Dynamical Modeling and Dynamic Characteristics Analysisof a Coaxial Dual-Rotor System

The dual-rotor structure serves as the primary source of vibration in aero-engines. Understanding itsdynamical model and analyzing dynamic characteristics, such as critical speed and unbalanced response, arecrucial for rotor system dynamics. Previous work introduced a coaxial dual-rotor-support scheme for aeroengines,and a physical model featuring a high-speed flexible inner rotor with a substantial length-to-diameter ratiowas designed. Then a finite element (FE) dynamic model based on the Timoshenko beam elements and rigid bodykinematics of the dual-rotor system is modeled, with the Newmark method and Newton–Raphson method used forthe numerical calculation to study the dynamic characteristics of the system. Three different simulation models,including beam-based FE (1D) model, solid-based FE (3D) model, and transfer matrix model, were designed tostudy the characteristics of mode and the critical speed characteristic of the dual-rotor system. The unbalancedresponse of the dual-rotor system was analyzed to study the influence of mass unbalance on the rotor system. Theeffect of different disk unbalance phases and different speed ratios on the dynamic characteristics of the dual-rotorsystem was investigated in detail. The experimental result shows that the beam-based FE model is effective andsuitable for studying the dual-rotor system.

Analysis on Nonlinear Dynamic Properties of Dual-Rotor System

In order to clarify the effects of support structure on a dual-rotor machine,a dynamic model is established which takes into consideration the contact force of ball bearing and the cubic stiffness of elastic support. Bearing clearance,Hertz contact between the ball and race and the varying compliance effect are included in the model of ball bearing. The system response is obtained through numerical integration method,and the vibration due to the periodic change of bearing stiffness is investigated. The motions of periodic,quasiperiodic and even chaotic are found when bearing clearance is used as control parameter to simulate the response of rotor system. The results reveal two typical routes to chaos: quasi-periodic bifurcation and intermittent bifurcation. Large cubic stiffness of elastic support may cause jump and hysteresis phenomena in resonance curve when rotors run at the critical-speed region. The modeling results acquired by numerical simulation will contribute to understanding and controlling of the nonlinear behaviors of the dual-rotor system.

VIBRATION CHARACTERISTIC INVESTIGATION OF COUNTER-ROTATING DUAL-ROTOR IN AERO-ENGINE

Two methods for vibration characteristic investigation of the counter-rotating dual-rotors in an aero-en- gine are put forward. The two methods use DAMP tool on the MSC. NASTRAN platform and develope the re- solving sequence. Vibration characteristics of a turbofan engine are analyzed by using the two methods. Com- pared with results calculated using transfer matrix method and test results, the two methods are valuable and have great potential in practical applications for vibration characteristic investigation of aero-engines with high thrust-weight ratio.

Modal analysis strategy and nonlinear dynamic characteristics of complicated aero-engine dual-rotor system with rub-impact

This paper aims to gain insight into the nonlinear modal characteristics and the possible influence of the modes on the responses for the practical dual-rotor system with rub-impact in aero-engine.The finite solid element method combined with a constraint stiffness model produced by rub-impact is introduced to build the governing equation of the complicated nonlinear dual-rotor system.In order to deal with the efficiency and numerical divergence in the process of solving the nonlinear modes of this large-scale nonlinear system,an analysis strategy is proposed by integrating a two-layer reduction technique into the harmonic balance method.The effectiveness of the analysis strategy is validated by applying to a simple rotor system,which can easily obtain the theoretical result.Based on the modeling method and analysis strategy,the modal characteristics of an aero-engine dual-rotor system with rub-impact are revealed.The results show that the modal frequency of the dual-rotor system increases when rub-impact occurs and has the feature of interval,which allows us to obtain the critical speeds of the rubbing system by traditional Campbell diagram.The rotation direction is an important factor since it can not only affect the gyroscopic effect but also change the friction effect of the rub-impact.It is found that the modal frequencies of the counter-rotation dual-rotor are less than those of co-rotation condition.More importantly,the forward modes of the counter-rotation dual-rotor may be instable when rub-impact occurs at a certain rotor,while the corresponding modes under the co-rotation condition are always stable.Furthermore,by analyzing the rubbing response of the dual-rotor,it is found that the modal characteristics have an important influence on rotor’s response.The instable forward modes existing in the counter-rotation dual-rotor may lead to the divergence of the response when passing the corresponding critical speed.

Nonlinear resonance characteristics of a dual-rotor system with a local defect on the inner ring of the inter-shaft bearing

In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing.The local defect is modelled as an inverted isosceles trapezoidal groove,which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing.The motion equations of the dual-rotor system are formulated by using the Lagrange equation.The Runge-Kutta method is employed to solve the motion equation.The amplitude-frequency response curve of the dual-rotor system is obtained,the abnormal resonance characteristics are analyzed.In addition,the influence of defect parameters,rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed.The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing.Through analyzing the vibration response of the abnormal resonance peaks,it is found that the first two abnormal resonances are caused by the combined resonance,which are related to the inner ring fault and the rotational speed of high or low pressure rotors,and the last two resonances are caused by the induced resonance of the inner ring fault.At the same time,when the parameters of defect,rotors and support and inter-shaft bearing change,the resonance of the system also shows the corresponding change law.

A 5-DOF Model for Aeroengine Spindle Dual-rotor System Analysis

This paper develops a five degrees of freedom（5-DOF） model for aeroengine spindle dual-rotor system dynamic analysis.In this system,the dual rotors are supported on two angular contact ball bearings and two deep groove ball bearings,one of the latter-mentioned bearings works as the inter-shaft bearing.Driven by respective motors,the dual rotors have different co-rotating speeds.The proposed model mathematically formulates the nonlinear displacements,elastic deflections and contact forces of bearings with consideration of 5-DOF and coupling of dual rotors.The nonlinear equations of motions of dual rotors with 5-DOF are solved using Runge-Kutta-Fehlberg algorithm.In order to investigate the effect of the introduced 5-DOF and nonlinear dy-namic bearing model,we compare the proposed model with two models：the 3-DOF model of this system only considering three translational degrees of freedom（Gupta,1993,rotational freedom is neglected）;the 5-DOF model where the deep groove ball bearings are simplified as linear elastic spring（Guskov,2007）.The simulation results verify Gupta＇s prediction（1993） and show that the rotational freedom of rotors and nonlinear dynamic model of bearings have great effect on the system dynamic simula-tion.The quantitative results are given as well.

Rubbing-Induced Vibration Response Analysis of Dual-Rotor-Casing System

Considering gyroscopic effects caused by rotational speed,torsional vibration as well as coupling effects among inner rotor,out rotor and casing,a dynamic model of the dual-rotor-casing system is established using finite element(FE)method.By comparing the natural characteristics obtained from MATLAB and ANSYS,the developed model is verified.Then rubbing-induced vibration responses in dual-rotor-casing system are analyzed.The effects of rotational speed and speed ratio on rubbing vibration responses of the system are discussed.Results show that different combined frequency components will appear in the spectrum except two unbalanced excitation frequencies and their multiple frequency components,and these frequencies can be used as the dual-rotor aero-engine rubbing failure diagnosis frequencies when rubbing occurs.Besides,the amplitude of torsional vibration is larger than that of lateral vibration under the same working condition,and speed ratio has a great impact on the periodicity of the system rubbing-induced motion trajectory.The amplitude of rubbing-induced responses under counter-rotation is less than that under co-rotation with the same parameters.

Synchronous impact phenomenon of a high-dimension complex nonlinear dual-rotor system subjected to multi-frequency excitations

The“synchronous impact”is a phenomenon that increases the dynamic load of the inter-shaft bearing,when the frequency of the aerodynamic excitation is close to the contact frequency of the inter-shaft bearing.This work addresses the“synchronous impact”phenomenon of an aero-engine.The 104 degree-of-freedom dynamical model of an aero-engine is established by the finite element method,in which the complex nonlinearity of the Hertzian contact force of the inter-shaft bearing with clearance is included,and the multi-frequency excitations such as the unbalanced excitations of the high-and low-pressure rotors and the aerodynamic excitation are considered.A harmonic balance method combined with the alternating frequency time-domain method(HB-AFT)is introduced to obtain periodic responses of the high-dimension complex nonlinear dual-rotor system.The results show that there emerges a peak value of the amplitude-frequency response for the contact frequency harmonic component of the outer ring of the inter-shaft bearing,when the aerodynamic excitation frequency is close to the contact frequency.In addition,the dynamic load of the inter-shaft bearing increases significantly.Moreover,the parametric analysis shows that the“synchronous impact”phenomenon is sensitive to the change of the speed ratio of the high-and low-pressure rotors.The dynamic load of inter-shaft bearing can be significantly reduced by changing the speed ratio by 1%.The results obtained in this paper not only provide more insight into the mechanism of the“synchronous impact”phenomenon but also demonstrate the HBAFT method as a potential semi-analytical tool to explore the high-dimension complex nonlinear system.

Effect of Hub-Ratio on Performance of Asymmetric Dual-Rotor Small Axial Fan

Currently, domestic and abroad scholars put more attention on contra-rotating dual-rotor axial fan. But there is less scholars study on asymmetric dual-rotor small axial fan, which is one of the contra-rotating dual-rotor axial fans. Like axial fan, many factors have influence on the performance of the asymmetric dual-rotor small axial flow fan, such as the wheel hub ratio, blade shape, blade number, stagger angle and the tip clearance. Because wheel hub ratio has great impact on the performance of the fan, we choose the size of wheel hub ratio as a variable factor to study the model change. There is a different wheel hub ratio between front stage impeller and rear stage of asymmetric dual-rotor small axial fan, so it is very beneficial to select the greater wind area that the fan area of external diameter minuses the area occupied by the blades and the hub as front stage impeller. In this paper, the hub-ratio of front stage impeller is 0.72, and that of rear stage is 0.72, 0.67 and 0.62 respectively along with the front stage impeller. Three kinds of models with different hub ratio of rear stage are simulated using the CFD software and the static characteristics are obtained. Based on the experimental test results, the internal flow field of the asymmetric dual-rotor small axial fan is analyzed in detail, the impact trends of different hub-ratio on the performance of asymmetric dual-rotor small axial fan are obtained and the argument of structure optimization for dual-rotor small axial fan is provided.

双转子-中介轴承系统动力学仿真与实验研究

针对双转子系统复杂的动力学特性以及总是存在的质量不平衡现象,建立内外双转子系统动力学模型,通过轴心轨迹图、时域图、频谱图、庞加莱截面图和分岔图分析其振动特性,并通过双转子系统实验台升速和不平衡实验验证了理论和仿真结果。结果表明:双转子系统在升速过程中会发生2次振幅突然加剧的现象,2次主共振分别由内、外转子转速达到系统固有频率引起;双转子系统在不同的转速下会呈现出不同的振动特性;增大内转子的不平衡量,不仅会影响内转子系统振动响应,还会影响外转子系统振动响应,并且对前者的影响更显著。

能量轨道下带碰摩的双转子系统振动特性分析

为提高航空发动机的推重比和燃油效率,调整转子与机壳间的间隙变小,易发生碰摩故障问题,本文针对带碰摩双转子系统的非线性振动特性开展了定性、定量分析。建立了具有非线性弹簧特性和带碰摩故障双转子系统的非线性数学模型,通过仿真与数值分析调查了该模型复杂的碰撞、振动特性。对碰摩故障发生后和即将脱离时该系统的能量交换进行了定量分析,基于振动能量轨道的迁移过程分析了非线性振动特征和诱发机理。使用转子实验验证了数值仿真、理论分析结果和振动能量轨道。本文揭示了带碰摩故障的非线性双转子系统运行时振动变化规律,更好地分析了双转子系统的振动特征。

含中介轴承波纹度的双转子系统振动特性分析

针对双转子系统中存在中介轴承波纹度的问题,以含变截面外转子的双转子-轴承系统为研究对象,考虑中介轴承滚动体和内、外圈滚道波纹度,基于有限元法建立了双转子-轴承系统的动力学模型,采用四阶Runge-Kutta数值解法求解方程,分析了波纹度激励对系统频谱特征和幅频响应曲线的影响。结果表明:内、外圈滚道存在波纹度时系统会出现内、外转子转频和保持架转频的组合频率,滚动体存在波纹度时系统会出现偶数倍的滚动体自转频率;考虑转子不平衡激励,外圈滚道波纹度会增大外转子主激励的共振区域的振动,且随着波纹度幅值的增加,系统的振动会在整个转速范围内增大,而内圈滚道波纹度与不平衡激励两者的振动响应会在内转子主激励的第二次共振区域出现近似同频反相的现象,系统的振动会随着波纹度幅值的增加而降低,在其他区域的振动会增大,相对于高转速区域,滚动体波纹度对低转速区域的振动特性会有较大影响。

微转速差双转子系统对自动液力变速器车型怠速抽动的影响研究

为分析液力变矩器与曲轴组成的微转速差双转子系统对自动液力变速器(AT)车型怠速抽动的影响,通过对双转子系统动不平衡耦合激励力进行希尔伯特变换(Hilbert Transform),揭示出部件拍振是导致有规律怠速抽动的根本原因,其抽动激励幅值最大值为激励力之和,抽动间隔频率为激励力频率之差。建立包括发动机、变速器、悬置等系统的机械系统动力学自动分析(ADAMS)模型并进行仿真,结果表明,动力总成垂向刚体模态频率与激励频率越接近,液压悬置垂向一阶动刚度越大,振动幅值越大。因此,可通过动力总成Z向模态频率与曲轴动不平衡激励频率间的避频设计、降低液压悬置垂向动刚度、提高悬置系统的隔振性能等方式改善怠速抽动。

基于联轴器不对中的磁悬浮双转子系统不平衡响应分析

为探讨联轴器不对中故障对磁悬浮双转子系统振动响应的影响,基于有限元法构建包含不对中故障的磁悬浮双转子系统动力学模型,利用Newmark-β法求解其运动方程,通过时域和频域分析不对中情况下转子系统的振动响应。研究结果表明:在不对中引起的附加力作用下,磁悬浮双转子系统的响应会呈现显著的二倍频分量,且随着不对中程度的增加,二倍频分量的幅值也相应增大;内转子由于不对中故障引起的二倍频分量会通过中介轴承传递到外转子上;在不同控制参数下不对中故障对系统的影响有所不同,通过选取合适的比例系数和较大的微分系数,可以有效降低不对中故障对系统振动响应的影响。

支承刚度各向异性对双转子系统进动状态的影响

为提高航空发动机的推重比,航空发动机静子系统的工程解决方案常引起转子系统支承刚度各向异性,进而对转子系统的动力学特性产生显著影响。针对支承刚度各向异性的双转子系统,建立动力学特性计算模型,在验证计算模型准确性的基础上,研究支承刚度各向同性和各向异性对双转子系统固有频率、进动状态和不平衡响应的影响。研究结果表明:支承刚度各向同性时,双转子系统Campbell图中的低阶固有频率线出现交叉,而支承刚度各向异性使低阶固有频率线具有相互分离的趋势。支承刚度各向同性时,不平衡力仅触发转子系统的正进动运动,转子进动轨迹为圆形;而支承刚度各向异性时,转子系统的反/正进动均被不平衡力触发,转子进动轨迹为椭圆形。支承刚度各向异性时,在某些转速下转子系统不同位置处的进动方向可能不同。支承阻尼减小转子系统反/正进动的振幅及反进动的转速区间,降低支承刚度各向异性对双转子系统动力学特性的不利影响。

在能量空间中实现非线性双转子系统的碰摩振动机理表征

碰摩是转子系统发生失稳的一个重要原因。在碰摩故障发生时,转子与机壳随时间的推移在碰撞和脱离等状态间变化,容易产生能量交换,并引发复杂的振动现象。通过构建带碰摩故障的非线性双转子系统模型及动力学方程,采用龙格-库塔法进行数值仿真,在相空间中分析系统的非线性振动特性。在振动能量空间中使用非线性能量供给函数模拟碰摩故障发生后系统的转子振动能量变化,利用振动能量轨道的迁移表征碰摩振动机理。研究结果更好地揭示了非线性双转子系统发生碰摩故障后的碰摩振动机理,提出的方法为双转子系统的振动机理分析提供了新的视角。

双转子系统碰摩有限元接触分析模型及故障诊断

针对常用碰摩力模型的不足,应用AN SY S软件在求解转静子之间的碰摩力与法向相对位移之间的关系的基础上得到了碰摩力模型,并与整体传递系数法相结合建立转静件碰摩的动力学方程。采用整体传递系数法计算转子系统的动力特性,进而求解双转子系统的瞬态响应。利用时域波形、频谱分析和小波变换对响应进行了分析,得出并分析了相关的故障特征。

航空发动机双转子系统的拍振分析

在双转子航空发动机中,由于转子系统不可避免地存在不平衡量,当两个转子的转速比较接近时,发动机会出现拍振现象,拍振将引起振动强度过大问题。对双转子系统的拍振进行了研究,分析了拍振的周期性、信号强度及其反向转子特性,阐明了拍振产生的机理和特征,并采用数值仿真和试验对拍振进行了定量分析和验证。研究表明,拍振与双转子转速差和不平衡量的相位因素有关,当转速差小于工作转速的20%时,双转子系统拍振信号的强度较大。

内外双转子系统支撑轴承不对中分析

针对航空发动机内外双转子系统不对中问题,以某航空发动机转子系统为对象,运用转子动力学有限元分析方法,给出内外双转子系统中介轴承的处理方法,建立内外双转子系统动力学模型。通过数值计算,得到该双转子系统的固有频率和振型,对比分析考虑外转子(高压转子)支撑轴承不对中的转子振动响应。

反向旋转双转子系统非线性分析

以双转子系统中介轴承刚度的非线性为简化模型,推导了反向旋转双转子系统振动响应的非线性动力学方程。研究了转子转速、不平衡量和中介轴承径向间隙对系统响应特性的影响。结果表明:转速、不平衡量等对转子-轴承系统的非线性振动有较大的影响;减少中介轴承的径向间隙,有利于系统的非周期运动转变为周期运动,提高系统运动的平稳性。