A rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty

Abstract

The application provides a rotor assembly geometry precision prediction and optimization method considering multi-source uncertainty, comprising: analyzing uncertainty affecting assembly precision in a rotor assembly process; representing the uncertainty as random variables and interval variables respectively through a random model and an interval model; establishing a precision prediction model considering random-interval hybrid uncertainty to predict rotor assembly coaxiality error; solving the uncertainty model based on a Monte Carlo method to obtain probability statistical results of upper and lower bounds and midpoint values of the coaxiality error interval; performing coaxiality out-of-tolerance probability interval estimation, constructing a rotor coaxiality double-layer optimization model under hybrid uncertainty, and optimizing to obtain optimal installation phases of each stage disk. The application applies an uncertainty quantification method to prediction and optimization of rotor assembly geometry precision, can realize accurate prediction and reliable optimization of rotor assembly geometry precision, and meets high-reliability assembly requirements of an aero-engine rotor.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aero-engine assembly, and particularly relates to a rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty. BACKGROUND

[0002] In the assembly of an aero-engine, rotor assembly precision is an important indicator affecting the safety and performance of the aero-engine, and insufficient rotor assembly geometric precision will cause a large eccentricity and tilt of a rotor assembly, resulting in severe vibration and wear of the aero-engine during high-speed operation, and seriously affecting the performance and service life of the aero-engine. Precise prediction of rotor assembly geometric precision is a prerequisite for aero-engine assembly parameter optimization and improvement of aero-engine assembly process reliability.

[0003] Currently, there are two kinds of rotor assembly precision prediction and optimization models: 1) a deterministic model based on error transmission principle; and 2) a random probability model considering single uncertainty form. However, due to the complexity of the rotor assembly process and the large number of parts involved, various uncertainty factors inevitably exist in the measurement and process execution process, resulting in a large dispersion of the assembly precision of the rotor assembly. The former does not consider the uncertainty factors in the assembly process, and therefore the reliability of the prediction and optimization results is insufficient. The latter considers the influence of random errors on the assembly precision of the rotor assembly, and to some extent, improves the prediction accuracy and optimization reliability. However, the uncertainty factors are all represented as random distributions according to the design tolerance or precision level, and the uncertainty sources are extensive and diverse in engineering practice. Therefore, the latter is also difficult to reliably predict the assembly precision, and cannot meet the high-reliability assembly requirements. SUMMARY

[0004] The purpose of the present application is to solve the problem that the existing aero-engine rotor assembly precision prediction and optimization method is difficult to obtain reliable assembly precision results, and to provide a rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty by considering multi-source and mixed uncertainty in the prediction and optimization of rotor assembly geometric precision.

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

[0006] The present application provides a rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty, comprising the following steps:

[0007] Step 1: analyzing the uncertainty affecting the rotor assembly geometric precision in the aero-engine rotor stacking assembly process;

[0008] Step 2: representing the uncertainty analyzed in step 1 as a random variable and an interval variable through a random model and an interval model, respectively;

[0009] Step 3, taking the uncertainty variables characterized in step 2 as input variables, a rotor assembly geometric accuracy prediction model considering random-interval mixed uncertainty is established to predict the rotor assembly coaxiality error under mixed uncertainty conditions;

[0010] Step 4, based on the Monte Carlo method, the random-interval mixed uncertainty model established in step 3 is solved in a double-layer nested manner to obtain the probability statistical results of the upper and lower bounds and the midpoint value of the coaxiality error interval;

[0011] Step 5, the coaxiality tolerance probability interval is estimated, a double-layer optimization model of rotor coaxiality under mixed uncertainty is constructed, and the optimal installation phase of each disc is obtained by optimization to minimize the upper bound value of the coaxiality tolerance probability interval and the mean value of the midpoint of the coaxiality error interval.

[0012] Further, in step 1, according to the different sources of uncertainty, the uncertainty affecting the geometric accuracy of the rotor assembly is divided into single-stage disc manufacturing error uncertainty, measurement uncertainty and assembly process execution uncertainty;

[0013] Single-stage disc manufacturing error uncertainty includes disc stop port fitting cylindrical runout and stop port fitting end face runout;

[0014] Measurement uncertainty includes centering and tilting error of the turntable, disc clamping error and sensor installation error;

[0015] Assembly process execution uncertainty includes bolt tightening torque, assembly process temperature and axial pressing force uncertainty.

[0016] Further, in step 2, the single-stage disc manufacturing error uncertainty and the measurement uncertainty jointly cause the uncertainty of the single-stage disc stop port centroid coordinates and the end face normal vector as the model input variables, which is classified as random uncertainty and characterized as a random variable; the single-stage disc manufacturing error uncertainty and the assembly process execution uncertainty jointly cause the uncertainty of the stop port assembly eccentricity and the stop port assembly skew angle as the model input variables, which is classified as cognitive uncertainty and characterized as an interval variable.

[0017] Further, in step 2, the random variable is characterized by step 2.1, which includes:

[0018] Step 2.1.1, using the same measuring instrument, multiple measurements are performed on the same feature on the same part under the same installation clamping to obtain the measurement variation, which is defined as repeatability;

[0019] Step 2.1.2, the variation of the measurement average is obtained by repeating the measurement on the same feature on the same part under the same measuring instrument and multiple mounting clamps, which is defined as the repeatability;

[0020] Step 2.1.3, the unbiased estimation of the repeatability variance σ 2 and the reproducibility variance ε 2 is respectively represented as:

[0021]

[0022] wherein, l is the number of mounting clamps, m is the number of repeated measurements for one mounting clamp, y kj is the jth repeated measurement result of the kth mounting clamp, is the average of the m repeated measurements of the kth mounting clamp, is the average of all repeated measurements of the l mounting clamps, i.e. the average of l×m measurement results;

[0023] Step 2.1.4, the total variance α 2 = σ 2 + ε 2 is calculated, and the measurement uncertainty is characterized as a random normal distribution Δ~N(0,α 2 ) with 0 as the mean value and α as the standard deviation;

[0024] Step 2.1.5, under the same measurement conditions, a measurement point on a feature surface of a part is measured, and the measurement value is t, then the true value of the measurement point is contained in a random normal distribution with t as the mean value and α as the standard deviation, i.e. the value distribution of multiple measurements on the measurement point is T~N(t,α 2 );

[0025] Step 2.1.6, the probability distribution of the measurement values of all measurement points is obtained, and the random distribution model of the fitting after the joint center coordinate vector d and the end face normal vector p is obtained by the Monte Carlo method, which is respectively represented as:

[0026]

[0027] wherein, the superscript "R" represents a random variable, and the subscript "i" represents the ith wheel disc, "U" represents the upper joint, and "L" represents the lower joint.

[0028] Further, in step 2, the interval variable is characterized by step 2.2, and step 2.2 includes:

[0029] Step 2.2.1, the following interval model is established:

[0030]

[0031] In the formula, a I Let 'a' be an interval variable, and 'a' be the lower bound of the interval number of the variable. This is the upper bound of the variable interval number;

[0032] Step 2.2.2, let F(a) I ) is an interval vector a I If the function is an interval-valued function, then the solution interval of the function is:

[0033]

[0034] In the formula, F(a) I )=min{F(a I )},

[0035] Furthermore, in step 2.2.1, the interval model can be replaced as follows:

[0036]

[0037] In the formula, a c The value is the midpoint of the interval. a r Let be the radius of the interval.

[0038] Furthermore, step 3 includes:

[0039] Step 3.1: Correct the benchmark alignment error. Establish a single-level wheel coordinate system at the lower stop of the i-th level wheel. Through coordinate transformation, obtain the coordinate vector of the centroid of the upper stop of the i-th level wheel in the single-level wheel coordinate system. and end face normal vector They are represented as follows:

[0040]

[0041] In the formula, This is the rotation transformation matrix for transforming from the measurement system coordinate system to a single-level wheel coordinate system. and Let these be the normal vector of the upper stop face of the i-th level wheel, the coordinate vector of the upper stop centroid, and the coordinate vector of the lower stop centroid in the coordinate system of the measurement system. and Let X, Y, and Z be the components of the centroid coordinate vector of the i-th level wheel's upper stop in the X, Y, and Z directions in the single-level wheel coordinate system, respectively. and These are the components of the normal vector of the upper stop end face of the i-th level wheel in the X, Y, and Z directions in the single-level wheel coordinate system;

[0042] Step 3.2, the single-stage wheel disc error model is established to obtain the rotation transformation matrix from the upper stop port fitting plane coordinate system to the reference coordinate system where the reference coordinate system is a single-stage wheel disc coordinate system established at the lower stop port of the i-th stage wheel disc;

[0043] Step 3.3, the stop port assembly deviation model is established to obtain the stop port assembly eccentricity vector the interval expression in the i-1-th stage wheel disc upper stop port fitting plane coordinate system and the rotation transformation matrix E' from the i-th stage wheel disc reference coordinate system to the i-1-th stage wheel disc upper stop port fitting plane coordinate system i I ;

[0044] Step 3.4, taking the 1st stage wheel disc lower stop port reference coordinate system as the assembly coordinate system O-XYZ, the coordinate vector of the i-th stage wheel disc upper stop port centroid in the assembly coordinate system is obtained when the n-stage wheel discs are stacked

[0045]

[0046] In the formula, the superscript "M" represents a mixed uncertainty variable, O iL and O iU are the fitting centroids of the lower stop port and the upper stop port of the i-th stage wheel disc respectively, is the stop port assembly eccentricity vector the rotation transformation matrix from the i-1-th stage wheel disc upper stop port fitting plane coordinate system to the assembly coordinate system, is the centroid offset vector of the upper and lower stop ports of the i-th stage wheel disc the rotation transformation matrix from the single-stage wheel disc reference coordinate system to the assembly coordinate system, S zi is a rotation matrix considering assembly phase change;

[0047] Step 3.5, taking the centroid connecting line of the rotor front and rear support journal sections as the reference axis for evaluating the rotor coaxiality error, i.e. establishing a rotation coordinate system with the connecting line as the Z-axis direction, and obtaining the i-th stage wheel disc upper stop port centroid coordinate vector in the rotation coordinate system through rotation transformation:

[0048]

[0049] In the formula, is the rotation transformation matrix from the assembly coordinate system to the rotation coordinate system, and are the components of the i-th stage wheel disc upper stop port centroid coordinate vector in the X, Y and Z directions in the rotation coordinate system respectively;

[0050] Step 3.6, the coaxiality error of the stacked multi-stage wheel discs is expressed as:

[0051]

[0052] Further, in step 4, the outer layer adopts probability theory to represent random uncertainty, and the inner layer adopts interval theory to represent cognitive uncertainty, and the calculated rotor assembly coaxiality error is presented in the form of N interval numbers, and the upper limit, lower limit and interval midpoint value of the interval number are respectively subjected to probability statistics.

[0053] Further, step 5 includes:

[0054] Step 5.1, the coaxiality excess probability is calculated, and the coaxiality excess probability is P f The lower limit of the coaxiality excess probability is The upper limit of the coaxiality excess probability is

[0055] Step 5.2, taking the circumferential installation phase of each stage of the disc as the control variable, the rotor assembly coaxiality error is adjusted, and a double-layer optimization mode is adopted, that is, in the case that the inner layer optimization ensures that the upper limit of the coaxiality excess probability is minimum, the optimal installation phase of each stage of the disc is found through the outer layer optimization, and finally the mean value of the coaxiality error interval midpoint is minimum.

[0056] Step 5.3, the optimization model is solved by an intelligent optimization algorithm, and the disc installation phase combination mode meeting the minimum upper limit of the coaxiality excess probability and the minimum mean value of the interval midpoint is obtained.

[0057] Further, the double-layer optimization model adopted in step 5.2 is:

[0058]

[0059] In the formula, A best is the optimal installation phase combination, is the mean value of the coaxiality error interval midpoint, W is the installation phase combination number for minimizing the upper limit of the excess probability, θ zi is the circumferential installation phase of the i-th stage of the disc, s i is the number of bolt holes for the joint connection.

[0060] The advantages of the present application are:

[0061] 1. The rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty of the application applies an uncertainty quantification method to the prediction and optimization of rotor assembly geometric precision, and can realize accurate prediction and reliable optimization of the geometric precision of an aero-engine rotor assembly. Compared with the existing rotor assembly geometric precision prediction and optimization random probability model considering only single uncertainty, the application considers multi-source uncertainty in the rotor assembly process, establishes a rotor coaxiality error prediction and optimization model under random-interval mixed uncertainty, statistically analyzes the upper limit, lower limit and midpoint value of the coaxiality error interval, more comprehensively and accurately describes the distribution and range of the rotor coaxiality error, and obtains the optimal installation phase of each disc through an uncertainty optimization algorithm, so that the mean value of the midpoint of the rotor coaxiality error interval obtained by assembling at the installation phase is minimized, the accuracy of the rotor assembly geometric precision is improved, and the high-reliability assembly requirement of the aero-engine rotor can be met.

[0062] 2. The uncertainty optimization method proposed in the application also minimizes the upper limit value of the coaxiality error tolerance probability interval, can quantify the possibility of the rotor assembly tolerance obtained by assembling at the given optimal phase combination, improves the rotor assembly geometric precision, ensures that the coaxiality error tolerance probability after assembly is minimized, and improves the reliability and stability of the aero-engine rotor assembly. BRIEF DESCRIPTION OF DRAWINGS

[0063] The above and / or other features and advantages of the application will become more apparent by describing in following reference to the accompanying drawings, in which:

[0064] Figure 1 is a flowchart of the rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty of the application;

[0065] Figure 2 is an analysis of the sources of uncertainty in the rotor assembly of the application;

[0066] Figure 3 is a rotor assembly geometric precision prediction process under mixed uncertainty in the application;

[0067] Figure 4 is a schematic diagram of a rotor structure simulated in an example of the application;

[0068] Figure 5 is a comparison of the uncertainty prediction, deterministic prediction and measured coaxiality error under the optimal installation phase combination in the example of the application;

[0069] Figure 6 is a comparison of the uncertainty prediction, deterministic prediction and measured coaxiality error under the existing high-low point assembly in the example. DETAILED DESCRIPTION

[0070] The present application will be described in detail below with reference to the accompanying drawings by means of exemplary embodiments of the present application. It should be noted that the following detailed description of the present application is merely for illustrative purposes and is not limiting on the present application.

[0071] The present application provides a rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty, which is used for predicting and optimizing the assembly precision of an aero-engine rotor and improving the assembly precision of the rotor.

[0072] With reference to Figure 1 The rotor assembly geometric precision prediction and optimization method considering multi-source uncertainty as the exemplary embodiment of the present application comprises the following steps:

[0073] Step S1: analyzing the uncertainty affecting the geometric precision of the rotor assembly in the stacking assembly process of the aero-engine rotor;

[0074] Step S2: representing the uncertainty analyzed in step S1 as a random variable and an interval variable respectively through a random model and an interval model;

[0075] Step S3: taking the uncertainty variables represented in step S2 as input variables, establishing a rotor assembly geometric precision prediction model considering random-interval mixed uncertainty, and predicting the rotor assembly coaxiality error under the mixed uncertainty condition;

[0076] Step S4: based on the Monte Carlo method, solving the random-interval mixed uncertainty model established in step S3 in a double-layer nested manner to obtain the probability statistical results of the upper limit, lower limit and midpoint value of the coaxiality error interval;

[0077] Step S5: performing coaxiality out-of-tolerance probability interval estimation, constructing a rotor coaxiality double-layer optimization model under mixed uncertainty, and obtaining the optimal installation phase of each disc through optimization so as to minimize the upper limit value of the coaxiality out-of-tolerance probability interval and the mean value of the coaxiality error interval midpoint.

[0078] For step S1, the rotor assembly uncertainty analysis is as follows Figure 2As shown, the uncertainty affecting the rotor assembly geometry precision can be divided into single-stage disk manufacturing error uncertainty, measurement uncertainty and assembly process execution uncertainty according to different sources of uncertainty. Among them, the single-stage disk manufacturing error uncertainty is caused by the dispersion of machining deviation, and the main uncertain influencing factors include the jump of the stop port fitting cylindrical surface and the end surface jump. The measurement uncertainty refers to the uncertainty caused by human operation, consistency problem of part clamping and installation error of measuring instrument when measuring the stop port assembly surface jump, and the main uncertain influencing factors include the centering and tilting error of the rotary table, the disk clamping error and the sensor installation error. The assembly process execution uncertainty refers to the uncertainty caused by the dispersion of assembly process execution such as temperature difference assembly, press assembly and bolt tightening during the disk stacking process, and the main uncertain factors include the assembly process parameters such as bolt tightening torque, process temperature and axial press assembly force.

[0079] The single-stage disk manufacturing error uncertainty and the measurement uncertainty jointly cause the uncertainty of the rotor assembly geometry precision prediction model input variables such as the single-stage disk stop port centroid coordinates and the end surface normal vector. During the disk stacking process, the assembly process execution and the part surface shape deviation have a direct impact on the elastic deformation and contact balance state of the contact surface, which further affects the prediction model input variables such as the stop port assembly eccentricity and the skew angle. The single-stage disk uncertainty variables such as the stop port centroid coordinates and the end surface normal vector can be obtained by multiple measurements to obtain sufficient statistical information, and a probability statistical model of the uncertainty variable can be constructed according to a large amount of measurement data, which belongs to random uncertainty and is characterized as a random variable. Limited by the measurement means, the uncertainty variables caused by the single-stage disk manufacturing error uncertainty and the assembly process execution uncertainty during the disk stacking process can only obtain interval information according to experience and simulation, which can be classified as cognitive uncertainty and is expressed as an interval variable.

[0080] Step S2 characterizes the uncertainty in the above-mentioned rotor stacking assembly process, including random uncertainty characterization (step S2.1) and interval uncertainty characterization (step S2.2).

[0081] In step S2.1, without considering the part selection, the single-stage disk uncertainty variable is mainly affected by the measurement uncertainty. In order to simplify the workload of random uncertainty quantification and make it easy for engineering application, the measurement uncertainty is directly characterized by referring to the variance analysis method (ANOVA) in measurement system analysis (MSA). The specific characterization method is as follows:

[0082] Using the same measuring instrument, the measurement variation of the same feature on the same part is obtained by multiple measurements under the same installation clamping, and is defined as repeatability.

[0083] The variation of the measurement average value is obtained by repeatedly measuring the same feature on the same part using the same measuring instrument and under multiple mounting and clamping, and is defined as the repeatability.

[0084] The unbiased estimation of the measurement system repeatability variance σ 2 and the repeatability variance ε 2 is respectively represented as:

[0085]

[0086] In the formula, l is the number of mounting and clamping, m is the number of repeated measurements for one mounting and clamping, y kj is the jth repeated measurement result of the kth mounting and clamping, represents the average value of the m repeated measurements of the kth mounting and clamping, represents the average value of all repeated measurements of the l mounting and clamping, i.e., the average value of l×m measurement results.

[0087] The total variance α 2 of the measurement system is calculated as σ 2 + ε 2 , and the measurement uncertainty is characterized as a random normal distribution Δ~N(0,α 2 ) with 0 as the mean value and α as the standard deviation.

[0088] Under the same measurement conditions, a measurement point on a feature surface of a part is measured, and the measurement value is t, then the true value of the measurement point is contained in a random normal distribution with t as the mean value and α as the standard deviation, i.e., the value distribution of multiple measurements of the measurement point is T~N(t,α 2 ).

[0089] The probability distribution of the measurement values of all measurement points is obtained, and the random distribution model of the fitted joint core coordinate vector d and the end face normal vector p is obtained by the Monte Carlo (MC) method, and is respectively represented as:

[0090]

[0091] In the formula, the superscript “R” represents a random variable, and the subscript “i” in the subscript represents the i-th wheel, “U” represents the upper joint, and “L” represents the lower joint.

[0092] In step S2.2, the interval model is generally defined as follows:

[0093]

[0094] In the formula, a I is an interval variable, a is the lower limit of the variable interval number, and b is the upper limit of the variable interval number.

[0095] ​The interval variable can also be denoted by the center interval representation as

[0096] (5)

[0097] where a c is the midpoint value of the interval, a r is the radius of the interval,

[0098] If F(a I ) is an interval-valued function of the interval vector a I , then the solution interval of the function is:

[0099]

[0100] where F(a I ) = min{F(a I )},

[0101] The eccentricity and the skew of the joint fit can be characterized by the interval variables of the joint fit eccentricity distance the joint fit eccentricity angle the joint fit skew angle δ i I and the skew minimum point phase , where the superscript "I" represents the interval variable.

[0102] In step S3, a rotor assembly geometric precision prediction model considering random-interval hybrid uncertainty is established.

[0103] First, the reference alignment error is corrected. The single-stage disk coordinate system is established at the lower joint of the i-th stage disk, and the center of mass coordinate vector of the upper joint of the i-th stage disk in the single-stage disk coordinate system is obtained through coordinate transformation and the end face normal vector are respectively expressed as:

[0104]

[0105]

[0106] wherein is the rotation transformation matrix from the measurement system coordinate system to the single-stage disk coordinate system, which can be expressed as equation (9); and are the end face normal vector, the center of mass coordinate vector and the center of mass coordinate vector of the lower joint of the i-th stage disk in the measurement system coordinate system, respectively; and are the components of the center of mass coordinate vector of the upper joint of the i-th stage disk in the X, Y and Z directions in the single-stage disk coordinate system, respectively; and are the components of the end face normal vector of the upper stop of the i-th stage in the X, Y and Z directions of the single stage coordinate system, respectively. It should be pointed out that since the datum error is corrected, the datum coordinate system is changed from the measurement system coordinate system to the single stage coordinate system established at the lower stop of the i-th stage, and the center coordinates and the end face normal vector of the lower stop are no longer needed to be considered in the subsequent calculation, therefore, in order to distinguish the notations of the center coordinates and the end face normal vector of the upper stop in different coordinate systems, the subscript U is removed.

[0107]

[0108] wherein,

[0109]

[0110] wherein, and are the components of the end face normal vector of the lower stop of the i-th stage in the X, Y and Z directions of the measurement system coordinate system, respectively, and are the angles of rotation of the coordinate system around the X and Y axes in the measurement system coordinate system.

[0111] Secondly, the error model of the single stage is established. The rotation transformation matrix from the fitting plane coordinate system of the upper stop to the datum coordinate system (the single stage coordinate system established at the lower stop of the i-th stage) is obtained

[0112]

[0113] wherein,

[0114]

[0115] wherein, and are the components of the end face normal vector of the upper stop of the i-th stage in the X, Y and Z directions of the single stage coordinate system, respectively, and are the angles of rotation of the coordinate system around the X and Y axes in the measurement system coordinate system. Then, the assembly deviation model of the stop is established. The assembly eccentricity vector of the stop is obtained

[0116] the interval expression (as shown in equation (14)) in the fitting plane coordinate system of the upper stop of the i-1-th stage and the rotation transformation matrix from the datum coordinate system of the i-th stage to the fitting plane coordinate system of the upper stop of the i-1-th stage wherein,

[0117] ​

[0118] are the interval representations of the assembly tilt angle and the tilt minimum phase of the lower stop of the i-th stage disk relative to the upper stop of the i-1-th stage disk, respectively, and are the interval representations of the assembly eccentricity and the eccentric angle of the lower stop of the i-th stage disk relative to the upper stop of the i-1-th stage disk, respectively. and are the angles of the i-th stage disk reference coordinate system rotating around the X axis and the Y axis, respectively.

[0119]

[0120] are the interval representations of the assembly tilt angle and the tilt minimum phase of the lower stop of the i-th stage disk relative to the upper stop of the i-1-th stage disk, respectively, and are the interval representations of the assembly eccentricity and the eccentric angle of the lower stop of the i-th stage disk relative to the upper stop of the i-1-th stage disk, respectively.

[0121] Next, taking the lower stop reference coordinate system of the 1st stage disk as the assembly coordinate system O-XYZ, the coordinate vector of the center of the upper stop of the i-th stage disk in the assembly coordinate system is obtained when the n-stage disk stack is assembled

[0122]

[0123] wherein the superscript "M" represents the mixed uncertainty variable, O iL and O iU are the fitting centers of the lower stop and the upper stop of the i-th stage disk, respectively. is the stop assembly eccentricity vector is the rotation transformation matrix from the fitting plane coordinate system of the upper stop of the i-1-th stage disk to the assembly coordinate system, is the center offset vector of the upper and lower stops of the i-th stage disk is the rotation transformation matrix from the single-stage disk reference coordinate system to the assembly coordinate system; S zi is the rotation matrix considering the assembly phase change, as shown in equation (16).

[0124]

[0125] wherein θ zi is the circumferential installation phase of the i-th stage disk relative to the i-1-th stage disk, and is positive when installed counterclockwise.

[0126] Finally, assuming that the centers of the front and rear support circles of the rotor are the centers of the upper and lower stops of the assembly O n and O, the rotation coordinate system is established with the center line OO n as the Z axis direction, and the coordinate vector of the center of the upper stop of the i-th stage disk in the rotation coordinate system is obtained through coordinate rotation transformation:

[0127]

[0128] where, is the rotation transformation matrix from the assembly coordinate system to the rotation coordinate system, and are the components of the i-th level wheel disc's center of the orifice in the X, Y and Z directions in the rotation coordinate system, respectively, where:

[0129]

[0130] where, and are the coordinate values of the n-th level wheel disc's center in the X, Y and Z directions in the assembly coordinate system, respectively, and are the angles of rotation of the assembly coordinate system around the X and Y axes, respectively.

[0131] At this time, the coaxiality error of the multi-level wheel disc stack is expressed as:

[0132]

[0133] Step S4 solves the random-interval hybrid uncertainty model.

[0134] Since both random and cognitive uncertainties exist in the assembly accuracy prediction model, a double-layer nested method is used to propagate the hybrid uncertainty based on the Monte Carlo method. The outer layer uses probability theory to represent random uncertainty, and the inner layer uses interval theory to represent cognitive uncertainty. The overall solution process is shown in Figure 3 The calculated rotor assembly coaxiality error is in the form of N interval numbers, and the upper and lower bounds of the interval numbers and the interval midpoint value can be statistically analyzed.

[0135] The sub-interval combination method is introduced to suppress the "interval expansion" in the interval operation process. First, monotonicity analysis shows that the coaxiality error is not monotonic with respect to the orifice assembly eccentric angle η i and the deflection minimum point phase τ i Then, according to the calculation accuracy requirement, the interval variables η i I and τ i I are decomposed into g sub-intervals of equal length; finally, the end point values of the decomposed sub-intervals are combined and traversed to solve the total number of solutions h = [2(g+1)] 2(n-1) The maximum and minimum values obtained are the upper and lower limits of the coaxiality error solution interval.

[0136] In step S5, a double-layer optimization model of the rotor coaxiality under hybrid uncertainty is constructed.

[0137] The installation phase of each stage of the wheel disc is obtained by optimization, while ensuring that the upper bound of the coaxiality error probability and the mean value of the midpoint of the coaxiality error interval are minimized. The specific process is as follows:

[0138] First, the coaxiality error probability is estimated. Since the input variables of the prediction model include both random variables and interval variables, the coaxiality error probability changes from a single value to an interval value where P f is the lower bound of the coaxiality error probability, is the upper bound of the coaxiality error probability:

[0139]

[0140] In the formula, C max is the upper limit value of the rotor assembly coaxiality error; X q represents the qth random simulation set of the input variable; C and respectively represent the lower bound and the upper bound of the coaxiality error interval obtained by each random simulation; I is an indicator function, which is 1 if the function inside the “[]” is true, and 0 otherwise.

[0141] Then, the circumferential installation phase of each stage of the wheel disc is taken as the control variable to control the rotor assembly coaxiality error. A double-layer optimization method is used to find the optimal installation phase of each stage of the wheel disc through outer optimization while ensuring that the upper bound of the coaxiality error probability is minimized in the inner optimization, so as to finally realize the minimum mean value of the midpoint of the coaxiality error interval. In particular, the double-layer optimization model is:

[0142]

[0143] In the formula, A best is the optimal installation phase combination; is the mean value of the midpoint of the coaxiality error interval; W is the number of installation phase combinations that minimize the upper bound of the error probability; θ zi is the circumferential installation phase of the i-th stage of the wheel disc; s i is the number of bolt holes used for the joint connection.

[0144] Finally, the optimization model is solved by an intelligent optimization algorithm to obtain the wheel disc installation phase combination that satisfies the minimum upper bound of the coaxiality error probability and the minimum mean value of the midpoint. Thus, the optimization algorithm can quantify the possibility of the rotor assembly exceeding the error after assembly according to the given optimal phase combination, improve the geometric precision of the rotor assembly, ensure that the coaxiality error probability after assembly is minimized, and improve the reliability and stability of the rotor assembly of the aero-engine.

[0145] Therefore, as described above, compared with existing random probability models for predicting and optimizing rotor assembly geometric accuracy that only consider a single uncertainty, this invention considers multi-source uncertainties in the rotor assembly process, establishes a rotor coaxiality error prediction and optimization model under random-interval mixed uncertainty, and describes the distribution and range of rotor coaxiality error more comprehensively and accurately by performing probability statistics on the upper bound, lower bound and midpoint value of the coaxiality error interval. The optimal installation phase of each stage of the rotor is obtained through an uncertainty optimization algorithm, so that the mean value of the midpoint of the rotor coaxiality error interval obtained by assembling with this installation phase is minimized, thereby improving the accuracy of rotor assembly geometric accuracy and meeting the high reliability assembly requirements of aero-engine rotors.

[0146] The following examples will further illustrate the rotor assembly geometric accuracy prediction and optimization method considering multi-source uncertainties provided by this invention.

[0147] This example uses a multi-stage disk simulator of a high-pressure compressor rotor as the research object, and its structure is as follows: Figure 4 As shown, this includes level 5 & 6 disks, level 4 disks, level 3 disks, level 2 disks, and level 1 disks. Figure 4 The line connecting the support truncated circle at the bearing mounting location and the centroid of the lower stop of the 5&6 grade disc is used as the reference axis for evaluating the rotor coaxiality error.

[0148] First, the measurement uncertainty was characterized. The part was clamped 10 times. Each time it was clamped, the runout of the end face and cylindrical surface of the upper and lower stops of the wheel was measured 30 times. The maximum value of the runout data of each characteristic surface was taken in each measurement. According to Equations (1) and (2), the measurement repeatability variance and reproducibility variance of the measurement system for the four measurement surfaces were calculated respectively. Then, the random distribution of the four measurement errors was obtained and listed in Table 1.

[0149] Table 1 Measurement Error Distribution

[0150]

[0151] The range of values ​​for the eccentricity and skew angle of the stop assembly can be estimated based on the rough surface contact simulation, and the specific range values ​​are shown in Table 2.

[0152] Table 2. Range of deviation values ​​for edge assembly

[0153]

[0154] Then, the runout of the end faces and cylindrical surfaces of the upper and lower stops of each level of wheel parts was measured. The measured runout data was used as input, and the coaxiality error of the components was optimized according to the two-layer optimization model of Equation (21). The upper limit of the allowable coaxiality error was set to 0.06 mm. The optimization model was solved using an intelligent optimization algorithm to obtain the upper bound of the minimum coaxiality deviation probability. Mean of midpoint of minimum coaxiality error interval min(μ Cc ) and corresponding optimal installation phase combination A best As shown in Table 3.

[0155] Table 3 uncertain optimization results

[0156]

[0157] Finally, according to the rotor assembly geometry precision prediction process under mixed uncertainty shown in Figure 3 , the wheel disc stacking prediction and assembly measurement are performed according to the optimal phase combination, and the comparison of the rotor coaxiality error measured value, uncertainty prediction and certainty prediction result is shown in Figure 5 . The uncertainty prediction result contains the measured result and the certainty prediction result, which shows that the rotor assembly geometry precision can be accurately predicted by the method. Figure 6 The prediction result obtained by using the existing high-low point assembly method is compared with the prediction result shown in Figure 6 . It can be seen that the rotor coaxiality error after assembly according to the optimal phase combination is significantly reduced, and the measured value of the rotor coaxiality error after optimization assembly is reduced by 57.28% compared with the measured value of the high-low point assembly. Therefore, the example verifies the effectiveness of the rotor assembly geometry precision prediction and optimization method considering multiple source uncertainties provided by the present application.

[0158] Finally, it should be noted that the features mentioned and / or shown in the above description of the exemplary embodiments of the present application can be combined in the same or similar manner into one or more other embodiments, combined with or replaced by the features in other embodiments. The technical solutions obtained by combining or replacing should also be considered to be included in the protection scope of the present application.

Claims

1. A method for rotor assembly geometric accuracy prediction and optimization considering multi-source uncertainty, characterized in that, The method comprises the following steps: Step 1, analyzing the uncertainty affecting the rotor assembly geometry precision in the aero-engine rotor stack assembly process; Step 2, representing the uncertainty analyzed in step 1 as a random variable and an interval variable respectively through a random model and an interval model; Step 3, taking the uncertainty variables represented in step 2 as input variables, establishing a rotor assembly geometry precision prediction model considering random-interval hybrid uncertainty, and predicting the rotor assembly coaxiality error under the hybrid uncertainty, comprising the following sub-steps: Step 3.1, correct the reference alignment error, in the first stage disk lower stop, establish a single stage disk coordinate system, through the coordinate transformation, get the single stage disk coordinate system in the first stage disk upper stop centroid coordinate vector And the end face normal vector , respectively, as follows: wherein R is a rotation transformation matrix from the measurement system coordinate system to the single stage disk coordinate system, , and are the upper lip end face normal vector, the upper lip centroid coordinate vector and the lower lip centroid coordinate vector of the nth stage disk in the measurement system coordinate system, respectively, , , and are the components of the upper lip centroid coordinate vector of the nth stage disk in the single stage disk coordinate system in the directions of , , and , , and are the components of the upper lip end face normal vector of the nth stage disk in the single stage disk coordinate system in the directions of , , and . Step 3.2, establish a single-level wheel disc error model to obtain a rotation transformation matrix from the upper stop fitting plane coordinate system to the reference coordinate system where the reference coordinate system is a single-level wheel disc coordinate system established at the first level wheel disc lower stop Step 3.3, the model of the assembly deviation of the joint is established, and a joint assembly eccentricity vector is obtained In the first Interval representation of the joint fitting plane coordinate system on the first Rotation transformation matrix from the reference coordinate system of the first grade wheel disc to the joint fitting plane coordinate system on the first grade wheel disc Step 3.4, take the 1st stage disk lower stop base coordinate system as the assembly coordinate system , get When the stage disk is stacked, the coordinate vector of the 1st stage disk upper stop center in the assembly coordinate system , , =1, 2, …, : where the superscript "M" represents the mixed uncertainty variable, and are the first and second order wheel disk lower and upper stop fitting centroid, is the stop fitting eccentricity vector is the rotation transformation matrix from the first order wheel disk upper stop fitting plane coordinate system to the assembly coordinate system, is the centroid offset vector of the first and second order wheel disk upper and lower stop fitting is the rotation transformation matrix from the single stage wheel disk reference coordinate system to the assembly coordinate system, is the rotation matrix considering assembly phase change; Step 3.

5. The center line of the intersection circle of the front and rear support shaft necks of the rotor is taken as the reference axis for evaluating the coaxial error of the rotor, i.e. the center line is taken as The rotational coordinate system is established in the axial direction, and the first The center point coordinate vector of the upper stop of the stage wheel disc wherein is the rotation transformation matrix from the assembly coordinate system to the rotating coordinate system, , and are the components of the first order wheel disk stop center point coordinate vector in the rotating coordinate system in the directions , and , respectively. Step 3.6, representing the coaxiality error of the multi-stage disk stack as: ； Step 4, based on the Monte Carlo method, solving the random-interval hybrid uncertainty model established in step 3 in a double-layer nested manner to obtain the probability statistical results of the upper limit, lower limit and midpoint value of the coaxiality error interval; Step 5, estimating the coaxiality error probability interval, constructing a double-layer optimization model of the rotor coaxiality under the hybrid uncertainty, and obtaining the optimal installation phase of each stage disk through optimization to minimize the upper limit value of the coaxiality error probability interval and the mean value of the coaxiality error interval midpoint.

2. The method for rotor assembly geometric accuracy prediction and optimization considering multi-source uncertainty according to claim 1, characterized in that, In step 1, the uncertainty affecting the rotor assembly geometry precision is divided into single-stage disk manufacturing error uncertainty, measurement uncertainty and assembly process execution uncertainty according to different sources of uncertainty; The single-stage disk manufacturing error uncertainty includes disk stop port fitting cylindrical runout and stop port fitting end face runout; The measurement uncertainty includes the centering and tilting error of the rotary table, the disk clamping error and the sensor installation error; The assembly process execution uncertainty includes the uncertainty of bolt tightening torque, assembly process temperature and axial pressing force.

3. The method for rotor assembly geometric accuracy prediction and optimization considering multi-source uncertainty according to claim 2, characterized in that, In step 2, the single-stage disk manufacturing error uncertainty and the measurement uncertainty jointly cause the uncertainty of the single-stage disk stop port centroid coordinates and end face normal vector as model input variables, which are classified as random uncertainty and represented as random variables; the single-stage disk manufacturing error uncertainty and the assembly process execution uncertainty jointly cause the uncertainty of the stop port assembly eccentricity and the stop port assembly skew angle as model input variables, which are classified as cognitive uncertainty and represented as interval variables.

4. The method for rotor assembly geometric accuracy prediction and optimization considering multi-source uncertainty according to claim 3, characterized in that, In step 2, the random variables are represented through step 2.1, and step 2.1 comprises: Step 2.1.1, using the same measuring instrument, measuring the same feature on the same part multiple times under the same installation clamping to obtain the measurement variation, which is defined as repeatability; Step 2.1.2, using the same measuring instrument, repeatedly measuring the same feature on the same part under multiple installation clamping to obtain the variation of the measurement average, which is defined as reproducibility; Step 2.1.3, the unbiased estimates of the repeatability variance σ 2 and the reproducibility variance ε 2 are denoted by: In the formula, For the number of clamping cycles, The number of repeated measurements for a single clamping operation. For the first The first clamping Results of repeated measurements Indicates the first Secondary clamping The average of repeated measurements express The average of all repeated measurements in each clamping, i.e. The average of the measurements; Step 2.1.4, calculation of total variance The measurement uncertainty is characterized as a random normal distribution with a mean of 0 and a standard deviation of ;​​ Step 2.1.5, a measurement point on a certain feature surface of a certain part is measured under the same measurement conditions, and the measurement value is , the true value of the measurement point is contained in the random normal distribution with as the mean value and as the standard deviation, that is, the value distribution of multiple measurements on the measurement point is ~ ;​ Step 2.1.6, obtaining the probability distribution of all measured point measurements, the fitted center of the notch coordinate vector is obtained by the Monte Carlo method and the random distribution model of the end face normal vector is respectively expressed as: where the superscript "R" represents a random variable, the subscript "i" represents the i-th "U" represents an upper stop, and "L" represents a lower stop.​ 5. The method for rotor assembly geometric accuracy prediction and optimization considering multi-source uncertainty according to claim 4, characterized in that, In step 2, the interval variables are represented through step 2.2, and step 2.2 comprises: Step 2.2.1, the following interval model is established: wherein is the lower bound of the interval number of the variable, is the lower bound of the interval number of the variable, is the upper bound of the interval number of the variable; Step 2.2.2, another is an interval vector is an interval value function of the interval vector , then the solution interval of the function is In the formulae, , .

6. The method for rotor assembly geometric precision prediction and optimization considering multi-source uncertainty according to claim 5, characterized in that, In step 2.2.1, the interval model can replace the following: wherein is the midpoint of the interval, , is the radius of the interval, .

7. The method for rotor assembly geometry precision prediction and optimization considering multi-source uncertainty according to claim 6, characterized in that, In step 4, the outer layer uses probability theory to represent random uncertainty, and the inner layer uses interval theory to represent cognitive uncertainty. The calculated rotor assembly concentricity error is presented in the form of N interval numbers. The upper bound, lower bound and midpoint value of the interval number are subjected to probability statistics.

8. The method for rotor assembly geometric precision prediction and optimization considering multi-source uncertainty according to claim 7, characterized in that, Step 5 includes: Step 5.1, perform coaxiality out-of-tolerance probability estimation, the coaxiality out-of-tolerance probability is , is a lower bound of the coaxiality out-of-tolerance probability, is an upper bound of the coaxiality out-of-tolerance probability; Step 5.2, taking the circumferential installation phase of each stage of the wheel disc as the control variable, regulating the rotor assembly concentricity error, using a double-layer optimization method, in the case of ensuring the minimum upper bound of the concentricity error probability, the optimal installation phase of each stage of the wheel disc is found through the outer layer optimization, and finally the minimum mean value of the interval midpoint of the rotor assembly concentricity error is realized; Step 5.3, the optimization model is solved by an intelligent optimization algorithm to obtain the wheel disc installation phase combination mode that satisfies the minimum upper bound of the concentricity error probability and the minimum mean value of the interval midpoint.

9. The method for rotor assembly geometry precision prediction and optimization considering multi-source uncertainty according to claim 8, characterized in that, The double-layer optimization model used in step 5.2 is: In the formula, is the optimal installation phase combination, is the average of the coaxiality error interval midpoint, is the number of installation phase combinations that minimize the upper bound of the probability of exceeding the tolerance, is the number of installation phase combinations that minimize the upper bound of the probability of exceeding the tolerance, is the circumferential installation phase of the nth wheel disc, is the number of bolt holes for the joint connection.

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