circular radial gas bearing, providing a design basis for developing high-performance gas hydrodynamic bearings. Attached Figure Description

[0025] Figure 1 A schematic diagram of the bearing rotor and stator (inner contour of the circular stator);

[0026] Figure 2 This is a diagram showing the bearing clearance development (inner contour of a circular stator);

[0027] Figure 3 Schematic diagram of bearing rotor and stator (Implementation Case 1, taking m = 1, 3, 5 as an example);

[0028] Figure 4 The bearing clearance development diagram (Implementation Case 1, taking m = 1, 3, 5 as an example);

[0029] Figure 5 For the distribution of lubricating gas film pressure (Implementation Case 1, taking mm=1,3,5 as an example);

[0030] Figure 6 Schematic diagram of bearing rotor and stator (Implementation Case 2, taking b=3, a=0.1, 0.3, 0.5 as an example);

[0031] Figure 7 The bearing clearance diagram is shown in Implementation Case 2, with b=3 and a=0.1, 0.3, 0.5 as an example.

[0032] Figure 8 Schematic diagram of bearing rotor and stator (Implementation Case 2, taking a=0.5, b=2,3,4 as an example);

[0033] Figure 9 The bearing clearance development diagram is shown in Implementation Case 2, with a = 0.5 and b = 2, 3, 4 as an example.

[0034] Figure 10 For the distribution of lubricating gas film pressure (Implementation Case 2, taking b=3, a=0.1, 0.3, 0.5 as an example);

[0035] Figure 11 The distribution of lubricating gas film pressure (Implementation Case 2, taking a=0.5, b=2,3,4 as an example). Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0037] The present invention provides a design method for the inner contour of the stator of a non-circular radial gas hydrodynamic bearing by setting the sine and cosine functions of the offset angle θ in the lubrication film thickness equation (Equation (2)) on which the circular radial gas hydrodynamic bearing is based, or by adding a correction coefficient, or by setting both a power factor and adding a correction coefficient, so as to obtain the design basis for the inner contour of the stator of the non-circular radial gas bearing.

[0038] Implementation Case 1:

[0039] Its lubricating film thickness equation is:

[0040] h=C0[1+ε(cosθ) m (3)

[0041] Where m is a power of cosθ, 1≤m≤5. When m=1, equation (3) is reduced to the air film thickness equation (equation (2)) based on the inner contour of the circular stator.

[0042] For a bearing designed according to equation (3), the schematic diagram of the bearing rotor and stator (taking m=3 as an example) is as follows. Figure 3 As shown, the bearing clearance development diagram (taking m=3 as an example) is as follows. Figure 4 As shown.

[0043] Equation (1) is numerically solved using Newton's iteration method. Here, the thickness of the lubricating gas film is controlled by equation (3). The lubricating gas is air, the ambient temperature is 1100K, the rotor radius is r=2000μm, and the rotor speed is N=3×10 6 rpm and eccentricity ε = 0.9.

[0044] When the power of cosθ is m = 1, 3, 5, the gas film pressure distribution during the extrusion process is as follows: Figure 5 As shown. Here, m = 1 is the pressure distribution in equation (2). It can be seen that as m increases, the pressure distribution of the lubricating gas film gradually increases. Furthermore, it can be proven that the inner contour shape of the non-circular gas dynamic bearing stator designed according to equation (3) has obvious advantages.

[0045] Implementation Case 2:

[0046] The equation for the thickness of the lubricating gas film is:

[0047] h=C0[1+εcosθ+a(|sinθ|) b (4)

[0048] Where a is the coefficient of (|sinθ|)b, 0≤a≤0.5; b is the power of |sinθ|, 2≤b≤4. When a=0, equation (4) is reduced to equation (2) based on the inner contour of the circular stator.

[0049] For a bearing designed according to equation (4), a schematic diagram of the bearing rotor and stator is shown below, taking b = 3 and a = 0, 0.1, 0.3, 0.5 as an example. Figure 6 As shown, the bearing clearance development diagram is as follows, taking b=3 and a=0, 0.1, 0.3, 0.5 as examples. Figure 7 As shown, a schematic diagram of the bearing rotor and stator with a = 0.5 and b = 2, 3, 4 is given. Figure 8 As shown, the bearing clearance development diagram with a = 0.5 and b = 2, 3, 4 is as follows. Figure 9 As shown.

[0050] Equation (1) is numerically solved using Newton's iteration method. Here, the thickness of the lubricating gas film is controlled by equation (4), the lubricating gas is air, the ambient temperature is 1100K, the rotor radius is r=2000μm, and the rotor speed is N=3×10 6 rpm and eccentricity ε = 0.9.

[0051] When (|sinθ|) b When the coefficient a = 0, 0.1, 0.3, 0.5, the air film pressure distribution during the extrusion process is as follows: Figure 10 As shown. Here, a = 0 represents the pressure distribution in equation (2). It can be seen that as a increases, the pressure distribution of the lubricating gas film gradually increases. When the power of |sinθ| is b = 2, 3, 4, the gas film pressure distribution during the extrusion process is as follows. Figure 11 As shown, we can see that as b increases, the lubricating gas film pressure distribution also gradually increases. Whether a or b increases, the gas film pressure they generate is much greater than the gas film pressure generated by the inner contour of the circular stator. This proves that the inner contour shape of the non-circular gas dynamic bearing stator designed according to equation (4) has obvious advantages.

[0052] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing the inner contour of a non-circular radial gas hydrodynamic bearing stator, characterized in that, The offset angle in the lubricating film thickness equation used for current circular radial gas hydrodynamic bearings By setting the power of the sine and cosine functions, or adding a correction coefficient, or both, the equation for the thickness of the lubricating gas film on which the non-circular radial gas hydrodynamic bearing is based is obtained, thereby designing the inner profile of the stator of the non-circular radial gas bearing. The equation for the lubricating film thickness upon which the current circular radial gas hydrodynamic bearing is based is: （2） in, This is the thickness of the lubricating gas film, measured in μm. It is the average radial clearance between the stator and rotor. It is the inner contour radius of the stator, in μm. This is the rotor radius, in μm; It is the bearing eccentricity; It is the offset angle, and the unit is rad; The equation for the lubricating film thickness upon which the non-circular radial gas hydrodynamic bearing is based is: （3） in, yes powers of, .

2. The design method for the inner contour of a non-circular radial gas hydrodynamic bearing stator according to claim 1, characterized in that, The equation for the lubricating film thickness upon which the non-circular radial gas hydrodynamic bearing is based is: （4） in, yes coefficient, ; yes powers of, .

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