Rotor assembly geometric accuracy prediction and optimization method considering multi-source uncertainty

Abstract

The invention provides a rotor assembly geometric accuracy prediction and optimization method considering multi-source uncertainty. The method comprises the following steps: analyzing uncertainty influencing assembly accuracy in a rotor assembly process; respectively representing the uncertainty as a random variable and an interval variable through a random model and an interval model; establishing a precision prediction model considering random-interval hybrid uncertainty, and predicting the coaxiality error of the rotor assembly; solving the uncertainty model based on a Monte Carlo method to obtain probability statistical results of an upper bound value, a lower bound value and a midpoint value of a coaxiality error interval; and carrying out coaxiality out-of-tolerance probability interval estimation, constructing a rotor coaxiality double-layer optimization model under hybrid uncertainty, and carrying out optimization to obtain the optimal installation phase of each stage of wheel disc. According to the method, the uncertainty quantification method is applied to prediction and optimization of the rotor assembly geometric accuracy, accurate prediction and reliable optimization of the rotor assembly geometric accuracy can be achieved, and the high-reliability assembly requirement of an aero-engine rotor is met.

Description

Technical Field

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

[0002] In the assembly of aircraft engines, rotor assembly accuracy is an important indicator that affects engine safety and performance. Insufficient rotor assembly geometric accuracy will cause large eccentricity and tilt of the rotor assembly, resulting in severe vibration and wear of the aircraft engine during high-speed operation, seriously affecting the performance and service life of the aircraft engine. Accurately predicting the rotor assembly geometric accuracy is a prerequisite for optimizing aircraft engine assembly parameters and improving the reliability of aircraft engine assembly processes.

[0003] There are currently two main models for predicting and optimizing rotor assembly accuracy: 1) a deterministic model based on the principle of error transmission; 2) a random probability model that considers a single form of uncertainty. However, due to the complexity of the rotor assembly process and the large number of parts involved, various uncertainties inevitably exist in the measurement and process execution process, resulting in a large dispersion in the assembly accuracy of the rotor assembly. The former does not consider the uncertainties in the assembly process, so the reliability of the prediction and optimization results is insufficient. Although the latter takes into account the impact of random errors on the assembly accuracy of the rotor assembly, and improves the accuracy of the prediction and the reliability of the optimization to a certain extent, it characterizes the uncertainty factors as random distributions according to the design tolerance or accuracy level. In engineering practice, the sources of uncertainty are extensive and the manifestations are diverse. Therefore, the latter is also difficult to reliably predict the assembly accuracy and cannot meet the requirements of high-reliability assembly. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the existing methods for predicting and optimizing the assembly accuracy of aircraft engine rotors are difficult to obtain reliable assembly accuracy results, and to take multi-source and mixed uncertainty representations into consideration in the prediction and optimization of rotor assembly geometric accuracy, thereby providing a method for predicting and optimizing rotor assembly geometric accuracy taking multi-source uncertainty into consideration.

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

[0006] The present invention provides a method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties, comprising the following steps:

[0007] Step 1, analyzing the uncertainty affecting the geometric accuracy of rotor assembly during the stacking assembly of aero-engine rotors;

[0008] Step 2, characterize 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, using the uncertainty variables characterized in step 2 as input variables, establishing a rotor assembly geometric accuracy prediction model considering random-interval mixed uncertainty, and predicting the coaxiality error of the rotor assembly under mixed uncertainty conditions;

[0010] Step 4: Based on the Monte Carlo method, a double-layer nested method is used to solve the random-interval mixed uncertainty model established in step 3, and the probability statistical results of the upper bound, lower bound and midpoint value of the coaxiality error interval are obtained;

[0011] Step 5, estimate the probability interval of coaxiality excess tolerance, construct a two-layer optimization model for rotor coaxiality under mixed uncertainty, and obtain the optimal installation phase of each level of the wheel through optimization, so that the upper limit value of the coaxiality excess tolerance probability interval and the mean of the midpoint of the coaxiality error interval are minimized.

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

[0013] The manufacturing error uncertainty of a single-stage wheel includes the cylindrical runout of the wheel stop and the end runout of the stop;

[0014] The measurement uncertainty includes the centering and tilting error of the turntable, the wheel clamping error and the sensor installation error;

[0015] The assembly process execution uncertainty includes the uncertainty of bolt tightening torque, assembly process temperature and axial press force.

[0016] Furthermore, in step 2, the single-stage wheel manufacturing error uncertainty and measurement uncertainty jointly cause the uncertainty of the single-stage wheel stop centroid coordinates and end face normal vector as model input variables, which are classified as random uncertainty and characterized as random variables; the single-stage wheel manufacturing error uncertainty and assembly process execution uncertainty jointly cause the uncertainty of the stop assembly eccentricity and stop assembly deflection angle as model input variables, which are classified as cognitive uncertainty and characterized as interval variables.

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

[0018] Step 2.1.1, use the same measuring instrument, under the same installation and clamping, to measure the same feature on the same part multiple times, and obtain the measurement variation, which is defined as repeatability;

[0019] Step 2.1.2, using the same measuring instrument, repeatedly measure the same feature on the same part under multiple mounting and clamping conditions, and obtain the variation of the measurement mean value, which is defined as reproducibility;

[0020] Step 2.1.3, replace the repeatability variance σ 2 and reproducibility variance ε 2 The unbiased estimates of are expressed as:

[0021]

[0022] In the formula, l is the number of installation and clamping times, m is the number of repeated measurements for one installation and clamping, and y is kj is the jth repeated measurement result of the kth clamping, It represents the average value of m repeated measurements in the k-th clamping. It represents the average value of all repeated measurements of l clampings, that is, the average value of l×m measurement results;

[0023] Step 2.1.4, calculate the total variance α 2 =σ 2 +ε 2 , the measurement uncertainty is characterized as a random normal distribution Δ~N(0,α 2 );

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

[0025] Step 2.1.6, obtain the probability distribution of the measured values ​​of all measuring points, and obtain the random distribution model of the fitting stop centroid coordinate vector d and the end surface normal vector p by Monte Carlo method, which are expressed as:

[0026]

[0027] In the formula, the superscript "R" represents a random variable, the subscript "i" represents the i-th level wheel, "U" represents the upper stop, and "L" represents the lower stop.

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

[0029] Step 2.2.1, establish the following interval model:

[0030]

[0031] In the formula, a I is an interval variable, a is the lower bound of the variable interval number, is the upper bound of the variable interval number;

[0032] Step 2.2.2, another F(a I ) is the interval vector a I If it 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 is the midpoint value of the interval, a r is the interval radius,

[0038] Further, step 3 includes:

[0039] Step 3.1, correct the benchmark alignment error, establish a single-stage wheel coordinate system at the lower stop of the i-th wheel, and obtain the centroid coordinate vector of the upper stop of the i-th wheel in the single-stage wheel coordinate system through coordinate transformation. and the end normal vector Respectively expressed as:

[0040]

[0041] In the formula, is the rotation transformation matrix from the measurement system coordinate system to the single-stage wheel coordinate system, and are the normal vector of the upper stop end face, the coordinate vector of the upper stop centroid and the coordinate vector of the lower stop centroid in the coordinate system of the i-th level wheel, respectively. and are the components of the centroid coordinate vector of the stop on the i-th wheel in the X, Y and Z directions in the single-stage wheel coordinate system, and are the components of the normal vector of the end face of the stopper on the i-th wheel in the X, Y and Z directions in the single-stage wheel coordinate system;

[0042] Step 3.2: Establish a single-stage wheel error model and obtain the rotation transformation matrix from the upper stop fitting plane coordinate system to the reference coordinate system. The reference coordinate system is a single-stage wheel coordinate system established at the lower stop of the i-th wheel;

[0043] Step 3.3, establish the stopper assembly deviation model and obtain the stopper assembly eccentricity vector The interval representation in the i-1th level wheel upper stop fitting plane coordinate system and the rotation transformation matrix E′ from the i-1th level wheel reference coordinate system to the i-1th level wheel upper stop fitting plane coordinate system i I ;

[0044] Step 3.4, using the reference coordinate system of the lower stop of the first-level wheel as the assembly coordinate system O-XYZ, obtain the coordinate vector of the centroid of the upper stop of the i-th wheel in the assembly coordinate system when the n-level wheels are stacked

[0045]

[0046] In the formula, the superscript “M” represents the mixed uncertainty variable, O iL and O iU are the fitting centroids of the lower stop and upper stop of the i-th level wheel, Eccentricity vector for stopper assembly The rotation transformation matrix from the i-1th level wheel upper stop fitting plane coordinate system to the assembly coordinate system, is the centroid offset vector of the upper and lower stoppers of the i-th level wheel The rotation transformation matrix from the single-stage wheel reference coordinate system to the assembly coordinate system, S zi is the rotation matrix that takes into account the assembly phase change;

[0047] Step 3.5, take the centroid line of the front and rear support journal sections of the rotor as the reference axis for evaluating the coaxiality error of the rotor, that is, take the line as the Z-axis direction to establish a rotating coordinate system, and obtain the centroid coordinate vector of the upper stop of the i-th level wheel in the rotating 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 centroid coordinate vector of the stop on the i-th level wheel in the X, Y and Z directions in the rotating coordinate system respectively;

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

[0051]

[0052] Furthermore, in step 4, the outer layer uses probability theory to characterize random uncertainty, and the inner layer uses interval theory to characterize epistemic uncertainty. The calculated coaxiality error of the rotor assembly is presented in the form of N interval numbers, and probability statistics are performed on the upper limit, lower limit and midpoint value of the interval number.

[0053] Further, step 5 comprises:

[0054] Step 5.1, estimate the probability of coaxiality exceeding the tolerance. The probability of coaxiality exceeding the tolerance is P f is the lower bound of the probability of coaxiality exceeding the tolerance, is the upper bound of the probability of coaxiality exceeding the tolerance;

[0055] Step 5.2, taking the circumferential installation phase of each level of wheel disc as the control variable, regulating the coaxiality error of the rotor assembly, adopting a double-layer optimization method, while the inner layer optimization ensures the minimum upper bound of the probability of coaxiality deviation, the outer layer optimization is used to find the optimal installation phase of each level of wheel disc, and finally the mean value of the midpoint of the coaxiality error interval of the rotor assembly is minimized;

[0056] Step 5.3, solve the optimization model through the intelligent optimization algorithm to obtain the wheel installation phase combination that satisfies the minimum upper bound of the probability of coaxiality deviation and the minimum mean value of the midpoint of the interval.

[0057] Furthermore, the two-layer optimization model used in step 5.2 is:

[0058]

[0059] In the formula, A best For the optimal installation phase combination, is the mean of the midpoint of the coaxiality error interval, W is the number of installation phase combinations that minimizes the upper bound of the probability of exceeding the tolerance, θ zi is the circumferential installation phase of the i-th wheel disc, s i is the number of bolt holes used for the stop connection.

[0060] The advantages of the present invention are:

[0061] 1. The rotor assembly geometric accuracy prediction and optimization method considering multi-source uncertainty of the present invention applies uncertainty quantification method to the prediction and optimization of rotor assembly geometric accuracy, which can realize accurate prediction and reliable optimization of aero-engine rotor assembly geometric accuracy. Compared with the existing rotor assembly geometric accuracy prediction and optimization random probability model that only considers single uncertainty, the present invention considers multi-source uncertainty in the rotor assembly process, establishes a rotor coaxiality error prediction and optimization model under random-interval mixed uncertainty, and more comprehensively and accurately describes the distribution and range of rotor coaxiality error by performing probability statistics on the upper bound, lower bound and midpoint value of the coaxiality error interval respectively. The optimal installation phase of each level of wheel is obtained through the uncertain optimization algorithm, so that the mean value of the midpoint of the rotor coaxiality error interval obtained by assembly 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.

[0062] 2. The uncertain optimization method proposed in the present invention also minimizes the upper limit of the probability interval of coaxiality excess tolerance, and can quantify the possibility of excess tolerance of the rotor assembly obtained by assembling according to a given optimal phase combination. While improving the geometric accuracy of the rotor assembly, it can ensure that the probability of coaxiality excess tolerance after assembly is minimized, thereby improving the reliability and stability of the aircraft engine rotor assembly. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The above and / or other features and advantages of the present invention will become more easily understood through the following description with reference to the accompanying drawings, in which:

[0064] Figure 1 is a flow chart of a method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties of the present invention;

[0065] Figure 2 It is the analysis of the sources of uncertainty in rotor assembly in the present invention;

[0066] Figure 3 It is the prediction process of rotor assembly geometric accuracy under mixed uncertainty in the present invention;

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

[0068] Figure 5 It is the comparison of uncertain prediction, deterministic prediction and measured coaxiality error under the optimal installation phase combination in the example of the present invention;

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

[0070] 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.

[0071] The present invention provides a rotor assembly geometric accuracy prediction and optimization method taking into account multi-source uncertainties, which is used to predict and optimize the assembly accuracy of an aero-engine rotor and improve the rotor assembly accuracy.

[0072] Reference Figure 1 , as an exemplary embodiment of the present invention, a method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties comprises the following steps:

[0073] Step S1, analyzing the uncertainty affecting the geometric accuracy of rotor assembly during the stacking assembly of the aircraft engine rotor;

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

[0075] Step S3, using the uncertainty variable represented by step S2 as an input variable, establishing a rotor assembly geometric accuracy prediction model considering random-interval mixed uncertainty, and predicting the coaxiality error of the rotor assembly under mixed uncertainty conditions;

[0076] Step S4, based on the Monte Carlo method, a double-layer nested method is used to solve the random-interval mixed uncertainty model established in step S3, and the probability statistical results of the upper bound, lower bound and midpoint value of the coaxiality error interval are obtained;

[0077] Step S5, estimate the probability interval of coaxiality excess tolerance, construct a two-layer optimization model of rotor coaxiality under mixed uncertainty, and obtain the optimal installation phase of each level of wheel by optimization, so that the upper limit value of the coaxiality excess tolerance probability interval and the mean of the midpoint of the coaxiality error interval are minimized.

[0078] For step S1, the rotor assembly uncertainty analysis is as follows: Figure 2As shown in the figure, according to the different sources of uncertainty, the uncertainty affecting the geometric accuracy of rotor assembly can be divided into: single-stage disc manufacturing error uncertainty, measurement uncertainty and assembly process execution uncertainty. Among them, the single-stage disc manufacturing error uncertainty is caused by the dispersion of processing deviations, and the main uncertainties include the cylindrical runout and end face runout of the stopper. Measurement uncertainty refers to the uncertainty caused by human operation, consistency of parts clamping and installation error of measuring instruments when measuring the surface runout of the stopper assembly. The main uncertainties include the centering and tilting error of the turntable, disc clamping error and sensor installation error. Assembly process execution uncertainty refers to the uncertainty caused by the dispersion of assembly processes such as temperature difference assembly, press fitting and bolt tightening during the disc stacking process, mainly including the uncertainty of assembly process parameters such as bolt tightening torque, process temperature and axial press fitting force.

[0079] The combined effect of manufacturing error uncertainty and measurement uncertainty of a single-stage wheel causes uncertainty in the input variables of the rotor assembly geometric accuracy prediction model, such as the centroid coordinates of the stopper and the end face normal vector. During the wheel stacking process, the assembly process execution and part surface shape deviation have a direct impact on the elastic deformation and contact equilibrium state of the contact surface, which in turn affects the input variables of the prediction model, such as the stopper assembly eccentricity and deflection angle, on a macro level. Sufficient statistical information can be obtained from multiple measurements of single-stage wheel uncertainty variables such as the stopper centroid coordinates and the end face normal vector. The probability statistical model of uncertainty variables is constructed based on a large amount of measurement data, which belongs to random uncertainty and is characterized as a random variable. Limited by the measurement method, the uncertainty variables caused by the combined effect of manufacturing error uncertainty and assembly process execution uncertainty of a single-stage wheel, such as the stopper assembly eccentricity and deflection angle, can only obtain interval information based on experience and simulation, and can be classified as cognitive uncertainty, expressed as interval variables.

[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 selection of parts, the uncertainty variable of the single-stage wheel is mainly affected by the measurement uncertainty. In order to simplify the workload of random uncertainty quantification and make it easier for engineering applications, the measurement uncertainty is directly characterized by the variance analysis method (ANOVA) in the measurement system analysis (MSA). The specific characterization method is as follows:

[0082] Repeatability is the measurement variation obtained by measuring the same feature on the same part multiple times using the same measuring instrument in a single setup and fixture.

[0083] Reproducibility is the variation in the average value of repeated measurements of the same feature on the same part using the same measuring instrument under multiple mounting and clamping conditions.

[0084] The measurement system repeatability variance σ 2 and reproducibility variance ε 2 The unbiased estimates of are expressed as:

[0085]

[0086] In the formula, l is the number of installation and clamping times, m is the number of repeated measurements for one installation and clamping, and y is kj is the jth repeated measurement result of the kth clamping, It represents the average value of m repeated measurements in the k-th clamping. It represents the average value of all repeated measurements of l clampings, that is, the average value of l×m measurement results.

[0087] Calculate the total variance α of the measurement system 2 =σ 2 +ε 2 , the measurement uncertainty is characterized as a random normal distribution Δ~N(0,α 2 ).

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

[0089] The probability distribution of the measured values ​​of all measuring points is obtained, and the random distribution models of the fitting stop centroid coordinate vector d and the end surface normal vector p are obtained by the Monte Carlo (MC) method, which are expressed as follows:

[0090]

[0091] In the formula, the superscript "R" represents a random variable, the subscript "i" represents the i-th level wheel, "U" represents the upper stop, and "L" represents the lower stop.

[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 bound of the variable interval number, is the upper bound of the variable interval.

[0095] You can also use the central interval notation to write the interval variable as

[0096] (5)

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

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

[0099]

[0100] In the formula, F(a I )=min{F(a I )},

[0101] The eccentricity and deflection of the stop assembly can be determined by the eccentricity of the stop assembly. Eccentric angle of stopper assembly Deflection angle of stopper assembly δ i I and the phase of the lowest point of deflection The superscript “I” represents an interval variable.

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

[0103] First, correct the benchmark alignment error. Establish a single-stage wheel coordinate system at the lower stop of the i-th wheel, and obtain the centroid coordinate vector of the upper stop of the i-th wheel in the single-stage wheel coordinate system through coordinate transformation. and the end normal vector Respectively expressed as:

[0104]

[0105]

[0106] In the formula, is the rotation transformation matrix from the measurement system coordinate system to the single-stage wheel coordinate system, which can be expressed as formula (9); and are the normal vector of the upper stop end face, the coordinate vector of the upper stop centroid and the coordinate vector of the lower stop centroid of the i-th level wheel in the coordinate system of the measurement system respectively; and are the components of the centroid coordinate vector of the stop on the i-th wheel in the X, Y and Z directions in the single-stage wheel coordinate system; and are the components of the end face normal vector of the upper stop of the i-th level wheel in the X, Y and Z directions in the single-level wheel coordinate system. It should be pointed out that after the reference error is corrected, the reference coordinate system is transformed from the measurement system coordinate system to the single-level wheel coordinate system established at the lower stop of the i-th level wheel. The centroid coordinates and end face normal vector of the lower stop no longer need to be considered in subsequent calculations. Therefore, in order to distinguish the codes of the centroid coordinates and end face normal vector of the upper stop in different coordinate systems, the U in the subscript is removed.

[0107]

[0108] in,

[0109]

[0110] In the formula, and are the components of the normal vector of the end face of the lower stopper of the i-th wheel in the X, Y and Z directions in the coordinate system of the measurement system, and They are the angles of rotation of the measurement system coordinate system around the X-axis and Y-axis respectively when the coordinate system is rotated and transformed.

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

[0112]

[0113] in:

[0114]

[0115] In the formula, and are respectively the normal vectors of the end face of the stopper on the i-th level wheel The components in the X, Y and Z directions in the single-stage wheel coordinate system, and are the rotation angles of the fitting plane coordinate system of the upper stop of the i-th level wheel around the X-axis and Y-axis respectively.

[0116] Then, the stopper assembly deviation model is established. The stopper assembly eccentricity vector is obtained. The interval representation in the i-1th level wheel upper stop fitting plane coordinate system (such as formula (14)) and the rotation transformation matrix from the i-th level wheel reference coordinate system to the i-1th level wheel upper stop fitting plane coordinate system in:

[0117]

[0118] In the formula, and They are the interval representation of the assembly deflection angle of the lower stop of the i-th level wheel relative to the upper stop of the i-1-th level wheel and the phase of the lowest point of deflection, and are the rotation angles of the i-th level roulette reference coordinate system around the X-axis and Y-axis respectively.

[0119]

[0120] In the formula, and They are respectively the intervals of the assembly eccentricity and eccentricity angle of the lower stop of the i-th stage wheel relative to the upper stop of the i-1-th stage wheel.

[0121] Next, the reference coordinate system of the lower stop of the first-level wheel is used as the assembly coordinate system O-XYZ to obtain the coordinate vector of the centroid of the upper stop of the i-th wheel in the assembly coordinate system when the n-level wheels are stacked

[0122]

[0123] In the formula, the superscript “M” represents the mixed uncertainty variable, O iL and O iU are the fitting centroids of the lower stop and upper stop of the i-th level wheel, Eccentricity vector for stopper assembly The rotation transformation matrix from the i-1th level wheel upper stop fitting plane coordinate system to the assembly coordinate system, is the centroid offset vector of the upper and lower stoppers of the i-th level wheel The rotation transformation matrix from the single-stage wheel base coordinate system to the assembly coordinate system; S zi is the rotation matrix considering the assembly phase change, as shown in formula (16).

[0124]

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

[0126] Finally, assume that the centroids of the front and rear support circles of the rotor are the centroids of the upper and lower stoppers of the assembly, respectively. n and O, connecting the centroids OO n A rotating coordinate system is established in the Z-axis direction, and the coordinate vector of the centroid of the upper stop of the i-th level wheel in the rotating coordinate system is obtained through coordinate rotation transformation:

[0127]

[0128] In the formula, is the rotation transformation matrix from the assembly coordinate system to the rotation coordinate system, and are the components of the centroid coordinate vector of the stop on the i-th level wheel in the X, Y and Z directions in the rotating coordinate system, in:

[0129]

[0130] In the formula, and are the coordinate values ​​of the centroid of the nth level wheel in the X, Y and Z directions of the assembly coordinate system, and They are the rotation angles of the assembly coordinate system around the X-axis and Y-axis respectively.

[0131] At this time, according to the definition of coaxiality error, the coaxiality error of the multi-stage wheel stack is expressed as:

[0132]

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

[0134] Since there are two types of uncertainty variables, random and cognitive, in the assembly accuracy prediction model, a double-layer nested approach is used to propagate mixed uncertainty based on the Monte Carlo method. The outer layer uses probability theory to characterize random uncertainty, and the inner layer uses interval theory to characterize cognitive uncertainty. The overall solution process is as follows: Figure 3 The calculated coaxiality error of the rotor assembly is presented in the form of N interval numbers, and the probability statistics of the upper limit, lower limit and midpoint value of the interval number can be performed respectively.

[0135] The sub-interval combination method is introduced to suppress the "interval expansion" in the interval operation process. First, through monotonicity analysis, it is known that the coaxiality error is relative to the eccentricity angle η of the stop assembly. i and the phase of the lowest point of deflection τ i Not monotonic; then according to the calculation accuracy requirements, the interval variable η that does not have monotonicity i I and τ i I Decompose into g subintervals of equal length; finally, perform combined traversal to solve the endpoint values ​​of the decomposed subintervals, and the total number of solutions is 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 for rotor coaxiality under mixed uncertainty is constructed.

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

[0138] First, the probability of coaxiality exceeding the tolerance is estimated. Since the input variables of the prediction model contain both random variables and interval variables, the probability of coaxiality exceeding the tolerance changes from a single value to an interval value. Among them, P f is the lower bound of the probability of coaxiality exceeding the tolerance, The upper bound of the probability of coaxiality exceeding the tolerance is:

[0139]

[0140] In the formula, C max X is the upper limit of the coaxiality error of the rotor assembly; q represents the qth random simulation set of input variables; C and They represent the lower and upper bounds of the coaxiality error interval obtained in each random simulation respectively; I is the indicator function, if the function in “[]” is judged as “true”, its value is 1, otherwise its value is 0.

[0141] Then, the circumferential installation phase of each level of wheel disc is used as the control variable to regulate the coaxiality error of the rotor assembly. A double-layer optimization method is adopted. While the inner layer optimization ensures the minimum upper bound of the probability of coaxiality deviation, the outer layer optimization is used to find the optimal installation phase of each level of wheel disc, and finally the mean value of the midpoint of the coaxiality error interval of the rotor assembly is minimized. In particular, the double-layer optimization model is:

[0142]

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

[0144] Finally, the optimization model is solved by an intelligent optimization algorithm to obtain the disc installation phase combination that satisfies the minimum upper bound of the probability of coaxiality exceeding tolerance and the minimum mean of the midpoint of the interval. Therefore, the optimization algorithm can quantify the possibility of the rotor assembly exceeding tolerance obtained by assembling according to the given optimal phase combination, while improving the geometric accuracy of the rotor assembly, it can ensure the minimum probability of coaxiality exceeding tolerance after assembly, and improve the reliability and stability of the aircraft engine rotor assembly.

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

[0146] Next, the rotor assembly geometric accuracy prediction and optimization method considering multi-source uncertainties provided by the present invention is further explained with reference to examples.

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

[0148] First, the measurement uncertainty is characterized. The part is clamped repeatedly 10 times. Each time the end face and cylindrical runout of the upper and lower stoppers of the wheel are measured 30 times. The maximum value of the runout data of each feature surface is taken each time. The measurement repeatability variance and reproducibility variance of the measurement system for the four measurement surfaces are calculated according to equations (1) and (2), and then the random distribution of the four measurement errors is obtained, which is listed in Table 1.

[0149] Table 1 Measurement error distribution

[0150]

[0151] The range of the eccentricity and deflection 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 The deviation range of the stopper assembly

[0153]

[0154] Then, the end face and cylindrical runout of the upper and lower stoppers of the wheel parts at each level are measured respectively. The measured runout data is used as input to optimize the component coaxiality error according to the double-layer optimization model of formula (21), and the upper limit of the coaxiality error is set to 0.06mm. The optimization model is solved using the intelligent optimization algorithm to obtain the upper limit of the minimum coaxiality error probability. The mean value of the minimum coaxiality error interval midpoint min (μ Cc ) and the corresponding optimal installation phase combination A best As shown in Table 3.

[0155] Table 3 Uncertain optimization results

[0156]

[0157] Finally, according to Figure 3 The rotor assembly geometric accuracy prediction process under mixed uncertainty is shown in the figure. The disk stacking prediction and component measurement are performed according to the optimal phase combination to obtain the comparison of the rotor coaxiality error measured value, uncertainty prediction and deterministic prediction results. Figure 5 As shown, the uncertainty prediction results include both measured results and deterministic prediction results, indicating that the proposed method can accurately predict the rotor assembly geometric accuracy. Figure 6 The prediction results obtained by using the existing high-low point assembly method are compared with Figure 6 The comparison of the prediction results shown shows that the rotor coaxiality error is significantly reduced after the present invention is assembled according to the optimal phase combination, and the measured value of the rotor coaxiality error of the optimized assembly is 57.28% less than the measured value of the high and low point assembly. Therefore, this example verifies the effectiveness of the rotor assembly geometric accuracy prediction and optimization method considering multi-source uncertainty provided by the present invention.

[0158] Finally, it should be noted that the features mentioned and / or shown in the above description of the exemplary embodiments of the present invention may be combined in the same or similar manner into one or more other embodiments, combined with the features in other embodiments or substituted for the corresponding features in other implementations. The technical solutions obtained by these combinations or substitutions shall also be deemed to be included in the protection scope of the present invention.

Claims

1. A method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties, characterized in that: The following steps are involved: Step 1, analyzing the uncertainty affecting the geometric accuracy of rotor assembly during the stacking assembly of aero-engine rotors; Step 2, characterize the uncertainty analyzed in step 1 as a random variable and an interval variable through a random model and an interval model respectively; Step 3, using the uncertainty variables characterized in step 2 as input variables, establishing a rotor assembly geometric accuracy prediction model considering random-interval mixed uncertainty, and predicting the coaxiality error of the rotor assembly under mixed uncertainty conditions; Step 4: Based on the Monte Carlo method, a double-layer nested method is used to solve the random-interval mixed uncertainty model established in step 3, and the probability statistical results of the upper bound, lower bound and midpoint value of the coaxiality error interval are obtained; Step 5, estimate the probability interval of coaxiality excess tolerance, construct a two-layer optimization model for rotor coaxiality under mixed uncertainty, and obtain the optimal installation phase of each level of the wheel through optimization, so that the upper limit value of the coaxiality excess tolerance probability interval and the mean of the midpoint of the coaxiality error interval are minimized.

2. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 1, characterized in that: In step 1, according to the different sources of uncertainty, the uncertainty affecting the geometric accuracy of rotor assembly is divided into single-stage disk manufacturing error uncertainty, measurement uncertainty and assembly process execution uncertainty; The manufacturing error uncertainty of the single-stage wheel disc includes the cylindrical runout of the wheel disc stop and the end face runout of the stop; The measurement uncertainty includes the centering and tilting error of the turntable, the wheel clamping error and the sensor installation error; The assembly process execution uncertainty includes uncertainties in bolt tightening torque, assembly process temperature and axial press force.

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

4. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 3 is characterized in that: In step 2, the random variable is characterized by step 2.1, which includes: Step 2.1.1, use the same measuring instrument, under the same installation and clamping, to measure the same feature on the same part multiple times, and obtain the measurement variation, which is defined as repeatability; Step 2.1.2, using the same measuring instrument, repeatedly measure the same feature on the same part under multiple mounting and clamping conditions, and obtain the variation of the measurement mean value, which is defined as reproducibility; Step 2.1.3, replace the repeatability variance σ 2 and reproducibility variance ε 2 The unbiased estimates of are expressed as: In the formula, l is the number of installation and clamping times, m is the number of repeated measurements for one installation and clamping, and y is kj is the j-th repeated measurement result of the k-th clamping, It represents the average value of m repeated measurements in the k-th clamping. It represents the average value of all repeated measurements of l clampings, that is, the average value of l×m measurement results; Step 2.1.4, calculate the total variance α 2 =σ 2 +ε 2 , the measurement uncertainty is characterized as a random normal distribution Δ~N(0,α 2 ); Step 2.1.5: Under the same measurement conditions, a measurement point on a feature surface of a part is measured, and the measured indication is t. The true value of the measurement point is contained in the random normal distribution with t as the mean and α as the standard deviation. That is, the indication distribution of multiple measurements of the measurement point is T~N(t,α 2 ); Step 2.1.6, obtain the probability distribution of the measured values ​​of all measuring points, and obtain the random distribution model of the fitting stop centroid coordinate vector d and the end surface normal vector p by Monte Carlo method, which are expressed as: In the formula, the superscript "R" represents a random variable, the subscript "i" represents the i-th level wheel, "U" represents the upper stop, and "L" represents the lower stop.

5. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 4, characterized in that: In step 2, the interval variable is characterized by step 2.2, which includes: Step 2.2.1, establish the following interval model: In the formula, a I is an interval variable, a is the lower bound of the variable interval number, is the upper bound of the variable interval number; Step 2.2.2, another F(a I ) is the interval vector a I If it is an interval-valued function, then the solution interval of the function is: In the formula, F (a I )=min{F(a I )}, 6. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 5, characterized in that: In step 2.2.1, the interval model can be replaced as follows: In the formula, a c is the midpoint value of the interval, a r is the interval radius, 7. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 5, characterized in that: Step 3 includes: Step 3.1, correct the benchmark alignment error, establish a single-stage wheel coordinate system at the lower stop of the i-th wheel, and obtain the centroid coordinate vector of the upper stop of the i-th wheel in the single-stage wheel coordinate system through coordinate transformation. and the end normal vector Respectively expressed as: In the formula, is the rotation transformation matrix from the measurement system coordinate system to the single-stage wheel coordinate system, and are the normal vector of the upper stop end face, the coordinate vector of the upper stop centroid and the coordinate vector of the lower stop centroid in the coordinate system of the i-th level wheel, respectively. and are the components of the centroid coordinate vector of the stop on the i-th wheel in the X, Y and Z directions in the single-stage wheel coordinate system, and are the components of the normal vector of the end face of the stopper on the i-th wheel in the X, Y and Z directions in the single-stage wheel coordinate system; Step 3.2: Establish a single-stage wheel error model and obtain the rotation transformation matrix from the upper stop fitting plane coordinate system to the reference coordinate system. The reference coordinate system is a single-stage wheel coordinate system established at the lower stop of the i-th wheel; Step 3.3, establish the stopper assembly deviation model and obtain the stopper assembly eccentricity vector Interval representation in the i-1th level wheel upper stop fitting plane coordinate system and the rotation transformation matrix from the i-th level wheel reference coordinate system to the i-1th level wheel upper stop fitting plane coordinate system Step 3.4, using the reference coordinate system of the lower stop of the first-level wheel as the assembly coordinate system O-XYZ, obtain the coordinate vector of the centroid of the upper stop of the i-th wheel in the assembly coordinate system when the n-level wheels are stacked i=1,2,……,n: In the formula, the superscript "M" represents the mixed uncertainty variable, O iL and O iU are the fitting centroids of the lower stop and upper stop of the i-th level wheel, Eccentricity vector for stopper assembly The rotation transformation matrix from the i-1th level wheel upper stop fitting plane coordinate system to the assembly coordinate system, is the centroid offset vector of the upper and lower stoppers of the i-th level wheel The rotation transformation matrix from the single-stage wheel reference coordinate system to the assembly coordinate system, S zi is the rotation matrix that takes into account the assembly phase change; Step 3.5, take the centroid line of the front and rear support journal sections of the rotor as the reference axis for evaluating the coaxiality error of the rotor, that is, take the line as the Z-axis direction to establish a rotating coordinate system, and obtain the centroid coordinate vector of the upper stop of the i-th level wheel in the rotating coordinate system through rotation transformation: In the formula, is the rotation transformation matrix from the assembly coordinate system to the rotation coordinate system, and are the components of the centroid coordinate vector of the stop on the i-th level wheel in the X, Y and Z directions in the rotating coordinate system respectively; Step 3.6, the coaxiality error of the stacked multi-stage discs is expressed as:

8. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 7, characterized in that: In step 4, the outer layer uses probability theory to characterize random uncertainty, and the inner layer uses interval theory to characterize epistemic uncertainty. The calculated coaxiality error of the rotor assembly is presented in the form of N interval numbers, and probability statistics are performed on the upper limit, lower limit and midpoint value of the interval number.

9. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 8, characterized in that: Step 5 includes: Step 5.1, estimate the probability of coaxiality exceeding the tolerance. The probability of coaxiality exceeding the tolerance is P f is the lower bound of the probability of coaxiality exceeding the tolerance, is the upper bound of the probability of coaxiality exceeding the tolerance; Step 5.2, taking the circumferential installation phase of each level of wheel disc as the control variable, regulating the coaxiality error of the rotor assembly, adopting a double-layer optimization method, while the inner layer optimization ensures the minimum upper bound of the probability of coaxiality deviation, the outer layer optimization is used to find the optimal installation phase of each level of wheel disc, and finally the mean value of the midpoint of the coaxiality error interval of the rotor assembly is minimized; Step 5.3, solve the optimization model through the intelligent optimization algorithm to obtain the wheel installation phase combination that satisfies the minimum upper bound of the probability of coaxiality deviation and the minimum mean value of the midpoint of the interval.

10. The method for predicting and optimizing rotor assembly geometric accuracy considering multi-source uncertainties according to claim 9, characterized in that: The two-level optimization model used in step 5.2 is: find A best =(θ z2 ,i z3 ,…,θ zn ) best s.t.A w ∈{A1,A2,…,A W } find A w =(θ z2 ,i z3 ,…,θ zn ) w ,w=1,2,…,W i=2,3,…,n In the formula, A best For the optimal installation phase combination, is the mean of the midpoint of the coaxiality error interval, W is the number of installation phase combinations that minimizes the upper bound of the probability of exceeding the tolerance, θ zi is the circumferential installation phase of the i-th wheel disc, s i is the number of bolt holes used for the stop connection.

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