Aero-engine rotor blade tip assembly clearance prediction method considering multi-source uncertainty

Abstract

The invention provides an aero-engine rotor blade tip assembly clearance prediction method considering multi-source uncertainty, and the method comprises the steps: analyzing the uncertainty affecting the rotor blade tip assembly clearance, and determining that the level of the rotor blade tip assembly clearance is divided into a phase layer, a blade layer and a blade disc layer; the uncertainty is quantized into an uncertainty variable; and in combination with the deterministic prediction model, calculating to obtain a prediction response of a phase layer by taking the uncertainty variable as input, then calculating to obtain a prediction response of a leaf layer by taking the prediction response of the phase layer as input, and finally calculating to obtain a prediction response of a leaf disc layer by taking the prediction response of the leaf layer as input. According to the method, the multi-source uncertainty in rotor blade tip assembly is considered and quantified, the quantified result serves as input, the blade tip assembly clearance is predicted gradually and progressively from the blade phase to the blade to the blade disc in three levels, the rotor blade tip assembly clearance under the uncertainty condition can be predicted accurately, and the accuracy of the rotor blade tip assembly clearance prediction is improved. And the high-reliability assembly requirement of the blade tip is met.

Description

Technical Field

[0001] The invention belongs to the technical field of aero-engine assembly, and in particular relates to a method for predicting assembly clearance of an aero-engine rotor blade tip taking into account multi-source uncertainties. Background Art

[0002] In the assembly of aircraft engine rotors, the rotor tip clearance is an important indicator that affects the engine safety and performance. Excessive or uneven distribution of the rotor tip assembly clearance will increase the risk of collision and friction of the engine in operation, or reduce its aerodynamic performance. Accurately predicting the rotor tip assembly clearance is a prerequisite for achieving precise control of the assembly clearance.

[0003] At present, there are two main prediction methods for the assembly clearance of the blade tip of an aircraft engine rotor: 1) a deterministic prediction method based on the error transfer principle; 2) an interval prediction method based on interval calculation. However, due to the limited measurement data of part manufacturing deviations, such as the runout data of the casing stop and the runout data of the front and rear pivots, it is difficult to accurately characterize the part manufacturing deviations; at the same time, the assembly process execution is usually based on experience, which introduces a lot of uncertainty, making it difficult for the two existing methods to accurately predict. The former ignores various uncertainty factors and only considers deterministic results; although the latter quantifies the uncertainty into intervals, it is impossible to determine the probability distribution of the blade tip clearance within the interval, and it is still difficult to guide the optimization of process parameters through prediction, and it cannot meet the requirements of high-reliability assembly. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of inaccurate prediction of the assembly clearance of an aero-engine rotor blade tip under uncertainty conditions in the prior art, and to provide an aero-engine rotor blade tip assembly clearance prediction method taking into account multi-source uncertainty.

[0005] To achieve the above purpose, the technical solution provided by the present invention is:

[0006] The present invention provides a method for predicting the assembly clearance of an aero-engine rotor blade tip considering multi-source uncertainties, comprising the following steps:

[0007] Step 1, analyzing the uncertainty affecting the rotor blade tip assembly clearance and determining the rotor blade tip assembly clearance level;

[0008] The blade tip assembly clearance level is divided into phase layer, blade layer and blade disk layer. The phase layer represents the tip clearance of the jth blade of the i-th blade disk at the δ phase. The blade layer is the cumulative amount of the phase layer, which represents the tip clearance of the jth blade of the i-th blade disk at all phases. The blade disk layer is the cumulative amount of the blade layer, which represents the cumulative amount of all blades of the i-th blade disk at all phases.

[0009] Step 2: Based on the uncertainty analysis results of step 1, design a corresponding uncertainty quantification algorithm to quantify the uncertainty into uncertainty variables;

[0010] Step 3, combining the deterministic prediction model, constructing the rotor blade tip assembly clearance prediction model of the jth blade of the i-th blade disk at the δ phase, taking the uncertainty variables in step 2 as input, and calculating the predicted response of the phase layer;

[0011] Step 4, combining the deterministic prediction model, constructing the prediction model of the rotor blade tip assembly clearance of the jth blade of the i-th blade disk, taking the phase layer prediction response obtained in step 3 as input, and calculating the prediction response of the blade layer;

[0012] Step 5, combining the deterministic prediction model, constructing the i-th level blade disk rotor blade tip assembly clearance prediction model, using the blade layer prediction response obtained in step 4 as input, and calculating the blade disk layer prediction response.

[0013] Furthermore, in step 1, the uncertainty affecting the rotor blade tip assembly clearance is analyzed to include part / component uncertainty and assembly execution uncertainty; part / component uncertainty includes blade disk assembly uncertainty and casing uncertainty, blade disk assembly uncertainty includes blade tip manufacturing uncertainty and blade disk assembly centroid uncertainty, casing uncertainty includes casing stop manufacturing uncertainty, front and rear support manufacturing uncertainty and compressor casing internal flow channel manufacturing uncertainty; assembly execution uncertainty includes adjustment gasket selection uncertainty and bearing clearance uncertainty.

[0014] Furthermore, in step 1, the uncertainty affecting the rotor blade tip assembly clearance is divided into sparse mixed uncertainty, random uncertainty and interval uncertainty; the sparse mixed uncertainty includes the manufacturing uncertainty of the casing stop and the manufacturing uncertainty of the front and rear support points; the random uncertainty includes the manufacturing uncertainty of the blade tip, the centroid uncertainty of the blade disk assembly and the manufacturing uncertainty of the flow path surface in the compressor casing; the interval uncertainty includes the uncertainty of adjusting the gasket selection and the uncertainty of the bearing clearance.

[0015] Furthermore, in step 2, for sparse mixed uncertainty, assuming that the sparse data set is D sd , then the sparse mixed uncertainty quantification method includes the following steps:

[0016] Step 2.1.1, calculate the data set D sd The positive proportion pp sd , construct D sd The absolute value data set D sdi ;

[0017] Step 2.1.2, another D sdiIt obeys six distributions: uniform distribution, normal distribution, lognormal distribution, exponential distribution, extreme value distribution and Weibull distribution. The distribution parameters of the six distributions are estimated by maximum likelihood estimation method.

[0018] Step 2.1.3, another D sdi It obeys mixed weighted distribution, and its probability density function is as follows. Its distribution parameters are estimated by genetic algorithm:

[0019]

[0020] In the formula, ω i represents the weight of the i-th probability density function, δ i is the probability density function indicator parameter, f i (x) represents the i-th probability density function;

[0021] Step 2.1.4, calculate the goodness of fit p of the above seven distributions by KS test method. If the maximum goodness of fit p max ≥α, α is the predetermined goodness of fit judgment threshold, then D sdi Obey p max Corresponding distribution, otherwise, D is estimated by kernel density estimation sdi The probability density function of D sdi The probability density function f output,sd (x);

[0022] Step 2.1.5, calculate D as follows sd The positive and negative function f sign,sd :

[0023]

[0024] Where n represents the sampling dimension and k represents the number of positive values.

[0025] Furthermore, in step 2, the quantification method of random uncertainty is similar to the quantification method of sparse mixed uncertainty, except that step 2.1.2 is omitted and the probability density function f of the random variable is obtained. output,rd (x) and the positive and negative function f sign,rd .

[0026] Furthermore, in step 2, for the quantification of interval uncertainty, the uncertainty of adjusting gasket selection and bearing clearance is quantified into interval variables according to the design tolerance, which are recorded as and

[0027] Further, step 3 includes:

[0028] Step 3.1, obtain measurement data and quantify uncertainty, where XR represents the random variable of the manufacturing error of the i-th level internal flow channel, X S Represents the sparse variables of the receiver stop and front and rear pivots, X I represents the interval uncertainty of assembly execution;

[0029] Step 3.2: discretize the interval variable of the adjustment shim, denoted as Set the adjustment shim interval variable to a fixed value q=1,2,…,m, the outermost loop traverses all adjustment shim interval variables;

[0030] Step 3.3, discretize the bearing clearance interval variable and record it as Let the bearing clearance interval variable be a fixed value p=1,2,…,k, the second layer loops through all bearing clearance interval variables;

[0031] Step 3.4, through the probability density function f output,sd (x) and f output,rd (x) respectively for X S and X R The value of is sampled by the positive and negative function f sign,sd and f sign,rd The positive and negative samples are sampled for n times, each sampling dimension is l, and the sampled data sets are recorded as and Let the random variables and sparse variables have fixed values and in, The innermost loop traverses the samples n times;

[0032] Step 3.5, the deterministic prediction model of the rotor tip clearance of the jth blade of the i-th blade disk at the δ phase is expressed as:

[0033]

[0034] In the formula, X D represents deterministic variables, including rotor blade tip manufacturing errors and blade disk centroid position;

[0035] Step 3.6, the deterministic prediction model of the rotor tip clearance expressed by the driver is used, and after three cycles, the rotor tip clearance prediction response tip considering uncertainty is obtained. i,j,δ , the dimension of the response dataset and the number of loops are m×k×n.

[0036] Further, step 4 includes:

[0037] Step 4.1, calculate the predicted response of the jth blade of the i-th blade disk at 360 phases and use it as input to construct the response matrix of the jth blade of the i-th blade disk, with a dimension of m×k, recorded as:

[0038]

[0039] In the formula, tip i,j is the predicted response of the jth blade of the i-th level blade disk, with a total of m×k subsets, and the dimension of each subset is 360×n.

[0040] Further, step 5 comprises:

[0041] Step 5.1, calculate the tip assembly clearance prediction response of the z blades of the i-th blade disk and use it as input to construct the response matrix of the i-th blade disk, with a dimension of m×k, recorded as:

[0042]

[0043] In the formula, tip i is the predicted response of the i-th level leaf disk, with a total of m×k subsets, and the dimension of each subset is 360×n×z.

[0044] Furthermore, step 5 also includes:

[0045] Step 5.2: Fit the CDF curve, obtain m×k CDF curves, and find their upper limit and lower limit Construct the probability box of the blade tip assembly clearance of the i-th level blade disk and calculate the mean interval of the blade tip clearance and tip clearance variance interval in and denote the lower and upper limits of the mean value of the tip clearance, respectively. and They represent the lower and upper limits of the tip clearance variance respectively.

[0046] The advantages of the present invention are:

[0047] 1. The method for predicting the assembly clearance of the rotor blade tip of an aero-engine considering multi-source uncertainties of the present invention quantifies the multi-source uncertainties brought about by manufacturing, measurement and process execution, divides the rotor blade tip assembly clearance into layers, and progressively divides it into phase layer, blade layer and blade disk layer according to different scales. The deterministic prediction model is used to calculate the predicted response of the phase layer with the quantified uncertainty variables as input, and then the predicted response of the blade layer is obtained with the predicted response of the phase layer as input, and finally the predicted response of the blade disk layer is obtained with the predicted response of the blade layer as input. Therefore, the present invention takes the multi-source uncertainties in the assembly of the rotor blade tip into consideration and quantifies them, and uses the quantified results as input to progressively predict the blade tip assembly clearance in three levels from blade phase to blade and then to blade disk, so as to accurately predict the rotor blade tip assembly clearance under uncertainty conditions and meet the high-reliability assembly requirements of the blade tip.

[0048] 2. The present invention combines a deterministic prediction model to express the rotor blade tip assembly clearance in the form of a probability box, and the result of the deterministic prediction is a point data, and the result of the interval prediction provides a range value without probability, both of which are inconsistent with the actual situation. The method provided by the present invention describes the probability of the rotor blade tip assembly clearance taking values ​​within a certain range through the upper and lower limits of the CDF curve, thereby more objectively and comprehensively evaluating the risk of out-of-tolerance of the rotor blade tip assembly clearance, helping engineers to make more reliable decisions on process parameters, thereby further improving the assembly reliability of the rotor blade tip. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The above and / or other features and advantages of the present invention will become more easily understood through the following description with reference to the accompanying drawings, in which:

[0050] Figure 1 It is a flow chart of the method for predicting the assembly clearance of an aero-engine rotor blade tip considering multi-source uncertainties of the present invention;

[0051] Figure 2 It is the analysis of the uncertainty affecting the rotor blade tip assembly clearance in the present invention;

[0052] Figure 3 is a flow chart of the sparse mixed uncertainty quantization algorithm of the present invention;

[0053] Figure 4 is a flow chart of the prediction of the rotor blade tip assembly clearance of the jth blade of the i-th blade disk at the δ phase in the present invention;

[0054] Figure 5 It is a schematic diagram of the engine structure in an example of the present invention;

[0055] Figure 6 It is the prediction result of the first stage rotor blade tip assembly clearance in the example of the present invention. DETAILED DESCRIPTION

[0056] The present invention will be described in detail below with reference to the accompanying drawings by means of exemplary embodiments of the present invention. It should be noted that the following detailed description of the present invention is only for the purpose of illustration, and is not intended to limit the present invention.

[0057] The present invention provides an aero-engine rotor blade tip assembly clearance prediction method considering multi-source uncertainties, which is used to accurately predict the blade tip assembly clearance by considering various uncertainties in the rotor blade tip assembly process.

[0058] Overall reference Figure 1 As an exemplary embodiment of the present invention, a method for predicting the assembly clearance of an aero-engine rotor blade tip considering multi-source uncertainty comprises the following steps:

[0059] Step S1, analyzing the uncertainty affecting the rotor blade tip assembly clearance and determining the rotor blade tip assembly clearance level;

[0060] The blade tip assembly clearance level is divided into phase layer, blade layer and blade disk layer. The phase layer represents the tip clearance of the jth blade of the i-th blade disk at the δ phase. The blade layer is the cumulative amount of the phase layer, which represents the tip clearance of the jth blade of the i-th blade disk at all phases. The blade disk layer is the cumulative amount of the blade layer, which represents the cumulative amount of all blades of the i-th blade disk at all phases.

[0061] Step S2, designing a corresponding uncertainty quantification algorithm for the uncertainty analysis result of step S1, and quantifying the uncertainty into uncertainty variables;

[0062] Step S3, combining the deterministic prediction model, constructing a rotor blade tip assembly clearance prediction model for the jth blade of the i-th blade disk at the δ phase, taking the uncertainty variables in step S2 as input, and calculating the predicted response of the phase layer;

[0063] Step S4, combining the deterministic prediction model, constructing a prediction model for the assembly clearance of the jth blade rotor tip of the i-th blade disk, taking the phase layer prediction response obtained in step S3 as input, and calculating the prediction response of the blade layer;

[0064] Step S5, combining the deterministic prediction model, constructing the i-th level blade disk rotor blade tip assembly clearance prediction model, taking the blade layer prediction response obtained in step S4 as input, and calculating the blade disk layer prediction response.

[0065] In step S1, the uncertainty affecting the rotor blade tip assembly clearance is analyzed. Figure 2As shown in the figure, according to the uncertainty source, the uncertainty affecting the rotor blade tip assembly clearance can be divided into: part / component uncertainty and assembly execution uncertainty. Among them, part / component uncertainty mainly includes blade disk assembly uncertainty and casing uncertainty. The uncertainty of blade disk assembly mainly includes: blade tip manufacturing uncertainty and blade disk assembly centroid uncertainty; casing uncertainty mainly includes: casing stop manufacturing uncertainty, front and rear support manufacturing uncertainty and compressor casing flow channel manufacturing uncertainty. Assembly execution uncertainty mainly includes: adjustment gasket selection uncertainty and bearing clearance uncertainty.

[0066] Since the blade disk assembly measurement equipment is highly intelligent, a large amount of high-precision blade tip runout data and blade disk assembly radial runout data can be obtained during the assembly process. Therefore, the blade tip manufacturing uncertainty and blade disk assembly centroid uncertainty can be regarded as random uncertainty. Given the high measurement accuracy, the blade tip manufacturing uncertainty and blade disk assembly centroid uncertainty can be ignored.

[0067] The degree of automation of the casing stop measurement equipment is low. The radial runout and end face runout of the casing stop, as well as the radial runout of the front and rear pivots, are only measured at 8-16 points during the assembly process. This introduces both random uncertainty of the measuring equipment and cognitive uncertainty caused by insufficient data. The manufacturing uncertainty of the casing stop and the manufacturing uncertainty of the front and rear pivots can be regarded as sparse mixed uncertainty. The inner flow surface of the compressor casing is an important mating surface, so a large amount of high-precision data can be obtained from the manufacturing error of the inner flow surface. Therefore, the manufacturing uncertainty of the inner flow surface can be regarded as random uncertainty. In the uncertainty of assembly execution, due to lack of knowledge and other reasons, the uncertainty of adjusting the gasket selection and the uncertainty of the bearing game can be regarded as interval uncertainty.

[0068] Therefore, the uncertainties affecting the rotor blade tip assembly clearance include: sparse mixed uncertainty, random uncertainty and interval uncertainty.

[0069] In addition, in step S1, the rotor tip assembly clearance level is analyzed, and the rotor tip assembly clearance can be divided into three levels, namely, phase level, blade level and blade disk level. The phase level represents the tip clearance of the jth blade of the i-th blade disk at the δ phase, the blade level is the cumulative amount of the phase level, which represents the tip clearance of the jth blade of the i-th blade disk at all phases, and the blade disk level is the cumulative amount of the blade level, which represents the cumulative amount of all blades of the i-th blade disk at all phases.

[0070] Based on step S1, a corresponding uncertainty quantification algorithm is designed in step S2. The uncertainty quantification method includes: step S2.1, a sparse uncertainty quantification method; step S2.2, a random uncertainty quantification method; and step S2.3, an interval uncertainty quantification method.

[0071] Step S2.1 The sparse uncertainty quantification method may specifically include:

[0072] Assume that the sparse dataset is D sd , its value is described by the distribution of its absolute value, and its positive and negative shape is described by the binomial distribution. Its uncertainty quantification method is as follows Figure 3 As shown, it can be divided into the following 5 sub-steps:

[0073] Step S2.1.1, calculate the data set D sd The positive value ratio in is denoted as pp sd , construct D sd The absolute value data set is denoted as D sdi ;

[0074] Step S2.1.2, another D sdi It obeys 6 common distributions (uniform distribution, normal distribution, lognormal distribution, exponential distribution, extreme value distribution, Weibull distribution), and estimates the parameters of the 6 distributions through maximum likelihood estimation (MLE);

[0075] Step S2.1.3, another D sdi It obeys the mixed weighted distribution, and its probability density function is as follows, and its distribution parameters are estimated by genetic algorithm:

[0076]

[0077] In the formula, ω i represents the weight of the i-th probability density function, which can be determined by the Akaike Information Criterion (AIC), δ i is the probability density function indicator parameter. In order to reduce the complexity of the function, the probability density function with a weight less than 0.1 will be ignored. i (x) represents the i-th probability density function;

[0078] Step S2.1.4, calculate the goodness of fit of the above 7 distributions by KS test method, denoted as p. If the maximum value of the goodness of fit p max ≥α, α is the predetermined goodness of fit judgment threshold, then D sdi Obey the corresponding distribution, otherwise, D is estimated by the kernel density estimation (KDE) method sdi The probability density function of D sdi The probability density function f output,sd (x);

[0079] Step S2.1.5, output D sdi The positive and negative function of sign,sd , as shown in the following formula:

[0080]

[0081] Where n represents the sampling dimension, pp sd represents the proportion of positive values ​​in the data set, and k represents the number of positive values.

[0082] The random uncertainty quantification method in step S2.2 is similar to the sparse uncertainty quantification method in step S2.1, but since a large amount of jump data can be obtained, step S2.1.2 can be omitted, thereby estimating the probability density function f of the random variable output,rd (x) and the positive and negative function f sign,rd .

[0083] Step S2.3: Quantification method of interval uncertainty: For the uncertainty of adjusting gasket selection and bearing clearance, they can be quantified into interval variables according to the design tolerance, which are recorded as: and

[0084] In step S3, the rotor blade tip assembly clearance deterministic prediction model can be divided into four sub-models, namely:

[0085] (1) Data preprocessing sub-model:

[0086] Rotor blade tip beating treatment: The beating amount and beating angle of the i-th level j-th blade can be recorded as tr i,j and λ i,j , then the initial position vector of the rotor blade tip can be expressed as:

[0087]

[0088] In the formula, x IT,i,j ,y IT,i,j and z IT,i,j Represent the theoretical coordinates of the blade tip, h rs Represents the blade adjustment shim thickness.

[0089] Inner channel runout processing: The coordinates of any point on the i-th level inner channel can be recorded as: P i,δ,z =[x P,i,δ,z ,y P,i,δ,z ,z P,i,δ,z ,1], which can be calculated by the following formula:

[0090]

[0091] In the formula, ir i,δ,z represents the internal flow channel runout, h cs represents the thickness of the casing adjustment gasket, ρ i,δ,z represents the theoretical radius of the i-th level inner flow channel at δ phase and z height, where ρ i,δ,z It can be calculated by the following formula:

[0092] ρ i,δ,z =f is,i (δ,z) (5)

[0093] In the formula, f is,i (δ,z) represents the theoretical equation of the i-th level internal flow channel.

[0094] Data processing of the radial runout of the blade disk assembly and the front and rear pivots: The radial runout of the blade disk assembly and the front and rear pivots is usually used to describe the eccentricity error of the blade disk assembly and the front and rear pivots. The pose vector can be obtained by least squares fitting.

[0095] Data processing of the receiver stopper runout: The end face runout and radial runout of the receiver stopper are often used to characterize the manufacturing error of the stopper, which can usually be expressed as the receiver stopper characteristic matrix as shown in the following formula:

[0096]

[0097] In the formula, e and θ e Represent the eccentricity and eccentricity angle, θ l represents the lowest point angle, θ t Represents the reference surface inclination angle.

[0098] Finite element simulation processing: The deformation amount and deformation angle of the compressor casing caused by bolt tightening can be recorded as: lim =[x lim ,y lim ,z lim ,0] and θ h .

[0099] (2) Sub-model of flow channel position in casing:

[0100] The actual position of the flow channel in the casing is affected by the actual position of the compressor casing and the manufacturing error of the flow channel in the casing. The actual position of the compressor casing can be obtained by T cc Expression, which can be calculated by the following formula:

[0101] T cc =L fc ·G fc ·L cc ·G cc (7)

[0102] In the formula, z fc and z cc Represent the actual height of the front casing and the compressor casing, G fc represents the front receiver stop feature matrix, G cc represents the compressor case stop feature matrix, G fc and G ccIt can be constructed by formula (6).

[0103] Combined with T cc and O lim The unit pose vector of the compressor casing can be obtained, denoted as n cc =[n x,cc ,n y,cc ,n z,cc ,1]. Then the rotation matrix around the x-axis and y-axis is obtained as follows:

[0104]

[0105] In the formula, and Represent the deflection angles around the x-axis and y-axis respectively.

[0106] Then the actual position of the i-th level inner flow channel at the δ phase and z height can be expressed as:

[0107]

[0108] (3) Rotor blade tip posture sub-model:

[0109] The actual position of the rotor blade tip is determined by the concentricity of the front and rear support points, the centroid position of the blade disk and the manufacturing error of the blade tip.

[0110] The centroid coordinates of the i-th blade disk are: R i =[x R,i ,y R,i ,z R,i +h rs ,1], the deflection matrices around the x-axis and y-axis can be recorded as TR i (α i,x ) and TR i (α i,y ), where α i,x is the rotation angle of the i-th leaf disk around the x-axis, α i,x =arcsin(y R,i / z R,i ), α i,y is the rotation angle of the i-th leaf disk around the y-axis, α i,y =arcsin(x R,i / z R,i ).

[0111] The rotation axis of the blade disk assembly is determined by the front and rear pivot positions, and the front and rear pivot position vectors can be recorded as: fp =[x fp ,y fp ,z fp ,1] and O rp =[x rp +x lim·cosθ h ,y rp +y lim sinθ h ,z rp ,1].

[0112] The actual posture matrix of the rear receiver can be calculated by the following formula:

[0113] T rc =L fc ·G fc ·L cc ·G cc ·L rc ·G rc (10)

[0114] In the formula, z rc Indicates the height of the rear receiver, G rc represents the feature matrix of the rear receiver stop, which is constructed according to formula (6).

[0115] Through T rc The direction vector of the rear receiver can be obtained by unitization, which is recorded as: n rc =[n x,rc ,n y,rc ,n z,rc ,1]. Then the actual position of the rear support can be calculated by the following formula:

[0116] OT rp =O rp ·D rc (θ x )·D rc (θ y ) (11)

[0117] Where D rc (θ x ) and D rc (θ y ) represent the deflection matrix of the rear receiver, and their forms refer to formula (8),

[0118] θ x =arcsin(n y,rc / n z,rc ) and θ y =arcsin(n x,rc / n z,rc ) are the deflection angles of the rear receiver around the x-axis and y-axis respectively.

[0119] Therefore, the direction vectors of the front and rear pivots can be expressed as: Then the actual position of the jth blade of the i-th level blade disk can be expressed as:

[0120] RT′i,j =R i,j ·D fr (β x )·D fr (β y )·TR i (α i,x )·TR i (α i,y ) (12)

[0121] In the formula, R i,j represents the initial position of the jth blade of the i-th blade disk, D fr (β x ) and D fr (β y ) represent the front and rear support deflection matrices respectively, and their forms refer to formula (8), β x =arcsin(n y,fr / n z,fr ) and β y =arcsin(n x,fr / n z,fr ) represent the deflection angles of the front and rear pivots around the x-axis and y-axis respectively.

[0122] (4) Rotor blade tip assembly gap sub-model:

[0123] The initial rotor tip assembly clearance can be determined by RT′ i,j and PT i,δ,z The calculation is as follows:

[0124] initial cle i,j =||PT i,δ,z -RT′ i，j || (13)

[0125] Due to the non-coaxiality between the rotor's rotation axis and the centroid axis, the position of the rotor tip will change with the change of phase. Therefore, the phase variable δ is introduced to describe the different phases of the rotor blade tip assembly gap. The theoretical rotation center of the i-th blade disk can be recorded as: Ri =[0,0,z RT,i,j ,1], its actual rotation center can be expressed as:

[0126] O RTi =O Ri ·D fr (β x )·D fr (β y ) (14)

[0127] Then formula (12) can be updated as follows:

[0128] RT′ i,j,δ=RT′ i,j ·Tr i (ω x )·Tr i (ω y )·T z (δ) (15)

[0129] In the formula, Tr i (ω x ) and Tr i (ω y ) represents the deflection matrix of the i-th blade disk, and its form refers to formula (8), ω x and ω y Represent the deflection angles around the x-axis and y-axis, T z (δ) represents the phase rotation matrix, as follows:

[0130]

[0131] Therefore, formula (13) can be updated to the following formula, from which the rotor blade tip assembly clearance at any phase is calculated:

[0132] cle i,j,δ =||PT i,δ,z -RT′ i,j,δ || (17)

[0133] The prediction model is driven by various uncertainties quantified in step S2 to obtain a predicted response of the phase layer.

[0134] Since it contains two interval variables, we can build a prediction process based on the probability box, as shown in the following figure: Figure 4 As shown, the specific steps are as follows:

[0135] Step S3.1, obtain uncertainty data set, where X R represents the random variable of the manufacturing error of the i-th level internal flow channel, X S Represents the sparse variables of the receiver stop and the front and rear pivots, a total of 8 sparse variables, X I represents the interval uncertainty of assembly execution;

[0136] Step S3.2, discretize the interval variable of the adjustment gasket, recorded as Set the adjustment shim interval variable to a fixed value The outermost loop iterates over all adjustment shim interval variables;

[0137] Step S3.3, discretize the bearing game interval variable, recorded as Let the bearing clearance interval variable be a fixed value The second layer loops through all bearing clearance interval variables;

[0138] Step S3.4, by f output,sd (x) and f output,rd (x) respectively for X S and X R The value of is sampled by the positive and negative function f sign,sd and f sign,rd Sampling the positive and negative, a total of n samplings are performed, each sampling dimension is l, combining each numerical sampling and positive and negative sampling, taking sparse variables as an example, the sampling combination method is as follows: One sampling can get a numerical sampling data set and positive and negative sampling datasets Multiply the elements at corresponding positions in the two data sets to obtain the hth sampling data set of the sparse variable

[0139] Then the sampling data set can be constructed and recorded as: and Let the random variables and sparse variables have fixed values and in, The innermost loop traverses the samples n times;

[0140] Step S3.5, the deterministic prediction model of the rotor tip clearance of the jth blade of the i-th blade disk at the δ phase can be expressed as:

[0141]

[0142] In the formula, X D represents deterministic variables, including rotor blade tip manufacturing error, blade disk centroid position, etc.;

[0143] The deterministic prediction model of the drive rotor blade tip clearance is used to obtain the predicted response after three cycles, which is recorded as tip. i,j,δ , the dimension of the response data set and the number of cycles are: m×k×n.

[0144] Considering that the result of the existing deterministic prediction is a point data, and the result of the interval prediction provides a range value without probability, both of them are inconsistent with the actual situation. Therefore, in the preferred embodiment of the present invention, step S3 may also include step S3.6 after step S3.5: fitting the CDF curve to obtain m×k CDF curves, finding their upper and lower limits, which are respectively recorded as and Construct the rotor tip assembly clearance probability box of the jth blade of the i-th blade disk at the δ phase, and calculate the mean interval and variance interval of the tip clearance, which are recorded as and and are the lower and upper limits of the mean tip clearance of the jth blade of the i-th blade disk at the δ phase, respectively. and are the lower limit and upper limit of the variance of the tip clearance of the jth blade of the i-th blade disk at the δ phase, respectively. In this way, the present invention describes the probability of the rotor blade tip assembly clearance taking values ​​within a certain range at the phase layer level through the upper and lower limits of the CDF curve with a probability box, which can more objectively and comprehensively evaluate the risk of the rotor blade tip assembly clearance exceeding the tolerance.

[0145] In step S4, a prediction model for the tip assembly clearance of the jth blade of the i-th blade disk is constructed, and the prediction response of the jth blade of the i-th blade disk is calculated using the prediction response in step S3 as input, which specifically includes:

[0146] Step S4.1, calculate the predicted response of the jth blade of the i-th blade disk at 360 phases and use it as input to construct the response matrix of the jth blade of the i-th blade disk, with a dimension of m×k, which can be recorded as:

[0147]

[0148] In the formula, tip i,j is the predicted response of the jth blade of the i-th level blade disk, with a total of m×k subsets, and the dimension of each subset is 360×n.

[0149] Furthermore, step S4 may also include step S4.2: fitting the CDF curve to obtain m×k CDF curves, and finding their upper and lower limits, which are recorded as and Construct the rotor tip assembly clearance probability box of the jth blade of the i-th blade disk, and calculate the mean interval and variance interval of the tip clearance, which are recorded as and and are the lower and upper limits of the mean tip clearance of the jth blade of the i-th blade disk, respectively. and are the lower and upper limits of the tip clearance variance of the jth blade of the i-th blade disk, respectively. Therefore, the present invention describes the probability of the rotor tip assembly clearance taking values ​​within a certain range at the blade layer level by using the upper and lower limits of the CDF curve with a probability box, which can more objectively and comprehensively evaluate the risk of the rotor tip assembly clearance exceeding the tolerance.

[0150] In step S5, a prediction model for the assembly clearance of the blade tip of the i-th blade disk is constructed, and the prediction response of the i-th blade disk is calculated using the prediction response in step S4 as input, which specifically includes:

[0151] Step S5.1, assuming that the i-th level blade disk has z blades, calculate the blade tip assembly clearance response of z blades and use it as input to construct the i-th level blade disk response matrix with a dimension of m×k, which can be recorded as:

[0152]

[0153] In the formula, tip i is the predicted response of the i-th blade disk, with a total of m×k subsets, and the dimension of each subset is 360×n×z. So far, the present invention has obtained the predicted response of the assembly clearance of the blade tip of the aircraft engine rotor from the phase layer to the blade layer and then to the blade disk layer, and has realized the prediction of the assembly clearance of the blade tip of the aircraft engine rotor in a progressive manner.

[0154] Step S5 of the present invention particularly includes step S5.2: fitting the CDF curve to obtain m×k CDF curves, finding their upper and lower limits, which are respectively recorded as and Construct the probability box of the blade tip assembly clearance of the i-th level blade disk, and calculate the mean interval and variance interval of the blade tip clearance, which are recorded as: and in and They represent the lower and upper limits of the mean tip clearance of the i-th blade disk, respectively. and The lower and upper limits of the variance of the blade tip clearance of the i-th blade disk are respectively represented. Therefore, the present invention describes the probability of the rotor blade tip assembly clearance taking values ​​within a certain range by using the upper and lower limits of the CDF curve with a probability box, which can more objectively and comprehensively evaluate the risk of the rotor blade tip assembly clearance exceeding the tolerance.

[0155] Therefore, as described above, the method for predicting the assembly clearance of the rotor blade tip of an aero-engine considering multi-source uncertainty of the present invention quantifies the multi-source uncertainty caused by manufacturing, measurement and process execution, divides the rotor blade tip assembly clearance into levels, and progressively divides it into phase layer, blade layer and blade disk layer according to different scales, and uses a deterministic prediction model to take the quantified uncertainty variable as input to calculate the predicted response of the phase layer, and then take the phase layer predicted response as input to obtain the predicted response of the blade layer, and finally take the blade layer predicted response as input to obtain the predicted response of the blade disk layer. Therefore, the present invention takes into account the multi-source uncertainty in the assembly of the rotor blade tip and quantifies it, takes the quantified result as input, and gradually and progressively predicts the blade tip assembly clearance in three levels from blade phase to blade and then to blade disk, which can accurately predict the rotor blade tip assembly clearance under uncertainty conditions and meet the high reliability assembly requirements of the blade tip.

[0156] In addition, the present invention combines the deterministic prediction model to express the rotor blade tip assembly clearance in the form of a probability box, and the result of the deterministic prediction is a point data, and the result of the interval prediction provides a range value without probability, both of which are inconsistent with the actual situation. The method provided by the present invention describes the probability of the rotor blade tip assembly clearance taking values ​​within a certain range through the upper and lower limits of the CDF curve, thereby more objectively and comprehensively evaluating the out-of-tolerance risk of the rotor blade tip assembly clearance, helping engineers to make more reliable decisions on process parameters, thereby further improving the assembly reliability of the rotor blade tip.

[0157] Next, the method for predicting the assembly clearance of an aero-engine rotor blade tip taking into account multi-source uncertainties provided by the present invention is further described with reference to examples.

[0158] This example takes the first-stage rotor tip assembly clearance of an axial-flow aircraft engine as the research object to illustrate the method of the present invention. Figure 5 As shown. The first-stage theoretical rotor blade tip assembly clearance is: [0.6, 1.1] mm, the adjustment gasket tolerance range is: [0, 1.4] mm, and the bearing clearance tolerance range is: [-0.05, 0.05] mm. There are 8 measurement data for the end face runout, radial runout, and radial runout of the front and rear pivots of the casing, so they can be regarded as sparse mixed uncertainties; the first-stage inner flow channel manufacturing error runout measurement data contains 24 points, so it can be regarded as random uncertainty; the above runout data are shown in Table 1.

[0159] Table 1 Runout data during assembly

[0160]

[0161] According to the uncertainty quantification method proposed in the present invention, the uncertainty quantification results can be obtained as shown in Table 2.

[0162] Table 2 Uncertainty quantification results

[0163]

[0164]

[0165] The final prediction result is as follows Figure 6 As shown, the red curve on the left describes the lower limit of the probability distribution of the rotor blade tip assembly clearance, and the blue curve on the right describes the upper limit of the probability distribution of the rotor blade tip assembly clearance. Inside the two curves are all possible possibilities of the rotor blade tip assembly clearance. Figure 6It shows that the mean interval of the first-stage rotor blade tip assembly clearance is: [0.5832, 0.8913], and the variance interval is: [0.09, 0.18]. The probability box model of the rotor blade tip assembly clearance is predicted, which effectively reflects the upper and lower limits of the probability distribution of the rotor blade tip assembly clearance value. Therefore, this example verifies the effectiveness of the blade tip assembly clearance prediction method provided by the present invention.

[0166] Finally, it should be noted that the features mentioned and / or shown in the above description of the exemplary embodiments of the present invention may be combined in the same or similar manner into one or more other embodiments, combined with the features in other embodiments or substituted for the corresponding features in other implementations. The technical solutions obtained by these combinations or substitutions shall also be deemed to be included in the protection scope of the present invention.

Claims

1. A method for predicting the assembly clearance of an aero-engine rotor blade tip considering multi-source uncertainty, characterized in that: The following steps are involved: Step 1, analyzing the uncertainty affecting the rotor blade tip assembly clearance and determining the rotor blade tip assembly clearance level; The blade tip assembly clearance level is divided into phase layer, blade layer and blade disk layer. The phase layer represents the blade tip clearance of the jth blade of the i-th blade disk at the δ phase. The blade layer is the cumulative amount of the phase layer, which represents the blade tip clearance of the jth blade of the i-th blade disk at all phases. The blade disk layer is the cumulative amount of the blade layer, which represents the cumulative amount of all blades of the i-th blade disk at all phases. Step 2: Based on the uncertainty analysis results of step 1, design a corresponding uncertainty quantification algorithm to quantify the uncertainty into uncertainty variables; Step 3, combining the deterministic prediction model, constructing the rotor blade tip assembly clearance prediction model of the jth blade of the i-th blade disk at the δ phase, taking the uncertainty variables in step 2 as input, and calculating the predicted response of the phase layer; Step 4, combining the deterministic prediction model, constructing the prediction model of the rotor blade tip assembly clearance of the jth blade of the i-th blade disk, taking the phase layer prediction response obtained in step 3 as input, and calculating the prediction response of the blade layer; Step 5, combining the deterministic prediction model, constructing the i-th level blade disk rotor blade tip assembly clearance prediction model, using the blade layer prediction response obtained in step 4 as input, and calculating the blade disk layer prediction response.

2. The method for predicting the assembly clearance of an aero-engine rotor blade tip considering multiple sources of uncertainty according to claim 1, characterized in that: In step 1, the uncertainty affecting the rotor blade tip assembly clearance is analyzed, including part / component uncertainty and assembly execution uncertainty; The part / assembly uncertainty includes the blade disk assembly uncertainty and the casing uncertainty. The blade disk assembly uncertainty includes the blade tip manufacturing uncertainty and the blade disk assembly centroid uncertainty. The casing uncertainty includes the casing stop manufacturing uncertainty, the front and rear support manufacturing uncertainty and the compressor casing inner flow channel manufacturing uncertainty. The assembly execution uncertainty includes adjustment shim selection uncertainty and bearing clearance uncertainty.

3. The method for predicting the assembly clearance of an aero-engine rotor blade tip considering multiple sources of uncertainty according to claim 2, characterized in that: In step 1, the uncertainty affecting the rotor blade tip assembly clearance is divided into sparse mixed uncertainty, random uncertainty and interval uncertainty; The sparse mixed uncertainty includes the manufacturing uncertainty of the casing stop and the manufacturing uncertainty of the front and rear pivots; The random uncertainty includes manufacturing uncertainty of blade tip, uncertainty of centroid of blade disk assembly and manufacturing uncertainty of flow path surface in compressor casing; The interval uncertainty includes the uncertainty of adjusting shim selection and the uncertainty of bearing clearance.

4. The method for predicting the assembly clearance of an aircraft engine rotor tip considering multi-source uncertainty according to claim 3, characterized in that: In step 2, for sparse mixed uncertainty, assume that the sparse dataset is D sd , then the sparse mixed uncertainty quantification method includes the following steps: Step 2.1.1, calculate the data set D sd The positive proportion pp sd , construct D sd The absolute value data set D sdi ; Step 2.1.2, another D sdi It obeys six distributions: uniform distribution, normal distribution, lognormal distribution, exponential distribution, extreme value distribution and Weibull distribution. The distribution parameters of the six distributions are estimated by maximum likelihood estimation method. Step 2.1.3, another D sdi It obeys mixed weighted distribution, and its probability density function is as follows. Its distribution parameters are estimated by genetic algorithm: In the formula, ω i represents the weight of the i-th probability density function, δ i is the probability density function indicator parameter, f i (x) represents the i-th probability density function; Step 2.1.4, calculate the goodness of fit p of the above seven distributions by KS test method. If the maximum goodness of fit p max ≥α, α is the predetermined goodness of fit judgment threshold, then D sdi Obey p max Corresponding distribution, otherwise, D is estimated by kernel density estimation sdi The probability density function of D sdi The probability density function f output,sd (x); Step 2.1.5, calculate D as follows sd The positive and negative function f sign,sd : Where n represents the sampling dimension and k represents the number of positive values.

5. The method for predicting the assembly clearance of an aircraft engine rotor tip considering multi-source uncertainty according to claim 4, characterized in that: In step 2, the quantification method of random uncertainty is similar to the quantification method of sparse mixed uncertainty, the difference is that step 2.1.2 is omitted and the probability density function f of the random variable is obtained output,rd (x) and the positive and negative function f sign,rd .

6. The method for predicting the assembly clearance of an aircraft engine rotor tip considering multi-source uncertainty according to claim 5, characterized in that: In step 2, for the quantification of interval uncertainty, the uncertainty of adjusting gasket selection and bearing clearance is quantified into interval variables according to the design tolerance, which are recorded as and 7. The method for predicting the assembly clearance of an aircraft engine rotor tip considering multi-source uncertainty according to claim 6, characterized in that: Step 3 includes: Step 3.1, obtain measurement data and quantify uncertainty, where X R represents the random variable of the manufacturing error of the i-th level internal flow channel, X S Represents the sparse variables of the receiver stop and front and rear pivots, X I represents the interval uncertainty of assembly execution; Step 3.2: discretize the interval variable of the adjustment shim, denoted as Set the adjustment shim interval variable to a fixed value The outermost loop iterates over all adjustment shim interval variables; Step 3.3, discretize the bearing clearance interval variable and record it as Let the bearing clearance interval variable be a fixed value The second layer loops through all bearing clearance interval variables; Step 3.4, through the probability density function f output,sd (x) and f output,rd (x) respectively for X S and X R The value of is sampled by the positive and negative function f sign,sd and f sign,rd The positive and negative samples are sampled for n times, each sampling dimension is l, and the sampled data sets are recorded as and Let the random variables and sparse variables have fixed values and in, The innermost loop traverses the samples n times; Step 3.5, the deterministic prediction model of the rotor tip clearance of the jth blade of the i-th blade disk at the δ phase is expressed as: Where, X D represents deterministic variables, including rotor blade tip manufacturing errors and blade disk centroid position; Step 3.6, the deterministic prediction model of the rotor tip clearance expressed by the driver is used, and after three cycles, the rotor tip clearance prediction response tip considering uncertainty is obtained. i,j,δ , the dimension of the response dataset and the number of loops are m×k×n.

8. The method for predicting the assembly clearance of an aircraft engine rotor blade tip considering multi-source uncertainty according to claim 7, characterized in that: Step 4 includes: Step 4.1, calculate the predicted response of the jth blade of the i-th blade disk at 360 phases and use it as input to construct the response matrix of the jth blade of the i-th blade disk, with a dimension of m×k, recorded as: In the formula, tip i,j is the predicted response of the jth blade of the i-th level blade disk, with a total of m×k subsets, and the dimension of each subset is 360×n.

9. The method for predicting the assembly clearance of an aircraft engine rotor blade tip considering multi-source uncertainty according to claim 8, characterized in that: Step 5 includes: Step 5.1, calculate the tip assembly clearance prediction response of the z blades of the i-th blade disk and use it as input to construct the response matrix of the i-th blade disk, with a dimension of m×k, recorded as: In the formula, tip i is the predicted response of the i-th level leaf disk, with a total of m×k subsets, and the dimension of each subset is 360×n×z.

10. The method for predicting the assembly clearance of an aircraft engine rotor blade tip considering multi-source uncertainty according to claim 9, characterized in that: Step 5 also includes: Step 5.2: Fit the CDF curve, obtain m×k CDF curves, and find their upper limit and lower limit Construct the probability box of the blade tip assembly clearance of the i-th level blade disk and calculate the mean interval of the blade tip clearance and tip clearance variance interval in and denote the lower and upper limits of the mean value of the tip clearance, respectively. and They represent the lower and upper limits of the tip clearance variance respectively.

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