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Active bump-type foil bearings (ABFBs) enhance the rotordynamic characteristics of rotor–bearing systems with the advantage of controllable mechanical preloads. However, the coupling of controllable mechanical preloads, compressible gas film, and foil structures induce strong nonlinear characteristics and affect the dynamic responses of rotor. In this study, a nonlinear theoretical model that considers the gyroscopic effect of rotor, nonlinear Reynolds equation, complicated foil structures, and dynamic motions of active substructures is presented. This model is verified by a corresponding rotordynamic test. The nonlinear dynamic responses of a rotor–ABFB system are discussed on the basis of waterfall plots, orbit simulations, and Poincaré maps of rotor center, fast Fourier transform, minimum film thickness, and power loss during one cycle of journal orbit. The effects of voltage on piezoelectric actuators, nominal clearance, width of flexure hinge, and static load on the nonlinear rotordynamic responses of rotor are analyzed to provide guidelines on selecting the design and control parameters of rotor–ABFB systems.

Linearized dynamic bearing coefficients are commonly used to determine the vibration response of rotors supported by journal bearings. Journal bearings can, however, behave nonlinearly, particularly in the presence of bearing wear. This work was undertaken to examine the effect of bearing wear severity on the linear and nonlinear responses of a rigid rotor at low, moderately, and highly loaded operating regime. Numerical results showed that the center of the nonlinear orbit coincides with the center of the linear orbit for all three operating regimes in non-worn bearing. However, in worn bearings, the center of the nonlinear orbit shifts away from the center of the linear orbit for all three operating regimes. The nonlinear analysis also showed that super-synchronous vibration response may occur, particularly at highly loaded operating regimes and at the maximum wear depth investigated in this work.

Magnetic bearings are widely used in engineering for their remarkable advantages of low friction, no wear and high speed. In this paper, the dynamics and control of the magnetic bearing-rigid rotor system under the influence of multisource stochastic factors are studied. Firstly, a model of magnetic bearing-rigid rotor system driven by multiplicative noise and additive noise is established. Secondly, the stationary response probability density function (PDF) of the proposed magnetic bearing system is obtained by using the amplitude envelope stochastic average method. Then we analyze the influence of different system parameters and noise intensity on the magnetic bearing-rigid rotor system, and find that internal stochastic factors are the main factors affecting the stability of the bearing system. Finally, the fractional Proportional Integral Derivative (PID) control of the system is studied. Based on the numerical analysis, we verify the effectiveness of the control strategy and draw the conclusion that adjusting appropriately the parameters of fractional PID controller can make the magnetic bearing system control better.

Purpose Misalignment is one of the serious faults that occur in rotating machinery. This fault may be caused by the offset between the axis of the supported shaft and the bearings axis or the offset between two coupled shafts. Excessive vibration can be developed in the machines due to the misalignment fault, which can result in the breakdown of the complete machine. Therefore, there is a need to explore and analyze the vibrational behavior of a faulty rotor-bearing system and identify the fault for the untroubled performance of machines. Methods An innovative virtual trial misalignment approach based on trial bias current is proposed to study the dynamics of an unbalanced rigid rotor misaligned with the supported active magnetic bearings and eddy current proximity displacement sensors. The same approach has been also utilized to identify the residual offset amounts of displacement sensors located at active magnetic bearing locations. Results Numerical results are obtained by solving the system’s equations of motion on SIMULINKTM platform. The results demonstrate that the displacement and current signals are sinusoidal in nature due to the presence of unbalanced force. Moreover, the size of orbital responses gets enhanced with increments in the misalignment level and noise signal errors. The virtual trial misalignment strategy could also identify the offset amounts of sensors. Conclusions This paper proposes a virtual trial misalignment approach to analyze the effects of unbalance and AMBs as well as sensor residual misalignments on rotating machinery integrated with active magnetic bearings. For executing this motive, a rigid rotor linked with two discs (at offset positions) mounted on two misaligned AMBs at the end locations is considered and mathematically modeled. The dynamic effect of AMB and sensor residual misalignment on the vibrating nature of the rotor is presented for different misalignment levels, at a single spin speed of the rotor as well as ramp-up speed. The residual misalignments of eddy current proximity sensors are also identified with the help of mathematical modeling of misaligned sensors and virtual trial misalignments of the rotor. The proposed method is found to be more reliable and efficient as compared to traditional approaches for the identification of faults.

A precise characterization of molecular vibrations and thermodynamic properties is essential for applications in spectroscopy, computational modeling, and chemical process design. In this study, the q-deformed Tietz (qDT) oscillator is applied to examine vibrational energy spectra of diatomic molecules and thermodynamic properties of nonlinear symmetric triatomic molecules. Vibrational energy eigenvalues were obtained analytically using the improved Nikiforov-Uvarov method. The symmetric vibrational mode was described with the qDT oscillator, while asymmetric and bending modes were modeled using the rigid rotor harmonic oscillator (RRHO); translational and rotational contributions were incorporated from standard models. For diatomic molecules (BrF, CO+, CrO, ICl, KRb, NaBr), mean absolute percentage errors (MAPE) ranged from 0.53% to 1.73% for vibrational energy eigenvalues and 0.34% to 1.08% for potential fits. Extending the analysis to triatomic molecules, thermodynamic properties of AlCl2, BF2, Cl2O, OF2, O3, and SO2 were calculated with the qDT model, yielding low MAPE benchmarked against NIST-JANAF reference data: entropy 0.203% to 0.614%, enthalpy 1.792% to 5.861%, Gibbs free energy 0.419% to 1.270%, and constant-pressure heat capacity 1.475% to 4.978%. These results demonstrate the versatility and accuracy of the qDT oscillator as an analytical framework connecting molecular potentials, vibrational energies, and thermodynamic functions, providing a practical and tractable approach for modeling both diatomic and symmetric triatomic systems.

Energy levels for DNh-symmetrical cyclic polyenes with planar aromaticity were obtained using two-dimensional (2D) rigid rotor as the zeroth approximation. The addition of nuclei was simulated by the cosine-type potential and treated at the first-order perturbation theory. The result is qualitatively equivalent to that obtained using Hückel’s molecular orbital theory. As an addition, the energetic shift between σ and π orbitals is obtained using the model of electron oscillating around the center of a positively charged ring.

The controlled dynamics of the rotor of an axial pump arranged in conical active magnetic bearings is studied. Bearings of this type make it possible to miniaturize the geometry of the rotor suspension structure, which is an important factor when designing ann auxiliary mechanical blood circulation apparatus. In such facilities, the problem of rotor positioning plays an important role. The essence of this work is in selecting the control coefficients of proportional-integral-differential control to stabilize the rotor.

The pop-up progress of the coaxial rigid rotor helicopter was decomposed into 5 stages. Quasi-steady flow assumption was adopted to analyze the helicopter performance. XH-59A helicopter was regarded as a solid body. Flow interactions between fuselage and rotor, rotor and tail were ignored. The aerodynamic performance of coaxial rotor, fuselage and horizontal tail were calculated based on Blade element moment theory, wind tunnel test data and theoretical calculation correspondingly. The Pitt/Peters inflow model was used to represent the inflow velocity on the rotor and flow interaction between upper and lower rotor were considered using interference factor. The net force and moment on the helicopter was derived and formulated into flight mechanics equations. To validate the calculation, a wind tunnel test of a coaxial rigid rotor helicopter was employed. The rotor lift coefficient, helicopter pitching and rolling moment coefficients were close to the experimental data. The controlled variables of the helicopter was composed of helicopter pitch angle (shaft angle), collective pitch, cyclic pitch of both rotors, deflection angle of the horizontal tail during the pop-up progress. The mathematical model presented in this paper provides the basic system structure to analyze the pop-up progress. The required power of the helicopter were formulated with altitude, rotor thrust, flight velocity, which help to obtain a rapid and primary evaluation of the integral performance of the progress.

This study develops a hybrid solver with reversed overset assembly technology (ROAT), a viscous vortex particle method (VVPM), and a CFD program based on the URNS method, in order to study the aerodynamic and acoustic characteristics of coaxial rigid rotors. The aerodynamic load of the “AH-1G” helicopter rotor is first calculated based on the hybrid method and compared with available experimental data. The prediction of the linear noise of the OLS rotor is then performed and the obtained results are compared with available experimental data. These results allow the evaluation of the accuracy of the hybrid method for emulating rotor aerodynamics and acoustics. Afterwards, the hybrid and CFD methods are applied to obtain the aerodynamic and acoustic characteristics of the given coaxial rigid rotor model, while taking into account the trim of the collective pitch. The obtained results demonstrate that the hybrid method has high proficiency in capturing blade–vortex-interaction impulsive loads and high computational efficiency in predicting associated loading noise characteristics. Furthermore, the effect of the hybrid method on the noise characteristics of coaxial rigid rotors under a different advance ratio, blade tip speed, shaft angle, and other conditions, as well as the impact of the upper and lower rotors on the noise contribution of the coaxial rotor are analyzed. Finally, the impacts of the initial phase and the vertical spacing on the sound pressure level are studied.

The main helium circulator is the core component of the High Temperature Reactor (HTR). Mechanical machining errors and assembly errors can cause uneven distribution of rotor mass. When the rotor rotates, the unbalanced mass will generate unbalanced force which will change the rotor's axis trajectory. By coupling the rotor dynamics method and the electromagnetic bearing system control theory, the motion of the rotor is modeled. Three representative unbalanced conditions of the impeller position, the bearing position and the centroid position are assumed to simulate the unbalance response of the rotor, and the influence of changes in the stiffness and damping on the unbalance response of the rotor is analyzed by adjusting the stiffness and the damping of the rotor. The results of the analysis show that the bearings farther from the unbalanced position (UBP) have larger rotor displacements and bearing loads. Increasing Active Magnetic Bearings (AMBs) stiffness and damping will increase the bearing load and reduce the response displacement of the rotor. Therefore, the stiffness and damping of AMBs must be designed by considering the bearing capacity and the displacement limit of the rotor.