Static performance design method of high-speed oil-air lubricated hydrodynamic stepped thrust bearing

Abstract

The application relates to a high-speed oil-gas lubricated hydrodynamic step thrust bearing static performance design method, which comprises the following steps: establishing an oil-gas mixture viscosity and density expression; based on the oil-gas mixture viscosity and density expression, establishing a step thrust bearing Reynolds equation and an energy equation in a polar coordinate; solving the Reynolds equation and the energy equation to calculate the static performance of the thrust bearing; carrying out static performance parameter calculation of the oil-gas lubricated hydrodynamic thrust bearing under different oil-gas mixture gas contents and working rotating speeds to obtain the influence law of oil-gas lubrication on the static performance of the thrust bearing; and taking the friction torque, the bearing capacity and the temperature rise of the hydrodynamic thrust bearing as design targets, determining the structure parameters of the bearing through sensitivity analysis of the structure parameters on the static performance. The high-speed oil-gas lubricated hydrodynamic step thrust bearing static performance design method can greatly improve the static design precision of the bearing and shorten the design cycle.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bearing static performance design, and particularly relates to a static performance design method of a high-speed oil-gas lubricated dynamic pressure stepped thrust bearing. BACKGROUND

[0002] Oil-gas lubrication is a kind of lubrication mode using oil-gas mixture as lubricating medium, which has excellent lubrication performance such as low friction power consumption, low temperature rise and controllable static performance, and has broad application prospects in the field of dynamic pressure sliding bearing. However, there is no consensus on the design method of the static performance of high-speed oil-gas lubricated dynamic pressure sliding bearing, and the conclusions obtained by different methods are even contradictory. This is because the static performance calculation of high-speed oil-gas lubricated dynamic pressure sliding bearing must be completed first, and the viscosity model needs to be used for static performance calculation. The existing viscosity models have great differences and are only limited to the range of low shear rate, that is, due to the lack of viscosity parameters at high shear rate, the static design requirements of high-speed oil-gas lubricated dynamic pressure sliding bearing cannot be met.

[0003] At present, there are three kinds of viscosity models used for the calculation and structural design of the static performance of oil-gas lubricated dynamic pressure sliding bearing: 1) equivalent model, the equivalent density and viscosity model of oil-gas mixture are established by theoretical or experimental methods, and are substituted into the classical Reynolds equation to calculate the performance of oil-gas lubricated bearing. This method is direct and simple to solve the model. However, due to the difference in viscosity model, the obtained conclusions have great differences. 2) Two-fluid model, considering the momentum and energy transmission effect of gas phase and liquid phase on the interface, a generalized Reynolds equation considering the interface effect is established, and the calculation result shows that oil-gas lubrication can improve the bearing capacity. 3) Mixed theory, based on the interaction force between oil and gas bubbles, the classical Reynolds number equation is modified, and a non-Newtonian fluid lubrication model consistent with the motion law of oil-gas mixture is derived. It is found that oil-gas lubrication has a great influence on the pressure distribution of the bearing, but the size of the gas bubble has little effect on the pressure of the bearing. Overall, the static performance of dynamic pressure sliding bearing calculated by the above three viscosity models of oil-gas mixture has certain calculation error or does not completely match the theoretical calculation value and engineering practice. SUMMARY

[0004] In view of the deficiencies of the prior art, based on a large number of viscosity tests in the early stage, an oil-gas mixture viscosity model with large shear rate, gas content and temperature as independent variables is fitted, and an oil-gas mixture density model is given. Based on the viscosity and density models of oil-gas mixture, the Reynolds equation and energy equation of stepped thrust bearing in polar coordinates are established, and a static performance calculation theory and method of high-speed oil-gas lubricated dynamic pressure stepped thrust bearing is proposed. On this basis, a static performance design method of high-speed oil-gas lubricated dynamic pressure stepped thrust bearing is provided.

[0005] The technical solutions adopted by the present application are as follows:

[0006] A static performance design method of a high-speed oil-gas lubricated dynamic pressure stepped thrust bearing, comprising:

[0007] An oil-gas mixture viscosity and density expression is established;

[0008] A Reynolds equation and an energy equation of the dynamic pressure stepped thrust bearing under polar coordinates are established based on the oil-gas mixture viscosity and density expression;

[0009] The Reynolds equation and the energy equation are solved based on a difference method, and the static performance of the dynamic pressure stepped thrust bearing is calculated, including oil film thickness, friction torque, load capacity and temperature rise;

[0010] The static performance parameters of the oil-gas lubricated dynamic pressure thrust bearing under different oil-gas mixture gas contents and working speeds are calculated, and the influence law of oil-gas lubrication on the static performance of the thrust bearing is obtained;

[0011] Taking the friction torque, load capacity and temperature rise of the dynamic pressure stepped thrust bearing as design targets, the structure parameters of the bearing are determined through sensitivity analysis of the bearing structure parameters on the static performance.

[0012] Further technical solutions are as follows:

[0013] The oil-gas mixture viscosity and density expression is established, comprising:

[0014] Experimental data obtained by measuring the viscosity of the oil-gas mixture under a large shear rate are fitted based on the least square principle to obtain the viscosity expression of the oil-gas mixture:

[0015]

[0016] In the above formula, μ is the viscosity of the oil-gas mixture, T is the temperature, γ is the shear rate, a, b, c and d are parameters related to the gas content of the oil-gas mixture;

[0017] The equivalent dimensionless density of the oil-gas mixture is defined as:

[0018]

[0019] In the above formula, represents the dimensionless density, λ represents the ratio of the volume of the gas bubble to the volume of the pure oil, T is the temperature, p oil represents the pressure of the pure oil, σ represents the surface tension of the gas bubble, r air represents the radius of the gas bubble, which is obtained by the state of the gas bubble at the oil inlet.

[0020] The Reynolds equation is established by the flow balance relationship of the oil film flowing into and out of the finite volume, and the flow relationship expression is:

[0021]

[0022] In the above formula, the subscripted numbers represent the numbers of the four control volumes near a certain control node, Q r and Q θ respectively represent the radial mass flow and the circumferential mass flow of the control volume, and the expressions are as follows:

[0023]

[0024]

[0025] In the above two formulas, h represents the oil film thickness, p represents the oil film pressure, r represents the radial coordinate, theta represents the circumferential coordinate, omega is the bearing angular velocity; r1 and r2 are respectively the starting and ending radial coordinates of the finite volume, theta1 and theta2 are respectively the starting and ending circumferential coordinates of the finite volume; mu is the viscosity of the oil-gas mixture, and rho is the density of the oil-gas mixture.

[0026] The energy equation is as follows:

[0027]

[0028] In the above formula, c v represents the specific heat capacity, q r is the radial mass flow, q θ is the circumferential mass flow, p represents the oil film pressure, r is the radius, T m is the average temperature of the oil film in the temperature field, mu is the viscosity of the oil-gas mixture, and rho is the density of the oil-gas mixture.

[0029] The beneficial effects of the present application are as follows:

[0030] The present application fits an oil-gas mixture viscosity model with large shear rate, gas content and temperature as independent variables, and derives an oil-gas mixture density model. In particular, the oil-gas mixture viscosity model is a fitting mathematical expression based on a large number of viscosity test results, which can truly describe the viscosity characteristics of the oil-gas mixture. Based on the oil-gas mixture viscosity model and the density model, the Reynolds equation and the energy equation of the stepped thrust bearing under polar coordinates are established, which can greatly improve the calculation accuracy of the static performance of the high-speed oil-gas lubricated hydrodynamic stepped thrust bearing, and shorten the design cycle. On this basis, based on the sensitivity analysis of the key structural parameters, a reliable technical method is provided for the design of this type of bearing.

[0031] Other features and advantages of the present application will be set forth in the following description, and in part will become apparent to those skilled in the art from the description, or can be learned by practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 A dynamic pressure stepped thrust bearing structure diagram of an embodiment of the present application.

[0033] Figure 2 A mass flow diagram of a finite volume of a dynamic pressure stepped thrust bearing of an embodiment of the present application.

[0034] Figure 3 Changes of film thickness, friction torque and temperature rise of a bearing under oil-air lubrication with different gas contents of an embodiment of the present application with an external load.

[0035] Figure 4 Changes of bearing carrying capacity, bearing friction torque and bearing temperature rise of a bearing under oil-air mixture lubrication with a gas content of 26% of an embodiment of the present application with a stepped depth.

[0036] Figure 5 A flowchart of a design method of an embodiment of the present application. DETAILED DESCRIPTION

[0037] The specific embodiments of the present application are described below with reference to the accompanying drawings.

[0038] Referring to Figure 5 The present application provides a static performance design method of a high-speed oil-air lubricated dynamic pressure stepped thrust bearing, comprising:

[0039] An oil-air mixture viscosity and density expression is established;

[0040] A Reynolds equation and an energy equation of a dynamic pressure stepped thrust bearing under polar coordinates are established based on the oil-air mixture viscosity and density expression;

[0041] The Reynolds equation and the energy equation are solved based on a difference method, and the static performance of the dynamic pressure stepped thrust bearing is calculated, including oil film thickness, friction torque, carrying capacity and temperature rise;

[0042] The static performance parameters of the oil-air lubricated dynamic pressure thrust bearing under different gas contents and working speeds of the oil-air mixture are calculated, and the influence law of oil-air lubrication on the static performance of the thrust bearing is obtained;

[0043] The friction torque, carrying capacity and temperature rise of the dynamic pressure stepped thrust bearing are taken as design targets, the structure parameters of the bearing are determined through sensitivity analysis of the structure parameters of the bearing on the static performance, the high-speed oil-air lubricated dynamic pressure stepped thrust bearing design is completed, and the requirements of the static performance are met.

[0044] The technical solutions of the present application are further described below with specific embodiments.

[0045] Step 1: The viscosity expression under different gas contents is obtained by fitting the test data based on the least square principle using the test results of the oil-air mixture viscosity under a large shear rate:

[0046] The viscosity expression for an oil-gas mixture is:

[0047]

[0048] In the formula, μ is the viscosity of the oil-gas mixture, T is the temperature, γ is the shear rate, and a, b, c, d are parameters related to the gas content of the oil-gas mixture.

[0049] Using No. 20 machine oil as the liquid phase, the parameters a, b, c, and d vary with the gas content under different gas contents, as shown in Table 1.

[0050] Table 1. Viscosity Model Parameters for Oil-Gas Mixtures (No. 20 Machine Oil)

[0051]

[0052]

[0053] Define the equivalent dimensionless density of an oil-gas mixture:

[0054]

[0055] In the formula, ρ represents the dimensionless density, and ρ represents the density of the oil-gas mixture. oil ,m oil ,v oil Let m represent the density, mass, and volume of pure oil, respectively. air ,v air These represent the mass and volume of the bubble, respectively.

[0056] Introducing the bubble volume and oil volume ratio λ, the ideal gas equation, and the relationship between bubble pressure and surface tension:

[0057]

[0058]

[0059]

[0060] In the formula, λ represents the ratio of bubble volume to pure oil volume, and p air ,p oil The pressure inside the bubble and the pure oil is represented by R, which is a universal constant, and σ represents the surface tension of the bubble. air Indicates the bubble radius.

[0061] Substituting equations (3), (4), and (5) into equation (2) yields:

[0062]

[0063] Bubble radius r in formula (6) air The bubble state at the oil inlet needs to be obtained, i.e.:

[0064]

[0065] In the formula, r inlet ,p inlet ,T0 respectively represent the radius, pressure and temperature of the bubble in the oil-gas mixture at the oil inlet.

[0066] Step 2: Establish the Reynolds equation and energy equation of the dynamic pressure stepped thrust bearing in polar coordinates, and the bearing structure diagram is as shown in Figure 1 , Figure 1 In (a), the front view is shown, and the bearing includes a thrust pad 1 and a thrust disc 2, Figure 1 In (b), the Figure 1 In (a), the cross-sectional view of the A-A section is shown. The thrust disc 2 is provided with uniformly spaced groove areas 21 and platform areas 22 in the circumferential direction.

[0067] The bearing parameters are shown in Table 2:

[0068] Table 2: Parameter table of dynamic pressure stepped thrust bearing

[0069]

[0070]

[0071] Specifically includes:

[0072] The Reynolds equation of the dynamic pressure stepped thrust bearing of the steady-state, compressible fluid lubrication in polar coordinates can be established by the flow balance relationship of the fluid flowing into and out of the finite volume, and the flow relationship is as shown in Figure 2 , and the expression is:

[0073]

[0074] Wherein, the subscripts 1-4 represent the regions of the control volume, Q r and Q θ respectively represent the radial mass flow and circumferential mass flow of the control volume, and the expressions are:

[0075]

[0076]

[0077] In the formula, h represents the film thickness, p represents the oil film pressure, r represents the radial coordinate, θ represents the circumferential coordinate, and ω is the bearing angular velocity. r1 and r2 represent the starting and ending radial coordinates of the finite volume, and θ1, θ2 are the starting and ending circumferential coordinates of the finite volume, respectively.

[0078] The energy equation of the dynamic pressure stepped thrust bearing in polar coordinates is established:

[0079] The energy equation of the dynamic pressure stepped thrust bearing in polar coordinates is established:

[0080]

[0081] In the formula, c v represents the specific heat capacity, q r represents the radial mass flow rate, and is expressed as:

[0082]

[0083] q θ represents the circumferential mass flow rate, and is expressed as:

[0084]

[0085] T m is the average temperature of the oil film in the temperature field, and can be expressed as:

[0086]

[0087] In the formula, z represents the film thickness direction coordinate.

[0088] Step 3: Solve the Reynolds equation and the energy equation to calculate the static performance of the dynamic pressure stepped thrust bearing, specifically including:

[0089] The difference method is used to solve the Reynolds equation and the energy equation to calculate the static performance of the dynamic pressure stepped thrust bearing, and the friction torque M, the load capacity W, and the temperature rise T are obtained as follows:

[0090]

[0091]

[0092]

[0093] In the formula, r in represents the inner diameter of the bearing, r out is the outer diameter of the bearing, τ represents the shear stress of the oil film, represents the temperature of the outer diameter of the bearing. The local structure of the divided grid based on the difference method is shown in Figure 2 .

[0094] Step 4, the static performance calculation of the oil-gas lubricated dynamic pressure stepped thrust bearing, including:

[0095] The formulas (1)-(14) are used to calculate the static performance parameters of the dynamic pressure stepped thrust bearing under oil-gas lubrication, Figure 3Figures (a), (b), (c) show the changes of bearing film thickness, friction torque and temperature difference with external load under the action of oil-gas mixture with different gas contents.

[0096] Step 5, taking the friction torque, load capacity and temperature rise of the hydrodynamic step thrust bearing as the design target, the sensitivity analysis of the bearing structure (including step depth) parameters on the static performance is carried out, and the results are shown in Figure 4 Figure 4 Figures (a), (b), (c) respectively show the changes of bearing load capacity, bearing friction torque and bearing temperature rise with step depth under the lubrication of oil-gas mixture with a gas content of 26%. It can be seen from Figure 4 that the load capacity has a maximum value, while the friction torque and temperature rise have a minimum value. According to the static performance design indicators required by the oil-gas lubricated hydrodynamic step thrust bearing, the structure parameters such as step depth of the bearing can be selected and determined according to the calculation results of Figure 4 , and the structure parameter design of the high-speed oil-gas lubricated hydrodynamic step thrust bearing is completed.

[0097] Those skilled in the art can understand that the above description is only preferred embodiments of the present application, and is not used to limit the present application, although the present application has been described in detail with reference to the foregoing embodiments, and those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to some technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.​

Claims

1. A method for static performance design of a high-speed oil-air lubricated hydrodynamic stepped thrust bearing, characterized in that, include: Establish expressions for the viscosity and density of oil-gas mixtures; Based on the viscosity and density expressions of the oil-gas mixture, the Reynolds equation and energy equation of the hydrodynamic stepped thrust bearing in polar coordinates are established. The static performance of the hydrodynamic stepped thrust bearing, including oil film thickness, frictional torque, load capacity, and temperature rise, is calculated by solving the Reynolds equation and energy equation using the finite difference method. Static performance parameters of oil-gas lubricated hydrodynamic thrust bearings under different oil-gas mixtures with varying gas content and operating speeds were calculated to obtain the influence law of oil-gas lubrication on the static performance of thrust bearings. With the frictional torque, load capacity, and temperature rise of the dynamic pressure stepped thrust bearing as design objectives, the structural parameters of the bearing are determined through sensitivity analysis of the bearing structural parameters on static performance. The establishment of expressions for the viscosity and density of oil-gas mixtures includes: The viscosity expression of the oil-gas mixture was obtained by fitting the experimental data obtained from measuring the viscosity of the oil-gas mixture at high shear rates based on the least squares principle: ， In the above formula, The viscosity of the oil-gas mixture. For temperature, Shear rate, , , , It is a parameter related to the gas content of the oil-gas mixture; Define the equivalent dimensionless density of an oil-gas mixture: ， In the above formula, Represents dimensionless density. This indicates the ratio of bubble volume to pure oil volume. For temperature, Indicates the pressure of pure oil. This represents the surface tension of the bubble. This indicates the bubble radius, which is obtained by observing the bubble state at the oil inlet.

2. The static performance design method for high-speed oil-air lubricated hydrodynamic stepped thrust bearing according to claim 1, characterized in that, The Reynolds equation is established through the flow balance relationship of the oil film within a finite volume, and the flow relationship expression is as follows: ， In the above formula, the subscript numbers represent the numbers of the four control volumes near a certain control node. and The radial and circumferential mass flow rates of the control volume are expressed as follows: ， ， In the above two equations, Indicates the thickness of the oil film. Indicates oil film pressure, Represents radial coordinates, Represents circumferential coordinates. The bearing angular velocity; and These are the radial coordinates of the start and end points of the finite volume, respectively. These are the starting and ending circumferential coordinates of the finite volume, respectively; The viscosity of the oil-gas mixture. The density of the oil-gas mixture.

3. The static performance design method for high-speed oil-air lubricated hydrodynamic stepped thrust bearing according to claim 2, characterized in that, The energy equation is as follows: ， In the above formula, Indicates specific heat capacity. Radial mass flow rate, For circumferential mass flow rate, Indicates oil film pressure, For radius, The average temperature of the oil film in the temperature field. The viscosity of the oil-gas mixture. The density of the oil-gas mixture.

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