Dynamic behavior of aero-engine rotor with fusing design suffering blade of f

Cun WANG,Dayi ZHANG,Yanhong MA,Zhichao LIANG,Jie HONG

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

Dynamic behavior of aero-engine rotor with fusing design suffering blade of f

Cun WANG,Dayi ZHANG*,Yanhong MA,Zhichao LIANG,Jie HONG

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

Available online 8 May 2017

*Corresponding author.

E-mail address:dayi@buaa.edu.cn(D.ZHANG).

Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

http://dx.doi.org/10.1016/j.cja.2017.03.015

1000-9361©2017 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/).

Fan blade off(FBO)from a running turbofan rotor will introduce sudden unbalance into the dynamical system,which will lead to the rub-impact,the asymmetry of rotor and a series of interesting dynamic behavior.The paper first presents a theoretical study on the response excited by sudden unbalance.The results reveal that the reaction force of the bearing located near the fan could always reach a very high value which may lead to the crush of ball,journal sticking,high stress on the other components and some other failures to endanger the safety of engine in FBO event.Therefore,the dynamic influence of a safety design named ‘fusing”is investigated by mechanism analysis.Meantime,an explicit FBO model is established to simulate the FBO event,and evaluate the effectiveness and potential dynamic influence of fusing design.The results show that the fusing design could reduce the vibration amplitude of rotor,the reaction force on most bearings and loads on mounts,but the sudden change of support stiffness induced by fusing could produce an impact effect which will couple with the influence of sudden unbalance.Therefore,the implementation of the design should be considered carefully with optimized parameters in actual aero-engine.©2017 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/).

Aero-engine;

Blade off;

Finite element analysis;

Fusing design;

Rotor dynamics;

Sudden unbalance

1.Introduction

Fan blade off(FBO)from a turbofan rotor during operation is a major safety concern in commercial civil aviation.1The release of fragments or even the whole blade from the rotor will lead to the failure of different engine components.2The authorities request the manufacturers to run a successful fan blade loss test which is extremely expensive and costly to demonstrate the strength and integrity of the engine and the aircraft.3,4Therefore,analytical and numerical simulations get more attention in the industry to reduce the test cost and guide the structural safety design.

During the past decades,a significant amount of research has been done on the topics of blade off event including the sudden unbalance load generated on the rotor,5the asymmetry of inertia,6the deceleration of the damaged rotor from operating rotating speed to windmilling condition,7the rub-impact between blade and casing,8,9the interaction between fragments and containment casing,10,11and the transient vibration response.12,13

Among all of these,dynamical response of rotor system excited by sudden unbalance load is one of the important research topics.The amplitudes of transient displacements and loads generated are the main concern parameters,and influences due to different parameters such as internal damping,gyroscopic moment and support stiffness are analyzed.Kalinowski,5Genta,14Dzenan,15and Liang et al.16established dynamic equation to study the response caused by sudden unbalance.Their work demonstrated that the sudden unbalance could lead to amplification of vibration response instantaneously while the value is related to the operating state,and the low order natural frequencies exist in frequency content.

Due to the high vibration of rotor,the reaction force of bearings,especially the main bearing located near the fan,could usually reach a very high value,which exceeds the bearing capacity and may lead to the failure of system.Therefore,a safety design structure to relieve structural loading and improve the distribution of load during FBO event,named the breakage or fusing,17,18is used.Zheng et al.19designed an active fusing apparatus to improve the sensitivity of fusing and relieve loads transiently.Comprehensive study of the combined effect of all the behavior including fusing during FBO by theoretic or simulation method is carried out by many researchers.1,20,21Sinha and Sreekanth2used LS-DYNA as the solver to perform an analysis on FEO event with a complex finite element model of whole engine,and carried out a rotordynamic analysis of asymmetric turbofan rotor with contact-impact rub loads.Analysis of the response of aircraft structure,especially the failure of mounts caused by a propeller blade loss,was performed using the same program by Armendariz et al.22,23

In the existing analysis,the dynamic influence of the transient variation of support stiffness induced by fusing design is covered by other mechanisms,and the potential dynamic problems induced by fusing design are not well investigated.Therefore,the work presented in this paper aims at understanding the dynamic influence of the stiffness change caused by fusing design with mechanism analysis and a series of simulations carried out on an explicit FBO model which is based on an actual high bypass turbofan aero-engine.Finally,the paper will provide reference for safety design and corresponding analysis method.

2.Mechanism analysis of rotor system with sudden unbalance load

A typical low pressure rotor system of high bypass ratio aeroengine and associated parameters are shown in Fig.1,blade massmb=3 kg,radius of blade mass centerr=0.5 m,disk massmd=120 kg,polar inertia of diskJp=8 kg·m2,diameter inertia of diskJd=4 kg·m2, Elastic modulusE=2.1 × 105MPa,density ρ =7800 kg·m-3,Possion’s ratio μ=0.3,damping ratio ξ=0.1,shaft lengthl=2000 mm,l1=300 mm,l2=300 mm,l3=1400 mm,outer diameterD1=160 mm,D2=160 mm,D3=80 mm,inner diameterd1=140 mm,d2=140 mm,d3=70 mm,support stiffnessK1=4.0×108N·m-1,K2=6.0× 108N·m-1,K3=5.5×108N·m-1,damping of supportC1=C2=C3=0.

The dynamical equation is written as

whereqis the generalized degree of freedom,Mthe mass matrix,Cthe damping matrix,Ggyroscopic matrix,Kthe stiffness matrix,Q（t）the time variable load vector,mbthe blade mass,rthe radius of blade mass center and ω the rotating speed.The sudden unbalance load is generated at the momentto=0.25 s.In this part,the influence of deceleration and the asymmetry of inertia are not considered,and only the effect of sudden unbalance is investigated to make the results simplified and convenient for comparison.The response of the rotor excited by sudden unbalance is analyzed in Matlab through Newmark’s method of direct integration,and Eq.(1)is formed by finite element method.The calculated orbits,amplitude response and frequency contents at the fan disk are summarized in Fig.2.The vibration increases instantaneously to a peak value,and then attenuates to a steady amplitude in several periods,which indicates that sudden unbalance produces an impact on the rotor.As shown in Fig.2(c),despite the rotating speed frequency(79.15 Hz,4749 r/min,1 r/min-≈ 0.105 rad/s),the natural frequencies ω1，ω2are excited by sudden unbalance load.16It should be noticed that in this part,the rub-impact between rotor and casing,and the interaction between lost blade and other blades are neglected.

Fig.3 gives the reaction force of supports in time history,and the amplitude of transient and steady response is marked.The time history properties of reaction force is consistent with that of vibration response.The value increases instantaneously to a peak,and then attenuates to be steady.One can observe that the reaction force decreases obviously with the increasing distance between fan and bearings.The 1st bearing located near the fan has the maximum value of reaction force which exceeds 500 kN,while the reaction force of the 2nd and 3rd bearing is far below.Therefore,the 1st bearing and corresponding load-carrying structure are most likely to be damaged,which may lead to a journal sticking failure.Until now,the worldwide jet engine manufacturers have presented some patents to improve the distribution of load and protect the bearing,and the patent will be discussed in detail in the following part.

3.Mechanism analysis of rotor system with safety design structure

3.1.Principle of safety design structure

According to Section 2,the load on the bearing located near the fan is maximum in FBO event.In order to decrease the load transmitted to the engine and protect bearings,some safety design strategies had been adopted.Among them,the fusing design which is easy to implement in structure is shown as follows.18

Fig.4 gives two typical structures to reduce support stiffness once the reaction force exceeds a threshold value.A weak conical shell is arranged on the force transmitting line from the 1st bearing to the middle casing(Fig.4(a)),and the conical shell will break due to extremely high load.The support of middle casing to the 1st bearing is disabled,and the number of supports reduces,which will totally change the dynamics of system.Different from the design that the support is totally disabled,the structure shown in Fig.4(b)could provide a relatively small stiffness in FBO event.During the normal operation,the 1st bearing is supported by parallel installed shells with high stiffness,but only supported by inner shell with smaller stiffness when the breakable connection element is cut off and the shell with high radius do not transmit load.Although the structures are different,the principles are basically the same that the weak part fails at a predetermined load to reduce support stiffness and relieve load.

Despite improving the distribution of load of the system,the fusing design could also improve the dynamic properties of rotor in windmilling state.Fig.5 shows steady response of rotor which indicates that the lower stiffness will distance the critical speed from windmilling speed,and decrease the vibration response at windmilling speed.Meantime,as the unbalance load is proportional to the square of rotating speed,the unbalance load produced at critical speed will decrease greatly,which will be beneficial to the engine in deceleration.

In conclusion,the fusing design could improve the dynamic properties of system in windmilling state and safety of engine.However,due to the demand of low cost and easier implementation,the fusing design is realized by the break of fragile stator component,which will lead to the sudden change of support stiffness and may generate other dynamic problems.In fact,some active control methods24with smart materials have been investigated,which shows a new light on safety design,but the application is limited by response speed,costs and size of structure.Therefore,in a long time of the future,the fusing design will still be used,and the mechanism of sudden stiffness change needs to be further investigated.

3.2.Mechanical model

Based on the principle of fusing design,a time variable stiffness matrixKb（t）is inserted to Eq.(1)to consider the change of stiffness.Eq.(1)is revised as follows:

λ is the ratio of remnant stiffness to the original support stiffness,tfthe moment of fusing,）the local support stiffness matrix,kxthe horizontal stiffness of bearing,kythe vertical stiffness of bearing andTthe transformation matrix from local coordinate system to global coordinate system.The threshold value is set as 300 kN in the analysis,and once the reaction force exceeds the value,the 1st bearing do not support the rotor system(λ=0).In fact,the load capacity of ball bearings is far above this value which is chosen to verify the feasibility of the safety design structure.All the other parameters and the algorithm used are the same with those in Section 2.

The reaction force of all the bearings and the variation of amplitude are summarized in Fig.6 and Table 1.According to the result,the reaction force of the1st bearing exceeds 300 kN at the moment 0.2546 s and the stiffness changes to zero at this moment suddenly.

The 1st bearing is no longer loaded,while the transient and steady amplitudes of the 2nd bearing increase 64.8%and 29.2%respectively,and the reaction force of the 3rd bearing which locates at turbine reduces.The results indicate that the 1st bearing is protected and the load is redistributed.Fusing design proposes a higher requirement to other bearings,and the impact of sudden unbalance and stiffness change may produce a combined effect on the displacement response.The calculated orbits and amplitude response at the fan disk is shown in Fig.7,while the difference of response characteristics is shown in Table 2.The decay time means the time that the response amplitude needs to be steady(the variation of amplitude is less than 1.0 mm).

Table 1 Amplitude of reaction force without fusing design.

Table 2 Response amplitude of fan.

Table 2 Response amplitude of fan.

Response Transient amplitude(mm)Steady amplitude(mm)Decay time(s)Sudden unbalance 32.20 14.20 0.45 Fusing design 37.50 8.74 2.29 Rate of change(%)16.4 -38.5 408.9

The slight increase of transient amplitude is identical to authors’expectation and may lead to a more severe rubimpact between blade and casing,while the steady amplitude decreases obviously,and the decay time is substantially extended compared to the results with constant support stiffness.The results demonstrate that the fusing design will induce negative dynamic influence to the system,and the influence of key parameters should be investigated.

3.3.Influence of key parameters on dynamic properties

The influence of stiffness ratio of the 1st bearing to the rotor system is analyzed firstly.The value of stiffness ratio λ is chosen as 0,0.2,0.4,0.6,0.8 and 1.0,while 0 corresponds to the complete failure of the support and 1.0 corresponds to the structure without fusing.The vibration response of fan and reaction force of bearings are summarized in Figs.8 and 9 respectively.In order to compare the results with different stiffness ratios,the moment of sudden unbalance load applied is set with time interval in Fig.8.The threshold value of reaction force is assumed to be 300 kN.

Contrary to the expectations,the transient amplitude do not monotonically increase with the decrease of stiffness ratio.The minimum value of transient amplitude occurs when λ=0.8,and the maximum value occurs when λ=0.0.The steady amplitude decreases monotonically,due to the reduction of critical speed of the rotor system.

According to the result in Table 1,the stiffness change of the 1st bearing will lead to the increase of reaction force of the 2nd bearing,which may influence the safe operation,while the consequence is clearly a breach of the original purpose of fusing design.Therefore,the influence of stiffness ratio on the reaction force of the 2nd bearing should be analyzed.

The following is shown in Fig.9:

(1)The steady amplitude of reaction force of the 1st bearing decreases almost linearly,while the transient amplitude decreases rapidly to the value slightly above 300 kN(310 kN with λ=0.3)and decreases slowly to the threshold value.

(2)The transient and steady amplitudes of the 2nd bearing increase monotonically with the decrease of λ,and the transient amplitude increases with large slope when λ＜0.3.The reason is that the impact induced by sudden unbalance and stiffness change of bearing is suffered by all the bearings;when λ is lower than 0.3,the load on the 1st bearing is relatively small,but the impact caused by stiffness change is aggravated.

(3)The decay time increases obviously for the decrease of stiffness ratio,which means that the impact of the stiffness change is more serious.

Fig.10 gives the influence of the 1st support stiffness and threshold value on the transient amplitude of reaction force of the 1st and 2nd bearings.It could be observed that the increase of the 1st support stiffness and decrease of threshold value will reduce the transient amplitude of reaction force of the 2nd bearing.In fact,the value of support stiffness is usually determined in the early design phase to satisfy the design requirements of critical speeds and vibration.This part only provide the response characteristics as a reference.In actual engine,the value of parameters should be chosen carefully by optimized analysis which will be presented in further study to consider the vibration response and reaction force at the same time,and the influence of the change speed of stiffness will be investigated.

4.Simulation of engine FBO event

4.1.Explicit FBO model

A simplified generic engine model was established in LSDYNA.The model includes high pressure rotor,low pressure rotor,five bearings(one innershaft bearing)and other stator components(Fig.11).Some acronyms commonly used in the turbomachinery industry should be introduced,such as low pressure turbine(LPT),high pressure turbine(HPT)and high pressure compressor(HPC).The number following the acronym means which stage it is,for example,HPC1 is the first stage of high pressure compressor.It should be noticed that in order to avoid the chaos of description,the bearings in this Section are named as 1#to 5#,while the 5#bearing is actually the 3rd bearing in mechanism analysis.Typically,full FBO models usually have millions of elements and degrees of freedom to represent a realistic aero engine.In this investigation,the model is not as elaborate as the full engine models that are used by manufacturers in their explicit simulation,21but is sufficiently detailed to capture the physics of the problem and enhance the computing efficiency.

The blades of fan,booster,compressor and HPT are constructed by shell elements with various thickness across their width and length to make the mass,stiffness and rotational inertia equivalent to the characteristics of actual blades,while the blades of LPT and stator are constructed by mass elements.The FBO model has a total of 15,328 elements and 15,387 nodes.The distribution of mass,rotational inertia and stiffness is compared to the actual data to ensure the accuracy of model.

Table 3 Material properties.

The main materials used in typical aero engine are titanium alloy,aluminum alloy,high temperature alloy and composite material which are shown in Fig.12.The linear material used in rotor dynamic analysis is not suitable in FBO due to the large deformation and penetration of materials.The bilinear elastic–plastic constitutive model(Fig.13)is adopted to simulate the nonlinear properties,while the main properties are listed in Table 3.

The predefined lost blade is connected to the disk by the card‘*CONTACT_TIED_NODES_TO_SURFACE”,while the moment of blade off is defined by DT(death time of the contact)at 0.02 s.The contact caused by FBO should be considered carefully,especially the contact between the blades and inner surface of the fan case,and the contact between lost blade and blades still on the fan,which are defined by the card ‘*CON TACT_AUTOMATIC_SURFACE_TO_SURFACE”and‘*CONTACT_TIED_NODES_TO_SURFACE”.The initial rotating speeds of high pressure rotor and low pressure rotor are 4383 rev/min and 14,018 rev/min respectively.The blades are rotating about the engine axis using ‘*BOUNDARY_PRE SCRIBED_MOTION_NODE”for the nodes,where the shaft or the disk is being driven by some external means,and the deceleration is defined that low pressure rotor will decelerate from 4383 rev/min at 0.02 s to 1000 rev/min at 0.1 s.The‘*INITIAL_VELOCITY_NODE” card is used for all other nodes which will simply rotate as a result of prescribed angular velocity at the boundary nodes.

In order to handle the rigid body rotations of the spinning rotor,the major challenge is how to deal with the interface involving the bearing surfaces between the rotating shaft and the outer-race bearing connected to stator surface,and the inner shaft bearing surfaces between high pressure rotor and low pressure rotor.Sinha2assumed an elastic material model to make the 3D bearing structure have a stiffness equivalent to the actual bearing,and the card ‘*CONTACT_TIED_N ODES_TO_SURFACE” is used.Gunther25used the cards ‘‘*CONSTRAINED_JOINT_SPHERICAL_ID” and ‘*CON STRAINED_JOINT_CYLINDRICAL_ID”to define the ball bearings and roller bearings respectively,while ‘*CON STRAINED_JOINT_STIFFNESS_TRANSLATIONAL”is used to define the stiffness of bearings.Different from these methods, ‘*CONSTRAINED_EXTRA_NODES_NODE”is used to connect nodes to rigid parts which represent the inner or outer race of bearings,and spring elements(‘*ELEMENT_DISCRETE”)are defined between these nodes with determined stiffness.This method is easier to define the support stiffness,while the fusing of support structure is defined by the card ‘*MAT_ADD_EROSION” with a failure time definition.In the simulation,no specific hourglass control parameter or penalty factor,other than the default values built into the code already,is used.

In fact,the stiffness of bearing is nonlinear with such huge load.Despite the nonlinearity of bearing,there are many sources of nonlinearity in the simulation including the rubimpact between rotor and casing,and the interaction between lost blade and other blades.The nonlinearity of bearing stiffness which may lead to a more complex response is not the primary focus of the research.Therefore,the influence of nonlinear stiffness is neglected.In the mechanism analysis presented in Section 2,all the nonlinearity are neglected,which makes the effect of the sudden unbalance load be more obvious.

4.2.Reaction force of bearings

Different from the usual explicit analysis which has been presented,this paper focuses on the vibration response of rotor,reaction force of bearings and loads transmitted to the wing instead of the containment of the fan.The load generated on the rotor is mainly transmitted to the mounts through bearings and support casing,and meantime,the fan casing adds a load path to absorb a part of the unbalance loads and behaves like a bearing due to the rub-impact.As shown in Fig.11,despite the innershaft bearing,there are four bearings locating inside the support casing,including the 1#,2#,3#and 5#bearings.

Fig.14 gives the time history response of reaction force of bearings,while the influence of fusing design could be observed directly by the comparison in Table 4.Conclusions could be drawn as follows.

(1)The simulation results coincide with the results of mechanism analysis.The transient amplitude of reaction force of 1#bearing is maximum,which could reach 1094 kN.The 1#bearing is in a severe environment.Because the threshold value is assumed as 500 kN,the load path of 1#bearing will be cut off at 0.026 s when fusing design is implemented.

(2)Fusing design has a great influence on 2#bearing,and the transient amplitude increases by31.4% from 330 kN to 481 kN,while the steady amplitude almost has no change.The results demonstrate that the fusing design will generate a coupling effect caused by sudden unbalance load and sudden stiffness change,which may affect the normal operation of other bearings.But the transient amplitude of reaction force of 2#bearing is still far below that of 1#bearing when fusing design is not used,which means that the result is acceptable.

(3)Different from the variation tendency of reaction force of 2#bearing,the transient and steady amplitudes of 5#bearing sharply decrease from 703 kN and 469 kN to 184 kN and 109 kN respectively.The decrease of steady amplitude is corresponding to the analysis inSection 3 that the fusing will change the dynamic properties of rotor system and lead to the decrease of critical speed.

Table 4 Amplitude of reaction force with fusing design.

(4)The fusing design has little influence on the reaction force of 3#bearing which is the front bearing of high pressure rotor,and the response between 0.02 s and 0.2 s almost coincides.In conclusion,the reaction force of all the bearings are reduced below 500 kN,and the essence of the fusing design is to average the unbalance load from 1#bearing to other bearings.Although some potential negative influence will be generated,especially the increase of reaction force of 2#bearing which is nearest to the 1#bearing and locates at the spline joint of low pressure rotor,in the analysis that this paper presented,the reaction force of all bearings is kept within a safe limit.

4.3.Loads on mount system

The load will finally be transmitted to the wing through mount system.As shown in Fig.11,the mount system of a typical high bypass ratio turbofan aero-engine is composed of main mount and rear mount.Usually only the main mount transmits the axial load to the wing by the design of constraint.

Figs.15 and 16 indicate that the load on main mount is higher than that on rear mount because the main mount is close to the fan component where the large unbalance is generated,and the load in horizontal direction is higher than that in vertical direction because the lost blade strikes the containment casing in horizontal direction in this analysis.

As shown in Table 5,the transient response amplitude of main mount drops from 1470 kN and 2360 kN to 780 kNand 1210 kN in vertical and horizontal directions respectively.The transient response amplitude of rear mount decreases from 1370 kN to 630 kN in horizontal direction,while the response in vertical direction is relatively small.Despite the steady response amplitude of main mount,the response amplitude almost drops about 50%.All the results demonstrate the effectiveness of fusing design on the point that the load transmitted to the airplane decreases sharply.

Table 5 Load on mounts.

4.4.Vibration response of rotor

Fig.17(a)gives the time history of vertical displacement of fan without fusing design,and the horizontal displacement is not given due to the similar properties.It is assumed that there is no unbalance load in rotor before the FBO happens.Once the FBO happens at 0.02 s,the vibration intensif i es to the maximum amplitude 25.64 mm at 0.054 s.

Because the duration of initial speed 4383 r/min(73.1 Hz)is very short(0.02 s),the initial speed frequency could not be observed in the frequency content,but the amplitude of windmilling rotating speed 1000 r/min(16.7 Hz)is obvious.As shown in Fig.17(b),despite the windmilling rotating speed frequency,abundant components including precession and subharmonic frequencies(19.9 Hz,31.5 Hz,38.3 Hz,46.6 Hz,54.9 Hz and 66.5 Hz)exist.

Fig.18 gives the response of fan when fusing design is implemented,and the attenuation of vibration could not be found before 0.6 s(Fig.18(a)).Because most of the vibration energy will transmit to the middle casing through 1#bearing when the fusing structure is not implemented,the fan has a relatively high vibration amplitude and vibration energy when 1#bearing is not valid.It should be noticed that the results in Figs.17 and 18 are the vibration response of the center of disk,and the amplitude is far above the clearance between blade and casing due to the deformation of blade.The number of frequency components is fewer,while the main component is the windmilling rotating speed frequency(16.7 Hz).The frequency components also have a significant change due to the variation of dynamic properties of rotor system(26.9 Hz,39.8 Hz and 49.8 Hz).

Different from the result presented in Sections 2 and 3 that the vibration amplitude almost has no oscillation(Figs.2(b)and 3),the simulation result acquired by explicit model in LS-DYNA has significant amplitude oscillation(Fig.14).The main reason is that the explicit model takes the rubimpact into consideration,which makes the response complex with many frequency components.

Fig.19 gives the time history of response at other locations of rotor,and the vibration response amplitude of HPC is far below the amplitude at other locations,which corresponds to the low reaction force of 3#bearing.The vibration amplitude of turbine has a sharp decrease compared to that without fusing design,and the impact effect is not obvious.

4.5.Influence of threshold value

The influence of threshold value is analyzed.Fig.20 gives the time history of response of reaction force of bearings,while the response of 3#bearing is not given due to its non-sensitivity to the fusing design.The threshold value varies from 250 kN to 750 kN,and according to Fig.14(a),the moment at which the support stiffness changes is 0.023 s and 0.035 s respectively.It could be observed that the threshold value almost has no influence on the steady amplitude,while the transient amplitude of 2#bearing increases from 4330 kN to 6110 kN(4810 kN with threshold value 500 kN)as threshold value rises.Similarly,the transient amplitude of 5#bearing increases from 1720 kN to 2890 kN(1840 kN with threshold value 500 kN).

Fig.21 gives the load on main mount in vertical direction.Once the fusing design is implemented,the steady amplitude with different threshold values is similar,while the transient amplitude achieves a minimum(0.78×103kN)when threshold value is 500 kN.

Based on the results,the fusing design and its dynamic influence could be simulated correctly through explicit analysis,and the results coincide well with the mechanism analysis.The fusing of support structure of 1#bearing could reduce the vibration amplitude of rotor,the steady amplitude of reaction force on bearings and the loads on mounts to ensure the safety of engine and aircraft.But the fusing design which leads to the transient variation of stiffness in mechanics could produce an impact effect on the system,especially increasing the load of 2#bearing greatly.

5.Conclusions

The paper focuses on the safety design of aero-engine rotor system with severe load induced by FBO,firstly analyzes the mechanism of sudden unbalance,then introduces a safety design structure named ‘fusing”,and analyzes the effectiveness and possible dynamic problems induced.Finally,the paper establishes an explicit FBO model to simulate the FBO event with fusing design.The following conclusions could be drawn:

(1)FBO produces a violent impact on the engine,which could be observed in the vibration response of fan and the reaction force.The reaction force of 1#bearing could exceed its capacity.The fusing design,which means cutting off the load path when the force exceeds a threshold value,could protect the bearings and prevent possible failures.The explicit FBO model established in LS-DYNA with corresponding simulation method could be capable to capture the dynamic properties and describe mechanical processes including rotation of rotor,blade off,rub-impact,deceleration and fusing of support structure.

(2)Both the mechanism analysis and simulation results demonstrate that the fusing design of support structure could reduce the vibration amplitude of rotor when its operational speed is above critical speed,and redistribute the reaction force on bearings and loads of mounts indeed to ensure the safety of engine.Meantime,the sudden change of support stiffness will produce an impact effect which will couple with the influence of sudden unbalance.It means that the parameters of fusing design should be considered carefully,including the support stiffness,stiffness ratio and threshold value in actual aero-engine,and the influence of the change speed of stiffness should be investigated further.In addition,as the related whole engine experimental data and operation experience are published in future,the comparison between simulation and experiments or operation experience will be beneficial to validate the model and improve its accuracy.

Acknowledgements

The authors would like to acknowledge the f i nancial support from the National Natural Science Foundation of China(Nos.51575022 and 51475021).

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25 February 2016;revised 12 May 2016;accepted 23 August 2016