A method for predicting rotor / stator rub fault of an aero-engine rotor system

Abstract

The application provides a rotating / stationary rubbing fault prediction method for an aero-engine rotor system, the relationship between the rotating speed and the amplitude is determined by collecting rotating speed and amplitude data of the rotor system, and a competitive failure system modeling and reliability evaluation method considering the coupling effect of dynamic environment and regional impact is proposed through mechanism analysis, the rotor speed is studied in sections, and the reliability evaluation model of the rotating / stationary rubbing phenomenon is further refined, the analytical result of the first failure time is given, and the precision level of the reliability evaluation of the rotor system is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of reliability analysis of aero-engine rotor-casing, and relates to a method for failure prediction of rotor-casing rub-impact failure of an aero-engine rotor system under a dynamic environment. BACKGROUND

[0002] An aero-engine is a device for providing power for an aircraft and propelling the aircraft forward, and is a decisive factor for performance, reliability and cost of the aircraft. The aero-engine technology is an important symbol of a country's military equipment level, scientific and industrial strength and comprehensive national power. A rotor-casing system is a core component of an aero-engine, and is subjected to the action of complex environments such as mechanical excitation, aerodynamic excitation and thermal field in work, which leads to many failure modes of the rotor system, mainly including rotor-stator rub-impact failure, thermal bending failure, vibration failure, looseness failure, fatigue crack failure, rolling bearing failure and misalignment failure. Among them, the rotor-stator rub-impact is a serious failure often occurring in rotating machinery. The commonly said rotor-stator rub-impact phenomenon refers to that when the relative displacement of the rotor and the casing exceeds the installation gap of the two, the rotor and the casing will collide, contact and rub. The rub-impact makes the vibration intensified, the gradual evolution of local rub-impact will lead to whole rub-impact, and even cause the destruction of the whole shaft system, resulting in that the system cannot operate normally, and the direct and indirect economic losses are very huge. It can be seen that the research on the reliability analysis method has extremely important significance for the development of national economy and the progress of national defense.

[0003] The rotor system will experience a process from normal to degradation to failure during service, and a series of different performance degradation states will be experienced during this period. The accumulation of performance degradation will cause the gradual degradation of device function, the degradation of main performance indicators such as strength and stress in the system, and eventually the failure of the product. Specifically, as time goes on, the rotor and the casing are in constant contact and friction at the contact surface, which gradually leads to the system failure mode being called soft failure. During the constant friction of the system, unbalance, misalignment and different concentric phenomena occur in the rotor system, which leads to the collision between the rotor and the stator, and the range of collision gradually increases with the increase of the rotating speed, from local collision to full collision, and even shaft system failure. This sudden failure of the system due to random impact is called hard failure. However, the collision phenomenon will lead to dry friction, impact and other series of faults, so the two failure modes are dependent on each other and compete with each other. However, due to the harsh and variable working environment, the degradation speed of the equipment is getting faster and faster, and the rotor system is easily affected by unbalance excitation, disturbance, structural nonlinearity and other factors during work. These factors are prone to induce rotor system failure, and the efficiency of traditional vibration analysis method for rotor fault diagnosis is less than 70%, and it is helpless for accurate judgment of early (slight) fault. SUMMARY

[0004] The present application aims at the problem that the efficiency of traditional vibration analysis method for rotor fault diagnosis is low and it is difficult to accurately judge early (slight) fault, and proposes a rotor / stator rub-impact fault prediction method for aero-engine rotor system in dynamic environment, which analyzes the failure probability in a future period of time by calculating the reliability function of aero-engine rotor system.

[0005] The technical scheme of the present application is as follows:

[0006] A rotor / stator rub-impact fault prediction method for aero-engine rotor system, comprising the following steps:

[0007] Step 1: response characteristic analysis is carried out on the aero-engine rotor system of the same type as the actual aero-engine rotor system to obtain the corresponding relationship between the vibration displacement data of the aero-engine rotor system of this type and the rotor speed, determine the rub-impact form corresponding to different displacement intervals of the aero-engine rotor system of this type, and the speed interval corresponding to different rub-impact forms, and determine the total degradation amount expression corresponding to each rub-impact form;

[0008] Step 2: the speed and displacement of the actual aero-engine rotor system are collected, and the total degradation amount X(t) expression of the corresponding interval is brought into the calculation of MTTF according to the measured speed and displacement and the speed interval drawn in step 1:

[0009]

[0010] The mean time to failure (MTTF) of the actual aero-engine rotor system before the first failure of the system is calculated;

[0011] Wherein, F * (D s ,s) is the expression obtained after Laplace transform of F(D s ,t) with respect to t; and F(D s ,t) = 1-R(D s ,t), R(D s ,t) is the reliability function of the rotor system at time t, R(D s ,t) = ∑ i∈S R i (D s ,t) ; R i (D s ,t) is the conditional reliability function of the system, i.e. the reliability of the rotor system given that it has been running from the environment i; D s is the soft failure threshold;

[0012] Further, in step 1, the rubbing forms corresponding to different displacement intervals are divided into four sub-regions: a safe region, a partial damage region, a full damage region, and a dry friction region.

[0013] No rubbing occurs in the safe region, and when the impact size is in this region, it is considered to have no effect on the degradation process and will not produce additional degradation increments.

[0014] Partial rubbing occurs in the partial damage region, and when the impact size is in this region, it is considered to produce additional degradation increments with a probability ∈, and (1-∈) will not produce additional degradation increments.

[0015] Full rubbing occurs in the full damage region, and when the impact size is in this region, it is considered to definitely affect the degradation process and produce additional degradation increments.

[0016] Dry friction occurs in the dry friction region, and when the impact size is in this region, it is considered to directly cause damage to the rotor system and cause the system to fail.

[0017] Further, the conditional reliability function of the system is solved according to the formula

[0018]

[0019] ; wherein p4 represents the probability of the event of the impact falling into the fatal region, λ represents the number of events of the impact amplitude being less than D3 within a specified time, and D3 is a hard failure threshold.

[0020] ψij (D s The solution of (D ij (D s , t) (i≠j) and (D ii (D s , t) (i=j) is made about D s and t, and after double Laplace transformation, it is and Written in matrix form is:

[0021]

[0022] Where I is the unit matrix, is the matrix form of the double Laplace transformation of the total impact damage amount θ(t) of the system at t, Q1 is a transition rate matrix with all 0s on the diagonal, φ * (s) = e -p4λt ; Indicates the conditional probability About D s and t, double Laplace transformation, Indicates the conditional probability that the rotor system still works normally at t, and no environmental transition occurs from the environment i.

[0023] A computer readable storage medium stores a computer executable program, and the computer executable program is used to implement the above method when executed.

[0024] A computer system comprises one or more processors, the above computer readable storage medium, and one or more programs stored in the computer readable storage medium, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above method.

[0025] Advantages

[0026] The present application makes up for the deficiencies in the reliability modeling and evaluation method of the existing research that considers that impact will definitely affect the system, and innovatively proposes a modeling and reliability evaluation method of a competing failure system considering the coupling effect of dynamic environment and regional impact, further refines the reliability evaluation model of the rotor-stator rub-impact phenomenon, and innovatively divides the rotor speed into zones according to the influence of the rotor speed on the stator, thereby improving the precision level of the reliability evaluation of the rotor system.

[0027] Additional aspects and advantages of the present application will be in part apparent and in part pointed out hereinafter. BRIEF DESCRIPTION OF DRAWINGS

[0028] The above and / or additional aspects and advantages of the present application will become apparent and more readily appreciated from the following description, taken in conjunction with the following drawings of which:

[0029] Figure 1 : Schematic diagram of different situations of rotor rub-impact;

[0030] Figure 2 : Technology roadmap;

[0031] Figure 3 : Schematic diagram of rotor-blade-casing rub-impact test bed;

[0032] Figure 4 : Rub-impact test system; (a) acquisition test system, (b) DH5956 dynamic signal test analysis system;

[0033] Figure 5 : Rotational speed-displacement curve of rub-impact rotor;

[0034] Figure 6 : Schematic diagram of rotor rub-impact situation under different rotational speeds;

[0035] Figure 7 : State evolution path diagram of rotor system;

[0036] Figure 8 : Reliability result comparison of analytical method and Monte Carlo simulation method;

[0037] Figure 9 : Sensitivity analysis curve of system damage probability ∈;

[0038] Figure 10 : Sensitivity analysis curve of soft failure threshold D s

[0039] Figure 11 : Sensitivity analysis curve of hard failure threshold D3;

[0040] Figure 12 : Sensitivity analysis curve of impact arrival rate λ. DETAILED DESCRIPTION

[0041] ​The rotating / stationary rubbing phenomenon refers to that when the relative displacement of the rotor and the casing exceeds the installation gap of the two, the rotor and the casing will collide, contact and rub. In the reliability modeling evaluation of the rotor system, two aspects are considered. On the one hand, with the passage of time, the surfaces of the stator and the rotor are constantly rubbed, and when the amount of rubbing reaches a certain threshold, soft failure is caused. On the other hand, due to constant rubbing, the rotor system appears uneven mass distribution due to imbalance and misalignment, which causes the rotor to constantly collide with the stator during operation, and as the speed increases, the range of collision gradually increases, from local rubbing to whole rubbing, until hard failure is triggered.

[0042] With the passage of time, the contact surfaces are constantly rubbed, which increases the probability of the occurrence of the rubbing phenomenon, and the rubbing phenomenon brings a certain sudden increase in the degradation of the degradation process, thereby accelerating the occurrence of soft failure. It can be seen that the soft and hard failures are interdependent, and the occurrence of any failure will cause direct failure of the system, so they are also in a competitive relationship. In traditional research, it is generally believed that the rubbing phenomenon will affect the rubbing process, however, when the rotating speed is low, the rubbing phenomenon is very weak and will not have a significant impact on the system. At the same time, with the improvement of the material properties today, the system itself has the ability to resist part of the external impact. Therefore, the present application fully considers the above factors, and the impact of the rubbing phenomenon on the system is considered in combination with the size of the rotating speed to divide it into: a safe zone, a partially damaged zone, a whole damaged zone, and a fatal zone. The rotor rubbing phenomenon in different zones is as shown in Figure 1 .

[0043] In addition, today's rotating machinery is widely used in engine, centrifuge, steam turbine and other mechanical parts, and is an indispensable key equipment in the fields of aviation, transportation, railway and the like. Therefore, the system may need to work in a dynamic environment or perform various complex tasks, such as unmanned aerial vehicles operating in different seasons, or having multiple control modes. The degradation process of the rotor system will also be significantly affected by the environment. Therefore, normal use in different environments also becomes an important aspect affecting its reliability, and the dynamic environment is one of the key factors affecting the failure process, such as the humidity and temperature of the working environment of the engine. For example, the amount of debris generated between structures increases as the humidity decreases.

[0044] The following takes the aircraft engine rotor system as an object to completely describe the whole process of the present application:

[0045] I: Data acquisition and analysis of the aircraft engine rotor system

[0046] Friction impact between rotor and stator is one of the common faults in rotating machinery. Serious friction can cause rotor instability, blade fracture and engine structure damage. The occurrence of rub-impact fault can also cause unnecessary vibration of the rotor, and in severe cases, cause engine failure. Therefore, it is of great significance to study the friction impact between the rotor and the stator of the engine. The development of sensors makes it possible to monitor the equipment online. During the operation of the system, the time-domain amplitude data measured by the sensor is stored by arranging eddy current sensors inside the rotor structure to monitor the vibration displacement response of the rotating shaft. In this embodiment, the specific experimental composition and experimental test method are as follows:

[0047] The rotor system test bench is shown in Figure 3 , which is composed of a power system, a rotor system, a feeding system and a test system. The power system includes a motor and a coupling. The composition of the rotor system includes a rigid shaft and a rigid disc. The simulated blades are fixed on the disc by dovetail joints. The entire rotor system is installed on two ball bearings and driven by a motor. The feeding system is mainly composed of a screw guide device, and the feeding amount is controlled by a servo motor, with an accuracy of 1 μm. Connected above the screw is an elastic casing, which has an arc and its center is flush with the center of the rotor. The main parts of the test bench can be summarized as motor, coupling, bearing, stepped shaft, wheel disc and straight blade.

[0048] The measurement system is composed of two eddy current displacement sensors. The eddy current sensors are arranged near the rotating shaft close to the wheel disc to measure the horizontal and vertical displacement of the wheel disc vibration, respectively. The vibration test system used is shown in Figure 4 , which is mainly composed of a computer, a test analyzer, an eddy current displacement sensor (pre-amplifier and probe), a voltage measurement device and a speed regulation device. The test analyzer uses a DH5956 type 8 channel dynamic signal test analysis system, with a maximum continuous sampling rate of 100 kHz and an A / D accuracy of 24 bits, and a maximum analysis bandwidth of DC~40 kHz. The displacement sensor used is a DH902 eddy current sensor, with a probe (model: OD9008-03-04-50-00) range of 0.8mm~2.8mm, sensitivity of 5V / mm, and pre-amplifier (model: OD900800-50-05) providing ±15VDC power supply for the probe. The voltage measurement system uses a double-channel contact detector. The speed regulation system uses a Comau KV2000 non-inductive vector type frequency converter, which controls the speed by adjusting the frequency, with an adjustment accuracy of 0.1 Hz. The speed regulation motor is a Panasonic MINASA5E AC servo motor, with a maximum command pulse frequency of 4Mpps.

[0049] In the process of rotor system test, the rotor-stator gap, the speed range and the speed increasing rate are set, and then the test is carried out. The vibration signal is collected by the eddy current sensor and input into the dynamic signal test analysis system. The system can obtain the horizontal and vertical displacement of the real-time vibration of the measuring point and record it in the memory.

[0050] After obtaining the original experimental data, the collected data need to be preprocessed. In order to keep the connection between the data as much as possible, the polynomial fitting method is used to process the data, and the vibration displacement data and the rotor speed are corresponded, and the expression of the speed and amplitude is obtained as follows:

[0051] f(x) = 2.074 * 10 -15 *x 3 - 3.135 * 10 -11 *x 2 + 1.683 * 10 -7 *x - 1.48 * 10 -5

[0052] The fitted curve is drawn as shown in Figure 5 , where the abscissa is the rotor speed and the ordinate is the displacement. In addition, in order to show the relationship between the size of the rotor speed and the displacement size in different rub-impact phenomena, the curve is divided into four parts along the y-axis, which is marked at the right end of Figure 5 .

[0053] II. Analysis of the process of rotor rub-impact failure

[0054] In order to study the reliability of the rotor system in each process in detail, combined with the curve fitting results of the rotor speed-displacement in the first part, the region is divided, and the damage of the system is different in different regions. The dynamics characteristics of the corresponding structure are studied by simulation, and several possible cases are given, as shown in Figure 6 .

[0055] From Figure 6 , it can be known that when the rotor speed is lower than 1820 rpm, there is no rub-impact phenomenon, when the speed is in [1820 rpm, 3200 rpm), part of the rub-impact phenomenon begins to appear; when the speed is in [3200 rpm, 10700 rpm), the rub-impact phenomenon begins to gradually expand the range, and the full rub-impact phenomenon appears; when the rotor speed is further increased, higher than 10700 rpm, the dry friction whirl phenomenon appears, and the rotor system directly fails.

[0056] According to the rub-impact situation in different regions, the region is divided, and the non-negative random variable representing the strength of the i th impact process is defined, and the non-negative random variable represents the damage caused by the impact to the system, let X(t) represent the total degradation of the system at time t, W(t) represent the cumulative performance degradation of the system at time t, and ∈ represent the probability of damage caused by the impact to the system, and the specific sub-regions are represented as follows:

[0057] I. Safe region: no rubbing occurs, L i ∈ [0, 1820), when the impact size is in this region, due to the strength of the material and the structure, the rotor system's ability to resist impact is affected, so it is considered to have no effect on the degradation process and will not produce additional degradation increment Y i ; at this time, X(t) = W(t).

[0058] II. Partial damage region: partial rubbing occurs, L i ∈ [1820, 3200), when the impact size is in this region, due to the robustness of the system and the ability to resist impact, which will decrease with the degradation of the system, it is considered that with a probability ∈, additional degradation increment Y i ; at this time, X(t) = W(t) + (1-∈)Y i .

[0059] III. Full damage region: full rubbing occurs, L i ∈ [3200, 10700), when the impact size is in this region, as the micro-turbine deteriorates, its ability to resist impact also decreases, it is considered that it will definitely affect the degradation process and produce additional degradation increment Y i ; at this time, X(t) = W(t) + Y i .

[0060] IV. Dry friction region: dry friction occurs, L i ∈ [10700, ∞), when the impact size is in this region, it is considered to directly cause damage to the rotor system and cause system failure.

[0061] Three, establish a rotor system failure prediction model

[0062] In order to obtain the rotor reliability analysis and failure prediction model, the working mechanism and failure mode of the rotor system are modeled according to the above four different regions. The parameters involved in the model are summarized in Table 1.

[0063] Table 1. Parameter settings involved in the model

[0064]

[0065] 1. Basic failure model of rotor system and related assumptions

[0066] After obtaining the real-time monitoring data of the engine, a rotor system failure prediction model is established according to the working mode of the system. It is assumed that the initial degradation amount of the rotor system at t=0 is 0. With the passage of time, the system randomly experiences different working environments, such as high temperature, extreme cold, etc., and in each environment, the system experiences a performance degradation process with different degradation rates and a random shock process with different arrival rates. The system has two failure modes:

[0067] (1) Degradation failure: the performance degradation amount of the system is composed of two parts, which can be regarded as the sum of internal and external. The internal refers to the continuous performance degradation amount generated by the continuous friction between the stator and the rotor in the process of normal use of the rotor system over time, while the external is the sudden increase in performance degradation amount caused by each external random shock. The sum of the two parts is the total degradation amount of the system. When the total performance degradation amount exceeds the soft failure threshold D s of the rotor system, the system fails, which is called degradation failure, i.e. soft failure;

[0068] (2) Sudden failure: when the intensity of the random shock exceeds the hard failure threshold D3 of the rotor system, the system fails, which is called sudden failure, i.e. hard failure

[0069] In actual engineering, soft failure and hard failure exist at the same time, and the occurrence of any one of the two failure modes can lead to system failure, so this model is regarded as a competing failure reliability model. The related assumptions of the system that simultaneously experiences continuous degradation based on Gamma process and random shock in dynamic environment are described as follows:

[0070] Assumption 1: It is assumed that there are different working environments that randomly run over time, and the transition law between different environments can be described by a continuous-time Markov process {Z(t), t≥0} that is time-homogeneous. Z(t) is defined as a symbol representing the state of the environment at time t. Assuming that there are k time-switchable environments, the environment state space S composed of k time-switchable environments is S={1,2,...,k} and the matrix π(t)={π ij (t),i,j∈S}, Q={Q ij ,i,j∈S} and the vector v={v k ,k∈S} are the transition probability matrix, transition rate matrix and initial probability distribution of the process {Z(t), t≥0}, respectively.

[0071] Assumption 2: Over time, the system undergoes irreversible degradation after it begins operation, and this degradation process is influenced by the dynamic external environment. Assume the initial degradation at time t = 0 is zero, and the system's performance degradation accumulates continuously during operation. The system's performance degradation follows different patterns in different operating environments, specifically exhibiting a Gamma distribution with different parameters. When Z(t) = k (k ∈ S), the system operates in operating environment k, and its degradation follows a pattern with a shape parameter α. k >0, scale parameter is β k A stationary Gamma process >0 {W k The rotor system performance degradation rate is described by r (t), t≥0}. k =α k / β k In other words, for t>0 and time increment δ>0, the increment W k (t+δ)-W k (δ)>0 follows a shape parameter α k t, scale parameter β k The Gamma distribution has a probability density function that can be written as:

[0072]

[0073] Where, α k >0, β k >0; It is the Gamma function; I {A} This is an indicator function whose value is 1 only when event A occurs, and 0 otherwise. Then, the cumulative degradation of the system at time t is expressed as {W(t), t≥0}, where W(t)=W(h)+W k (th), where Z(h-) ≠ k, and for any s ∈ [h, t], Z(s) = k. It is important to note that the system does not undergo any degradation when t = 0, which means W(0) = 0. And define... This represents the probability that no soft failure occurs in the system at time t.

[0074] Hypothesis 3: When the system is subjected to a random shock, the dynamic environment has a significant impact on the following factors during the shock arrival process, and these impacts are specifically manifested as follows:

[0075] 1) Impact arrival time: Assume a homogeneous Poisson process {N(t), t≥0} is used to describe the impact process experienced by the system, where N(t) represents the number of impacts occurring within the time interval [0,t] under the given environment. Due to the influence of the working environment, in working environment k (k∈S), the impact process has an arrival rate of λ. k (λ kA homogeneous Poisson process with arrival rate λk= λk+ kλ, k ∈ S. That is, there is a correspondence When Z(t) = k, the arrival rate of the homogeneous Poisson process is λk k .

[0076] 2) Threshold of hard failure: the impact of the shock on the system is two- fold, on one hand, when the intensity of the shock exceeds a certain given value D3, the system fails, which is called sudden failure, i.e. hard failure.

[0077] 3) Threshold of soft failure: each shock results in a sudden increase of the performance degradation of the system, and the sum of the degradation caused by the continuous performance degradation and the sudden increase is the total degradation of the system. When the total degradation exceeds a certain preset value D s , the system fails, which is called degradation failure, i.e. soft failure.

[0078] 4) Impact of the shock: the performance degradation of the rotor system caused by each shock is represented by an independent and identically distributed non-negative random variable Yi, which represents the performance degradation caused by the i-th shock process, and is assumed to be subject to a normal distribution N(1, 0.1 i ), with a cumulative distribution function F 2 (y) = P{Y≤y} and a probability density function f Y (y). At the same time, an independent and identically distributed non-negative random variable Li, which represents the intensity of the i-th shock process, is assumed to be subject to a normal distribution N(1, 0.1 Y ), with a cumulative distribution function F L (x) = P{L≤x} and a probability density function f L (x). Therefore, the performance degradation of the system caused by the shock up to time t can be represented as

[0079]

[0080] where N(t) represents the total number of shocks up to time t. The total shock damage of the system at time t is represented as θ(t) = θ(h) + θ k (t-h), where Z(h - )≠k, and for any s ∈ [h, t], Z(s) = k.

[0081] 5) Competing failure mode: both sudden failure and degradation failure exist, and when either of the failure modes occurs, the system immediately fails, and the other failure mode no longer occurs, so the model can be regarded as a competing failure reliability model. Let X(t) represent the cumulative degradation of the system, therefore, based on the above assumptions, the total degradation of the performance of the rotor system at time t can be expressed as

[0082]

[0083] To make the model setting more clear, the possible state evolution path of the rotor system during operation is plotted as shown in Figure 7 Figure 7 It can be seen from the figure that the evolution path of the rotor system due to soft and hard failure is shown in the figure. In the first stage T1, the system is subjected to three impacts. The first impact L1∈[0, D1) falls into the safe region, so it has no effect on the system. The second impact L2∈[D1, D2) falls into the partial rubbing region, which causes damage to the system with a certain probability. As can be seen from the figure, the impact causes a sudden increase in the degradation amount, i.e., Y2. The third impact L3∈[D2, D3) indicates that full rubbing occurs. As can be seen from the figure, the impact causes a sudden increase in the degradation amount, i.e., Y3. With the natural degradation of the system, the degradation amount eventually exceeds the soft failure threshold D s , and the system fails due to soft failure. In the first stage T2, the system is subjected to two impacts. The first impact L4∈[D1, D2) causes damage to the system with a certain probability. As can be seen from the figure, the impact has no effect on the system. The second impact L5∈[D3, ∞) is the fatal region, and the system is directly damaged due to hard failure.

[0084] 2. Analytical calculation of the reliability of the rotor system

[0085] Based on the analysis of the failure modes of the rotor system in the foregoing, this part uses an analytical method to solve the analytical expressions of the system reliability function and the mean time to first failure on this basis.

[0086] According to the homogeneous Poisson assumption of the impact arrival rate, for any t>0, N(t)>0 is a non-negative random variable that obeys the Poisson distribution expression, which is

[0087]

[0088] where P{N(t)=0}=1 indicates that when t=0, no impact arrives.

[0089] Since the impact is divided into four regions for consideration, F L (x) is used here to represent the distribution function of different events x, and p1, p2, p3, and p4 represent the probability values of the events of the impact falling into the four intervals of the safe region, the partial damage region, the full damage region, and the fatal region, respectively. They can be represented as

[0090] p1=F L (D1), p2=F L (D2)-F L (D1), p3=F L (D3)-F L ​(D2), p4 = 1 - F L (D3)

[0091] Assume that the shocks in different zones obey Poisson distribution, N1(t), N2(t), N3(t), N4(t) represent the Poisson distribution of the shocks falling into different zones, for example, in the SZ zone, the homogeneous Poisson distribution {N1(t), t≥0} is obeyed. In addition, pi + p2 + p3 + p4 = 1.

[0092] According to the extreme shock model, when the stress is no longer less than the strength, the system failure is triggered. As described earlier, when the shock amplitude is greater than D3, i.e. falling into the FZ zone, the distribution N4(t) obeying p4λ will directly lead to the occurrence of hard failure, so the probability of no hard failure of the system before time t is

[0093]

[0094] where, represents the maximum shock amplitude suffered by the system up to time t. λ represents the number of events in which the shock amplitude is less than D3 within a specified time.

[0095] From the above formula, if only hard failure is considered, the failure of the system is inevitable during operation. At the same time, due to the uniformity of the Poisson process, we can get Let represent the probability of no hard failure up to time t.

[0096] The reliability function of the rotor system is the probability that neither soft failure nor hard failure has occurred up to time t, which can be expressed in the following form

[0097]

[0098] At the same time, without loss of generality, let P i {·} = P i {·|Z(0) = i} represents the conditional probability of the system starting from environment i at time t = 0. Therefore, if given starting from environment i, the conditional reliability function of the rotor system can be defined as

[0099]

[0100] Therefore, from formula (1), it can be seen that the key to solving the reliability function R i (D s , t) of the rotor system is to solve the conditional probability P

[0101] Proposition 1.

[0102] Conditional probability H i (D s ,t) is defined as the expression of the soft failure occurring and the hard failure not occurring before t, and the environmental state i starting from the beginning to t, without any change, as follows:

[0103]

[0104] The detailed proof of the corollary 1 is shown in Appendix A.

[0105] The expression in the corollary 1 is difficult to calculate due to the double convolution integral. The expression can be made more compact by using the double Laplace transform. Therefore, the double Laplace transform of H i (D s ,t) with respect to D s and t is

[0106]

[0107] where s and u are complex numbers. Therefore, the inverse Laplace transform of the above expression with respect to D s is

[0108]

[0109] Further, the Laplace transform of both sides of the above expression can be obtained as

[0110]

[0111] where

[0112]

[0113] Corollary 2.

[0114] The double Laplace transform of ψ ij (D s ,t) with respect to D s and t is

[0115]

[0116] The double Laplace transform of ψ ii (D s ,t) with respect to D s and t is

[0117]

[0118] where,

[0119]

[0120]

[0121] The detailed proof of Corollary 2 is given in Appendix B.

[0122] The expression in Corollary 2 above can be expressed as follows:

[0123]

[0124]

[0125]

[0126]

[0127] The above equation can be written in matrix form as follows.

[0128]

[0129] After sorting, we can obtain

[0130]

[0131] Theorem 1:

[0132] Because rotor systems subject to multi-dependency competition failure operate in dynamic environments, R(D) s ,t) do about D s The double Laplace transform of t can be written in the following form:

[0133]

[0134] Proof: According to formula (1), for R(D) s ,t) do about D s The double Laplace transform of t, written in matrix form, is:

[0135]

[0136] Therefore, Theorem 1 can be obtained by combining equations (1), (9) and (11).

[0137] Based on Theorem 1, we can use a system-based approach. To obtain the system, perform double inverse Laplace transforms on u and s respectively. The unconditional reliability function R(D) s ,t). At the same time, we can use R(D) s We obtain the distribution function of the first failure time (t). Assume T1 is a random variable representing the first failure time of the rotor system, then we have...

[0138]

[0139] F(D s ,t) is double Laplace transformed with respect to D s and t, and can be written as follows:

[0140]

[0141] In addition, in order to facilitate the decision maker to understand the system more comprehensively, the average time to failure (MTTF) of the system before the first failure can be obtained from the above, that is, when the conversion variable is zero, the expected negative value of the random variable is equal to the derivative of the Laplace transform of its probability density function. Therefore

[0142]

[0143] where F * (D s ,s) is the Laplace transform of the cumulative distribution function of the system lifetime F(D s ,s) with respect to t, which can be based on its relationship with the reliability function to obtain the formula of the average time to failure (MTTF) before the first failure of the system.

[0144] 3. Rotating system reliability failure prediction

[0145] In order to verify the correctness and universality of the above method, the data of the rotating system is sorted into the above model. Generally, the rotating system is put into use at t=0 and is considered to have no any pre-degradation. The working environment of the rotating system is affected by the dynamic change of the working environment during the operation, the working environment changes with time, and the natural degradation rate of the rotating system is different under different environments. The air humidity has a greater impact on the friction between the rotor and the stator. The higher the air humidity, the smaller the friction between the structures, and the lower the degradation rate. Conversely, the lower the air humidity, the greater the friction between the structures, and the higher the degradation rate.

[0146] Since the Markov process is always used to describe the change of external state, such as temperature, humidity, and the sojourn time in each state obeys the exponential distribution, it is considered to have Markov feature and is described by Markov process. Therefore, the Markov process Z(t) is defined to describe the evolution of air humidity, wherein the transition rate matrix between different environments is as follows

[0147]

[0148] It is assumed that the system is put into use from the lowest humidity, that is, the initial probability distribution of Z(t) is α=(1, 0, 0,.

[0149] Since the wear of the contact surface is irreversible and presents a monotonic increasing form with time, the Gamma process model is adopted to describe the process of debris generated by friction on the contact surface. Meanwhile, the generation of debris between the contact surfaces is significantly affected by air humidity. The higher the air humidity, the less debris is generated. Assuming that the system is put into use with the same probability from spring, summer, autumn and winter, that is, the seasonal rotation is controlled by the time-homogeneous Markov process {Z(t), t>0}, the degradation behavior of the rotor system in different environments follows different Gamma processes, and the degradation rates of the rotor system in different environments are assumed to be r i =α i / β i , α1=10, β1=100, α2=20, β2=100, α3=30, β3=100, α4=40, β4=100, that is, r=diag{0.1, 0.2, 0.3, 0.4}.

[0150] Based on the Gaver-Stehfest algorithm, combined with expression (1), the reliability function of the rotor system is drawn assuming D s =8 by using the numerical inversion of Laplace transform as shown in Figure 8 .

[0151] As can be seen from Figure 8 , the system reliability curves calculated by the analytical calculation method and the Monte Carlo simulation program are basically coincident, verifying the correctness of the method.

[0152] It is worth noting that in the partial damage region, when the probability of impact on the degradation process is set to ∈=1, ∈=0, ∈=(L i -D1) / (D2-D1), it corresponds to three cases that impact will definitely affect the system, will not affect the system and with the increase of the rotating speed, the probability of affecting the system also increases. In order to reflect the innovation and practicality of the method proposed in this paper, the reliability curves in the three cases are compared. As shown in Figure 9 .

[0153] 4. Sensitivity analysis of the failure prediction model

[0154] In order to evaluate the influence of model parameters on the reliability of the rotor system, the sensitivity analysis of the soft failure threshold D s , the hard failure threshold D3, the impact arrival rate λ and the system damage probability ∈ is carried out, and the results are shown in Figures 10 to 12 .

[0155] Through the sensitivity analysis of the soft failure threshold D sThe sensitivity analysis of the hard failure threshold D3, the shock arrival rate λ and the system damage probability ∈ shows that with the increase of D3 and the decrease of λ and ∈, the performance of the engine rotor system can be effectively improved. At the same time, with the decrease of λ and ∈, the reliability of the rotor system is also effectively improved. s The sensitivity analysis of the hard failure threshold D3, the shock arrival rate λ and the system damage probability ∈ shows that with the increase of D3 and the decrease of λ and ∈, the performance of the engine rotor system can be effectively improved. At the same time, with the decrease of λ and ∈, the reliability of the rotor system is also effectively improved.

[0156] Appendix:

[0157] Appendix A

[0158] Let P (t) denote the conditional probability that the rotor system is still working at time t, and no transition of the environment has occurred since the environment i. At the same time, let N h (t) denote the number of harmful shocks that have occurred in (0, t], so that the random shock obeys the homogeneous Poisson distribution {N h (t), t≥0} with the arrival rate p h λ, p h = p2+ p3+ p4. Therefore, we have

[0159]

[0160] Therefore, we have

[0161]

[0162] The proof is completed.

[0163] Appendix B

[0164] In order to solve R ij (D s ,t), we also need to solve ψ ij (D s ,t), so (1) first, consider when i = j,

[0165]

[0166]

[0167] (2) second, consider when i≠j,

[0168]

[0169]

[0170] For ψ ij (D s ,t), we do the double Laplace transform with respect to D s and t, which can be written as follows:

[0171]

[0172]

[0173] wherein,

[0174]

[0175] Q.E.D.

[0176] Although the embodiments of the present application have been shown and described above, it should be understood by those skilled in the art that the above embodiments are exemplary, and cannot be understood as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments without departing from the principles and spirits of the present application within the scope of the present application.

Claims

1. A method for predicting rotor / static rubbing faults in aero-engine rotor systems, characterized in that: Includes the following steps: Step 1: Analyze the response characteristics of an aero-engine rotor system of the same type as the actual aero-engine rotor system, obtain the correspondence between the vibration displacement data and the rotor speed of this type of aero-engine rotor system, determine the rubbing mode corresponding to different displacement ranges of this type of aero-engine rotor system, as well as the speed range corresponding to different rubbing modes, and determine the expression for the total degradation amount corresponding to each rubbing mode. Step 2: Collect the actual rotational speed and displacement of the aero-engine rotor system, and based on the measured rotational speed and displacement, combined with the rotational speed range defined in Step 1, substitute the expression for the total degradation amount X(t) of the corresponding range to calculate the MTTF: The mean time to failure (MTTF) before the first system failure of an actual aero-engine rotor system was calculated. in, for Do about The expression obtained after the Laplace transform; and , For the rotor system in The reliability function at time t. ; Let be the conditional reliability function of the system, i.e., given the environment. The reliability of the rotor system at the start of operation; This is the soft failure threshold; The conditional reliability function of the system is based on the formula: Solve the problem; where This indicates the probability of an event occurring where the victim falls into the lethal zone. This indicates that the impact amplitude is less than [a certain value] within the specified time. The number of times the event occurred. This is the hard failure threshold; right The solution is divided into two parts. and To make a statement about both and After the double Laplace transform, it becomes and In matrix form: ； in It is the identity matrix. Is the system in Total impact damage at time The matrix form after the double Laplace transform, It is a transition rate matrix where all values ​​on the diagonal are 0. ; Represents conditional probability about and The double Laplace transform, express The conditional probability that the rotor system will still operate normally at any given time, and from the environment Initially, no change in environment occurred.

2. The method for predicting rotor / static rubbing faults in an aero-engine rotor system according to claim 1, characterized in that: In step 1, the rubbing patterns corresponding to different displacement ranges are divided into four zones: safe zone, partial failure zone, full circumference failure zone, and dry friction zone. The safe zone is free from collisions. When the magnitude of an impact is within this zone, it is considered to have no effect on the degradation process and will not produce additional degradation increments. Partial contact occurs in the damaged area; when the impact magnitude is within this area, it is considered to occur with probability. This generates additional degradation increments, in order to It will not produce additional degradation increments; The full-circumference damage zone is where full-circumference impact occurs. When the impact magnitude is within this zone, it is believed that it will definitely affect the degradation process and produce additional degradation increment. Dry friction occurs in the dry friction zone. When the impact magnitude is within this zone, it is considered to directly cause damage to the rotor system, resulting in system failure.

3. A computer-readable storage medium storing a computer-executable program, which, when executed, is used to implement the method of any one of claims 1 to 2.

4. A computer system, comprising: One or more processors, the computer-readable storage medium of claim 3, for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 2.

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