A novel compilation method of comprehensive mission spectrum of aero-engine maneuvering load based on use-related mission segment

Xuming NIU, Qi LU, Zhigang SUN, Yingdong SONG,c

a Jiangsu Province Key Laboratory of Aerospace Power System and College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

b Laboratory of Aero-Engine Thermal Environment and Structure Ministry of Industry and Information Technology, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

c College of Energy and Power Engineering and State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

KEYWORDS Aero-engine;Comprehensive mission spectrum;Maneuvering load;Spectrum compilation;Typical mission segment

Abstract Comprehensive Mission Spectrum(CMS)of an aero-engine can reflect the usage characteristics of the engine.It can provide load input for engine life prediction and accelerated mission test.In this paper,a novel compilation method of CMS of aero-engine maneuvering load based on mission segment is proposed.Firstly,the use-related Typical Mission Segment(TMS)of maneuvering load is divided and identified according to spectral characteristics.Secondly, the mathematical model of different kinds of TMS are established based on stochastic process theory.Finally, the CMS of maneuvering load is compiled based on TMS.The proposed method can accurately quantify the compilation of CMS.The compiled CMS shows good agreement with the original load spectrum.According to damage consistency inspection, the compiled CMS is consistent with the damage caused by the original load spectrum in terms of low cycle fatigue.

1.Introduction

The load spectrum of an aero-engine covers the whole process of engine design, experiment and life prediction.The study of load spectrum is very important for improving the reliability of engine life assessment and ensuring the safety of engine usage.1The actual flight mission of an aero-engine undergoes innumerable changes,and thus it is impossible to analyze the stress and life in all flight missions, especially in the compilation of accelerated mission test spectrum.Therefore,it is often needed to synthesize all flight mission profiles into one or several profiles to carry out strength analysis and life research.2The maneuvering load of aero-engine originates from the inertial force generated by the aircraft maneuvering flight, and has a significant impact on the fatigue life of the loading bearing structure, such as installation joint, intermediate case, main shaft, bracket of appendix casing and main shaft bearing.Compiling a Comprehensive Mission Spectrum (CMS) of maneuvering loads is helpful to provide original load for analyzing the life of the above-mentioned structures.

In the field of load spectrum compilation, Li3established the program load spectrum of the numerical control turret under constant cutting torque based on the extrapolation frequency and the joint distribution model.Chen et al.4combined probability distribution function and determined the main wave center of multi-operating loads by weighted coefficient.Then, the load spectrum of wind turbine bearing multioperating loads was compiled by adding the eight levels amplitude to the main wave center.Gao et al.5made extrapolated the load data and weaved into an eight-program load spectrum.Zhang6studied the load-time course of the rotary cylinder and the lifter cylinder under single cycle, and then compiled the load spectrum of road header based on the rain flow counting method.Wu7proposed a compilation method of load spectrum based on hidden Markov model.Fang8used the distribution model to fit the load spectrum,but the damage equivalence is not examined.Repetto and Torrielli9conducted long-term simulation on wind-induced fatigue loadings.

However, aero-engines are susceptible to the harmful effects of widespread fatigue damage caused by the cyclic loading of structural component.10The load of an aircraft is unsmooth and random because it always needs to do many maneuver actions.In addition, aero-engines are always in the state of high pressure,high temperature and high speed of revolution, which makes the load spectrum of the aero-engine very complex.Therefore, the above methods are not suitable for the compilation of aero-engine load spectrum and some other methods have been proposed to deal with this problem.Song and Gao2gave out the principle and method for the qualitative derivation of the CMS,where too many empirical components were involved.Song11classified all maneuverable mission segments into one class and simulated a profile of the engine,which however could not reflect the entire use process of the aero-engine.Zhou12used the flight mission profiles as coding units to compile the standard load spectrum of aeroengine wheel based on the rain flow method.Zhao13proposed a general method for the preparation of standard test load spectrum.These methods consider only one profile of the aero-engine, which is not representative, because it is difficult to consider all maneuver actions.Therefore, it is necessary to establish an effective mathematical model of load spectrum for aero-engine,and put forward a quantitative method which considers all kinds of damage process to compile CMS.

The existing research on the compilation of load spectrum is summarized as follows.Song and Gao2,14took the flight profile as coding unit to give out the principle and method for the qualitative derivation of the CMS, where too many empirical components were involved.Sun and Sun15classified all the maneuver flight mission segments into one class to simulate the load spectrum.The spectrum pattern of simulated load spectrum was quite different from the measured load spectrum, and the difference of fatigue damage between them also existed when using rain flow counting method.16Song P and Song Y17simulated the profile of an engine based on the database, which however could not reflect the entire use of the aero-engine.Therefore, it is necessary to establish an effective mathematical model of load spectrum for aeroengine, and put forward a quantitative method that considers all kinds of damage process to compile CMS.Compared with the traditional block load spectrum, CMS can better simulate the entire history of engine use.It also provides the basis for stress analysis, life study and accelerated mission test of aero-engine, which is of great significance.18The maneuvering load has an important influence on the service life of the engine load-bearing structure.Taking the main shaft bearing as an example, the maneuvering load determines the radial force applied to it, which has a significant impact on its structural life.This effect needs to be taken into consideration during the structural life analysis and test process.At present, due to insufficient research on the load characteristics of aeroengine maneuvering loads, only equal-amplitude radial loads are applied to the bearing during fatigue life test,19which cannot fully reflect the load state that it is subjected to during service.The method proposed in this paper establishes an accurate characterization of the load characteristics of the aero-engine maneuvering load, which can provide load input for the compilation of the fatigue life test spectrum of the main shaft bearing in future.

Among many flight parameters of aero-engine, normal overload coefficient is the one that can mostly reflect the change of maneuver actions.In this research,first,the maneuvering load is divided into five kinds of Typical Mission Segment (TMS) according to spectral characteristics.Then, the mathematical model of TMS is constructed based on stochastic process theory.Finally, the CMS can be compiled by simulating and rearranging the TMS.The proposed use-related mission-segment-based CMS compilation method changes the compilation process from qualitative pattern to quantitative pattern.

2.TMS of maneuver flight

As illustrated in Fig.1,the key technology of the method is to extract the TMS and to compile the CMS based on TMS.

2.1.Extraction of TMS

Taking the normal overload coefficient as an example,the normal overload coefficient spectrum of 25 profiles of an aeroengine is divided into 742 segments with obvious changes in amplitude, which can be defined as mission segments.The original load spectrum segment is shown in Fig.2.On the basis of that, the load spectrum is pretreated, including filtering,removing the singular value and removing the random disturbance.20,21The processing result is shown in Fig.3.As illustrated in the figure, the load spectrum is divided into several mission segments.The 25 profiles of the engine contain 742 mission segments through statistics.

In the process of compiling the CMS, an important link is to extract TMS from many maneuver flight segments.It is directly related to the complexity of the CMS compilation and the rationality of the compiled load spectrum.22As the duration and peak value of the load can characterize fatigue damage,23the rules of combination of TMS in this paper are described as follows:

Fig.2 Original load spectrum of normal overload coefficient.

(1) The spectrum pattern of the mission segment is similar,which means the number of peaks contained in the mission segment is the same;

(2) The damage to the engine caused by the mission segments of the same kind is smaller than others, which means that the duration and peak value meet the following condition:

where Diand Aiare the duration and peak value of any mission segment in the same kind of TMS, respectively, εDis the critical duration, and εAis the critical peak value.The parameters can be resolved by the mean of the duration and peak value of the mission segments which are participated in the division.

(3) The damage to the engine caused by the mission segments of the same kind is more than others, which means that the duration and peak value meet the following condition:

In this way,the low cycle fatigue damage,the creep damage and the thermal shock damage caused by the same kind of TMS can be similar, which makes the division of TMS be of practical importance.

Firstly, the maneuver flight segments are divided into four kinds of TMS according to rule (1), including:

(A) Mission segment with single peak accounts for 81.3%of the total number of mission segments.

(B) Mission segment with two peaks accounts for 11.7% of the total number of mission segments.

(C) Mission segment with three peaks accounts for 3.5% of the total number of mission segments.

(D) Mission segment with several peaks,which contains four or more than four peaks in every mission segment,accounts for 3.5% of the total number of mission segments.

At this time, εD=19.6132 and εA=2.3265.The mission segments with two peaks,three peaks and several peaks all satisfy the third rule after preliminary division,as shown in Fig.4.Therefore, further division is meaningless for mission segment with more than two peaks.

Fig.3 Pretreat process of load spectrum.

However, the mission segment with single peak accounts for a higher proportion of the total number of mission segments,which is about 80%.In addition,there is a great difference between the peak value and the duration of the mission segment.As shown in Fig.5, both mission segments 1 and 2 belong to the mission segment with single peak.However,due to the great difference between the peak value and the duration of the mission segment, the damage of the engine caused by the two mission segments is obviously different.So,they should not be classified into the same kind.Therefore,the further division of the task segment with single peak is carried out.The purpose is to classify the mission segment according to damage conducted to the engine.The duration and peak value of the mission segments with single peak are analyzed,with the statistical result shown in Table 1.

Fig.4 Validation of three kinds of TMS after preliminary division.

Fig.5 Mission segments with single peak.

The mission segments with single peak are shown in Fig.4.Due to the great difference between the duration and peak value, the damage to the engine caused by mission segments 1 and 2 is obviously different.So, they cannot be classified as one kind, and further division is necessary.At this time,only the mission segments with single peak are participated in the division.By statistics, we have εD=6.9121 and εA=2.1248.According to Eqs.(2) and (3), the mission segments with single small peak and the mission segments with single big peak can be divided.

Finally,the maneuvering load spectrum can be divided into five kinds, as illustrated in Fig.6.

(a) Mission segments with single small peak.Each mission segment contains one peak and the peak value is smaller than 2, as shown in Fig.6(a).It accounts for 44.1% of the total number of the mission segments.

(b) Mission segments with single big peak.Each mission segment contains one peak and the peak value is larger than 2, as shown in Fig.6(b).It accounts for 37.2% of the total number of the mission segments.

(c) Mission segments with two peaks.Each mission segment contains two peaks, as shown in Fig.6(c).It accounts for 11.7% of the total number of the mission segments.

Table 1 Statistics of mission segments with single peak.

Fig.6 Five kinds of different mission segments.

(d) Mission segments with three peaks.Each mission segment contains three peaks, as shown in Fig.6(d).It accounts for 3.5% of the total number of the mission segments.

(e) Mission segments with several peaks.Each mission segment contains four or more peaks,as shown in Fig.6(e).It accounts for 3.5% of the total number of the mission segments.

These five kinds of TMS are called TMS1, TMS2, TMS3,TMS4 and TMS5 in the following part of this article.

Through the above steps, the maneuver flight load spectrum is divided into five TMS.This method of division can accurately reflect the load information of the original spectrum, and the basic flowchart is shown in Fig.7.

2.2.Establishment of mathematical model of TMS

A typical snippet of maneuvering load spectrum is shown in Fig.8.As illustrated in Fig.8,Di,Tiand Aiare duration,arrival time and peak value of the mission segment, respectively;Wiis the waiting time between the (i-1)th mission segment and the i th mission segment.As long as the peak value A and any two parameters of D,T, W are determined, the entire mission segment is determined.Therefore, waiting time W,duration D and peak value A are selected15to describe the TMS in this paper.

Fig.7 Flowchart of the extraction of five TMSs.

Fig.8 Load spectrum fragment of maneuver spectrum load.

The stochastic theory holds the view that the Poisson random process is suitable for describing the waiting time and duration of the use-related random process.24,25

If the random variable Tn(n ≥1)represents the time interval between the (n-1)th event and the n th event, Tnobeys exponential distribution.They are independent of each other,but they have the same distribution parameters.26

On the basis of this theory,the distribution of duration time Diof five kinds of TMS and waiting times are linearly fitted by exponential distribution.The Cumulative Distribution Function (CDF) of the exponential distribution is defined as.

where η is the position parameter, α is the proportion parameter, and β is the shape parameter.Taking the logarithm of both sides of Eq.(5), we can obtain the linear fitting formula of three-parameter Weibull distribution, as defined by.

The linear fitting result of exponential distribution and three-parameter Weibull distribution are illustrated in Figs.9–11.It can be seen from the figure that the selected distribution model can characterize the distribution characteristics of each parameter with good accuracy.

The results show that the waiting time and duration meet the exponential distribution, while the peak value satisfies the Weibull distribution of three parameters.The distribution parameters are shown in Table 2.

There are some kinds of coupling relationship between the maneuvering load and the aerodynamic load, but the maneuvering load usually lags behind the aerodynamic load.Therefore, the traditional method based on data correlation analysis cannot correctly analyze the correlation between the two.In this thesis, we analyze the coupling relationship between the maneuvering load and the aerodynamic load by correlation analysis method based on rain-flow counting.The correlation coefficients between these parameters are shown in Table 3.It can be found that the correlation coefficient between Nyand N1is 0.8335, and it can be considered that there is a strong correlation between the two parameters.

Fig.9 Exponential distribution linear fitting result of duration time in TMS5.

Fig.10 Exponential distribution linear fitting result of waiting time.

Fig.11 Three-parameter Weibull distribution linear fitting of peak value in TMS5.

In Table 3, Nyis the normal overload coefficient, Nxis the longitudinal overload coefficient, Nzis the lateral overload coefficient, and N1is the rotating speed.

3.Compilation of CMS for maneuver flight

3.1.Principle of compilation

The CMS characterizes the entire engine use throughout a flight process.For the CMS of maneuvering load, whether it can effectively replace the complex load spectrum of outfield or not, it depends on the consistence of fatigue damage tothe engine.Low cycle fatigue damage is mainly caused by the repeated changes of engine throttle during flight.As long as the CMS and the measured load spectrum meet the following three conditions,

Table 3 Correlation coefficients between maneuvering load and aerodynamic load.

(1) the number of load cycles N is the same;

(2) the distribution of peak value is the same;

(3) the switch rate v of the throttle rod is the same in the mission section.

We can guarantee the same damage to the engine caused by the maneuvering CMS and the measured maneuvering load spectrum.

3.2.Compilation of CMS

Since the load spectrum is composed of several independent TMS, the simulation of the load spectrum is actually the simulation of the mission segments.When compiling the CMS,this research adopts the method of compiling five kinds of TMS respectively based on the premise that the total number of mission segments remains unchanged before and after the compilation.The specific steps are shown as follows:

(1) According to the mathematical distribution of three descriptive parameters in each TMS,15 random number sequences are generated.

(2) The random number of three descriptive parameters is selected in turn.Five kinds of TMS are generated by triangular wave.The spectral patterns of TMS are generated, as shown in Fig.12 and the TMSs are stored in database.

(3) Under the premise that the CMS and the actual flight load spectrum have the same number of mission segments, we extract the mission segments in the database according to the ratio of each kind of TMS to the totalnumber of mission segments.Then, they are combined randomly to obtain the CMS of the normal overload coefficient of the engine, as shown in Fig.13.

Table 2 Distribution parameter of five TMSs.

Fig.12 Simulation spectrum of TMS.

The CMS obtained by the above steps is similar to the measured load spectrum on the spectrum pattern, and the proposed method realizes the quantification and standardization of compilation process of CMS.The process is shown in Fig.14.

3.3.Results analysis

The purpose of load spectrum compilation is to establish an accurate characterization method for the dispersion characteristics of engine load spectrum.At present, the load spectrum compilation method based on Typical Mission Profiles(TMP)27is widely used in the aero-engine industry.However,this method will lead to large compilation errors in certain intervals.The reason is that:(A)the number of typical profiles is limited, so the number of sub-samples is insufficient, which will inevitably lead to non-random sampling; (B) the typical profile is used as the spectral unit,resulting in a large representation range,which cannot fully represent the characteristics of the same type of mission profile.In this paper, an aero-engine load spectrum compilation method based on task segment is established.By using a smaller but more accurate spectrum compilation unit, the characterization accuracy of the load characteristics is improved, the number of subsamples is enlarged, and finally, the spectrum compilation accuracy can be improved.

Fig.13 Maneuvering load CMS obtained by simulation.

Fig.14 Compilation process of CMS.

The normal overload coefficient spectrum of a total of 25 profiles is used as the measured data to verify the method proposed in this paper.

According to the comprehensive mission spectrum compilation method based on typical mission profiles,28the distribution of load can be calculated by.

where Dcis the distribution characteristic of spectrum,m is the number of typical subjects,fkis the mix frequency of the No.k subjects, and dskis the distribution characteristic of the No.k subjects.

The original load spectrum data are divided into 4 types of typical mission profiles by clustering algorithm.The mix frequency of each one is 9.54%, 20.40%, 25.50%, and 44.56%respectively.Then the amplitude cumulative probability of CMS based on TMP is illustrated in Fig.15 by blue triangle symbol.

Fig.15 Cumulative probability of rain flow counting.

During the process of CMs compilation by the method proposed in this thesis, the total number of mission segments of the CMS is the same to that of the original spectrum mission segments.The proportion of each TMS to the total mission segment is also the same as that of the original spectrum.The amplitude probability cumulative distribution of the CMS compiled by the method proposed in this thesis is illustrated by the red pentagram symbol in Fig.15.The result of simulated CMS in this thesis finds good agreement with the original spectrum data, as illustrated by black square symbol in Fig.15.However, the error of simulated CMS based on TMP is relatively large and lacks distribution information in some interval.Therefore, the CMS compilation method proposed in this thesis is more accurate than the traditional CMS compilation method based on TMP.

In order to check the damage consistency between the comprehensive task spectrum and the original load spectrum, the fatigue damage of the bracket of appendix casing is taken as the verification object.Assume that the maximum stress caused by unit’s normal overload coefficient on the bracket of appendix casing is 150 MPa, and the stress caused by the extreme value of the normal overload coefficient of 4.39 is 658.5 MPa.Assuming that the bracket material is Ti-6Al-4V,the structural damage due to normal overload can be calculated according to its S-N curve and Goodman curve.According to the calculation results of 25 profile data,the fatigue damage caused by the original spectrum, the CMS prepared by the method in this paper, and the CMS compiled based on TMP are 2.9211 × 10-4, 2.9182 × 10-4, and 2.3213 × 10-4, respectively.Based on the damage caused by the original load spectrum, the fatigue damage error of the CMS compiled by the method proposed in this thesis is-0.1%, while the fatigue damage error of CMS based on TMP is-20.5%.The result shows that the damage consistency CMS compilation by the method proposed in this thesis relative to the original spectrum data is quite good, while that of CMS based on TMP is relatively poor.

4.Conclusions

In this research, a novel compilation method of use-related mission segment CMS of aero-engine is proposed.The CMS simulates the entire history of the engine use throughout a flight process, which provides the basis for the stress analysis,life prediction and test of aero-engine.The conclusions are drawn as follows:

(1) According to the principle that the spectrum pattern,the peak value and the duration of the mission segment are similar, the load spectrum of maneuver flight can be divided into five kinds of TMS.

(2) Each TMS can be described by three parameters, i.e.,waiting time,duration and peak value.The waiting time and duration of the mission segment satisfy the exponential distribution, and the peak value of the mission segment satisfies three-parameter Weibull distribution.

(3) A novel CMS compilation method for maneuver flight based on the TMS is proposed, which is a great change from qualitative pattern to quantitative pattern,and can guarantee the consistency in low cycle fatigue damage caused by the CMS and the original load spectrum.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

Supports of this project provided by the National Science and Technology Major Project, China (J2019-IV-0017-0085) and the Jiangsu Province Key Laboratory of Aerospace Power System, China (CEPE2020004) are gratefully acknowledged.