Applications of structural efficiency assessment method on structural-mechanical characteristics integrated design in aero-engines

Jie HONG, Tinrng LI, Huqing ZHENG, Ynhong MA,*

a School of Energy and Power Engineering, Beihang University, Beijing 100083, China

b Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100083, China

c AECC Hunan Aviation Powerplant Research Institute, Zhuzhou 412002, China

KEYWORDS Aero-engines;Integrated design;Mechanical characteristics;Structural efficiency;Structural optimization

Abstract In the design process of advanced aero-engines, it is necessary to carry out an effective analysis method between structural features and mechanical characteristics for a better structural optimization. Based on the structural composition and functions of aero-engines, the concept and contents of structural efficiency can reflect the relation between structural features and mechanical characteristics. In order to achieve the integrated design of structural and mechanical characteristics,one quantitative analysis method called Structural Efficiency Assessment Method(SEAM)was put forward. The structural efficiency coefficient was obtained by synthesizing the parameters to quantitatively evaluate the aero-engine structure design level. Parameterization method to evaluate structural design quality was realized. After analyzing the structural features of an actual dual-rotor system in typical high bypass ratio turbofan engines,the mechanical characteristics and structural efficiency coefficient were calculated. Structural efficiency coefficient of high-pressure rotor (0.43) is higher than that of low-pressure rotor (0.29), which directly shows the performance of the former is better,there is room for improvement in structural design of the low-pressure rotor.Thus the direction of structural optimization was pointed out. The applications of SEAM shows that the method is operational and effective in the evaluation and improvement of structural design.©2020 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Aero gas turbine engine is a kind of complicated rotating mechanical system. Reasonable structural arrangements are a direct expression of the design level integrated with technological disciplines. For an advanced structural design,1it need to ensure the structural integrity and reliability requirements,and meet the goals of performance and fuel efficiency in service life.Unfortunately in modern aero-engines,loads increase substantially and operation environments are more harsh for the pursuit of high thrust weight ratio and high thermal efficiency.Thrust weight ratio is a common performance indicator for aero-engines. It has become particularly important in structural design on how to obtain the best engine performance by the least weight.However,trust weight ratio cannot directly evaluate the mechanical characteristics of structures, and also cannot clearly guide the structural optimization.

The processes of structure and its components design are interwoven and iterative in nature on account of meeting various requirements. The purpose of structural design is to obtain excellent mechanical characteristics,which are the function of the structure feature parameters such as mass,stiffness(Strictly, stiffness belongs to mechanical characteristic parameters, however, it can reflect the material and structural composition, so put it here.), etc. When mass or stiffness of the structures change, it can affect the response characteristics of the structural systems. Conversely, the loads generated by structural response can affect the design requirements of mass and stiffness. Therefore, the best mechanical characteristics can only be obtained by optimizing structural parameters,which is so called the structural-mechanical characteristics integrated design. The concept of structural efficiency is often used to represent the relation between structural features and mechanical characteristics in engineering design.It can quantitatively describe the payoffs of structural improvement design.Popularly speaking,its physical meaning is the performance to mass ratio, namely, the less mass used in structures to achieve specific performance requirements, the higher the structure efficiency.

In aviation field, the concept of structural efficiency was first proposed by NASA’s Dow et al.2,3and was applied to the structural design of aircraft support composite panels.Williams et al.4-6respectively, applied the structural efficiency to cylindrical shells subjected to axial compression for the weight optimization, and through the replacement of aluminum alloy using composite materials and the optimization of crosssection shape, a 42% weight loss could be achieved. In 1976,Fischler7of McDonnell Douglas also applied the structural efficiency evaluation method in the structural design of supersonic cruise vehicle. Jegley8compared the profits of different structural forms of the stiffened plates for the aircraft design by numerical calculation and experimentation with defining the structural efficiency as the ratio of the maximum loadcarrying capacity to the structural weight.Buckney et al.9optimized the topology of the wind turbine blade by defining the stress shape factor and the stiffness shape factor as structural efficiency evaluation parameters. Obviously in the literatures described above, the researchers mostly focused on the design and optimization of some aircraft components by the use of structural efficiency concepts.

In 1989,Storace10of General Electric Aircraft Engines first applied the structural efficiency to quantify the improvement design of the engine structure, focusing on analytical methods and design concepts developed to enhance the structural efficiency of turbine engines in considering the specific strength,engine system vibration and turbomachinery clearance closures.Zhang et al.11,12made a basic research about the concept and contents of structural efficiency aiming to assess the structural design quality in modern aero-engines. However, the exploration is limited to the establishment of evaluation parameters and calculation methods for specific objects, such as rotors, bearings, or the whole engine, and do not form an universal analysis method for structural assessment or integrated design technique of structural and mechanical characteristics.

In view of the above research, this paper established an analysis method considering the relation between structural features and mechanical characteristics based on structural efficiency for improvement design in aero-engines. An universal and relatively standardized evaluation procedure of Structural Efficiency Assessment Method (SEAM) was proposed.The calculation program of SEAM and structural efficiency coefficient algorithm were introduced. A typical high bypass ratio turbofan engine was taken as an example to analyze and discuss the application of SEAM in structural design quality evaluation and structural-mechanical characteristics integrated design from components to overall engine systems.

2. Structural and mechanical characteristics

2.1. Structural and mechanical parameters

Structural systems can be components or the overall machine assembled with several parts by connection interface in aeroengines. The most important structural systems in aeroengines including: rotor system, bearing system and overall structure system. Due to different roles and functions, their design goals are different.

In order to quantitatively describe the relation between structural features and mechanical properties, two types of parameters,structural parameters and mechanical characteristic parameters are set.

Structural parameters include geometric parameters and material parameters.Geometric parameters refer to the aspects of key dimension and configuration, such as length, crosssectional area, second moment of area etc. Material parameters refer to the physical properties of materials, such as density, elastic modulus, Poisson ratio etc.

Similarly, mechanical characteristic parameters are what reflect structural-mechanical properties. In aero-engines, there are many mechanical parameters,some of the most typical are stiffness, specific strength, mechanical impedance, modal participation factor etc.

2.2. Structural efficiency

Structural efficiency13,14is an quantitative expression of environmental adaptability and performances of structural systems. Its essence is to describe the influence of structural parameters(geometric and material)on its mechanical characteristic parameters (strength, stiffness, vibration mode, etc.),which aims to quantitatively assess the benefits of new structures and new materials used in the design of structural optimization.

Structural design of aero-engines is a repeated optimization process to structural weight, strength, stiffness, dynamic characteristics and aerodynamic performance in given working environments.Regularly,much of the weight is used to obtain the structural strength required to withstand huge static and vibrational loads. On the another hand, structures must also have sufficient stiffness to control rotor to stator clearance,which has significant impact on the aerodynamic efficiency and safety of aero-engines. Besides, in order to achieve high aerodynamic efficiency, a low dynamic sensitivity to rotor unbalance loads and other cases, such as airflow disturbance, is required. As a consequence, the structural efficiency method as an quantitative assessment of structural design quality must contain the following three aspects:

(1) Bearing capacity. Which is used to describe the relation between structural mass and strength property.The purpose is to reflect the stress distribution under designed loads, so as to find the minimum structural mass with the most reasonable stress distribution, that is, the optimal strength performance.

(2) Resistance to deformation (anti-deformation ability).Which is used to describe the relation between structural mass and stiffness property.The purpose is to reflect the deformation distribution under limit loads,so as to find the minimum structural mass with the coordinated rotor-stator deformation distribution, that is, the optimal stiffness performance.

(3) Dynamic environment adaptability. Which is used to describe the relation between response properties and dynamic environment. The purpose is to reflect the dynamic response of the structural system under complex dynamic loads,so as to find the minimum vibration response, that is, the optimal dynamic sensitivity.

Obviously, from the above three aspects, the contents of structural efficiency established the contact between structural features and mechanical characteristics. This analysis method of structural-mechanical characteristics integrated design is so called Structure Efficiency Assessment Method (SEAM).

2.3. Structural efficiency coefficient

Based on the contents of structural efficiency, structural efficiency coefficient15was used to quantitatively characterize structural efficiency. Definition of the structural efficiency coefficient in aero-engines is as follows:

where ESis engine strength item, representing the structural bearing capacity; DCis deformation coordination item, representing resistance to deformation;DSis the dynamic sensitivity item,representing the adaptability of the structure to dynamic environments. In order to facilitate the calculation and comparison of the coefficients, ES, DCand DSshould be normalized. The determination of normalized method depends on the specific evaluation purpose. In improvement design process, prototype engine can be chosen as the benchmark; in evaluation of new structures, design goals can be chosen as the benchmark. In consequence of different performances in specific structures, representing items ES, DCand DShave different contributions to the structural efficiency coefficient.This difference is revealed by the weight coefficient αi（i=1，2，3）,and it satisfies:

Usually, the weight coefficient is constant in improvement design process. For a new structure design procedure, it depends on the design systems or the accumulated engineering data.

3. Structural efficiency assessment method

3.1. Analysis purposes

The SEAM is substantially to obtain structural mechanical parameters with normalization methods and normalized parameters, which can represent the mechanical characteristic from three aspects, see Fig. 1. And then according to Eq. (1),the structural efficiency coefficient is calculated by synthesizing the parameters to quantitatively evaluate the structural design quality. Through carrying out integrated design of structuralmechanical characteristics, the weak link of structural design can be obtained.

For different structural systems, the content and scope of mechanical evaluation parameters are different, but they must include the above mentioned three aspects. Considering the difference in structural features and design requirements,mechanical characteristics assessment of the overall aeroengine and its components has different emphasis.

Fig. 1 Scheme of SEAM.

Fig. 2 Overall engine deformation in transverse overload.

Fig. 3 Mechanical characteristics on bearing system.

3.1.1. Overall engine

For overall engine analysis,16-19its emphasis is on the dynamic sensitivity of the whole structural system to internal and external excitation sources,and the coordination ability of rotor to stator deformation under the limit loads, such as overload,bird impact,20blade loss21etc. The former is to reduce modal coupling between the rotor and stator structures to allow the rotor speed to be increased to improve the thermodynamic efficiency.The latter is to achieve minimal tip clearance contributing to aerodynamic efficiency of the turbine, and successfully avoiding rubbing at the same time.

For example, the engine structure subjected to transverse overload will occur the deformation as shown in Fig. 2(a).Due to asymmetric constraints and loads, the stator components deformation may be different in the vertical and horizontal, as a consequence the total deformation tends to oval.Whereas the rotor rotates in circular shape as usual, leading to different clearance between the rotor and the stator in the circumference, which probably cause the local rubbing as shown in the Fig. 2(b).

3.1.2. Components

Component structures mainly include the rotor system and bearing system.For rotor system,it is mainly to assess control level in structural mass, deformation and vibration characteristics;for bearing system,the focus is to evaluate dynamic stiffness, vibration isolation or vibration attenuation ability of support frame structures.

For example, as shown in Fig. 3(a), ω is the operating speed, K is the stiffness. If working speed is close to the abruptly-dropping points of dynamic stiffness, it will greatly reduce the anti-deformation capability of bearing structures,which affects the clearance control. In addition, as shown in Fig.3(b),if the isolation efficiency is low or there exists vibration amplification in the operating speed range, the vibration response will not be effectively controlled, and the vibrations will be transmitted to the supporting structures, increasing vibration level of the whole engine as well as the aircraft.

3.2. Analysis procedures

Fig.4 shows the procedures of SEAM in structural-mechanical characteristics integrated design, which can be divided into four following steps:

Step. 1 Analyze the structural features and functions to determine the most close evaluation items related to its mechanical characteristics.

Step. 2 Take structural loads and design requirements into consideration, establish quantification parameters or subparameters for evaluation items.

Step. 3 Determine the normalization method, obtain normalized parameters of evaluation, take into account the synthesis method of detailed parameters.

Fig. 4 Analysis procedures of SEAM in integrated design of structural-mechanical characteristics.

Step.4 Analyze mechanical characteristics and calculate the structural efficiency coefficient, after obtaining the weak link of structures, carry out optimization design to meet the optimal structure performances.

This analysis method can quantitatively evaluate the design level of structural systems, if there are different structural schemes for comparison, the structural design quality can be uniformly quantified to determine the optimal structure scheme. What’s more, the evaluation parameters cannot violate the principle of strength design or dynamic design specifications.It notes that,just meeting the requirements of existing structural design standards can only ensure the performance of aero-engine structures,but cannot guarantee the optimal structural design.

3.3. Structural efficiency coefficient algorithm

From the above analysis, it can be seen that the evaluation parameters of mechanical characteristics include multiple layers.The structural efficiency coefficient is the top layer parameter, called the coefficient term. It covers three parameter items,namely bearing capacity,anti-deformation and dynamic environment adaptability. For each parameter item, it can be quantified through setting a number of evaluation parameters,collectively referred to as sub-parameters, further divided into single-state sub-parameters and all-state sub-parameters according to the calculation conditions. The single-state subparameters corresponding to one calculation condition. For example, in anti-deformation assessment for overall engine structural system, deformations respectively under translational loads (g-loads) and rotor gyroscopic loads are singlestate sub-parameters. Evidently, all-state sub-parameters need to synthesize all the single-state sub-parameters in the states.

To reflect the level of structural design intuitively,it is necessary to set up a unified algorithm to synthesize multi-levels parameters for the calculation of structural efficiency coefficient. According to the logical relation between different parameters, two algorithms are proposed: logic multiplication is used in the processing of single-state sub-parameters and allstate sub-parameters; logical addition is used between parallel representing items ES, DCand DS. The detailed calculation procedure is shown in Fig. 5.

4. Applications of SEAM in aero-engines

The mechanical characteristics of a typical dual-rotor system are calculated and analyzed by using the SEAM established in this paper to clarify the assessment procedures and point out the direction of structural-mechanical characteristics integrated design.

4.1. Structural features

Fig.6 is a typical high bypass ratio turbofan engine with dualrotor structural system, mainly including single-stage fan,3rd-stage booster, 9th-stage High-Pressure Compressor(HPC), 1st-stage High-Pressure Turbine (HPT), 4th-stage Low-Pressure Turbine(LPT),cases and bearing frames.These component structures transmit major static and dynamic loads associated with rotor imbalance, maneuvers, and internal engine loads etc.

The Low-Pressure Rotor(LPR) has an elongated structure designed as flexible rotor with the 0-2-1 supporting form. The High-Pressure Rotor (HPR) is designed as rigid rotor with a drum shape structure, and the 1-0-1 supporting form along with an inter-shaft bearing is used. The maximum design speeds for low and high-pressure rotors are 5280 r/min and 15,000 r/min respectively.

Fig. 5 Calculation procedure of structural efficiency coefficient.

Fig. 6 Typical high bypass ratio turbofan engine with dual-rotor system.

According to the dynamical modeling of aero-engines,22a three-dimensional finite element overall engine model was established in ANSYS,as shown in Fig.7,where different colors represent different materials.

The data of structural feature parameters of this analysis model can be achieved from the appendix or be available from the corresponding author upon request.

4.2. Mechanical characteristics

4.2.1. Bearing capacity

The bearing capacity mainly reflects the relation between structural mass and stress. From the perspective of structural efficiency, through optimizing the structural geometry to make full use of the material, the greatest bearing capacity can be obtained with the lightest mass cost.

Disk is the most important load-bearing component in rotors, which is chosen as the evaluation object of bearing capacity. In bearing capacity analysis in rotor systems, the load environment includes aerodynamic forces acting on blades, thermal stress distribution on disks and centrifugal loads. As the blades were simplified as mass and moment of inertia in the finite element model, aerodynamic loads acting on disks were ignored. In order to simplify the calculation,the thermal stress on the discs was neglected and only the influence of centrifugal stress was considered. In structural efficiency evaluation of specific objects, influences of aerodynamic forces and thermal stress should also be taken into account. Average stress coefficient and stress distribution were taken as the evaluation parameters.

Fig. 7 Finite element model for overall engine.

1) Average stress coefficient

Average stress of the rotor in working condition can directly reflect the structural bearing capacity. Increasing the average stress level can make full use of the material properties to achieve the reduction of structure mass. It is calculated as follows:

where σiand midenote the stress and mass of the ith element in the discretized structure, respectively.

For comparison purposes, a normalized treatment is performed to define the average stress coefficient:

where σbis the ultimate strength stress.

Zσmust be less than 1 because of strength design criteria.So Zσvaries from 0 to 1, and the greater the value, the higher the material utilization.

2) Stress distribution

Stress distribution is the volume proportion of different stress levels, calculated as:

where V（σi） denotes the element volume with σiin stress level and V is the total volume of the structure.

Stress distribution can accurately describe the proportion of the high-stress regions in the whole structure,so as to evaluate the level of optimization design, for further improving of the material use efficiency.

Fig. 8 shows the stress distribution in different disks,according to Eqs. (3) and(4), the average stress σaveand average stress coefficient Zσresults are shown in Table 1.

Fig. 8 and Table 1 illustrate the utilization rate of bearing capacity for LPR is low.The range of average stress coefficient is: 0.20 ≤Zσ≤0.54. Particularly, in the fan Zσ=0.20, in the 1st to 3rd stage of booster Zσ=0.25. To increase the structural use efficiency of fan disk, an multi-disc structure shown in Fig. 9(a) may be considered to be adopted. For the 1st to 3rd stage of booster,use circumferential dovetail groove structure to replace double-deck ring may be an optimization way to improve bearing capacity, shown as Fig. 9(b).

In order to analyze internal stress distribution, stress is divided into several intervals. Take low-pressure turbine disk as an example, according to Eq. (5), stress distributions of the 1st stage and 4th stage disk were calculated. In Fig. 10(a), the 1st stage turbine disk stress is mainly between 250 MPa and 350 MPa(85.85%).In Fig.10(b),stress distribution in the 4th stage turbine disk is relatively uniform, from 200 MPa to 550 MPa.As a result of small radius and low tangential velocity, stress level is not high in the 1th stage disk.However,the average stress may be higher in the actual condition, if thermal stress and aerodynamic force were taken into account.

4.2.2. Resistance to deformation

In maneuver flight of aircrafts, overload acting on the overall engine,and gyroscopic moment acting on the rotor system are the main causes of structural deformation. The change between rotor and stator clearance may lead the aerodynamic efficiency decline, even cause safety problems. The structural anti-deformation ability and the rotor-stator deformation compatibility play an important role in ensuring the normal operation of the engine.The evaluation of structural deformation is a standard to measure the quality of engine design.

The deformation coordination term DCin Eq. (1) is based on the worst maneuver flight condition which includes translational acceleration, angular acceleration load, and rotor gyroscopic moment. Fig. 11 shows the engine components centerline deflection in maneuver flight.Relatively large deformation values occur in the middle part of low-pressure rotor and turbine of high-pressure rotor, where clearance closure may occur.These are the key points in design to avoid rubbing and ensure aerodynamic efficiency.

Since rotational inertia of fan and turbine component is large in LPR, a significant angular deformation may occur in disk-shaft connection part during maneuver flight. The maxi-mum angular deformation θmaxwas set to be the evaluation parameter in anti-deformation ability analysis. Calculation results of fan and turbine under gyroscopic moment are shown in Table 2.

Table 1 Average stress and average stress coefficient.

As can be seen from Table 2,turbine has the largest angular deformation under the action of gyroscopic moment, which illustrates that the angular stiffness of turbine is lower than that of fan. An optimization scheme was proposed as shown in Fig. 12. Bolt connection was used in the original scheme,see Fig. 12(a). The bolt weight is heavy and the stiffness is low because of the connection sections. In the improved scheme, see Fig. 12(a), an integral structure was adopted instead of bolt joints, stiffness loss in connection section was avoided. The conical shell was also optimized to increase the bending stiffness. However, excellent material properties and processing techniques were required in the new structure.

For HPR system, compressor outlet and turbine inlet are the key sections which affect aerodynamic efficiency. Therefore, equivalent specific stiffness of these sections should be calculated as evaluation parameters in analysis of antideformation ability. Table 3 is the transverse equivalent stiffness and equivalent specific stiffness in compressor outlet and turbine inlet sections.

Fig. 8 Stress distribution shown by Von Mises stress contour.

Fig. 10 Stress distribution in LPT.

Fig. 11 Aero-engine components centerline deflection.

The results show that the equivalent stiffness of the calculated sections both reach to 108N/m with a high specific stiffness,implying that the HPR has high rigidity with a low mass level. But the integral rigidity may be further improved by geometry change of the drum structure, shown in Fig. 13.Besides,utilizing counter-rotating design may be a better direction for the reduction of loads and weight.

4.2.3. Dynamic environment adaptability

In modern aero-engines, it is common that rotor bending critical speed occurs in the operating range, especially for LPR.There are two main ways to ensure the stable operation of the engine in working speed: one is to drive the critical speed out of the operating speed range by adjusting the mass and stiffness distribution of the rotor; the other is to reduce the dynamic sensitivity of rotor systems to unbalance and other excitation sources.

Based on the above analysis,the analysis of dynamics environment adaptability in dual-rotor systems set evaluation parameters as follows:

1) Stiffness-mass coordination factor

Stiffness-mass coordination factor is defined as follows:

where kiand miare defined as equivalent stiffness and the equivalent mass of the ith sub-structure of the rotor system.Obviously,the dimension of fiis same with circular frequency.

For the sake of comparison, the dimensionless stiffnessmass coordination factor is used in the assessment process:

Table 2 Mechanical evaluation parameters for LPR.

Fig. 12 Structural optimization for LPT conical shell.

Table 3 Mechanical evaluation parameters for HPR.

where fminis the minimum value of fifor sub-structures.

The variation of stiffness-mass coordination factors along the rotor axis reflects coupling possibilities of the substructure dynamic characteristics. If stiffness-mass coordination factor of the sub-structure is lower than or close to the main shaft, local vibration may be generated during the operation. The physical meaning of high stiffness-mass coordination factor can be understood as the sub-structure has high resonance frequency, where vibrations will not easily occur.

For typical dual-rotor system in aero-engines, the recommended sub-structure division of LPR and HPR are shown in Fig. 14. The LPR was divided into four parts, 1 to 4 are sub-structure numbers. The HPR was divided into substructure No.1 and No.2. Stiffness-mass coordination factor calculation results for LPR and HPR are shown in Table 4.

Analyzing the stiffness-mass coordination factors of substructures, it can be drawn that the fan, booster and turbine components of LPR have higher numerical value (5.94, 8.12 and 4.24 respectively) compared with the main shaft part, so local vibration does not easily occur in these parts. For HPR,although the 1st and 2nd stage disk is a cantilever structure, the stiffness-mass coordination factor is relatively high(3.98). Vibration modes of the whole structure in operating speed will appear as the No.2 sub-structure of HPR. It can be verified from the free mode analysis. Where there are only the overall vibration modes without local vibration modes within 500 Hz, as shown in Fig. 15.

2) Strain energy distribution coefficient

Strain energy distribution coefficient is the ratio of rotor structure strain energy to the total rotor-support system strain energy at critical speed. It can be expressed as:

where i is the critical speed order,Wrotor，iand Wsys，irespectively represent the strain energy of rotor structure and rotorsupport system.

The ideal state is that the rotor system has no strain energy,all deformation energy is concentrated in the support structures and then consumed by damping. So strain energy ration of the support can be set as the evaluation parameter, which can be expressed as the percentage of support strain energy to total system energy:

where Wsup，iis the strain energy concentrated in support structures.The maximal value ofis 1,means all strain energy can be absorbed by support structures, there is no strain energy distribution in the rotor.

Fig. 13 Structural optimization for HPT shaft.

Fig. 14 Sub-structure division for LPR and HPR.

Table 4 Stiffness-mass coordination factor for dual-rotor system.

Fig. 15 First three order free modes of HPR.

For dual-rotor systems, LPR and HPR are coupled together through the inter-shaft bearing,so the coupling effect must be considered in calculation of critical speed for strain energy analysis. Using the Reduction Method23to calculate the critical speed of co-rotating dual-rotor system. Campbell diagram for critical speed analysis is shown in Fig. 16. The points AL, BL, AH, BH, etc. are critical speeds of the system,where subscript L, H means excited by LPR and HPR respectively. Strain energy distribution and vibration mode description are respectively shown in Table 5 and Fig. 17.

There are three-order critical speeds(AL,BL,FH)in operating speed range. For HPR, the dynamic environment adaptability is better with low strain energy distribution coefficient in each critical speed, 0.05, 1.24 and 13.06 respectively.Whereas for LPR,strain energy distribution coefficient is high in ALand BL,42.71% and 45.86%respectively, which implies that the bending strain energy probably has a great bad influence on the robustness of connecting structures. In structural design process, corresponding measures should be taken to reduce strain energy distribution for LPR,e.g.the use of damper or high-speed flexible rotor dynamic balancing technology.

4.3. Calculation of structural efficiency coefficient

In above analysis, structural-mechanical characteristics were evaluated form bearing capacity, resistance to deformation and dynamic environment adaptability three aspects. Evaluation parameters were calculated in each step of the analysis.According to the calculation procedure of structural efficiency coefficient shown in Fig.5,evaluation items ES,DCand DSfor LPR and HPR can be obtained and shown in Table 6. Then the final structural efficiency coefficient I was calculated according to Eq. (1).

Fig. 16 Campbell diagram for critical speed analysis in dual-rotor system.

Table 5 Strain energy distribution of dual-rotor system under critical speeds.

Fig. 17 Vibration modes of dual-rotor system under critical speeds.

From the results of structural efficiency evaluation, it can be concluded that the efficiency of LPR is relatively low,mainly embodied in low bearing capacity and nondeformability (0.20). It is also proved the coefficient term can reflect the evaluation items synthetically. In subsequent improvement design,it is necessary to optimize the above mentioned two aspects by integrated design of structural and mechanical characteristics, finally achieve high structural efficiency design.

5. Conclusions

Structural-mechanical characteristics integrated design is an efficient and effective way for structural optimization in designof aero-engines. Structural efficiency can evaluate the structural design quality quantitatively. SEAM was proposed to conduct the implementation of integrated design in a standard and uniform approach. The following conclusions can be drawn in this paper:

Table 6 Structural efficiency coefficient evaluation results.

1) The concept of structural efficiency was introduced to establish links between structural feature parameters and mechanical characteristic parameters. The way of optimizing mechanical characteristics by improving structural features was provided, which aims to quantitatively assess the design quality of structures and guide the direction of optimal design.

2) Procedures of SEAM and structural efficiency coefficient algorithm were presented.For different parts,components, overall structure systems in aero-engines, the method can be used to consider bearing capacity, antideformation ability and dynamics environment adaptability under static loads,quasi-static loads and dynamic loads. One parameter can be used to comprehensively quantify the structural design.

3) For applications in a typical dual-rotor system of aeroengines,structural efficiency coefficient of HPR(0.43)is higher than LPR (0.29). The mechanical weaknesses were manifested in bearing capacity (0.20) and antideformation ability (0.20). Base on structural features,functions and working conditions of analysis objects,the results can be a good visualized appraisal with appropriate evaluation parameters selection, ultimately achieve the integrated design of structural and mechanical characteristics.

Acknowledgements

The author is grateful to AECC Commercial Aircraft Engine Co., LTD for providing the financial support for this work and for giving permission to publish this work.