Response Of Rotor Research Articles

Numerical Study on Aerodynamic and Noise Responses of Rotor with Ramp Increase in Collective Pitch Based on Time-Accurate Free-Wake Method

Research on helicopter transient maneuvering flight noise is a hotspot and challenging topic in the fields of helicopter design and application. A new time-accurate free-wake (TAFW) method and the Fowcs Williams-Hawkings (FW–H) equations are applied to analyze the aerodynamic and noise responses of a rotor subjected to a ramp increase in collective pitch, in hover, and in forward flight. First, a TAFW algorithm suitable for rotor aerodynamic simulation in steady-state flight and transient maneuvers is developed using modified third-order upwind backward differentiation formulas. Then, to verify the effectiveness and accuracy of the proposed method, various parameters are calculated for two scenarios and compared with corresponding results from experiments by the University of Maryland: the Langley 2MRTS rotor and the NACA rotor with ramp increases in collective pitch. Finally, the influence of collective pitch increase rate, the total increase of collective pitch, and the start and stop azimuth of ramp increase on the aerodynamic and loading noise responses of the rotor are analyzed in hover and forward flight conditions. The results show the ramp increase in collective pitch will affect the loading noise in three timescales: short-term, medium-term, and long-term. The change of the loading noise is greater when the collective pitch increase rate is greater, and the start and stop azimuth angles of the ramp increase are also important factors affecting the aerodynamic load distribution and directionality of the noise.

Nonlinear Dynamic Responses of Rigid Rotor Supported by Thick Top Foil Bearings

This study focuses on thick top foil bearings (TTFBs), which can prevent top foil from sagging and significantly reduce the load capacity of gas foil bearings (GFBs). However, the limited research on the dynamic responses of TTFB-rotor systems has hindered their wide application of TTFBs with high load capacity. To address this, an integrated nonlinear dynamic model is developed to analyze the linear dynamic responses of a rigid rotor supported on TTFBs. The model incorporates time domain orbit simulation, considering unsteady Reynolds equations, foil deformation equations, thick top foil motion equations, and rotor motion equations. A symmetrical test rig is used to validate the model, and three types of TTFBs with different bump foil stiffness are tested, with experimental results aligning with the model predictions. This study also investigates the effects of nominal clearance, static load, and unbalance on TTFB-rotor systems. The results indicate that unbalance has minimal impact on subsynchronous vibrations. However, larger bump foil stiffness, increased normal clearance, and higher static load contribute to improved stability and higher maximum stable speed of the TTFB-rotor system. Moreover, other relevant parameters reducing the bearing attitude angle can further enhance the system’s stability.

Finite element analyses of rotor/bearing system using second-order journal bearings stiffness and damping coefficients

The rotor-bearing system is a crucial component of rotating machinery, such as turbines, pumps, compressors, and turbogenerators, which are widely used in various advanced engineering fields. This work presented a methodology for studying the behavior of an elastic Jeffcott rotor supported by two similar fluid film journal bearings. A finite element model using consistent matrix formulation was employed to simulate the shaft, including the external load, with four degrees of freedom per node. The small perturbation method was used to evaluate the second-order bearing coefficients of a journal bearing of finite length. These coefficients were further integrated with the finite element model to evaluate the dynamic response of the flexible rotors. Moreover, the system equations of motion were presented in dimensional form. The results of the second-order bearing coefficients analysis agreed with nonlinear analysis when the speed was less than the threshold speed, while there was a pronounced difference in second-order analysis when the speed was above the threshold speed. The behavior of the rotor-bearing system was studied using dynamic response and orbit diagrams, revealing that changes in rotational speed significantly affected the rotor’s stability.

Simplified transformation matrices of journal bearings in vertical application

Rotodynamic simulation of complex or/and large systems, for instance hydropower machines, may consist of models with many degrees of freedom and require multidisciplinary computations such as fluid-thermal-structure interactions or rotor-stator interactions due to electromagnetic forces. Simulating such systems is often computationally heavy and impractical, especially in the case of optimization or parametric study, where many iterations are required. This has, therefore, created a need for simplified dynamic models to improve computational efficiency without significantly affecting the accuracy of the simulation result. The purpose of this paper is to present simplified coordinate transformation matrices for journal bearings in vertical rotors, which require less computational effort. Matrix multiplications, which appear during coordinate transformation, were eliminated, and the bearing stiffness and damping matrices in the fixed reference frame were represented by local coefficients instead. The dynamic response of a vertical rotor with eight-shoe Tilting pad journal bearings was simulated using the proposed model for two operational conditions, i.e., when the rotor was spinning at constant and variable speeds. The results from the proposed model were compared to those from the original model and validated through experiments. The conclusion was that the presented simulation model is time efficient and can effectively be used in rotordynamic simulations and analyses.

Experimental and numerical investigation on the dynamic response of reactor coolant pump rotor under different inflow conditions

In pressurized water reactors, a reactor coolant pump (RCP) is crucial for circulating coolant through the primary loop. However, in advanced passive (AP) reactors, the steam generator and RCP are not connected by a long pipeline, creating a transition section that leads to a non-uniform inflow at the pump inlet. The non-uniform inflow can affect the operational status of a pump, which in turn affects the motion state of the rotor. In this study, the variation of the axis orbit under non-uniform inflow was analyzed through experiments, and it was found that the shape of the axis orbit had undergone significant changes, and the amplitude of the orbit had also increased significantly, particularly in the y direction, where it increased by 88.6%. Subsequently, a combined approach of pump computational fluid dynamics (CFD) analysis and rotor finite element analysis was used to analyze the cause of the axis orbit change. The study revealed the existence of a vortex with a pulsating frequency of approximately 16.4 Hz at the inlet of the non-uniform inflow. This vortex caused the impeller's attack angle to deviate from the design value, resulting in flow separation inside the impeller, an increase in the impeller's radial force, and radial force pulsation at the same frequency as the vortex. The change in the axis orbit was caused by the superposition of the rotor's unbalance mass and radial force pulsation under non-uniform inflow.

A Simplified Model for the On-Line Identification of Bearing Direct-Dynamic Parameters Based on Algebraic Identification (AI)

In this paper, a mathematical model is presented to identify the direct dynamic coefficients (kxx, kzz, cxx, czz) of a pressurized bearing in a rotor-bearing system. The presented mathematical model for online identification is the result of the application of the algebraic identification approach to a two-degree-of-freedom rotor-bearing model. The proposed identification model requires only the vibration response as the input data. The performance of the model was assessed by theoretically and experimentally testing the proposed identifier at different shaft frequencies and, for the experimental test, a pressurized bearing that has hydrodynamic and hydrostatic characteristics at a support pressure of 10 psi was considered. The working fluid is Chevron GST 32 oil. The results show negligible differences between the vibration response of the experimental rotor and those obtained numerically using the identified direct dynamic coefficients of the pressurized bearing. In addition, it is observed that the algebraic identifier determines the identified parameters in a time less than 0.2 s. The proposed identifier can be used in other types of bearings, which is a great advantage over other identifiers.

Research on the Influence of Rub-impact Buffer Stroke on the Dynamic Response of Two-section Rotor

The two-section rotor needs to go through multiple critical speeds in the process of speed increase. When the rotor approaches the critical speed, its amplitude increases rapidly, easily causing collision damage. The auxiliary over-critical device cushions and protects the rotor through rubbing, which makes it pass the critical speed under the safe amplitude. In this paper, the influence of buffer stroke, the key structural parameter of the auxiliary over-critical device, on the dynamic response of the two-section rotor at the first-order bending critical speed is analyzed, the influence of its buffer stroke on the over-critical dynamic response of the rotor is calculated and analyzed, and the impact and friction force on the rotor is calculated. The design principles and results of the buffer stroke parameters of the auxiliary supercritical device are proposed.

Dynamic modeling and analysis of high-speed aerostatic journal bearing-rotor system with recess

To analyze the dynamic properties of high-speed aerostatic journal bearing with recess, a bidirectional fluid-structure coupling dynamic model is established. The mathematical model is established by coupling the governing equation of the transient air film flow, the flow balance equation, and the rotor motion equation. Based on the trajectory of rotor axis, trajectory of rotor center, Poincare map, time response of rotor, frequency spectrum, mass flow rate, and bifurcation diagram, the influences of operating parameters on the coupling system are analyzed theoretically and experimentally. The results indicate that the system has abundant nonlinear behavior, and the instability parameters of the system are determined. This study provides guidance for the theoretical design and practical operation of this type of system.

A data driven method applied on nonlinear vibration of flexible rotor supported on centralized squeeze film damper

This paper discusses the application of Dynamic Mode Decomposition (DMD) on vibration response of flexible rotor supported by a Centralized Squeeze Film Damper (CSFD). The mathematics behind DMD and its applications to rotor vibration data such as linearization, reconstruction has been established. Vibration data from the flexible rotor system supported on CSFD exhibits both linear and nonlinear behavior. Further, DMD has been applied on periodic and quasi-periodic vibration data of CSFD for prediction and forecasting. DMD is observed to have successfully linearized a nonlinear system with the linear Henkel Matrix. The reconstruction and forecasting of time series data from rotor has been achieved with a maximum error of 0.2% even for nonlinear vibration data. Further, White Gaussian Noise has been intermixed with CSFD data to demonstrate the noise reduction capability of DMD method for nonlinear systems. Lastly, the application of DMD algorithm on experimental data from Jeffcott rotor based test setup has been shown.

Subcritical behaviour of short cylindrical journal bearings under periodic excitation

Rotating machinery supported on journal bearings is affected by forces due to rotating unbalance and pressure gradients in the oil film. The interaction of these forces can evoke nonlinear behaviour, including asynchronous motion and even chaos. This work attempts to characterise the sub-synchronous motion of the rigid rotor supported on cylindrical journal bearings due to the abovementioned interaction. The analysis focuses on the rotor behaviour at the rotor speeds lower than the threshold speed for oil whirl, associated with sub-synchronous vibration of magnitude equaling the bearing clearance. It is shown that the sub-synchronous vibration can occur well before reaching the threshold speed and that the underlying period-doubling bifurcation depends on the amount of the rotating unbalance. The rotor response and stability are analysed using a numerical continuation method employing the infinitely short journal bearing model. Continuation results are further validated by time simulations which utilise the finite difference method to compute the hydrodynamic forces. The validation process employs bifurcation diagrams, Poincaré sections and numerical estimates of the largest Lyapunov exponents.

Linear stability and nonlinear rotor responses of the gas foil bearing with multiple sliding beams

This article reports the stability and dynamic characteristics of a passive gas foil bearing (MSGFB) in which multiple sliding beams provide the elastic support and Coulomb damping. The linear and nonlinear dynamic models of rotor-MSGFB system are established, both considering the complex contact constraints inside foil structures. The instability mechanism of rotor-foil bearing system is revealed from the equivalent dynamic stiffness and the critical whirl speed. The half speed whirl and the frequency locked vibrations are both observed in the simulations, indicating the nonlinearities of gas film and foil structure respectively. The results also show that larger rotor preload of MSGFB help suppress the half speed whirl vibrations and assist improving high speed rotor stability especially under the friction effect.

Physics-based recalibration method of cup anemometers

Cup anemometer is the most widely used instrument in the natural environment. However, the accuracy of cup anemometer is not robust due to their inertial structures. In this study, the equation of motion (EOM) relating rotational motion of the cup rotor to aerodynamic force is investigated to reveal the cause of measurement error of cup anemometer. A new methodology is proposed to recalibrate cup anemometer based on theoretical analysis of the dynamic response of the cup rotor and random process theory. The unknown dynamic coefficients of the EOM are quantified by the numerical method using measurement results from inertial and non-inertial anemometers. A detailed example is presented to demonstrate the efficiency of this new method in which coefficients of the EOM are quantified from laboratory and field data. Both mean wind speed and the entire time history could be recalibrated using this new method. Comparing with the non-inertial anemometer results, the improvement rate of the recalibrated cup anemometer results is 29%–99%.

The Numerical Identification of Basins of Attraction for the Vibration Response of the Rigid Rotor with Squeeze Film Dampers

The article deals with the computational study of the rigid rotor coupled with squeeze film dampers. Various techniques such as the method of computation of the synchronous response with a circular centred orbit, the harmonic balance method, and the direct time integration method are used to analyse the nonlinear behaviour of the rotor system. The results indicate that the rotor system can exhibit both a synchronous circular response with a large orbit radius and a nonsynchronous response with a quasiperiodic character. However, both responses are undesirable in rotating machinery and should be avoided. The new results are presented to provide insight into the impact of initial conditions on the vibration response via basins of attraction. The simulations show that: (i) the basins of attraction are more sensitive to the choice of the initial velocities than displacements, (ii) the basins of attraction are noticeably dependent on the rotor speed in the region of a nonsynchronous response, and (iii) the border between the basins of attraction can be smooth or without a clear structure. The research brings clear conditions defined by parameters such as the dimensionless SFD constant, unbalance, and rotational speed for the suppression of undesirable nonlinear phenomena. The results suggest that the damper can effectively improve the vibration response of high-speed rotating machinery, but its design must be chosen appropriately.

Analysis of the Dynamic Characteristics of a Gear-Rotor-Bearing System with External Excitation

The dynamic response of the rotor system in a ring die granulator is complex and difficult to solve when it operates under joint external, support and gear mesh forces. To solve this problem, a finite element method and extrusion theory was applied in this study to develop a dynamic coupling model for a hollow overhung rotor with external load excitation. A Newmark-β numerical integration method was used to solve for the dynamic response of the overhung rotor under multiple excitation forces. The results included time-domain response diagrams, frequency-domain response diagrams, phase diagrams, Poincaré section diagrams, and bifurcation diagrams. The model and the method were verified by testing a ring die granulator. On this basis, the dynamic response of the system is predicted according to the influence of different parameters. As the bearing support distance increased, the roller eccentricity decreased, the bearing clearance decreased, the response of the rotor system was significantly optimized, and the system tended to stabilize gradually. Therefore, this paper provides a theoretical basis and experimental verification for the optimization of a pelleting machine transmission structure.

Security Study on Freestanding Minigrid with Multiple Rotary Energy Sources

Traditional grid has been extensively studied for system security. For freestanding renewable energy-based minigrid, a three-source stand-alone minigrid is in this study examined for system security under large disturbances. By real-time simulation, rotor responses of the generators and voltage characteristics of the buses are assessed at sudden load change and under fault condition. Post-perturbation behaviour of the system shows synchronism is not compromised by any of the generators and the bus voltage profiles remains within their pre-perturbation statutory limits. This implies that a number of rotating machine-based energy mini-sources could be interconnected into a freestanding minigrid without compromising the stability of the system. The assessment could find use in predictive and corrective compensation for stability issues in mini integrated power systems and serve as simple generic investigative approach that could be integrated into Minigrids Remedial Action Scheme or Minigrids Energy Management System for dynamic security assessment of multi-machine island minigrids.

Uniform Fault-Tolerant Control of a Quadcopter With Rotor Failure

This article provides a uniform fault-tolerant controller for a quadcopter without controller switching in case one rotor fails completely. The fault-tolerant control adopts control allocation based on an optimization method as the core of control. It will abandon the yaw channel when a rotor fails completely, for which the motion characteristics of the free-rotation quadcopter and the degree of controllability are analyzed. For practical implementation, the rotor dynamics have been further taken into consideration as first-order dynamics and then a compensator is used to improve the rotor response. To validate the proposed controller, first, digital simulation studies are conducted to verify the control logic. Second, the hardware-in-the-loop simulation highlights the feasibility and high efficiency of the fault-tolerant control method on an embedded system. Finally, an outdoor experiment with onboard sensors and GPS demonstrates that the fault-tolerant controller has the ability to make quadcopters fly safely when an arbitrary rotor fails completely.

Research on Dynamic Characteristics Analysis Method of Spindle-Flywheel Rotor System of Inertia Friction Welding Machine

A rotor is a special vibration system whose mechanical characteristics change with rotating speed. Taking the spindle-flywheel rotor system of inertia friction welding machine as the research object, in order to explore the variation law of critical speed and the unbalanced response of rotor system at different node positions, according to the special form of the spindle-flywheel rotor system, the combined flywheel set is simplified as a node of a lumped mass model, and the Riccati transfer matrix method and finite element method are used to calculate respectively. The error of the Riccati transfer matrix method is less than 4% compared with the finite element method, which proves the rationality of an equivalent flywheel node. Compared with the finite element method, the Riccati transfer matrix method, which simplifies the flywheel model, not only ensures accuracy but also shortens the calculation time. This method is obviously more suitable for calculating the spindle-flywheel rotor system model of an inertial friction welding machine. In addition, this method can also calculate the unbalanced response. When the unbalanced mass distribution is closer to the head end of the spindle, the unbalanced response vibrates more strongly at the second-order natural frequency, and the rotor response during vibration can be predicted.

On the rub-impact force, bifurcations analysis, and vibrations control of a nonlinear rotor system controlled by magnetic actuator integrated with PIRC-control algorithm

This article presents the Proportional Integral Resonant Controller (PIRC-controller) as a novel control strategy to suppress the lateral vibrations and eliminate nonlinear bifurcation characteristics of a vertically supported rotor system. The proposed control algorithm is incorporated into the rotor system via an eight-pole electromagnetic actuator. The control strategy is designed such that the control law (PIRC-controller) is employed to generate eight different control currents depending on the air-gap size between the rotor and the electromagnetic poles. Then, the generated electrical currents are utilized to energize the magnetic actuator to apply controllable electromagnetic attractive forces to suppress the undesired lateral vibrations of the considered rotor system. According to the suggested control strategy, the whole system can be represented as a mathematical model using classical mechanics' principle and electromagnetic theory, in which, the rub-impact force between the rotor and the stator is included in the derived model. Then, the obtained discrete dynamical model is analyzed using perturbation techniques and validated numerically through bifurcation diagrams, frequency spectrums, Poincare maps, time responses, and steady-state whirling orbit. The obtained results illustrate that the proposed control algorithm can mitigate the nonlinear vibration and eliminate the catastrophic bifurcations of the rotor system when the control gains are designed optimally. In addition, the system dynamics are analyzed when the rub-impact occurrence between the rotor and the pole housing is unavoidable. The acquired results revealed that the system may perform periodic-1, periodic-n, or quasiperiodic motion with one of two oscillation modes depending on both the impact stiffness coefficient and the dynamic friction coefficient.Article HighlightsNonlinearity dominates the uncontrolled rotor response, where it suffers from the jump phenomenon and multiple solutions.The proposed controller forces the Jeffcott rotor to respond as a linear system with small oscillation amplitudes.The rotor oscillates with full-annular-rub or partial-rub-impact mode when rub-impact occurs between the rotor and stator.

Stability of a Rotor Partially Filled With Fluid: Test Facility and Experimental Results

Abstract Fluid trapped in a hollow, rotating component may lead to subsynchronous vibrations, resulting in high vibration amplitudes. This asynchronous response is observed around 0.55–0.92× after passing through the first critical frequency and affects large rotating equipment such as centrifuges, fluid-cooled gas turbines, and jet engines. A test rig is designed to evaluate this self-excited asynchronous vibration. The high-speed rig comprises of a flexibly-mounted rotor partially filled with fluid, with an overhung test chamber providing an unobstructed view of the liquid surface. A squeeze film damper provides external damping and allows operation through the asynchronous response when the test chamber contains a large amount of fluid. The results show the rotor response with different fluid depths and external damping values as the rotor-bearing system transverses the first critical speed (cylindrical mode). The experiments show that only a small amount of oil (∼20 mL) is required to induce asynchronous excitations, and increasing the fluid depth increases the amplitude of vibration. External damping slightly decreases the response, but it also expands the range of frequencies where asynchronous vibrations occur. At a given speed ratio, the vibrations reach a limit cycle, and subsequently, begin to drop as the rotor speed increases past the first critical speed.

Parked aeroelastic field rotor response for a 20% scaled demonstrator of a 13‐MW downwind turbine

AbstractAeroelastic parked testing of a unique downwind two‐bladed subscale rotor was completed to characterize the response of an extreme‐scale 13‐MW turbine in high‐wind parked conditions. A 20% geometric scaling was used resulting in scaled 20‐m‐long blades, whose structural and stiffness properties were designed using aeroelastic scaling to replicate the nondimensional structural aeroelastic deflections and dynamics that would occur for a lightweight, downwind 13‐MW rotor. The subscale rotor was mounted and field tested on the two‐bladed Controls Advanced Research Turbine (CART2) at the National Renewable Energy Laboratory's Flatiron Campus (NREL FC). The parked testing of these highly flexible blades included both pitch‐to‐run and pitch‐to‐feather configurations with the blades in the horizontal braked orientation. The collected experimental data includes the unsteady flapwise root bending moments and tip deflections as a function of inflow wind conditions. The bending moments are based on strain gauges located in the root section, whereas the tip deflections are captured by a video camera on the hub of the turbine pointed toward the tip of the blade. The experimental results are compared against computational predictions generated by FAST, a wind turbine simulation software, for the subscale and full‐scale models with consistent unsteady wind fields. FAST reasonably predicted the bending moments and deflections of the experimental data in terms of both the mean and standard deviations. These results demonstrate the efficacy of the first such aeroelastically scaled turbine test and demonstrate that a highly flexible lightweight downwind coned rotor can be designed to withstand extreme loads in parked conditions.