Transient Thrust Analysis of Rigid Rotors in Forward Flight

The purpose of this study was to investigate and quantify the transient thrust response of two small rigid rotors in forward flight. This was accomplished using a distributed doublet-based potential flow method, which was validated against wind-tunnel experimentation and a transient CFD analysis. The investigation showed that for both rotors, advancing and retreating blade effects were predicted to contribute to transient thrust amplitudes of 5–30% of the mean rotor thrust. The thrust output amplitudes of individual rotors blades were observed to be 15–45% of the mean rotor thrust, indicating that it is not uncommon for the thrust output variation of an individual rotor blade to approach the same value as the mean thrust output of the rotor itself. In addition to this, the theoretical analysis also illustrated that higher blade thrust oscillations resulted in pronounced asymmetric rotor wake structures.

Nonlinear dynamic response and bifurcation of asymmetric rotor system supported in axial-grooved gas-lubricated bearings

Dynamic characteristics of the asymmetric rotor system supported in axial-grooved gas-lubricated bearings are studied. In order to solve nonlinear dynamic response of rotor system effectively, a hybrid numerical model is established by coupling the motion equation of rotor with the rational function model of the gas film forces. The rational function model of the gas film forces of gas-lubricated bearing is established based on vector fitting theory. By using the hybrid numerical model, the repeated calculations of the unsteady Reynolds equation and gas film forces are avoided; the continuous rotor trajectory and the dynamic gas film forces can be calculated simultaneously; and for the rotor system supported in the same bearings, the computing cost can be saved effectively. The nonlinear dynamic responses of asymmetric rotor system supported in axial-grooved gas-lubricated bearings are investigated by trajectory diagrams, frequency spectrum, Poincaré maps, and time series. The bifurcations are analyzed by the bifurcation diagrams with different rotating speeds and mass eccentricities. The dynamic behaviors of the asymmetric rotor system appear complex nonlinear dynamic phenomenon and specific bifurcation characteristics.

Torque ripple optimization for synchronous reluctance motors based on a virtual permanent magnet harmonic machine model

The torque ripple is affected by both the stator and the rotor magnetic field harmonics. In synchronous reluctance motors (SynRM), there are only rotor permeance harmonics existing on the rotor side for the absence of the rotor windings. Since the asymmetric rotor flux barriers are widely applied in the SynRM rotor, it is difficult to calculate the rotor permeance accurately by the analytical method. In this article, the effects of the rotor permeance harmonics on the air-gap magnetic field are studied by a virtual permanent magnet harmonic machine (VPMHM), which is a finite-element (FE) based magnetostatic analysis model. The air-gap flux density harmonics produced by the SynRM rotor are extracted from the VPMHM model and used as the intermediate variables for the torque ripple optimization. The proposed method does not need to solve the transient process of motor motion. Hence, the time of the optimization process can be significantly shortened. Finally, a full electric cycle is simulated by dynamic FE simulation, and the torque ripple is proved to be effectively reduced.

Rub-Impact Force Induces Periodic, Quasiperiodic, and Chaotic Motions of a Controlled Asymmetric Rotor System

This article aims to explore the oscillatory characteristics of a controlled asymmetric rotor system when subjected to rub and impact forces between the rotor and stator. Four electromagnetic poles are used to control the whirling motion of the rotor system through a linear proportional-derivative control law. The equations of motion that govern the whole system dynamics are derived including the rub and impact forces. The derived mathematical model is analyzed in two basic steps. Firstly, the obtained model is treated as a weakly nonlinear system using perturbation analysis to obtain the slow-flow modulating equations when neglecting the rub and impact forces. Depending on the obtained slow-flow equations, different response curves are plotted to explore the system’s periodic vibrations and determine the conditions at which the system can exhibit rub and impact force. Secondly, the whole system model including the rub and impact forces is investigated by using the bifurcation diagrams, Poincare map, frequency spectrums, and temporal oscillations. The obtained results revealed that the applied control law could mitigate the system whirling oscillations and prevent the rub and impact forces if the control gains are tuned properly. However, the system can perform period-n, quasiperiodic, or chaotic motion depending on the shaft spinning speed if the controller fails to eliminate the contact between the rotor and stator.

Predicting unbalance asymmetric rotor vibration behavior based on sensitivity analysis and using Response Surface Methodology method considering parallel misalignment

Mass unbalance, shaft misalignment, rotor asymmetry, and force due to rotor weight are the main causes of vibrations in rotary machines especially when the shaft is not symmetric. Although extensive researches have been carried out to determine the effect of each on the increase of vibration levels far, there has been no clear study on the simultaneous existence of all these parameters and their interactions. In this research, the model is a rotor composed of a rigid disk and a flexible asymmetric shaft. The general equations of motion are first derived by considering the effect of high order large deformation in bending. The equations are discretized using the Rayleigh–Ritz method. The obtained equations are nonlinear coupled differential equations that are solved using the numerical method. Sensitivity analysis has been utilized to identify the percentage of the contribution of each parameter to the increase of vibration. Then a DOE-based Response Surface Methodology (RSM) is applied to present a model to predict the vibration behavior of the system with good accuracy. Genetic algorithm is also used to optimize the effective parameters and to verify the results. A 3D model of the asymmetric rotor is carried out in experimental studies to attain more precise responses. The research shows that rotor asymmetry alone and also its combination with gravitational force has much more effects on the vibration amplitude. These effects are observed at frequencies both once and twice the rotational speed in spectral data, in comparison with other factors. The mass unbalance also plays a significant role in frequency equal to the rotational speed. In the end, the achieved results are validated with experimental simulations.

Multistage Asymmetric Rotors Coaxial Measurement Stacking Method Based on Minimization of Exciting Force

The unbalanced exciting force of high-speed rotary asymmetric rotor equipment is the main factor causing rotor vibration. In order to effectively suppress the vibration of the asymmetric rotor equipment, the paper establishes a multistage asymmetric rotor coaxial measurement stacking method that minimizes the exciting force. By analyzing the propagation process of the centroid of the multistage asymmetric rotor assembly and analyzing the relationship between the geometric center and the centroid of a single asymmetric rotor, a multistage asymmetric unbalanced rotor propagation model based on geometric center stacking is established. The genetic algorithm is used to optimize the unbalance of the multistage asymmetric rotors. Combined with the vibration principle under the exciting force, the vibration amplitude of the left bearing at different rotation speeds under the minimization of the exciting force and the random assembly phase is analyzed. Finally, the experimental asymmetric rotors are dynamically measured, combined with the asymmetric rotors’ geometric error measurement experiment. The experimental results confirm that the vibration amplitude of the assembly phase with the minimum exciting force is smaller than the vibration amplitude under the random assembly phase at three-speed modes, and the optimization rate reached 73.2% at 9000 rpm, which proves the effectiveness of the assembly method in minimizing the exciting force.