Method for predicting creep life of foil dynamic pressure radial gas bearing

Abstract

The invention discloses a method for predicting the creep life of a foil dynamic pressure radial gas bearing. The method comprises the following four steps of: 1, determining a creep part and a mechanism; 2, determining main factors of creep deformation; 3, establishing a prediction model of the gas film pressure suffered by the foil dynamic pressure radial gas bearing under a constant load; and 4, establishing a foil dynamic pressure radial gas bearing creep residual life prediction model. According to the method, the structure and the working principle of the foil dynamic pressure radial gas bearing are combined, a creep quantity and creep residual life prediction model of the foil dynamic pressure radial gas bearing is given by analyzing the influence of random factors such as a material process, a working environment and a use task on the bearing, maintenance personnel can conveniently handle problems in time, and the service life of the foil dynamic pressure radial gas bearing is prolonged. The utilization rate and the efficiency of the foil dynamic pressure radial gas bearing are improved, and the safety and the reliability of an equipment system caused by excessive creep deformation of the bearing are avoided. The method has practical value and good application prospect in the technical field of gas bearing reliability.

Description

Technical Field

[0001] The present invention relates to a method for predicting the creep life of a foil dynamic pressure radial gas bearing, and specifically to a method for predicting the creep life based on the physics of failure (PoF) technology. The prediction method utilizes the structural composition and working principle information of the foil dynamic pressure radial gas bearing, combined with the influencing factor models such as the bearing working environment and usage tasks, to predict the life of this type of bearing, and belongs to the field of gas bearing and reliability technology. Technical Background

[0002] The foil dynamic pressure radial gas bearing is a typical dynamic pressure bearing. It is a dynamic pressure air bearing with a good flexible surface composed of one or more layers of corrugated foil and top foil. It relies on the relative movement of the shaft and the bearing surface to squeeze a certain viscosity of gas to form a pressure lubricating gas film to achieve support and lubrication. The principle is that when there is a wedge-shaped space between two relatively moving surfaces, the surfaces moving against each other continuously drive the gas into the wedge-shaped groove, so that a dynamic pressure gas film with a certain pressure is formed in the wedge-shaped groove. When the air film pressure is large enough to support the load, the shaft is floated and the friction disappears. The foil dynamic pressure radial gas bearing uses gas as a lubricating medium. Its surface has a certain flexibility, low friction power consumption, and stable operation. It can operate in extreme environments such as low temperature, high temperature and high speed. It is widely used in mechanical equipment such as turbo compressors and turbo expanders. Because the foil of the foil dynamic pressure radial gas bearing is subjected to cyclic stress, the foil creeps, the foil height decreases and collapses, and the elasticity decreases. The creep of the foil will restrict the functional performance of the gas bearing, and its creep degree directly affects the working life of the foil dynamic pressure radial gas bearing.

[0003] At present, the life prediction of bearings or equipment containing bearing structures is mainly carried out by detecting the equipment status and using the creep amount exceeding the threshold to predict the remaining life of the equipment.

[0004] Therefore, the present invention aims at the creep problem of foil dynamic pressure gas bearing under cyclic stress, constructs the relationship between the single-turn creep amount of the wave foil and the gas film pressure and time; and establishes a creep life model of foil dynamic pressure radial gas bearing based on random process. Summary of the invention

[0005] 1. Purpose: To provide a method for predicting the creep life of a foil dynamic pressure radial gas bearing. This method combines the working principle of the bearing and effectively predicts the creep life of this type of bearing.

[0006] 2. Technical solution: The present invention provides a method for predicting the creep life of a foil dynamic pressure radial gas bearing. The specific steps of the method are as follows:

[0007] Step 1: Determine the creep location and mechanism

[0008] In the foil gas dynamic pressure radial bearing and rotor system, due to the repeated operation of the rotor, the foil of the foil gas dynamic pressure radial bearing is subjected to cyclic stress, which causes the foil to creep, the foil to drop in height and collapse, and the elasticity to decrease.

[0009] Step 2: Determine the main factors of creep

[0010] This patent application assumes that the air film pressure and time on the foil are the main factors affecting the creep amount during the deformation process. Therefore, quantifying the influence of air film pressure and time on the creep amount of the foil is the basis for establishing a creep life model of the foil dynamic pressure radial gas bearing.

[0011] Step 3: Establish a predictive model for the air film pressure of a foil dynamic pressure radial gas bearing under constant load

[0012] (1) To calculate the creep of the foil, we first need to calculate the air film pressure. The bearing structure parameters are input into the air film thickness formula. The air film thickness equation is:

[0013] h(θ)=C+ecos(θ-θ0)+δ(θ,z)

[0014] Where C is the clearance, e is the eccentricity between the bearing and the rotor, θ0 is the eccentricity angle, and δ(θ,z) is the deformation of the wave foil.

[0015] Solving the Reynolds equation

[0016]

[0017] Where P = P / P0 is the dimensionless air film pressure, H = h(θ) / C is the dimensionless air film, Z = Z / R is the dimensionless length of the bearing, Λ = 6μωR 2 / P0C 2 is the number of bearings, τ e =vt is the dimensionless time, P0 is the atmospheric pressure, C is the nominal bearing clearance, R is the bearing radius, μ is the friction coefficient, ω is the angular velocity, and ν is the excitation ratio;

[0018] Calculate the air film force F and determine whether it converges. If not, substitute the equilibrium position e and θ0 into the air film thickness equation, iterate repeatedly, and obtain a stable air film force F. The air film pressure at this time is the air film pressure P that the bearing is subjected to under the secondary load.

[0019] (2) Solve the deformation δ of the foil

[0020] The flexible structure can be modeled as a series of springs and dampers, with the damping characteristics derived from friction. The unstable deflection of the foil structure is written as

[0021]

[0022] In the formula, Kb is the standard foil stiffness, C b is the equivalent viscous damping, τ is the dimensionless time, the effective coverage area of ​​the foil A0 and the structural loss factor η are expressed as follows

[0023]

[0024]

[0025] The synchronous excitation frequency ratio γ = 1 adopts the equivalent viscous damping coefficient

[0026] In order to get K b The value of K is obtained by assuming that one end of the foil is fixed and the other end is in simple contact. b value

[0027]

[0028] In the formula, t b is the foil thickness, α is the bending angle of a single foil, ι is half the length of a single foil, E and ν are the elastic modulus and Poisson's ratio of the foil, respectively, and I(α) is expressed as follows

[0029]

[0030]

[0031] (3) Solving the air film force

[0032] After solving for the gas pressure, the resultant force can be obtained from one-third of the Simpson integral equation

[0033]

[0034]

[0035]

[0036] (4) Solving creep

[0037] Creep of corrugated foil material obeys Norton creep rate model

[0038]

[0039] in is the creep rate, σ is the stress, E is the material constant, and n is the creep exponent;

[0040] Derivation

[0041]

[0042]

[0043]

[0044] N is the number of revolutions of the rotor

[0045] Step 4: Establish a creep remaining life prediction model for foil dynamic pressure radial gas bearings.

[0046] The creep amount of corrugated foil is solved by using Norton creep formula;

[0047] Structural equation of wave foil

[0048] Original y = ax 2 +h bump

[0049] Decompose the air film pressure on the foil and calculate the creep amount of each section separately

[0050] P=P1+P2+…P 2n

[0051] Substitute into the creep formula

[0052]

[0053] Then the creep amount of each segment is brought into the shape formula of the single segment corrugated foil for solution;

[0054] After creep y = a′x 2 +h′ bump

[0055] δ cr =h bump -h′ bump

[0056] Perform loop iterations to determine the creep amount δ cr Whether it exceeds the threshold, solve the bearing foil failure after the rotor rotates N times, and obtain the bearing creep life. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a comparison diagram of the structure and creep of the foil dynamic pressure radial gas bearing

[0058] Figure 2 This is a flowchart of the present invention DETAILED DESCRIPTION

[0059] See Figure 2 The present invention provides a method for predicting the creep life of a foil dynamic pressure radial gas bearing, and the specific implementation method includes:

[0060] Step 1: Determine the creep location and mechanism

[0061] The foil dynamic pressure radial gas bearing uses the elastic deformation of the foil to form a wedge-shaped gap between the rotor and the bearing working surface to support the load. The foil dynamic pressure radial gas bearing structure consists of three parts: bearing shell, corrugated foil and top foil. The foil mainly provides support for the bearing. Take the corrugated foil type dynamic pressure radial gas bearing as an example. Figure 1 The foils in this type of bearing are divided into wave foil and top foil. Their leading edge is spot welded or clamped on the bearing housing, which is the fixed end; the trailing edge is the free end. The wave foil provides support for the single top foil. The wave foil not only provides stiffness to the bearing like a spring, but also provides damping; the smooth top foil provides the bearing surface.

[0062] In the foil gas dynamic pressure radial bearing and rotor system, due to the repeated operation of the rotor, the foil of the foil gas dynamic pressure radial bearing is subjected to cyclic stress, which causes the foil to creep, the foil to drop in height and collapse, and the elasticity to decrease.

[0063] Step 2: Determine the main factors of creep

[0064] This patent application assumes that the air film pressure and time on the foil are the main factors affecting the creep amount during the deformation process. Therefore, quantifying the influence of air film pressure and time on the creep amount of the foil is the basis for establishing a creep life model of the foil dynamic pressure radial gas bearing.

[0065] Step 3: Establish a predictive model for the air film pressure of a foil dynamic pressure radial gas bearing under constant load

[0066] (1) To calculate the creep of the foil, we first need to calculate the air film pressure. The bearing structure parameters are input into the air film thickness formula. The air film thickness equation is:

[0067] h(θ)=C+ecos(θ-θ0)+δ(θ,z)

[0068] Where C is the clearance, e is the eccentricity between the bearing and the rotor, θ0 is the eccentricity angle, and δ(θ,z) is the deformation of the wave foil.

[0069] Solving the Reynolds equation

[0070]

[0071] Where P = P / P0 is the dimensionless air film pressure, H = h(θ) / C is the dimensionless air film, Z = Z / R is the dimensionless length of the bearing, Λ = 6μωR 2 / P0C 2 is the number of bearings, τ e =vt is the dimensionless time, P0 is the atmospheric pressure, C is the nominal bearing clearance, R is the bearing radius, μ is the friction coefficient, ω is the angular velocity, and ν is the excitation ratio;

[0072] Calculate the air film force F and determine whether it converges. If not, substitute the equilibrium position s into the air film thickness equation and iterate it repeatedly to obtain a stable air film force F. The air film pressure at this time is the air film pressure P that the bearing is subjected to under the secondary load.

[0073] (2) Solve the deformation δ of the foil

[0074] The flexible structure can be modeled as a series of springs and dampers, with the damping characteristics derived from friction. The unstable deflection of the foil structure is written as

[0075]

[0076] In the formula, K b is the standard foil stiffness, C b is the equivalent viscous damping, τ is the dimensionless time, the effective coverage area of ​​the foil A0 and the structural loss factor η are expressed as follows

[0077]

[0078]

[0079] The synchronous excitation frequency ratio γ = 1 adopts the equivalent viscous damping coefficient

[0080] In order to get K b The value of K is obtained by assuming that one end of the foil is fixed and the other end is in simple contact. b value

[0081]

[0082] In the formula, t b is the foil thickness, α is the bending angle of a single foil, ι is half the length of a single foil, E and ν are the elastic modulus and Poisson's ratio of the foil, respectively, and I(α) is expressed as follows

[0083]

[0084]

[0085] (3) Solving the air film force

[0086] After solving for the gas pressure, the resultant force can be obtained from one-third of the Simpson integral equation

[0087]

[0088]

[0089]

[0090] (4) Solving creep

[0091] Creep of corrugated foil material obeys Norton creep rate model

[0092]

[0093] Where creepRate is the creep rate, σ is the stress, E is the material constant, and n is the creep exponent

[0094] Derivation

[0095]

[0096]

[0097]

[0098] N is the number of revolutions of the rotor

[0099] Decompose the air film pressure and calculate the creep amount of each section separately

[0100] P=P1+P2+…P 2n

[0101] Step 4: Establishing a creep residual life prediction model for foil dynamic pressure radial gas bearings

[0102] The creep amount of corrugated foil is solved by using Norton creep formula;

[0103] Structural equation of wave foil

[0104] Original y = ax 2 +h bump

[0105] Decompose the air film pressure on the foil and calculate the creep amount of each section separately

[0106] P=P1+P2+…P 2n

[0107] Substitute into the creep formula

[0108]

[0109] Then the creep amount of each segment is brought into the shape formula of the single segment corrugated foil for solution;

[0110] After creep y = a′x 2 +h′ bump

[0111] δ cr =h bump -h′ bump

[0112] Perform loop iterations to determine the creep amount δcr Whether it exceeds the threshold, solve the bearing foil failure after the rotor rotates N times, and obtain the bearing creep life.

Claims

1. A method for predicting creep life of a foil dynamic pressure radial gas bearing, characterized in that: The specific steps of this method are as follows: Step 1: Determine the creep location and mechanism In the foil gas dynamic pressure radial bearing and rotor system, the rotor runs many times, and the foil of the foil gas dynamic pressure radial bearing is subjected to cyclic stress, the foil creeps, the foil height decreases and collapses, and the elasticity decreases. Step 2: Determine the main factors of creep Assuming that the air film pressure and time on the foil are the main factors affecting the creep amount during the deformation process, quantifying the influence of air film pressure and time on the creep amount of the foil is the basis for establishing the creep life model of the foil dynamic pressure radial gas bearing. Step 3: Establish a predictive model for the air film pressure of a foil dynamic pressure radial gas bearing under constant load (1) Creep of corrugated foil material obeys Norton creep rate model is the creep rate, σ is the stress, E is the material constant, and n is the creep exponent; Derivation (2) To calculate the creep of the corrugated foil, we first need to calculate the air film pressure: The film thickness equation is: h(θ)=C+e cos(θ-θ0)+δ(θ,z) C is the clearance, e is the eccentricity between the bearing and the rotor, θ0 is the eccentricity angle, and δ(θ,z) is the deformation of the wave foil. The Reynolds equation is P = P / P0 is the dimensionless air film pressure, H = h(θ) / C is the dimensionless air film, Z = Z / R is the dimensionless length of the bearing, Λ = 6μωR 2 / P0C 2 is the number of bearings, τ e =vt is the dimensionless time, P0 is the atmospheric pressure, C is the nominal bearing clearance, R is the bearing radius, μ is the friction coefficient, ω is the angular velocity, and ν is the excitation ratio; The dynamic dimensional gas pressure supported by the corrugated foil can be expressed as Calculate the air film force F and determine whether it converges. If not, substitute the equilibrium position e and θ0 into the air film thickness equation, iterate repeatedly, and obtain a stable air film force F. The air film pressure at this time is the air film pressure P that the bearing is subjected to under the secondary load. Step 4: Establish a creep remaining life prediction model for foil dynamic pressure radial gas bearings. The creep amount of corrugated foil is solved by using Norton creep formula; Structural equation of wave foil Original y = ax 2 + h bump Decompose the air film pressure on the foil and calculate the creep amount of each section separately P=P1+P2+…P 2n Substituting into the creep formula Then the creep amount of each segment is brought into the shape formula of a single segment of corrugated foil for solution; After creep y = a′x 2 +h′ bump δ cr =h bump -h′ bump Perform loop iterations to determine the creep amount δ cr Whether it exceeds the threshold, solve the bearing foil failure after the rotor rotates N times, and obtain the bearing creep life.

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