Bio: Qihan Li is an academic researcher from Beihang University. The author has contributed to research in topics: Natural frequency & Parametric statistics. The author has an hindex of 6, co-authored 9 publications receiving 87 citations.
TL;DR: In this paper, the existence of rub-impact periodic motions in an eccentric rotor system is considered and a criterion for the periodicity condition of n-periodic impacts is derived and other conditions for real rub impacts are also discussed.
Abstract: The existence of rub-impact periodic motions in an eccentric rotor system is considered. A criterion for the periodicity condition of n-periodic impacts is derived and other conditions for real rub-impacts are also discussed. A method consisting of analytical and numerical techniques is presented to solve the existence problem of rub-impact periodic motions. Some special results are obtained by theoretical analyses for rub-impact rotor systems, including the existence of grazing circle motions and that of single-impact periodic motions.
01 Aug 2009
TL;DR: In this article, a torsional parametric vibration model for a spur gear pair system is established and the periodically time-varying mesh stiffness is approximated linearly by trapezoidal waveforms and rectangular waves.
Abstract: In spur gear dynamic analysis, rectangular waves are often used to approximate the mesh stiffness alternating between one and two pairs of teeth in contact. But in actual practice, extended tooth contact (ETC) occurs due to gear tooth deflection under load. Considering the effect of ETC, the mesh stiffness in the pre-mature and post-mature contact regions is gradually rather than abruptly varying with time, which would influence the parametric stability of the geared system significantly. Therefore, research on parametric stability for a spur gear pair system considering the effect of ETC is carried out in this article. First, a torsional parametric vibration model for a spur gear pair system is established and the periodically time-varying mesh stiffness is approximated linearly by trapezoidal waveforms (with the effect of ETC) and rectangular waves (without the effect of ETC). Then, the Floquet theory for stability analysis (including two key elements: one is the derivation of state transition m...
TL;DR: In this article, intentional and random mistuning is introduced into a simplified 12-bladed disk model by varying the stiffness of the blades, and the combined effects of intentional mistuning, damping and coupling are examined.
Abstract: Blade-to-blade mistuning is always inevitable in bladed disk assemblies due to imperfections in the manufacturing progress as well as wear during operation. As a result, the forced response of a mistuned bladed disk may be drastically larger than that of the nominal or tuned design. The attendant increase in stress can lead to premature high cycle fatigue (HCF) of the blades. Therefore, it is of great importance to predict and, ultimately, to reduce the blade forced response levels caused by mistuning. In this paper, intentional and random mistuning is introduced into a simplified 12-bladed disk model by varying the stiffness of the blades. The combined effects of intentional mistuning, damping and coupling are examined. The numerical results indicate that there is some threshold value of intentional mistuning and coupling that leads to maximum mistuning effects and certain relations among intentional mistuning strength, integer harmonics, damping and coupling can suppress the response levels of bladed di...
TL;DR: In this article , the authors investigated the energy-conversion stability of hydropower energy conversion and provided a technical solution for fluid-induced vibration detection, which is critical to satisfy the growing demand for electricity.
Abstract: The energy-conversion stability of hydropower is critical to satisfy the growing demand for electricity. In low-head hydropower plants, a gravitational surface vortex is easily generated, which causes irregular shock vibrations that damage turbine performance and input-flow stability. The gravitational surface vortex is a complex fluid dynamic problem with high nonlinear features. Here, we thoroughly investigate its essential hydrodynamic properties, such as Ekman layer transport, heat/mass transfer, pressure pulsation, and vortex-induced vibration, and we note some significant scientific issues as well as future research directions and opportunities. Our findings show that the turbulent Ekman layer analytical solution and vortex multi-scale modeling technology, the working condition of the vortex across the scale heat/mass transfer mechanism, the high-precision measurement technology for high-speed turbulent vortexes, and the gas–liquid–solid three-phase vortex dynamics model are the main research directions. The vortex-induced vibration transition mechanism of particle flow in complex restricted pipelines, as well as the improvement of signal processing algorithms and a better design of anti-spin/vortex elimination devices, continue to draw attention. The relevant result can offer a helpful reference for fluid-induced vibration detection and provide a technical solution for hydropower energy conversion.
TL;DR: In this paper, the effects of the design parameters of an electromagnetic device on the instability of a cantilever beam with one or two electromagnetic excitations were studied experimentally and analytically.
Abstract: An electromagnetic device, acting like a spring with alternating stiffness, has been designed to parametrically excite the cantilever beam. However, only one parametric excitation (induced by one electromagnetic device) was considered in current research, and the effects of the design parameters of the device upon the instability were studied inadequately. Actually, multiple parametric excitations with various phases and amplitudes would bring significant impacts to the system instability. The electromagnetic device with various design parameters could cause the unstable regions to change evidently. Thus, the parametric instability of a cantilever beam subjected to two electromagnetic excitations is studied experimentally and analytically in the paper. The governing equations for the beam system are established utilizing the assumed mode method, and then verified through a DC current test. Based upon these, the instability experiments for the cantilever beam with one or two electromagnetic excitations are conducted in detail. Two design parameters of the device (magnet spacing and device location) are investigated, respectively, for their effects upon the instability regions. When two electromagnetic devices operate together to bring two parametric stiffness excitations with various phases and amplitudes to the cantilever beam, the variations of both simple and combination instability regions with coil current are observed and discussed. The above experimental results are all found to agree well with the analytical ones.
TL;DR: In this paper, an improved analytical method (IAM) suitable for gear pairs with tip relief is established to determine time-varying mesh stiffness (TVMS), where the effects of ETC, nonlinear contact stiffness, revised fillet-foundation stiffness, and tooth profile modification are considered.
Abstract: Due to the effects of gear flexibility, the extended tooth contact (ETC) can appear, which is the phenomenon that the incoming tooth pair gets into contact ahead of the theoretical start of contact and the outgoing tooth pair is out of contact later than the theoretical end of contact. A large calculation error for the time-varying mesh stiffness (TVMS) calculation can be caused if the effects of ETC are ignored, especially under the larger torques. In this paper, an improved analytical method (IAM) suitable for gear pairs with tip relief is established to determine time-varying mesh stiffness (TVMS), where the effects of ETC, nonlinear contact stiffness, revised fillet-foundation stiffness, and tooth profile modification are considered. Based on the improved analytical model, TVMS under different torques, lengths, and amounts of profile modification is compared with that obtained from analytical finite element approach  and from FE method. The results show that TVMS obtained from the IAM agrees well with that from FE method and from analytical FE approach , and the computational efficiency of the IAM is also much higher than that of FE method.
TL;DR: Considering the effects of the extended tooth contact and tooth root crack on the time-varying mesh stiffness (TVMS), a finite element (FE) model of a spur gear pair in mesh is established by ANSYS software as mentioned in this paper.
Abstract: Owing to the effect of gear flexibility, the extended tooth contact occurs, which is a phenomenon that the incoming tooth pair enters contact earlier than the theoretical start of contact, and the outgoing tooth pair leaves contact later than the theoretical end of contact. Considering the effects of the extended tooth contact and tooth root crack on the time-varying mesh stiffness (TVMS), a finite element (FE) model of a spur gear pair in mesh is established by ANSYS software. TVMS under different crack depths at constant rated torque (60 Nm) are calculated based on the FE model. Then, a FE model of a geared rotor system is developed by MATLAB software. Frequency-domain features, statistical features (Kurtosis and RMS) and instantaneous energies based on empirical mode decomposition (EMD) under different crack depths are calculated at 1000 rev/min and the corresponding measured results are also performed by model experiment. The results show that considering the effect of extended tooth contact, TVMS of crack gear pair becomes smooth from double-tooth engagement to single-tooth engagement; the gear crack has reduced the gear body rigidity, which leads to the reduction of stiffness of the healthy teeth and has little effect on the vibration response. The instantaneous energy can be chosen as a distinguishing indicator to qualitatively diagnose the gear cracks with different levels.
TL;DR: In this article, Ma et al. presented an improved analytical model for the time-varying mesh stiffness (TVMS) calculation of cracked spur gears, and compared the IAM, traditional analytical model (TAM) and finite element (FE) model under different torques and crack depths.
Abstract: Based on our previous work (Ma et al., 2014, Engineering Failure Analysis , 44, 179–194), this paper presents an improved analytical model (IAM) for the time-varying mesh stiffness (TVMS) calculation of cracked spur gears. In the improved analytical model, the calculation error of TVMS under double-tooth engagement due to repeatedly considering the stiffness of the fillet-foundation is revised, and the effects of reduction of fillet-foundation stiffness of cracked gears and extended tooth contact (ETC) are also considered, which have a great influence on TVMS, especially under the condition of large torques and crack levels. Moreover, the comparisons among the IAM, traditional analytical model (TAM) and finite element (FE) model are also carried out under different torques and crack depths. IAM is also verified by comparing TVMS and vibration responses obtained by FE model, which can be considered as a gauge to evaluate the calculation error. The results show that the maximum error of IAM is about 12.04%, however, that of TAM can be up to 32.73%.
TL;DR: In this article, an extended Jones-Harris stiffness model is presented to ascertain the stiffness of the angular contact ball bearing considering five degrees of freedom, and the effects of unbalanced force, bearing loads and damping on the instability regions are discussed thoroughly.
Abstract: Previous investigations have indicated that the finite number of balls can cause the bearing stiffness to vary periodically. However, effects of unbalanced force in a rotor–bearing system on the bearing stiffness have not received sufficient attention. The present work reveals that the unbalanced force can also make the bearing stiffness vary periodically. The parametric excitations from the time-varying bearing stiffness can cause instability and severe vibration under certain operating conditions. Therefore, the determination of the operating conditions of parametric instability is crucial to the design of high speed rotating machinery. In this paper, an extended Jones–Harris stiffness model is presented to ascertain the stiffness of the angular contact ball bearing considering five degrees of freedom. Stability analysis of a rigid rotor–bearing system is performed utilizing the discrete state transition matrix (DSTM) method. The effects of unbalanced force, bearing loads and damping on the instability regions are discussed thoroughly. Investigations mainly show that the time-varying bearing stiffness fluctuates sinusoidally due to finite number of balls and unbalanced force. The locations and widths of the instability regions caused by these two parametric excitations differ distinctly. Unbalanced force could change the widths of the instability regions, but without altering their central positions. The axial and radial loads of the bearing only change the positions of the instability regions, without affecting their widths. Besides, damping can reduce the widths of the instability regions.
TL;DR: In this article, an asymmetric support stiffness matrix with cross-coupling between the x and y direction stiffnesses is presented, and the influence of support asymmetry on nonlinear rotor response is shown using rotor orbits, frequency spectra, Poincare sections, and bifurcation diagrams.
Abstract: The efficiency of rotating machines can be improved via precisely manufactured bearings with reduced clearances; consequently, the proclivity for rotor–stator contact is increased. A common model used to investigate rotor–stator contact in previous studies is the two degree-of-freedom (DOF) rotor with symmetric support stiffness, where the contact assumes a linear elastic normal restoring force proportional to the rotor–stator interference and a tangential dry Coulomb friction force. Switching between the contacting and non-contacting states creates strong nonlinearity in the equations of motion, and the dynamic response displays a rich profile of behaviors including periodic, quasiperiodic, and chaotic responses via period-doubling, sudden transitions, quasiperiodicity, and intermittency. For the first time, this work emphasizes an asymmetric support stiffness matrix with cross-coupling between the x and y direction stiffnesses. The influence of support asymmetry on the nonlinear rotor response is shown using rotor orbits, frequency spectra, Poincare sections, and bifurcation diagrams. It is found that the cross-coupling stiffness coefficient kxy has negligible effect on the dynamic response until its magnitude is on the same order as the direct stiffness coefficients. Direct stiffness coefficient asymmetry is shown to affect the rotor׳s response, where even small asymmetries can qualitatively change the response. Additionally, the importance of including gravity is investigated, and a method is provided for determining the threshold shaft speed above which gravity can be ignored. The dominant route to chaos is period-doubling for the parameters considered here, though other routes to chaos are seen such as a direct transition from periodic to chaotic motion. Finally, observations pertaining to rotor modeling, design, and fault diagnostics are discussed.