A method for predicting the assembly clearance of aero-engine rotor blade tip considering multi-source uncertainties

Abstract

The present invention provides a method for predicting the assembly clearance of an aero-engine rotor blade tip that takes into account multi-source uncertainty, including: analyzing the uncertainty that affects the rotor blade tip assembly clearance and determining that the rotor blade tip assembly clearance is divided into a phase layer, a blade layer, and a blade disk layer; quantifying the uncertainty into uncertainty variables; combining a deterministic prediction model, using the uncertainty variables as input, calculating the predicted response of the phase layer, then using the phase layer predicted response as input, calculating the predicted response of the blade layer, and finally using the blade layer predicted response as input, calculating the predicted response of the blade disk layer. The present invention takes into account the multi-source uncertainty in the rotor blade tip assembly and quantifies it, using the quantified result as input, and gradually predicting the blade tip assembly clearance in three levels, from blade phase to blade and then to blade disk. It can accurately predict the rotor blade tip assembly clearance under uncertainty conditions and meet the high-reliability assembly requirements of the blade tip.

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] During aircraft engine rotor assembly, rotor tip clearance is a critical indicator affecting engine safety and performance. Excessive or uneven rotor tip clearance increases the risk of collision and friction during engine operation, or reduces aerodynamic performance. Accurately predicting rotor tip clearance is a prerequisite for precise control of assembly clearance.

[0003] Currently, there are two main methods for predicting the assembly clearance of aircraft engine rotor blade tips: 1) a deterministic prediction method based on the error propagation principle; and 2) an interval prediction method based on interval calculations. However, due to limited measurement data on part manufacturing deviations, such as casing stop runout data and front and rear pivot runout data, accurate characterization of part manufacturing deviations is difficult. Furthermore, assembly process execution is often based on empirical decisions, which introduces a significant amount of uncertainty, making accurate predictions difficult for both existing methods. The former ignores various uncertainties and only considers deterministic results. While the latter quantifies uncertainty as an interval, it cannot determine the probability distribution of the blade tip clearance within that interval, making it difficult to use predictions to guide process parameter optimization and failing to 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 that takes into account multi-source uncertainty.

[0005] To achieve the above objectives, the technical solutions provided by the present invention are:

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

[0007] Step 1: Analyze the uncertainty affecting the rotor blade tip assembly clearance and determine 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 phase δ. 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: Combined with the deterministic prediction model, a rotor blade tip assembly clearance prediction model for the jth blade of the i-th stage blade disk at the δ phase is constructed. The uncertainty variables in step 2 are used as input to calculate the predicted response of the phase layer.

[0011] Step 4: Combined with the deterministic prediction model, a prediction model for the rotor blade tip assembly clearance of the jth blade of the i-th stage blade disk is constructed, and the predicted response of the blade layer is calculated using the phase layer prediction response obtained in step 3 as input;

[0012] Step 5: Combined with the deterministic prediction model, a prediction model for the blade tip assembly clearance of the i-th level blade disk rotor is constructed. The blade layer prediction response obtained in step 4 is used as input to calculate the prediction response of the blade disk layer.

[0013] Furthermore, in step 1, the uncertainty affecting the rotor blade tip assembly clearance is analyzed, including 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 adjustment gasket selection uncertainty and the bearing clearance uncertainty.

[0015] Furthermore, in step 2, for sparse mixed uncertainty, assuming that the sparse dataset 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, and estimates the distribution parameters of the six distributions by maximum likelihood estimation method;

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

[0019]

[0020] Where, ω i represents the weight of the i-th probability density function, δ i is the indicator parameter of the probability density function, 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 method 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 of the random variable f 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] Furthermore, 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 support manufacturing, X I represents the interval uncertainty of assembly execution;

[0029] Step 3.2: Discretize the adjustment shim interval variable and record it 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, and the sampling dimension of each time is l. The sampled data sets are recorded as and Let the random variables and sparse variables be fixed values and in, The innermost loop traverses n samples;

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

[0033]

[0034] Where, 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 drive 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 cycles are m×k×n.

[0036] Furthermore, step 4 includes:

[0037] Step 4.1: Calculate the predicted response of the j-th blade of the i-th blade disk under 360 phases and use this as input to construct the response matrix of the j-th blade of the i-th blade disk, with dimensions of m × k, denoted 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] Furthermore, step 5 includes:

[0041] Step 5.1: Calculate the tip assembly clearance prediction response of the z blades of the i-th stage blade disk and use it as input to construct the response matrix of the i-th stage blade disk with dimensions of m × k, which is denoted as:

[0042]

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

[0044] Furthermore, step 5 further includes:

[0045] Step 5.2: Fit the CDF curve to 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 tip clearance, and represent the lower and upper bounds of the tip clearance variance, respectively.

[0046] The advantages of the present invention are:

[0047] 1. The present invention's method for predicting the assembly clearance of an aero-engine rotor blade tip, which takes into account multi-source uncertainty, quantifies the multi-source uncertainty brought about by manufacturing, measurement, and process execution, and divides the rotor blade tip assembly clearance into hierarchical levels, progressively dividing it into phase layer, blade layer, and blisk layer according to different scales. Using a deterministic prediction model, the quantified uncertainty variables are used as input to calculate the predicted response of the phase layer. The predicted response of the phase layer is then used as input to obtain the predicted response of the blade layer. Finally, the predicted response of the blade layer is used as input to obtain the predicted response of the blisk layer. Therefore, the present invention takes into account and quantifies the multi-source uncertainty in rotor blade tip assembly. Using the quantified results as input, the tip assembly clearance is progressively predicted in three levels, from blade phase to blade and then to blisk. This method can accurately predict the rotor blade tip assembly clearance under uncertainty conditions, meeting the requirements for high-reliability assembly of blade tips.

[0048] 2. The present invention combines the deterministic prediction model to express the rotor blade tip assembly clearance in the form of a probability box, while 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 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 readily understood through the following description with reference to the accompanying drawings, in which:

[0050] Figure 1 This is a flow chart of the method for predicting the assembly clearance of an aero-engine rotor blade tip considering multiple sources of uncertainty according to the present invention;

[0051] Figure 2 This is an 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 This is a flow chart for predicting the rotor blade tip assembly clearance of the jth blade of the i-th stage blade disk at the δ phase in the present invention;

[0054] Figure 5 1 is a schematic diagram of the engine structure in an example of the present invention;

[0055] Figure 6 This 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 uncertainty, 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 includes 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 phase δ. 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 based on 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 stage blade disk at the δ phase, using 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 rotor blade tip assembly clearance of the jth blade of the i-th stage blade disk, using the phase layer prediction response obtained in step S3 as input, and calculating the blade layer prediction response;

[0064] In step S5, a prediction model for the blade tip assembly clearance of the i-th level blade disk rotor is constructed in combination with the deterministic prediction model. The blade layer prediction response obtained in step S4 is used as input to calculate the prediction response of the blade disk layer.

[0065] In step S1, the uncertainty affecting the rotor blade tip assembly clearance is analyzed. Figure 2As shown in the figure, the uncertainty affecting rotor tip assembly clearance can be divided into part / component uncertainty and assembly execution uncertainty, based on the uncertainty source. Part / component uncertainty primarily includes blisk assembly uncertainty and casing uncertainty. The main sources of blisk assembly uncertainty are blade tip manufacturing uncertainty and blisk assembly centroid uncertainty. The main sources of casing uncertainty are casing stop manufacturing uncertainty, front and rear support manufacturing uncertainty, and compressor casing internal flow path manufacturing uncertainty. Assembly execution uncertainty primarily includes adjustment shim selection uncertainty and bearing clearance uncertainty.

[0066] Due to the high level of intelligence in blisk assembly measurement equipment, a large amount of high-precision blade tip runout and blisk assembly radial runout data can be obtained during assembly. Therefore, blade tip manufacturing uncertainty and blisk assembly centroid uncertainty can be considered random uncertainties. Given the high measurement accuracy, these uncertainties can be ignored.

[0067] The casing spigot measurement equipment has a low level of automation. The radial runout and end face runout of the casing spigot, as well as the radial runout of the front and rear pivots, are measured at only 8-16 points during the assembly process. This introduces both random uncertainty in the measurement equipment and cognitive uncertainty due to insufficient data. The manufacturing uncertainty of the casing spigot and the front and rear pivots can be considered sparse mixed uncertainty. The inner flow surface of the compressor casing is a critical mating surface, so a large amount of high-precision data can be obtained for its manufacturing errors. Therefore, the manufacturing uncertainty of the inner flow surface can be considered random uncertainty. Within the uncertainty of assembly execution, due to lack of knowledge and other factors, the uncertainty of adjusting the gasket selection and the bearing game can be considered 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 levels are analyzed. The rotor tip assembly clearance can be divided into three levels: phase level, blade level, and blisk level. The phase level represents the tip clearance of the jth blade of the i-th blisk at phase δ. The blade level is the cumulative amount of the phase level, representing the tip clearance of the jth blade of the i-th blisk at all phases. The blisk level is the cumulative amount of the blade level, representing the cumulative amount of all blades of the i-th blisk 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 numerical 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 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 a mixed weighted distribution, and its probability density function is as follows, and its distribution parameters are estimated by genetic algorithm:

[0076]

[0077] Where, 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 is 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, denoted as f 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 beating data can be obtained, step S2.1.2 can be omitted, and the probability density function f of the random variable is estimated. 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 shim selection and bearing clearance, they can be quantified into interval variables according to the design tolerance, which are respectively expressed as: and

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

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

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

[0087]

[0088] Where 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] Where ir i,δ,z Represents the inner 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 stage 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] Where, f is,i (δ,z) represents the theoretical equation of the i-th level internal flow channel.

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

[0095] Receiver spigot runout data processing: The receiver spigot end face runout and radial runout are often used to characterize the manufacturing error of the spigot. It can usually be expressed as the receiver spigot characteristic matrix as shown in the following formula:

[0096]

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

[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] Where, z fc and z cc Represents 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] Where, and Represents the deflection angle around the x-axis and y-axis respectively.

[0106] Then the actual position of the i-th stage 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 stage blade 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 limcosθ h ,y rp +y lim sinθ h ,z rp ,1].

[0112] The actual pose 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] Where, 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 normalization, 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 pivot points can be expressed as: Then the actual position of the jth blade of the i-th 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] Where 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 fulcrums around the x-axis and y-axis respectively.

[0122] (4) Rotor 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 stage 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] Where 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 respectively, 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 various uncertainties quantified in step S2 drive the prediction model to obtain the 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 example: Figure 4 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 support manufacturing, a total of 8 sparse variables, X I represents the interval uncertainty of assembly execution;

[0136] Step S3.2, discretize the adjustment shim interval variable, denoted 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 variables and record them 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 of positive and negative data is performed for n times, with a sampling dimension of l for each time. Combining the numerical sampling and positive and negative sampling for each time, taking sparse variables as an example, the sampling combination is as follows: One sampling can obtain 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 we can construct the sampling data set, which can be recorded as: and Let the random variables and sparse variables be fixed values and in, The innermost loop traverses n samples;

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

[0141]

[0142] Where, X D Represents deterministic variables, including rotor blade tip manufacturing errors, blade disk centroid position, etc.;

[0143] The deterministic prediction model of the drive rotor 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 dataset 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 a preferred embodiment of the present invention, step S3 may further include step S3.6 after step S3.5: fitting the CDF curve to obtain m×k CDF curves, and finding their upper and lower limits, which are respectively recorded as and Construct the rotor blade tip assembly clearance probability box of the jth blade of the i-th stage blade disk at the δ phase, and calculate the mean interval and variance interval of the blade 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 stage blade disk at the δ phase, and are the lower and upper limits of the tip clearance variance for the jth blade of the i-th stage blisk at phase δ, respectively. In this way, the present invention uses the upper and lower limits of the CDF curve to describe the probability of the rotor tip assembly clearance taking values ​​within a certain range at the phase level using probability boxes, allowing for a more objective and comprehensive assessment of the risk of rotor tip assembly clearance exceeding 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. The prediction response in step S3 is used as input to calculate the predicted response of the jth blade of the i-th blade disk. Specifically, the model includes:

[0146] In step S4.1, the predicted response of the j-th blade of the i-th blade disk under 360 phases is calculated and used as input to construct the response matrix of the j-th blade of the i-th blade disk. The dimension is m × k and can be expressed 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 further include step S4.2: fitting the CDF curve to obtain m×k CDF curves, and 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 level 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 stage blade disk, and are the lower and upper limits of the tip clearance variance for the jth blade of the i-th blade disk, respectively. Therefore, the present invention uses the upper and lower limits of the CDF curve to describe the probability of the rotor tip assembly clearance taking values ​​within a certain range at the blade level using a probability box, allowing for a more objective and comprehensive assessment of the risk of rotor tip assembly clearance exceeding tolerance.

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

[0151] In step S5.1, assuming that the i-th stage blade disk has z blades, the blade tip assembly clearance response of z blades is calculated and used as input to construct the i-th stage blade disk response matrix with dimensions m × k, which can be expressed as:

[0152]

[0153] In the formula, tip i is the predicted response for the i-th level blade disk, with a total of m × k subsets, each with dimensions of 360 × n × z. Thus, the present invention has obtained the predicted response for the aeroengine rotor tip clearance from the phase layer to the blade layer and then to the blade disk layer, achieving the prediction of the aeroengine rotor tip clearance in a progressive manner.

[0154] Step S5 of the present invention particularly further 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 stage blade disk, and The lower and upper limits of the variance of the blade tip clearance of the i-th stage blade disk are represented respectively. Therefore, 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 using a probability box, which can more objectively and comprehensively assess the risk of rotor blade tip assembly clearance exceeding tolerance.

[0155] Therefore, as described above, the present invention's method for predicting the assembly clearance of an aero-engine rotor blade tip that takes into account multi-source uncertainty quantifies the multi-source uncertainty brought about by manufacturing, measurement, and process execution, divides the rotor blade tip assembly clearance into hierarchical levels, and progressively divides it into a phase layer, a blade layer, and a blade disk layer according to different scales. Utilizing a deterministic prediction model, the quantified uncertainty variables are used as input to calculate the predicted response of the phase layer, and then the predicted response of the phase layer is used as input to obtain the predicted response of the blade layer, and finally the predicted response of the blade layer is used as input to obtain the predicted response of the blade disk layer. Thus, the present invention takes into account the multi-source uncertainty in the rotor blade tip assembly and quantifies it, and uses the quantified result as input to progressively predict the blade tip assembly clearance in three levels, from blade phase to blade and then to blade disk. This method 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, while 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 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 considering multi-source uncertainties provided by the present invention will be 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 The first-stage theoretical rotor tip assembly clearance is [0.6, 1.1] mm, the adjustment shim tolerance range is [0, 1.4] mm, and the bearing clearance tolerance range is [-0.05, 0.05] mm. The casing stopper end face runout, radial runout, and radial runout of the front and rear pivots have eight measurement data points and can be considered sparse mixed uncertainty. The first-stage internal flow passage manufacturing error runout measurement data consists of 24 points and can be considered random uncertainty. These 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 results are 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. The areas inside the two curves are all possible possibilities of the rotor blade tip assembly clearance. Figure 6The results show that the mean interval of the first-stage rotor blade tip clearance is [0.5832, 0.8913], and the variance interval is [0.09, 0.18]. The predicted probability box model of the rotor blade tip clearance effectively reflects the upper and lower limits of the probability distribution of the rotor blade tip clearance. Therefore, this example verifies the effectiveness of the blade tip clearance prediction method provided by the present invention.

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

Claims

1. A method for predicting the assembly clearance of an aero-engine rotor blade tip considering multiple sources of uncertainty, characterized in that: The following steps are involved: Step 1: Analyze the uncertainty affecting the rotor blade tip assembly clearance and determine the rotor blade tip assembly clearance level; The blade tip assembly clearance level is divided into 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. 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. 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: Combined with the deterministic prediction model, a rotor blade tip assembly clearance prediction model for the jth blade of the i-th stage blade disk at the δ phase is constructed. The uncertainty variables in step 2 are used as input to calculate the predicted response of the phase layer. Step 4: Combined with the deterministic prediction model, a prediction model for the rotor blade tip assembly clearance of the jth blade of the i-th stage blade disk is constructed, and the predicted response of the blade layer is calculated using the phase layer prediction response obtained in step 3 as input; Step 5: Combined with the deterministic prediction model, a prediction model for the blade tip assembly clearance of the i-th level blade disk rotor is constructed. The blade layer prediction response obtained in step 4 is used as input to calculate the prediction response of the blade disk layer.

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 tip assembly clearance is analyzed, including part / component uncertainty and assembly execution uncertainty; The part / assembly uncertainty includes the uncertainty of the blade disk assembly and the uncertainty of the casing. The uncertainty of the blade disk assembly includes the uncertainty of the manufacturing of the blade tip and the uncertainty of the centroid of the blade disk assembly. The uncertainty of the casing includes the uncertainty of the manufacturing of the casing stop, the uncertainty of the manufacturing of the front and rear support points, and the manufacturing uncertainty of the flow channel in the compressor casing. 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 support points; 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 in adjusting shim selection and the uncertainty in bearing clearance.

4. The method for predicting the assembly clearance of an aero-engine rotor blade tip considering multiple sources of 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, and estimates the distribution parameters of the six distributions by maximum likelihood estimation method; Step 2.1.3, another D sdi It obeys the mixed weighted distribution, and its probability density function is as follows. Its distribution parameters are estimated by genetic algorithm: Where, ω i represents the weight of the i-th probability density function, δ i is the indicator parameter of the probability density function, 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 method 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 aero-engine rotor blade tip considering multiple sources of 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, except that step 2.1.2 is omitted and the probability density function of the random variable f is obtained. output,rd (x) and the positive and negative function f sign,rd .

6. The method for predicting the assembly clearance of an aero-engine rotor blade tip considering multiple sources of 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 aero-engine rotor blade tip considering multiple sources of 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 support manufacturing, X I represents the interval uncertainty of assembly execution; Step 3.2: Discretize the adjustment shim interval variable and record it 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, and the sampling dimension of each time is l. The sampled data sets are recorded as and Let the random variables and sparse variables be fixed values and in, The innermost loop traverses n samples; In step 3.5, the deterministic prediction model of the rotor tip clearance of the jth blade of the i-th stage 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 drive 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 cycles are m×k×n.

8. The method for predicting the assembly clearance of an aero-engine rotor blade tip considering multiple sources of uncertainty according to claim 7, characterized in that: Step 4 includes: Step 4.1: Calculate the predicted response of the j-th blade of the i-th blade disk under 360 phases and use this as input to construct the response matrix of the j-th blade of the i-th blade disk, with dimensions of m × k, denoted 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 aero-engine rotor blade tip considering multiple sources of 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 stage blade disk and use it as input to construct the response matrix of the i-th stage blade disk with dimensions of m × k, which is denoted as: In the formula, tip i is the predicted response of the i-th level blade 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 aero-engine rotor blade tip considering multiple sources of uncertainty according to claim 9, characterized in that: Step 5 also includes: Step 5.2: Fit the CDF curve to 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 tip clearance, and represent the lower and upper bounds of the tip clearance variance, respectively.

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