A design method for key characteristic parameters of porous cage of space bearing

Abstract

The present invention discloses a method for designing key characteristic parameters of a porous cage of a spatial bearing, which solves the problem that the current design of key characteristic parameters of a porous cage is heavily dependent on experiments and has low design efficiency. The key points of the technical solution are to establish a mathematical model between key characteristic parameters and oil supply characteristics of the porous cage based on fractal theory, input the oil supply characteristic requirements of the porous cage of the spatial bearing, set the initial values ​​of the key characteristic parameters of the porous cage, calculate the oil supply characteristics of the porous cage under the process, and compare and judge with the oil supply characteristic requirements, iteratively update the key characteristic parameters until the oil supply characteristic requirements are met, and obtain the corresponding key characteristic parameters. The method for designing key characteristic parameters of a porous cage of a spatial bearing of the present invention can quickly obtain the key characteristic parameters under the target oil supply characteristic requirements through numerical calculation, thereby improving the design efficiency of the porous cage.

Description

Technical Field

[0001] The invention relates to a key characteristic parameter design of a porous cage, and in particular to a key characteristic parameter design method of a porous cage of a space bearing. Background Art

[0002] The country is developing highly reliable and long-life spacecraft, which places higher demands on bearing lubrication performance and life. Among them, the key features of porous cages play a vital role in bearing dynamics and lubrication performance. Porous cages are often used on bearings that are difficult to supply lubricating oil, especially space bearings. They use the loose internal pore structure to store lubricating oil, and provide lubricating oil to bearing components through centrifugal action or thermal effect, thereby increasing the service life of bearings. The key characteristic parameters of porous cages include the pore size and porosity of the holes, where porosity is the percentage of pore volume to the overall volume. Together, they affect the oil storage and supply performance of porous cages.

[0003] Existing research shows that precise control of pore size and porosity can be achieved by changing the preparation process, using molding powders of different particle sizes and adjusting molding process parameters. Since space bearings are difficult to repair and replace, in order to allow porous cages to provide lubricating oil for space bearings over a long period of time, engineers need to design the porosity and pore size so that the cages can provide lubrication and carry enough lubricating oil at the target speed, and avoid the oil supply at other speeds, which causes the lubricating oil stored in the porous cage to be consumed in the early stage of the bearing service, thus losing the function of extending the bearing lubrication life.

[0004] However, the current design process still relies heavily on experimental methods, which requires a lot of manpower and material resources to prepare cages with different porosity and pore size characteristics, and then conduct oil supply and oil storage tests. Finally, the structural parameters of the cage are updated and iterated according to the test results. The process involves cage forming technology, vacuum oil filling of porous cage materials, storage lubricating oil testing, lubricating oil supply testing and other processes, which seriously reduces the design efficiency of porous cages. Summary of the invention

[0005] The purpose of the present invention is to provide a method for designing key characteristic parameters of a porous cage of a spatial bearing, which can quickly obtain the key characteristic parameters of the porous cage under the target oil supply characteristic requirements through numerical calculation, thereby improving the design efficiency of the porous cage. The porous cage material is rich in pores and can be regarded as composed of capillaries that satisfy fractal distribution, and the pore diameter of these pores is the diameter of the capillary. For the convenience of description, the "capillary diameter" is abbreviated as "pore diameter" below.

[0006] The above technical objectives of the present invention are achieved through the following technical solutions:

[0007] A method for designing key characteristic parameters of a porous cage of a space bearing comprises the following steps:

[0008] Based on fractal theory, a mathematical model between key characteristic parameters and oil supply characteristics of porous cage is established;

[0009] Input space bearing porous cage oil supply characteristics requirements, including minimum oil supply speed, oil supply rate, effective oil supply quality;

[0010] Set the initial values ​​of the key characteristic parameters of the porous cage, including the initial minimum pore size, maximum pore size, average pore size, and porosity;

[0011] Based on the key characteristic parameters, the fractal parameters of capillary pore size distribution in the porous cage are calculated, including fractal dimension and density distribution parameters.

[0012] Based on the key characteristic parameters of the porous cage and the fractal parameters of the capillary pore size, the fractal parameters of the capillary length are calculated.

[0013] Based on the capillary aperture fractal parameters and length fractal parameters of the porous cage and the appearance geometric characteristics of the porous cage, the oil supply rate of the porous cage under this process is calculated.

[0014] When the capillary aperture is at its maximum, the minimum oil supply speed of the porous cage is calculated;

[0015] Based on the capillary aperture fractal parameters and length fractal parameters of the porous cage, the effective oil supply quality of the porous cage is calculated when the working speed is the highest;

[0016] Compare the obtained fuel supply characteristics with the input fuel supply characteristic requirements to determine whether the output fuel supply characteristics meet the fuel supply characteristic requirements;

[0017] If the requirements are met, the corresponding key characteristic parameters are output for design; if not, the key characteristic parameters are updated and the fuel supply characteristics are recalculated until the fuel supply characteristic requirements are met.

[0018] Preferably, the calculation of the fractal parameters of the capillary pore size distribution of the porous cage is specifically as follows:

[0019] Capillaries satisfy the following fractal characteristics:

[0020] The cumulative number of capillaries with diameters greater than λ satisfies

[0021]

[0022] Among them, λ max is the maximum aperture, D f is the fractal dimension of the capillary diameter;

[0023] The number of capillaries per unit area with a diameter of λ in the porous cage is f(λ):

[0024]

[0025] Among them, k c It is the density distribution parameter, which is related to the pore structure characteristics of the material;

[0026] The average pore size is obtained by integrating for:

[0027]

[0028] Among them, λ min is the minimum aperture, is the porosity;

[0029] The integral solution gives the area occupied by the pores in the plane with a cross-sectional area of ​​S:

[0030]

[0031] Based on setting the minimum pore size λ of the porous cage under a certain preparation process min , maximum aperture λ max , average pore size Porosity The fractal dimension D of the capillary pore size of the porous cage under this process is calculated by combining the formula of the average pore size and the area occupied by the pores in the plane with a cross-sectional area of ​​S. f And the density distribution parameter k c .

[0032] Preferably, the calculation of the fractal parameter of the capillary length of the porous cage distribution is specifically as follows:

[0033] The tortuosity of the capillary tube satisfies the fractal law and can be regarded as the actual length of the capillary tube l λ Ratio to characteristic length l0

[0034]

[0035] The capillary length also satisfies the fractal law. The total length of a capillary of a certain diameter is calculated as

[0036]

[0037] Among them, D T is the fractal dimension of tortuosity, l0 is the characteristic length of the material;

[0038] The volume of all capillaries with diameter λ within the integrated cross-sectional area S is:

[0039]

[0040] This volume should be equal to the total volume of the pores. Given the characteristic length l0, the total length calculation formula of a capillary of a certain diameter is combined to obtain the tortuosity fractal dimension D. T .

[0041] As a preferred method, the calculation of each parameter of the oil supply characteristic is specifically as follows:

[0042] Oil supply rate Q PS :

[0043]

[0044] In the formula, S c is the outer ring area of ​​the cage, λ is the capillary aperture, f(λ) is the density distribution parameter, and q is the flow rate of the lubricating oil at a certain moment;

[0045] Minimum fuel supply speedω min :

[0046]

[0047] ω min is the minimum oil supply speed of the capillary tube under any aperture λ, λ is taken as λ max is the minimum oil supply speed of the porous cage; where σ is the surface tension coefficient, ρ is the density of the lubricating oil, l0 is the characteristic length of the material, are the inner and outer diameters of the porous cage, respectively;

[0048] Effective oil supply quality M PS :

[0049]

[0050] In the formula, l λ is the actual length of the capillary, ω max is the maximum operating speed. When all the effective oil supply mass is ejected out of the cage under the centrifugal action, the q value in the oil supply rate calculation formula is 0.

[0051] As a preferred method, the factors involved in calculating the various parameters of the oil supply characteristic are:

[0052] The porous cage rotates at an angular velocity ω, generating a centrifugal acceleration a in the radial direction. At the same time, surface tension creates a pressure difference p inside the liquid. L ; Analysis of the working condition under the diameter of λ, length l λ The flow of liquid in the capillary; According to the Poiseuille flow model, the flow rate of lubricating oil at a certain moment is calculated to be

[0053]

[0054] Among them, ΔP is the pressure difference between the front and rear ends of the liquid in the pipeline, ρ is the density of the lubricating oil, μ is the viscosity of the lubricating oil, l t (λ) is the length occupied by the actual liquid volume in the capillary;

[0055] Considering the centrifugal acceleration field, ΔP is calculated as

[0056]

[0057] Among them, l λ is the actual length of the capillary, σ is the surface tension coefficient; is the pressure difference generated by capillary force, and the contact angle θ m The value is taken as 0 in calculation; when ΔP is greater than 0, there is flow, and when it is less than or equal to 0, the liquid does not flow relative to the capillary; is the pressure difference caused by centrifugal force; are the inner and outer diameters of the porous cage respectively; l t (λ) is the length of the liquid column in the capillary;

[0058] The mass of the liquid column m λ for

[0059]

[0060] but

[0061]

[0062] The rate of change of mass of the liquid column in the capillary is

[0063]

[0064] In summary, the present invention has the following beneficial effects:

[0065] Aiming at the oil supply characteristic requirements of porous cages of spatial bearings, a mathematical model between the key characteristic parameters of porous cages of bearings and their oil supply characteristics established based on fractal theory can be used as input to quickly obtain the key characteristic parameters of the target porous cage directly through numerical calculation. This parameter can be used as the basis for formulating the forming process parameters of porous cages, reducing the manpower and material costs caused by trial and error, and improving the design efficiency of porous cages. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 A schematic flowchart of the process of this method is shown in FIG.

[0067] Figure 2 Schematic diagram of capillary liquid flow under the action of centrifugal force. DETAILED DESCRIPTION

[0068] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0069] According to one or more embodiments, a method for designing key characteristic parameters of a porous cage of a spatial bearing is disclosed, such as Figure 1 As shown, the following steps are included:

[0070] S1. Based on fractal theory, a mathematical model between key characteristic parameters and the oil supply characteristics of porous cages is established.

[0071] S2. Input space bearing porous cage oil supply characteristics requirements, including minimum oil supply speed, oil supply rate, and effective oil supply quality.

[0072] S3. Set the initial values ​​of the key characteristic parameters of the porous cage, including the initial minimum pore size, maximum pore size, average pore size, and porosity. The initial values ​​can be selected based on past experience, and the initial values ​​mainly affect the speed of iterative convergence of subsequent numerical calculations.

[0073] S4. Based on the key characteristic parameters, the fractal parameters of the capillary pore size of the porous retainer are calculated, including the fractal dimension and density distribution parameters.

[0074] S5. Based on the key characteristic parameters of the porous retainer and the fractal parameters of the capillary pore size, the fractal parameters of the capillary length are calculated.

[0075] S6. Based on the capillary pore size fractal parameters and length fractal parameters of the porous retainer, combined with the appearance geometric characteristics of the porous retainer, the appearance geometric characteristics include the inner diameter, outer diameter, pocket diameter, and width, the oil supply rate of the porous retainer under this process is calculated.

[0076] S7. Calculate and obtain the minimum oil supply speed of the porous cage when the capillary aperture is at its maximum.

[0077] S8. Based on the capillary aperture fractal parameters and length fractal parameters of the porous cage, the effective oil supply quality of the porous cage is calculated when the working speed is the highest.

[0078] S9, comparing the calculated fuel supply characteristics with the input fuel supply characteristics requirements, and determining whether the output fuel supply characteristics meet the fuel supply characteristics requirements.

[0079] If the output oil supply characteristics meet the oil supply characteristics requirements, the current corresponding key characteristic parameters are output for design; if not, the Newton iteration method or other numerical algorithms can be used to update the key characteristic parameters of the porous cage, and then steps S4 to S9 are repeated to recalculate the oil supply characteristics until the oil supply characteristics requirements are met.

[0080] Specifically, fractal dimension refers to the coefficient of an exponential function where the number of units required to measure an object increases as ε decreases. For example, when measuring the length of a straight line, N(ε) = (1 / ε); when measuring the area of ​​a unit square, N(ε) = (1 / ε) 2 ; When measuring the volume of a unit cube, N(ε) = (1 / ε) 3 . The fractal dimensions of the above-mentioned unit line segment, square, and cube are 1, 2, and 3, respectively, which are the exponents of their formulas. For porous cages, the porous cage material is rich in pore structures, which can be regarded as capillary components that satisfy fractal distribution. The pore diameter of these pores is the diameter of the capillary. For the convenience of description, the "capillary diameter" is abbreviated as "pore diameter" below. These capillaries satisfy the following fractal characteristics: the cumulative number of capillaries with a diameter greater than λ satisfies:

[0081]

[0082] Among them, λ max is the maximum aperture, D f is the fractal dimension of the capillary diameter, so the number of capillaries with a diameter of λ per unit area in the porous cage, f(λ), can be obtained by differentiating the above formula:

[0083]

[0084] Among them, k c is the density distribution parameter, which is related to the pore structure characteristics of the material. At the same time, the average pore size can be obtained by integrating (2) for

[0085]

[0086] Among them, λ min is the minimum aperture, is the porosity. Integrating formula (2) yields the area occupied by the pores in the plane with a cross-sectional area of ​​S:

[0087]

[0088] Therefore, when the minimum pore size λ of the porous cage is set under a certain preparation process min , maximum aperture λ max , average pore size And porosity By combining equations (3) and (4), we can calculate the fractal dimension D of the capillary pore size of the porous cage under this process. f And the density distribution parameter k c .

[0089] On the other hand, the tortuosity of a capillary can be considered as the ratio of the actual length of the capillary to its characteristic length, which can be calculated as follows:

[0090] τ(λ)=l λ / l0 (5)

[0091] This parameter also satisfies the fractal law. Therefore, according to formula (5), the capillary length also satisfies the fractal law, and the total length of the capillary of a certain diameter can be calculated as:

[0092]

[0093] Among them, D T is the fractal dimension of tortuosity, and l0 is the characteristic length of the material. Then, by combining equations (6) and (1), we can get the volume of all capillaries with diameter λ in the integrated cross-sectional area S, and this volume should be equal to the total volume of the pores, as shown in the following equation:

[0094]

[0095] Therefore, based on the known characteristic length l0, the tortuosity fractal dimension D can be obtained by solving the above equation (6): T Generally, for a porous retainer, the width is taken as the characteristic length l0.

[0096] The hole structure inside the porous cage can be regarded as a combination of many capillaries. When the porous cage rotates at an angular velocity ω, the lubricating oil in the capillaries will flow under the combined action of centrifugal force and capillary force. According to its Reynolds number, the flow state is usually laminar flow, which can be analyzed according to the Poiseuille flow in the channel.

[0097] like Figure 2 As shown, the porous cage rotates at an angular velocity ω to generate a radial centrifugal acceleration a, and the surface tension will form a pressure difference p inside the liquid. L . Analyze the working condition with diameter λ and length l λ The flow of liquid in the capillary. According to the Poiseuille flow model, the flow rate of lubricating oil at a certain moment is calculated as:

[0098]

[0099] Among them, ΔP is the pressure difference between the front and rear ends of the liquid in the pipeline, ρ is the density of the lubricating oil, μ is the viscosity of the lubricating oil, l t (λ) is the length occupied by the actual liquid volume in the capillary. Considering the centrifugal acceleration field, ΔP is calculated as:

[0100]

[0101] Among them, l λis the actual length of the capillary, σ is the surface tension coefficient. The first term on the right is the pressure difference caused by the capillary force, and the contact angle θ m The value is taken as 0 in the calculation. When ΔP in formula (9) is greater than 0, flow exists. When it is less than or equal to 0, due to the action of capillary force and contact angle θ m The pressure difference generated by the centrifugal acceleration field will be overcome by the capillary force, so that the liquid does not flow relative to the capillary. Assuming that for any capillary, the tortuosity of each small section is equal, the projection of the unit length of the capillary on the characteristic length l0 is l0 / l λ , the corresponding capillary length is l t The projection of the liquid column (λ) in the characteristic length direction is l t (λ)l0 / l λ . Note that the direction of the acceleration field is consistent with the characteristic length direction and the pressure difference generated at the head and tail of the liquid column in the acceleration field is proportional to the projection length of the liquid column in the acceleration direction, and then the second term on the right side of the above equation, that is, the pressure difference generated by the centrifugal force, is calculated. The acceleration a in equation (9) can be approximately calculated as:

[0102]

[0103] in, are the inner and outer diameters of the porous cage respectively.

[0104] On the other hand, the mass of the liquid column m λ for:

[0105]

[0106] Combining equations (8), (9) and (11), we get:

[0107]

[0108] So the rate of change of the mass of the liquid column in the capillary is:

[0109]

[0110] The oil supply characteristics of the porous cage include the minimum oil supply speed, oil supply rate, and effective oil supply quality. Combined with the density distribution characteristics of the cage capillary diameter f(λ), the lubricating oil supply rate (oil supply rate) of the porous cage under centrifugal action is calculated as:

[0111]

[0112] The calculation of the pore size density distribution function f(λ) is based on formula (2), S c is the outer ring area of ​​the cage, calculated as:

[0113]

[0114] Among them, B c is the cage width, d p is the pocket diameter. In the calculation process, Q PS When it is less than 0, the value is 0, that is, the cage lubricating oil neither decreases nor increases.

[0115] For the lowest oil supply speed of the porous cage, that is, when the porous cage is filled with lubricating oil, the q value of equation (12) is exactly 0. Combining equations (5), (10), and (11), we can get:

[0116]

[0117] The above formula gives the minimum oil supply speed of the capillary tube under any aperture λ. For the cage as a whole, the above formula λ takes λ max It is the minimum fuel supply speed.

[0118] For the effective oil supply quality of the porous cage, that is, the cage at the maximum operating speed ω max The total mass of lubricating oil that can be supplied under the condition of centrifugal force. When the effective oil supply mass is just ejected out of the cage under the centrifugal force, the q value of equation (12) is exactly 0. Combining equations (10) and (11) yields:

[0119]

[0120] For the porous cage prepared by the same process, combined with equations (3) and (4), the minimum pore size λ of the cage capillary is modified to min , maximum aperture λ max , average pore size Cage porosity The density distribution parameter k of the porous cage will be changed c and fractal dimension D f , D T , thus affecting the hole diameter and its distribution function in equations (16) and (17), and ultimately achieving the control of effective oil supply quality and minimum oil supply speed.

[0121] At present, the existing design of key characteristic parameters of porous cages for space bearings requires multiple trials and errors, which consumes a lot of manpower and material resources and leads to low efficiency of porous cages. Based on the characteristics that the pore structure of porous cages obeys fractal distribution, the present invention proposes a key characteristic parameter design method for porous cages with centrifugal action as the main oil supply mechanism. By establishing a mathematical model between the key characteristic parameters of porous cages and their minimum oil supply speed and effective oil supply, the method can obtain the required key characteristic parameters of porous cages through simple numerical calculation.

[0122] Based on fractal theory, a model of the capillary pore size and length distribution parameters of the porous bearing cage with respect to the key characteristic parameters of the cage was established. These key characteristic parameters include porosity, minimum capillary pore size, maximum capillary pore size, and average capillary pore size. Based on fractal theory, considering the rotation speed and actual oil storage capacity of the cage, a mathematical model between the key characteristic parameters of the porous bearing cage and the cage oil supply characteristics was established. The cage oil supply characteristics include the minimum oil supply speed, oil supply rate, and effective oil supply quality.

[0123] Aiming at the oil supply characteristic requirements of porous cages of spatial bearings, based on the established mathematical model between the key characteristic parameters of porous cages of bearings and their oil supply characteristics, the oil supply characteristic requirements of porous cages of spatial bearings can be used as input, and the key characteristic parameters of the target porous cages can be quickly obtained directly through numerical calculation. The parameters can be used as the basis for formulating the forming process parameters of porous cages, reducing the manpower and material costs caused by trial and error, and improving the design efficiency of porous cages.

[0124] This specific embodiment is merely an explanation of the present invention and is not a limitation of the present invention. After reading this specification, those skilled in the art may make non-creative modifications to the present embodiment as needed. However, as long as they are within the scope of the claims of the present invention, they are protected by the patent law.

Claims

1. A method for designing key characteristic parameters of a porous cage of a space bearing, characterized in that: The following steps are involved: Based on fractal theory, a mathematical model between key characteristic parameters and oil supply characteristics of porous cage is established; Input space bearing porous cage oil supply characteristics requirements, including minimum oil supply speed, oil supply rate, effective oil supply quality; Set the initial values ​​of the key characteristic parameters of the porous cage, including the initial minimum pore size, maximum pore size, average pore size, and porosity; Based on the key characteristic parameters, the fractal parameters of capillary pore size distribution in the porous cage are calculated, including fractal dimension and density distribution parameters. Based on the key characteristic parameters of the porous cage and the fractal parameters of the capillary pore size, the fractal parameters of the capillary length are calculated. Based on the capillary aperture fractal parameters and length fractal parameters of the porous cage and the appearance geometric characteristics of the porous cage, the oil supply rate of the porous cage under this process is calculated. When the capillary aperture is at its maximum, the minimum oil supply speed of the porous cage is calculated; Based on the capillary aperture fractal parameters and length fractal parameters of the porous cage, the effective oil supply quality of the porous cage is calculated when the working speed is the highest; Compare the obtained fuel supply characteristics with the input fuel supply characteristic requirements to determine whether the output fuel supply characteristics meet the fuel supply characteristic requirements; If the requirements are met, the corresponding key characteristic parameters are output for design; if not, the key characteristic parameters are updated and the fuel supply characteristics are recalculated until the fuel supply characteristic requirements are met.

2. The key characteristic parameter design method of a porous cage of a spatial bearing according to claim 1 is characterized in that: The calculation of the fractal parameters of the capillary pore size distribution of the porous cage is as follows: Capillaries satisfy the following fractal characteristics: The cumulative number of capillaries with diameters greater than λ satisfies Where, L is the pore size of the capillaries distributed in the porous holder, λ max is the maximum aperture, D f is the fractal dimension of the capillary diameter; The number of capillaries per unit area with a diameter of λ in the porous cage is f(λ): Among them, k c It is the density distribution parameter, which is related to the pore structure characteristics of the material; The average pore size is obtained by integrating for: Among them, λ min is the minimum aperture, is the porosity; The integral solution gives the area occupied by the pores in the plane with a cross-sectional area of ​​S: Based on setting the minimum pore size λ of the porous cage under a certain preparation process min , maximum aperture λ max , average pore size Porosity The fractal dimension D of the capillary pore size of the porous cage under this process is calculated by combining the formula of the average pore size and the area occupied by the pores in the plane with a cross-sectional area of ​​S. f And the density distribution parameter k c .

3. The key characteristic parameter design method of a porous cage of a spatial bearing according to claim 2 is characterized in that: The calculation of the fractal parameters of the capillary length of the porous cage distribution is as follows: The tortuosity of the capillary tube satisfies the fractal law and can be regarded as the actual length of the capillary tube l λ Ratio to characteristic length l0 The capillary length also satisfies the fractal law. The actual length of a capillary with a certain diameter is calculated as Among them, D T is the fractal dimension of tortuosity, l0 is the characteristic length of the material; The volume of all capillaries with diameter λ within the integrated cross-sectional area S is: This volume should be equal to the total volume of the pores. Given the characteristic length l0, the total length calculation formula of a capillary of a certain diameter is combined to obtain the tortuosity fractal dimension D. T .

4. The key characteristic parameter design method of a porous cage of a spatial bearing according to claim 3 is characterized in that: The calculation of each parameter of the oil supply characteristic is as follows: Oil supply rate Q PS : In the formula, S c is the outer ring area of ​​the cage, λ is the capillary aperture, f(λ) is the density distribution parameter, and q is the flow rate of the lubricating oil at a certain moment; Minimum fuel supply speedω min : ω min is the minimum oil supply speed of the capillary tube under any aperture λ, λ is taken as λ max is the minimum oil supply speed of the porous cage; where σ is the surface tension coefficient, ρ is the density of the lubricating oil, l0 is the characteristic length of the material, are the inner and outer diameters of the porous cage, respectively; Effective oil supply quality M PS : In the formula, l λ is the actual length of the capillary, ω max is the maximum operating speed; when all the effective oil supply mass is ejected out of the cage under the centrifugal action, the q value in the oil supply rate calculation formula is 0.

5. The key characteristic parameter design method of a porous cage of a spatial bearing according to claim 4 is characterized by: The factors involved in the calculation of each parameter of the oil supply characteristic are: The porous cage rotates at an angular velocity ω, generating a centrifugal acceleration a in the radial direction. At the same time, surface tension creates a pressure difference p inside the liquid. L ; Analysis of the working condition under the diameter of λ, length l λ The flow of liquid in the capillary; According to the Poiseuille flow model, the flow rate q of the lubricating oil at a certain moment is calculated as Among them, ΔP is the pressure difference between the front and rear ends of the liquid in the pipeline, ρ is the density of the lubricating oil, μ is the viscosity of the lubricating oil, l t (λ) is the length occupied by the actual liquid volume in the capillary; Considering the centrifugal acceleration field, ΔP is calculated as Where, σ is the surface tension coefficient; is the pressure difference caused by capillary force, and the contact angle θ m The value is taken as 0 in calculation; when ΔP is greater than 0, there is flow, and when it is less than or equal to 0, the liquid does not flow relative to the capillary; is the pressure difference caused by centrifugal force; are the inner and outer diameters of the porous cage respectively; l t (λ) is the length of the liquid column in the capillary; The mass of the liquid column m λ for but The rate of change of mass of the liquid column in the capillary is

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