多种非线性力作用下不平衡弹性转子的分岔特性

研究了4自由度不平衡弹性转子在非线性油膜力、非线性内阻力和非线性弹性力联合作用下的动力学特性。结果表明，当只有非线性油膜力作用时，转子只存在由于油膜失稳而导致的倍周期分岔。而当非线性油膜力与非线性内阻力共同作用时，在油膜失稳后，转子产生低频振动。转速继续增加，还会诱发内阻失稳，产生概周期运动。在倍周期分岔中，存在分岔激变现象。本文发现的由于油膜涡动而导致的内阻失稳(概周期运动)是一种未见报道的转子失稳模式(组合失稳)，它与油膜失稳(倍周期运动)一起可作为转子故障诊断的典型失稳模式。     

非稳态非线性油膜力作用下柔性轴裂纹转子的动力特性分析

分析了在动载轴承非稳态非线性油膜力作用下，具有横向裂纹柔性轴Jeffcott转子在非线性涡动影响下的动力特性。通过数值计算表明，在油膜失稳转速前，随着裂纹轴刚度变化比的增大，系统在低转速区域内具有丰富的非线性动力行为，出现倍周期分叉及混沌现象，涡动振幅随转速升高而减小，直到非稳态非线性油膜失稳，在无裂纹转子油膜临界失稳点处发现了类Hopf分叉现象，系统运动由平衡变为拟周期运动；裂纹转子在油膜临界失稳时的系统运动亦为拟周期运动，裂纹转子轴刚度变化对油膜失稳点及油膜失稳之后转子的运动影响不大，转子系统作拟周期运动。     

汽轮机转子在气流力和油膜力作用下的非线性动力学特性

为了分析转子在油膜力和气流激振力共同作用下的非线性振动特性，本文以短轴承支撑的不平衡刚性对称Jeffcott转子系统为研究对象，首先分析转子在非稳态油膜力作用下的振动特性，然后分析转子在油膜力和气流激振力共同作用下的非线性振动特性。采用数值模拟的方法研究了系统的分岔和混沌特性，计算结果表明，考虑气流激振力和油膜力共同作用下的转子系统与仅考虑油膜力的转子系统相比，在相对进气速度v=30m／s时，随着无量纲转速ω的增加。二者都出现了周期运动和混沌运动多次交替出现的复杂运动特性，但是前者首次出现倍周期分岔和混沌运动时的转运提前，在定转速情况下，随着v的增大，系统最终在经历周期运动之后进入混沌运动，而且圆盘中心的最大振幅随着v的增大而增大。     

转子—轴承系统发生动静件碰摩时的混沌路径

分析了一个由油膜轴承支承的转子系统在发生动静件碰摩时的振动特性。转子转速与不平衡量被用来作为控制参数以研究进入和离开混沌区域的各种路径以及系统的各种形式的周期、拟周期与混沌运动。结果证明碰摩转子系统在进入和离开混沌区域时可经由倍周期分岔、阵发性和拟周期路径，以及一种由周期运动直接到混沌状态的突发路径。     

轴承-转子系统Hopf分叉及其后动力学行为研究

采用长轴承解析模型研究滑动轴承支承的平衡单盘柔性转子-轴承系统的自激振动,把结合打靶法的延续算法应用于柔性平衡转子-轴承系统Hopf分叉后周期解的追踪和求解上,基于Floquet理论对周期解的稳定性加以分析.通过持续追踪周期解频率变化并与失稳固有频率进行对比,分析了自激锁相现象,研究了非线性油膜力自激源对系统的作用机理.运用Poincare映射、分叉图、及Lyapnov指数对周期解分叉、混沌及进入和脱离混沌的过程进行了分析.     

碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

基于可观测状态的轴承-转子系统周期解计算及稳定性分析

分析了轴承-转子系统的稳定性和分岔,基于系统可观测状态信息给出1种求解系统周期解及识别周期解稳定性的方法,同时将该方法与Floquet理论相结合分析系统周期解的稳定性及失稳分岔形式,将转速作为分岔参数分析系统响应的周期、拟周期、多解共存和跳跃现象.结果表明,采用该方法计算系统周期解及稳定性时,利用系统可观测稳态和瞬态信息,即可求解出系统Jacobian矩阵而无需实时求解轴承非线性油膜力的Jacobian矩阵.与传统PNF方法相比,该方法不仅具有很高的精度而且可以节约计算量,同时可以预测追踪随控制参数变化的系统周期解及其稳定性,可用于指导轴承-转子系统的非线性动力学设计.     

磁浮轴承-转子系统非线性动态特性分析

考虑非线性电磁力对刚性Jeffcott转子系统的影响，采用Hopf分岔理论及CPNF法对系统平衡点解和周期解进行研究，数值仿真得到系统Jacobi矩阵特征值、轴心轨迹图和Poincare映射图。转子运动呈现Hopf分岔、倍周期分岔及拟周期运动等复杂的非线性动力学特征，其结果可为磁浮轴承-转子系统设计和运行状态控制提供理论依据。     

多自由度转子-轴承系统周期运动分岔及稳定性研究

建立考虑诸多因素的转子-轴承系统多自由度模型,将与Newmark结合的打靶法应用到多自由度转子-轴承系统的周期稳定性分析中。着重研究了转子-轴承系统失稳转速随系统偏心量、轴承间隙、润滑油动力粘度以及轴承长径比的变化规律,研究结果表明:提高系统偏心量、减小轴承间隙、增大润滑油动力粘度以及选择适当的轴承长径比均能提高转子-轴承系统的失稳转速;对于不同的参数值,系统表现出不同的分岔规律,系统发生半速涡动时表现为倍周期分岔或拟周期分岔,发生油膜振荡时则表现为拟周期分岔。     

流体动压滑动轴承-转子系统非线性动力特性及稳定性

根据油膜的物理特性,在动力积分、迭代过程中实时修正具有下游Reynolds边界条件的轴承流体润滑椭圆型变分方程,使其等价为变分不等式.运用八节点等参有限元方法,同时完成非线性油膜力及其Jacobian矩阵的计算.运用Newton-Raphson方法求得转子平衡点时,同时求得了作为副产品的轴承的刚度和阻尼系数.将预估-校正机理和Newton-Raphson方法相结合,提出了计算轴承-转子系统Hopf分岔点(对应于线性失稳转速)的方法.将预估-校正机理与Poincaré-Newton-Floquet方法相结合,分析了T周期运动的局部稳定性和分岔现象.结果表明,采用八节点等参有限元方法同时完成非线性油膜力及其Jacobian矩阵的计算时,同传统方法相比计算量减少,且精度协调一致;将预估-校正机理和Newton-Raphson方法相结合,可以方便地计算轴承-转子系统Hopf分岔点;将预估-校正机理与Poincaré-Newton-Floquet方法相结合,可以避免初值选取困难,快速求得系统周期解及其分岔点.所建立的计算方法具有省时、精度高等优点,可用于指导滑动轴承-转子系统设计.     

Turbocharger rotor dynamics with foundation excitation

To investigate the effect of foundation excitation on the dynamical behavior of a turbocharger, a dynamic model of a turbocharger rotor-bearing system is established which includes the engine’s foundation excitation and nonlinear lubricant force. The rotor vibration response of eccentricity is simulated by numerical calculation. The bifurcation and chaos behaviors of nonlinear rotor dynamics with various rotational speeds are studied. The results obtained by numerical simulation show that the differences of dynamic behavior between the turbocharger rotor systems with/without foundation excitation are obviously. With the foundation excitation, the dynamic behavior of rotor becomes more complicated, and develops into chaos state at a very low rotational speed.     

弹性支承滑动轴承不平衡转子系统非线性动力稳定性和分岔的研究

研究弹性支承滑动轴承不平衡转子系统的稳定性及分岔特性。建立了弹性支承-滑动轴承-转子非线性动力系统的力学模型，在油膜力非线性的情况下，应用数值模拟，采用打靶法计算了刚性转子系统的周期解，并与龙格-库塔法计算的结果进行了对比，依据Floquet理论，分析了周期解的稳定性，再结合龙格-库塔法、Poineare映射法作出了系统运动分岔图。最后，讨论了轴的柔性对转子系统运动稳定性的影响。     

Nonlinear behavior analysis of geared rotor bearing system featuring confluence transmission

In this paper, the nonlinear vibration characteristics of geared rotor bearing system and the interactions among gears, shafts, and plain journal bearings were studied. First, with the consideration of backlash, transmission error, time-varying mesh stiffness, and layout parameters, the dynamic model of geared rotor bearing system featuring confluence transmission was proposed. The nonlinear oil-film forces were computed with the Reynolds equation for finite-length journal bearings. Second, the responses of meshing vibration and bearing vibration were discussed. The numerical results revealed that the system exhibited a diverse range of periodic, sub-harmonic, and chaotic behaviors. Under different ranges of rolling frequency, the system got into chaos state through different roads. Moreover, in lower frequency, meshing vibration showed coexist of different periodic motions. Lastly, couplings of nonlinear oil-film force and nonlinear gear mesh force were discussed through a range of rolling frequencies. Gear-bearing dynamic interactions were demonstrated through the analysis of dynamic gear loads and dynamic bearing loads, and the coupling effect behaved different when rolling frequency changed.     

Robust control for MIMO hybrid dynamical system of underwater vehicles by composite adaptive fuzzy estimation of uncertainties

An organization structure of global oscillation with respect to a cracked rotor system with oil-film force is investigated in this paper. We profit from GPU cluster parallel computing to present a number of high-quality phase diagrams, and exhibit global dynamic characteristics of the system. An interesting scenario, “eye” of chaos, is discovered in this cracked rotor system, emerging as the accumulation limit of forward and reverse period-doubling bifurcation cascades. In this system, it is a common phenomenon that the vibration response of the rotor presents three typical characteristics in parameter space with the rotation speed increasing. Moreover, these phase diagrams assist us to identify multi-attractor coexisting that makes the dynamics behavior of this system become more enrich and complex. These results we represent get us better to understand the nonlinear response of the cracked rotor system and are beneficial to control and diagnose the crack.     

Dynamics and stability of turbocharger rotors

The paper discusses the bifurcation and stability behavior of (automotive) turbochargers with full-floating ring bearings. Turbocharger rotors exhibit a highly nonlinear behavior due to the nonlinearities introduced by the floating ring bearings. A flexible multibody model of the rotor/bearing system is presented. Numerical run-up simulations are compared with corresponding test rig measurements. The nonlinear oscillation effects are thoroughly investigated by means of simulated and measured rotor vibrations. The influence of various system parameters on the bifurcation behavior of the rotor/bearing system is analyzed. The article examines rotors supported in full-floating ring bearings with plain circular bearing geometry in the inner and outer oil gap. By recapitulating the well-known oil whirl and oil whip phenomena for single and double oil film bearings, the paper gives an overview on the fundamental dynamic effects occurring in turbocharger systems.     

Effects of thermo hydrodynamic (THD) floating ring bearing model on rotordynamic bifurcation

This paper introduces a numerical scheme for simulating instabilities of a nonlinear rotordynamic system including thermal effects in the fluid film bearings. The method utilizes shooting/arc-length continuation, and simultaneous, finite element based solutions of the variable viscosity Reynolds equation and the energy equation. This provides a means to investigate the effects of the thermo-hydrodynamic THD model on bifurcations and nonlinear rotordynamic stability. A “Jeffcott” type rigid rotor is modeled as supported on double-layered fluid film, floating ring bearings (FRB). The FRB are known to produce highly nonlinear forces as functions of relative and absolute internal displacements and velocities. Both autonomous (free vibration) and non-autonomous (mass unbalanced excitation) cases and algorithms are presented. The computational workload and execution time required for determining coexisting periodic solutions is significantly reduced by employing deflation and parallel computing methods. The THD model nonlinear responses and bifurcation diagrams are compared with isoviscous model results for various lubricant supply temperatures. The autonomous case, THD model orbit sizes and onset of Hopf and saddle–node bifurcations for coexisting steady state responses, may have significant differences relative to the isothermal model results. The onset of Hopf bifurcation is strongly dependent on thermal conditions, and the saddle–node bifurcation points are significantly shifted compared to the isothermal model. This tends to increase the likelihood of bifurcation from a machine operators standpoint. In the non-autonomous case, large unbalance forces create sub-synchronous and quasi-periodic responses at low spin speeds. The responses stability and onset of bifurcations of these responses are highly reliant on the lubricant supply temperature.     

Numerical and experimental analysis of the first-and second-mode instability in a rotor-bearing system

Aiming at the oil film instability of the sliding bearing at high speeds, a rotor test rig is built to study the non-linear dynamic behaviours caused by the first- and second-mode instability. A lumped mass model (LMM) of the rotor system considering the gyroscopic effect is established, in which the graphite self-lubricating bearing and the sliding bearing are simulated by a spring–damping model and a nonlinear oil film force model based on the assumption of short bearings, respectively. Moreover, a finite element model is also established to verify the validity of the LMM. The researches focus on the effects of two loading conditions (the first- and second-mode imbalance excitation) on the onset of instability and nonlinear responses of the rotor-bearing system by using the amplitude–frequency response, spectrum cascade, vibration waveform, orbit, and Poincaré map. Finally, experiments are carried out on the test rig. Simulation and experiment all show that oil film instability can excite complicated combination frequency components about the rotating frequency and the first-/second-mode whirl/whip frequency.     

Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow

A general model of a rub-impact rotor-bearing system with initial permanent bow is set up and the corresponding governing motion equation is given. The nonlinear oil-film forces from the journal bearing are obtained under the short bearing theory. The rubbing model is assumed to consist of the radial elastic impact and the tangential Coulomb type of friction. Through numerical calculation, rotating speeds, initial permanent bow lengths and phase angles between the mass eccentricity direction and the rotor permanent bow direction are used as control parameters to investigate their effect on the rub-impact rotor-bearing system with the help of bifurcation diagrams, Lyapunov exponents, Poincaré maps, frequency spectrums and orbit maps. Complicated motions, such as periodic, quasi-periodic even chaotic vibrations, are observed. Under the influence of the initial permanent bow, different routes to chaos are found and the speed when the rub happens is changed greatly. Corresponding results can be used to diagnose the rub-impact fault in this kind of rotor systems and this study may contribute to a further understanding of the nonlinear dynamics of such a rub-impact rotor-bearing system with initial permanent bow.