基于欧拉梁单元模型的裂纹转子变刚度特性分析

裂纹转子旋转过程中,由于裂纹的非线性开/合行为导致转子刚度的变化,进而导致转子复杂的非线性振动。文章研究存在横向表面裂纹转子的纵-弯-扭耦合振动建模,并对裂纹引发的转子变刚度特性进行综合分析。转子建模采用欧拉梁单元模型,并考虑了轴向力、截面剪力、弯矩以及扭矩作用下转子运动的六个方向的自由度。裂纹单元的刚度矩阵采用柔度系数法导出,而柔度系数则由应变能理论求得。在此基础上,对一些影响裂纹转子刚度变化的主要因素如裂纹深度,梁单元长度等进行了数值分析。所得研究结果,有助于理解和揭示具有横向表面裂纹转子的非线性振动响应特性。     

基于有限元的呼吸裂纹转子动力学特性

采用有限单元法建立了含裂纹Jeffcott转子的有限元模型,利用应变能释放率方法得到了裂纹单元的刚度矩阵,采用应力强度因子为零法模拟了裂纹的呼吸效应.计算分析了在一个稳态旋转周期内裂纹开闭的规律,以及直斜裂纹转子振动响应的特点.计算结果表明,斜裂纹开始张开以及闭合的时间迟后于直裂纹,斜裂纹处于全闭与全开状态所经历的时间比直裂纹长.直斜裂纹转轴的1X和2X倍频响应随着裂纹深度的增加而增加,但3X倍频分量变化不大.     

基于固有频率的呼吸式裂纹梁损伤识别方法

将呼吸裂纹梁简化为由扭转弹簧连接的两段弹性梁,在假定振动响应随振幅变化的基础上推导出呼吸裂纹梁的固有频率方程;考虑振动过程中呼吸裂纹的开合情况,假定裂纹梁的刚度是振幅的非线性函数,建立了呼吸裂纹梁的多项式刚度模型;结合等高线裂纹识别理论和方法,提出了一种基于固有频率的呼吸裂纹梁损伤识别方法,算例验证了方法的可行性与有效性。研究表明,该方法的识别精度取决于实验固有频率的精度。     

基于分段啮合刚度的双圆弧斜齿轮转子系统的振动响应分析

以双圆弧斜齿轮平行轴转子系统为研究对象,结合其啮合过程的变形特点,导出了其动能和势能的计算公式,根据拉格朗日方程建立了齿轮啮合的动力学模型;根据转子系统齿轮多点和多齿的啮合特点,采用分段式的方法计算其啮合刚度,将其与动力学模型相结合,采用有限元法,求解平行轴转子的弯曲振动和弯扭耦合振动特征值,并分析了系统在不平衡力作用下随激振频率变化的振动响应曲线.研究表明,采用分段式计算啮合刚度的方法来分析双圆弧齿轮是可行的,以此为根据求解的响应曲线符合转子动力学的振动规律,可为双圆弧齿轮平行轴转子系统的动力学分析提供理论基础.     

裂纹耦合双转子响应的非线性时间序列分析

建立了裂纹耦合双转子系统的动力学方程,分析了含有裂纹、支承在挤压油膜阻尼器上耦合双转子的复杂运动。采用非线性时间序列方法,对不同裂纹时系统的响应进行分析,估算了其最大Lyapunov指数和关联维数。结果表明,裂纹使轴的刚度下降到一定程度后,其响应由拟周期到周期运动,最后失稳。关联维数和Lyapunov指数相结合能为判断因裂纹变化引起的系统运动状态改变提供一种辅助方法。     

转子的瞬态响应特性研究

采用有限元法,研究了转子瞬态动力学特性。分析了转子在惯性载荷下对应的刚度矩阵设置问题,推导了转子工作状态下的振动方程。计算了在加速过程中转子裂纹处的最大应力,得到裂纹转子受加速冲击载荷作用时的变形曲线,并得到在给定转速下位移对频率的响应曲线。     

含裂纹转子的振动特性计算用于裂纹在线检测的研究

本文研究含裂纹转子的振动特性。文章首先根据裂纹结构的应力强度因子，得到含裂纹单元体的刚度矩阵，进而得到裂纹转子的整体刚度矩阵和质量矩阵，列写出裂纹转子的运动微分方程，导出裂纹引起转子系统刚度变化与系统振动特性参数变化间的关系，从而可由实时在线测得的振动参数判断裂纹的位置。通过对模拟转子的计算和实测，表明本文提出的方法是一种可用于大型旋转机械转子轴裂纹在线检测的极为有效的方法．     

基于时频分析的裂纹转子碰摩故障特征研究

为研究转子系统耦合故障特性,采用有限元方法建立了含有横向裂纹、转静碰摩的非线性转子动力学模型。首先研究了不同转速下裂纹、碰摩单一故障下转子系统的振动响应,其次研究了两种故障耦合情况下系统的振动响应特征。采用波形图、FFT谱图、瞬时频率和Hilbert-Huang时频谱(HHS)相结合的方法对故障转子振动信号进行了分析。分析结果表明:运用多种时频分析相结合的方法可以较为全面地了解转子的故障特征,裂纹转子在1/5、1/3临界转速时会发生较为明显的5X、3X谐波,且裂纹的产生会导致响应幅值增大,从而引起更为严重的碰摩。      

发动机转子系统碰摩-裂纹-松动耦合故障作用下动力学特性分析

建立了滚动轴承支承下的双跨转子系统非线性动力学模型,采用四阶-五阶定步长Runge-Kutta法分析比较了系统在无故障、碰摩故障、裂纹故障、一端松动故障以及碰摩-裂纹-松动耦合故障5种工况下随着转速变化的转子动力学响应。数值分析了在碰摩-裂纹-松动耦合故障工况下转子不平衡量、碰摩刚度、松动端轴承座质量对系统响应的影响。结果表明:当系统存在碰摩故障时,一阶临界转速有所提高,动力学行为更为复杂;存在裂纹故障时,一阶临界转速有所降低;存在松动故障时,响应混沌区域变大;存在三种耦合故障时,超一阶临界转速响应出现大面积混沌。随着转子不平衡量、碰摩刚度的增大,响应趋向于混沌,松动端轴承座质量在高速下响应具有敏感性。     

双盘裂纹转子非线性响应特性

研究了轴上含有横向裂纹 ,刚性支承带有居中盘和悬臂盘的双盘裂纹转子的非线性动态响应。考虑轴旋转过程中裂纹的开闭 ,推导出双盘裂纹转子的运动方程。采用仿真计算的方法 ,分析了转速、裂纹深度、外阻尼比的变化对响应的影响 ,并且研究了盘的摆振与横向振动的区别。结果表明 ,裂纹转子随转速变化 ,响应会出现丰富的非线性特征 ;裂纹深度的增大 ,会导致系统响应出现分叉与混沌 ;外阻尼可以有效抑制非线性响应 ;盘的摆振对于裂纹的出现 ,较之横向振动 ,包含有明显的高次谐波分量 ,易于识别     

Vibration analysis of periodically time-varying rotor system with transverse crack

This paper proposes the vibration analysis for the periodically time-varying rotor system with transverse crack based on the complex modal analysis by introducing the modulated coordinates. From the feasibility of the crack modeling by harmonically varying stiffness, for which the dynamic behaviors of breathing crack depending on two modeling structures are investigated, the vibration analysis associated with modal characteristics, whirling, instability, directional frequency response functions (dFRFs) and directional spectrum (dS) is carried out. Using the feature of the reverse dFRFs strongly representing the effect of the crack and the interpretation of the dS patterns, the effective method to identify the modes due to the presence or propagation of a transverse crack is suggested.     

Dynamic response of a cracked rotor with an unbalance influenced breathing mechanism

The vast majority of studies on cracked rotors assume that the breathing response of a fatigue crack is weight-dominant i.e. the effect of dynamic forces on the breathing response is negligible. In this study, the assumption of weight-dominance is removed and the coupling effect of unbalance angle and magnitude on the breathing behaviour of a crack is examined. The proposed breathing model is shown to be greatly influenced by unbalance eccentricity and rotor speed, whereas weight-dominant breathing models are unaffected by these factors. A significant difference in the vibration behaviour of a weight-dominant model and the proposed model was particularly seen around the critical speed of deeply cracked rotors. High unbalance eccentricity and a 180° placement of the unbalanced mass resulted in the disappearance of 2X and/or 3X harmonic components at one-half and one-third of the rotor critical speed when the vibration was predicted using the proposed model. This result suggests careful placement and size of the unbalance mass may allow for the isolation of rotor cracks from other rotor faults in the frequency domain by negating the effects of the crack breathing.     

The dynamic behavior of a rotor system with a slant crack on the shaft

For a Jeffcott rotor system with a 45° slant crack on the shaft, the motion equations are established with four directions, i.e. two transversal directions, one torsional direction and one longitudinal direction. It can be seen from the deducing process of the stiffness with the strain energy release approach that there are coupling stiffnesses of bending–torsion, bending–tension and torsion–tension for the slant-cracked shaft and only bending–tension for the transverse-cracked one. The paper shows that besides the coupling stiffnesses, there is bending–torsion coupling caused by the eccentricity. All these couplings affect the responses of the slant-cracked shaft and the transverse-cracked one. Comparing responses of a cracked shaft with an open crack model and those with a breathing crack model finds that there are the same prominent characteristic frequencies for these two kinds of shafts, even though the cracked shaft with a breathing crack model behaves much more non-linear than that with an open crack model. Therefore, almost all studies in this paper adopt the open crack model since it needs taking much longer time to compute responses of a breathing cracked shaft than that of an open cracked shaft. Analyses of steady responses indicate that the combined frequencies of the rotating speed and the torsional excitation in the transversal response and the frequency of the torsional excitation in the longitudinal response can be used to detect the slant crack on the shaft of the rotor system.     

Stability and dynamics of rotor system with 45° slant crack on shaft

Crack on a shaft is one of the common damages in a rotor system. In this paper, transverse vibrations are calculated to compare the influences of transverse crack and slant crack on the rotor system. Results show that the vibration amplitude of the rotor system with a 45° slant crack on the shaft is larger than that with a transverse crack when the two types of crack have the same depth and the rotor system runs in the same condition. Stability and dynamic characteristics of the rotor system with a 45° slant crack on the shaft under torsional excitation are analyzed by considering opening and closing of the crack. It is shown that the instability of the transverse vibration of the rotor system increases with increasing difference between the bending stiffness in two main directions, and the vibration is stable when the two bending stiffness are identical. The spectrum analysis of the steady-state response reveals that the gravity and the eccentricity produce different frequency components, and when the two bending stiffness are identical, the multiple frequency components of the torsional excitation disappear. Further investigation shows that the vibration amplitudes in combined frequencies increase rapidly in transversal, torsional, and axial vibration with increasing slant crack depth. The results are helpful for the understanding the dynamic behavior of a rotor system with a slant crack on a shaft and can be used for the detection of the slant crack on a shaft.     

Nonlinear vibrational response of a single edge cracked beam

The nonlinear vibrational response of a breathing cracked beam was investigated. The study was done by using a new crack stiffness model to examine some of the nonlinear behaviors of a cantilever beam with a breathing crack. The quadratic polynomial stiffness equation of the cracked beam was derived based on the hypothesis that the breathing process of a crack depends on the vibration magnitude. The Galerkin method combined with the stiffness equation was used to simplify the cracked beam into a Single-degree-of-freedom (SDOF) lumped system with nonlinear terms. The multi scale method was adopted to analyze the nonlinear amplitude frequency response of the beam. The applicability of the stiffness model was discussed and parameter sensitivity studies on the dynamic response were carried out by the SDOF model for a cantilever beam. Results indicate that the new stiffness model provides an efficient tool to study the vibrational nonlinearities introuduced by the breathing crack. Therefore, it might be used to develop a nonlinear identification method of a crack in a beam.     

含横向裂纹的Jeffcott转子刚度分析

根据断裂力学理论和转子动力学理论,考虑沿3个坐标轴方向6个载荷的作用,推导出了含裂纹的转轴刚度。裂纹的开闭状态由裂纹面的应力决定。通过数值仿真计算发现:刚度在3个坐标轴方向上随着裂纹深度的变化幅度有很大差异,轴向刚度变化以及小裂纹情况下垂直于裂纹方向的刚度变化可以不考虑;随着细长比的增大,裂纹轴的刚度减小。     

Condition monitoring of cracked rotors through transient response

In the present study a simple Laval rotor with a transverse crack is considered. The analysis assumes that the vibrations remain small in comparison to the sag of the rotor under its own weight. If a cracked shaft rotates slowly under the load of its own weight, then the crack will open and close once per revolution, i.e. it breathes. Considering a simple hinge model which is a very good model for small cracks with the breathing action of crack, the transient vibration response of a cracked rotor passing through its critical speed is analysed, as an attempt for crack detection and monitoring. Effects of different factors such as crack depth, unbalance eccentricity with phase and acceleration influencing vibration are investigated.     

On fault induced nonlinear rotary response and instability

Results of applying instantaneous frequency to the interpretation and characterization of bifurcation and evolution of instability are presented for a comprehensive rotor-journal bearing model incorporating translational and rotational inertia, bending stiffness, gyroscopic moments, shear deformation and disk imbalance. By designating rotor speed and the relative flexibility embodying the extent of surface crack development as the two controlled parameters, rich and complex nonlinear behaviors are observed as the model subjected to the combined exertion of slow crack breathing and bearing film pressure. Among them are that sub-harmonics attributable to the oil-film force are seen disappeared with crack opening and that the model system fails from one of the three possible scenarios: super-harmonic bifurcation, prolonged chaotic response, and large vibration amplitudes accompanied by no bifurcation. As a result of the investigation, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart.