Critical Rotational Speed Research Articles

Research on the Rotor of a Ducted Fan Propulsion System of MOSUPS Aircraft Taking into Account Self-Balance during Operation

The work concerns the research of a propulsion system for an unmanned aerial vehicle MOSUPS in joined wing configuration. Modeling, analysis and experimental research of a statically unbalanced rotor of a ducted fan propulsion system has been conducted.The aim of the analysis was to determine the critical rotational speeds of the rotor due to the probable excitation of oscillations. Due to the complex geometry, Finite Element Method has been used for the calculations. In the study, the critical frequencies (and also rotational speeds) of the rotor as well as precessional instability, flexibly mounted in the bearings have been calculated. Campbell and SAFE diagrams have been presented.Furthermore, the paper presents the idea for a device for automatic dynamic balancing of the mentioned rotor. A mechanism for changing the position of the correction weights has been developed, allowing for a long term operation of rotating parts without the need to stop the unit and correcting the unbalance.The main motivation for work was to fully understand the working conditions of the propulsion system and dynamic properties of the rotor in order to carry out a proper assessment of their impact on the safe operation of the aircraft.

Experimental and performance analyses of a turbomolecular pump rotor system

This study focuses on the experimental and performance analyses of a vertical turbomolecular vacuum pump (TMVP) rotor system. This approach can adopt various methods, such as numerical parametric analyses and experimental measurements. The analysis process can verify the finite element models of the rotor system under different boundary conditions by using pump system assembly testing data. Afterward, the dynamics characteristics of the rotor system must be calculated and compared with the experimental results to verify the models. Finally, the relationship between rotor critical speed and bearing stiffness can be established to study the design of the TMVP rotor system. The experimental analysis can adopt static modal and dynamic testing. Static modal testing can provide the natural frequencies of the rotor system. The waterfall diagram of dynamic testing can measure the operating critical speed of the vacuum pump system from 0 rpm to the operating speed and ensure that the operating speed is far from the critical speed or at least within 10% of the safe margin. In summary, results of the experimental testing and numerical parametric analysis can provide the basis for the design tool of the TMVP rotor system to identify and prevent vacuum pump vibrations.

The Shapes of Teeth of Circular Saw Blade and Their Influence on its Critical Rotational Speed

The main problems during cutting with circular saw blade are inaccurate cut, low quality of surface, high level of noise. These adverse effects are related to oscillation of circular saw blade. This oscillation cause adverse effects not only on workpiece but also on tool. In some case the circular saw blade reaches the value of critical rotational speed which leads to its instability and cause the oscillation of blade which may leads to destruction of tool. So the reduction of the amplitude of oscillation is essential for removing the adverse effects. This paper deals about influence of shapes of teeth as a type of modification that has positive effect oncritical rotational speed of circular saw blade. The parameters of studied models of circular saw blade were 42 number of teeth and the height of teeth with slice from sintered carbide was 14 mm. The variable parameter was the ratio between surface of teeth and surface of teeth gap. In this study was used computer software Creo Parametric 1.0 for obtaining natural frequencies of studied models. This software uses in analysis finite element method (FEM). There were done some steps to idealize the models. For calculating static and dynamics natural frequencies of modelswere used modal analysis. The critical rotational speed was calculated from obtained results by Creo Parametric 1.0 and compared on 5 models of tool.

Automatic PID Control Loops Design for Performance Improvement of Cryogenic Turboexpander

Cryogenics field involves temperature below 123 K which is much less than ambient temperature. In addition, many industrially important physical processes—from fulfilling the needs of National Thermonuclear Fusion programs, superconducting magnets to treatment of cutting tools and preservation of blood cells, require extreme low temperature. The low temperature required for liquefaction of common gases can be obtained by several processes. Liquefaction is the process of cooling or refrigerating a gas to a temperature below its critical temperature so that liquid can be formed at some suitable pressure which is below the critical pressure. Helium liquefier is used for the liquefaction process of helium gas. In general, the Helium Refrigerator/Liquefier (HRL) needs turboexpander as expansion machine to produce cooling effect which is further used for the production of liquid helium.Turboexpanders, a high speed device that is supported on gas bearings, are the most critical component in many helium refrigeration systems. A very minor fault in the operation and manufacturing or impurities in the helium gas can destroy the turboexpander. However, since the performance of expanders is dependent on a number of operating parameters and the relations between them are quite complex, the instrumentation and control system design for turboexpander needs special attention. The inefficiency of manual control leads to the need of designing automatic control loops for turboexpander. Proper design and implementation of the control loops plays an important role in the successful operation of the cryogenic turboexpander. The PID control loops has to be implemented with accurate interlocks and logic to enhance the performance of the cryogenic turboexpander. For different normal and off-normal operations, speeds will be different and hence a proper control method for critical rotational speed avoidance is must. This paper presents the design of PID control loops needed for the efficient performance of cryogenic turboexpander (Radial Inflow type) to ensure that the control systems meet the technical conditions and constraints more accurately and ensure the equipment safety.

Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer

We propose simple formulas for calibration of rheological parameters of Bingham fluid using a co-axial cylinder rheometer, in which the inner cylinder rotates at a constant speed, and the outer cylinder is stationary. A critical rotational speed exists due to existence of yield stress. If rotation speed exceeds the critical value, all fluid is fully sheared between the concentric cylinders. Plug flow exists only when rotation speed is less than the critical value. The effects of radius ratio and Bingham number are discussed. The rheometer with radius ratio very close to unity is discussed as a limiting case, and the result confirms previous research. Formulas for calibration are derived using Least Squares and perturbation methods for all values of radius ratio, based on measured rotation speed and torque. Two sets of experimental data are used for verification. The validation shows that the formulas derived here yield reasonable and accurate estimates of rheological parameters.

Electrospinning poly(ε-caprolactone) under controlled environmental conditions: Influence on fiber morphology and orientation

Reproducibility is a well-known issue in research involving electrospun materials, and, therefore, it is one of the main obstacles preventing this processing technique to prevail into the industry. Controlling environmental parameters during the electrospinning process helps in drastically reducing variability of results and, at the same time, has a strong impact on fiber characteristics. Using polycaprolactone (PCL) as a model system, in this work we investigated the influence of relative humidity and environmental temperature on the resulting mesh morphology for different PCL solutions. PCL solutions were electrospun on a rotating mandrel, for different rotational speeds and over a broad range of environmental conditions (30%–90% of relative humidity and temperature of 20 °C–40 °C) with different chloroform/tetrahydrofuran ratios in the solvent mixture. In this way we could assess the role of solvent water miscibility in determining surface features. While temperature changes have only a moderate effect on the resulting fibers, relative humidity does not only changes the surface morphology of electrospun fibers, but also the critical rotation speed of the collecting mandrel needed for obtaining alignment. Furthermore, we observed a self-assembled perpendicular monolayer-like fiber architectures when the electrospinning was performed above critical rotation speed required for aligned fibers.

Convective Transport Around a Rotating Square Cylinder at Moderate Reynolds Numbers

Two-dimensional numerical simulation is performed to analyze the thermofluidic transport around a rotating square cylinder in an unconfined medium. The convective transport originates as a consequence of the interaction between a uniform free-stream flow and the flow evolving due to the rotation of the sharp-edged body. A finite volume-based method and a body-fitted grid system along with the moving boundaries are used to obtain the numerical solution of the incompressible Navier–Stokes and energy equations. The Reynolds number based on the free-stream flow is considered in the range 10 ≤ Re ≤ 200, and the dimensionless rotational speed of the cylinder is kept 0 ≤ Ω ≤ 5. Depending on the Reynolds number and the rotational speed of the cylinder, the transport characteristics change. For the range 10 ≤ Re < 50, the flow remains steady irrespective of the rotational speed. In the range 50 ≤ Re ≤ 200, regular low-frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation (Ωcr ). Beyond Ωcr , the global convective transport shows a steady nature. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, the heat transfer behavior varies significantly with a rotating circular cylinder. Such thermofluidic transport around a spinning square in an unconfined free-stream flow is reported for the first time.

Study on the non-contact FBG vibration sensor and its application

A non-contact vibration sensor based on the fiber Bragg grating (FBG) sensor has been presented, and it is used to monitor the vibration of rotating shaft. In the paper, we describe the principle of the sensor and make some experimental analyses. The analysis results show that the sensitivity and linearity of the sensor are −1.5 pm/μm and 4.11% within a measuring range of 2 mm–2.6 mm, respectively. When it is used to monitor the vibration of the rotating shaft, the analysis signals of vibration of the rotating shaft and the critical speed of rotation obtained are the same as that obtained from the eddy current sensor. It verifies that the sensor can be used for the non-contact measurement of vibration of the rotating shaft system and for fault monitoring and diagnosis of rotating machinery.

An analytical insight into large-disturbance stability of doubly fed induction generators

This short communication presents an analytical method for assessing the stability of doubly fed induction generators. The method is based on the concept of critical rotor speed and it provides insights into the influence of the voltage applied to the rotor windings on the generator stability margin. This information can be useful to plan the converter rate and trace control strategies.

Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise

We present an experimental and theoretical study on the gravity-wave instability developing in a highly turbulent free-surface Taylor–Couette flow, for which only the inner cylinder rotates. Above a critical rotation speed, from an axisymmetric turbulent base state a non-axisymmetric fluctuating gravity-wave state develops, with an m = 1 azimuthal wave number. The bifurcation is discontinuous and presents hysteresis. In contrast to previously reported work (Mujica N and Lathrop D 2006 J. Fluid Mech. 51 49–62), here we compare our experimental results with a universal model based on a quintic subcritical amplitude equation with additive noise. In general, the model describes correctly the mean free-surface oscillation amplitude and its fluctuations, although differences exist in the bistability region width and the free-surface fluctuations in the gravity wave state. These differences are due to the finite time measurements and non-linear effects, respectively. Indeed, we show that longer measurement times allow the system to transit in either direction (from or to the base state), which results in the shrinking of the bistability region. For very long measurement times, and in a very narrow range of rotation rates, the system presents a series of random reversals between both states. Finally, by removing the mean wave and flow oscillations in the measured free-surface and bulk pressure signals, we demonstrate that their dynamic fluctuations depend on the system state.

The Dynamic Analysis of Two-Rotor Three-Bearing System

A finite element model considering the shear effect and gyroscopic effect is developed to study the linear and nonlinear dynamic behavior of two-rotor three-bearing system named N+1 configuration with rub-impact in this paper. The influence of rotational speed, eccentric condition, and the stiffness of coupling on the dynamic behavior of N+1 configuration and the propagation of motion are discussed in detail. The linear rotordynamic analysis included an evaluation of rotor critical speed and unbalance response. The results show that the critical speed and unbalance response of rotors are sensitive to coupling stiffness in N+1 configuration. In the nonlinear analysis, bifurcation diagram, shaft-center trajectory, amplitude spectrum, and Poincaré map are used to analyze the dynamic behavior of the system. The results of the research transpire that these parameters have the great effects on the dynamic behavior of the system. The response of the system with rub-impact shows abundant nonlinear phenomena. The system will exhibit synchronous periodic motion, multiperiodic motion, quasiperiodic motion, and chaotic motion patterns under rotor-stator rub interaction conditions. The dynamic response is more complicated for flexible coupling and two mass eccentricities than that of system with rigid coupling and one mass eccentricity.

Investigation of Copper Extraction from Aqueous Sulfate Solution in a Rotating Disc Contactor

The extraction of copper from aqueous sulfate solution with new extractant Cupromex-3302 (active substance is the 5-nonylsalicylaldoxime) using a rotating disc contactor (RDC) was investigated. It was observed from batch experiments that the best results were obtained with the initial aqueous pH and concentration of Cupromex-3302 of 1.9 and 10% (v/v) respectively. In continuous experiments, the first critical rotor speed based on drop breakage probabilities was determined. Then the effects of rotor speed, dispersed and continuous phase flow rates on hydrodynamic parameters such as static hold-up, mean drop sizes and extraction efficiency were studied. The experimental results were compared with the ones obtained by the empirical correlations for prediction of the dispersed phase static hold-up and mean drop sizes in terms of the operating variables and the physical properties. The results of experiments proved the feasibility of operating the solvent extraction of copper from the aqueous solution using rotating disc contactor.

Stochastic analysis of flow-induced dynamic instabilities of wind turbine blades

Wind turbine blades continue to grow in length to extract more energy from the wind. This trend results in more flexible blades that are more susceptible to flow-induced instabilities. Recent studies have shown that coupled-mode flutter can be a major concern for future wind turbine blades. In this work, we study the influence of uncertainty in system parameters on the onset of coupled-mode flutter for wind turbine blades. We consider two major sources of randomness: (i) flow forces through a random lift coefficient and (ii) structural properties through a random variation of the blade׳s torsional natural frequency. We use a linear stability analysis in order to predict the onset of instability and we apply the method to the NREL 5MW wind turbine blade. Both normal and uniform probability distributions are considered to describe the random parameters. For each case, the coefficient of variation (cov) is set to be equal to 0.1 and 0.2, which has been shown in the literature to be a plausible variability. We show that randomness in both the flow forces and the structural properties affect the onset of instability. In all the cases, the higher cov values result in non-negligible occurrence of instability at a blade critical rotor speed considerably lower than the value found in the absence of randomness. It is also found that the structural randomness can decrease the critical speed for the onset of coupled-mode flutter to speeds lower than the wind turbine׳s designed operational speed.

Multi-Objective Optimization of a Two-Disk Rotor System

A two-disk rotor system under the aero-engine support structure of typical 1-0-1 was established and the dynamical characteristics were analyzed. The two-disk rotor model was integrated to the Isight. The multi-objective design optimization of the transient process was then carried out with Evolutionary Optimization Algorithm. The optimum positions of the two-disk rotor system were obtained at the specified constraints. In order to verify the validity of the design optimization, the transient test was carried out on a high-speed flexible rotor mockup. The maximum amplitude of disk 1 cross the first critical rotation speed fell 50% and the maximum amplitude of disk 2 decreased by 20%. Experimental results indicated that the optimization method could obtain the position of the flexible rotor with the minimum amplitude and improve the design efficiency and quality, which had practical significance in the design of aero-engine rotor system.

An investigation into autobalancing devices with multireservoir system

Behaviour of a liquid-type automatic balancing device is modeled in this paper. To perform mathematical research the authors use a rotor model which contains a ring functioning as a reservoir coupled to a rigid shaft being rotatable in bearings. An autobalancer with several reservoirs is used for the mathematical investigation. The article provides the layout of forces acting in a multi-reservoir balancing system. Data on the effect of various factors on balancing accuracy as well as the main calculation features of a multi-reservoir autobalancer are presented. The obtained modeling results indicate that autobalancing efficiency is enhanced by increasing the number of reservoirs. An increase in the number of reservoirs causes a decrease in a critical rotor speed.

Numerical Study of the Laminar Flow Past a Rotating Square Cylinder at Low Spinning Rates

The fluid dynamic interaction between a uniform free stream flow and the rotation induced flow from a sharp edged body is numerically investigated. A two-dimensional (2D) finite volume based computation is performed in this regard to simulate the laminar fluid flow around a rotating square cylinder in an unconfined medium. Body fitted grid system along with moving boundaries is used to obtain the numerical solution of the incompressible Navier–Stokes equations. The Reynolds number based on the free stream flow is kept in the range 10≤Re≤200 with a dimensionless rotational speed of the cylinder in the range 0≤Ω≤5. At low Re=10, the flow field remains steady irrespective of the rotational speed. For 50≤Re≤200, regular low frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation (Ωcr). Beyond Ωcr, the global flow shows steady nature, although high frequency oscillations in the aerodynamic coefficients are present. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, significant differences can be seen at higher rotation. Such fluid dynamic transport around a spinning square in an unconfined free stream flow is reported for the first time.

Stationary Rotation of the Partially Liquid-Filled Unbalanced Rotor under External Friction Force Action

Rotor rotation with liquid layer on the chamber wall under viscoelastic action of the shaft within a planar model is examined in the article. The solution to the problem of determining the deflection of a rotating shaft with liquid filled chamber is given, which is important when designing an automatic balancing device. The issue of the cooperative motion of a solid body and liquid is considered in mathematical research. The set task is performed by applying D'Alembert's principle. The modeling results indicate that an increase in liquid’s mass in a rotor decreases its critical rotation speed; at the same time, the external friction accelerates the system’s self-centering. The developed mathematical models enable us to select the design parameters of a liquid-type autobalancer which operates within the set range of rotor’s angular velocity.

Efficiency of Balancing by Liquid-Type Automatic Balancing Devices

The article focuses on modelling the behaviour of a liquid-type automatic balancing device. To perform mathematical research the rotor model is used that contains a ring functioning as a vessel coupled to the rigid shaft being rotatable on bearings. Data on the influence of various factors on balancing accuracy are presented. The obtained modeling results indicate that the vibration amplitude at supercritical frequencies will decrease proportionally to the increase in the parameters of a liquid autobalancer. The performed calculation also reveals that the more the parameters of a liquid autobalancing device, the higher the efficiency of balancing. Provided the condition of the liquid sufficiency in the ring is satisfied, the independence of the rotor vibration amplitude from the mass of the liquid in the vessel is achieved. Critical rotor speed does not depend on the volume of the liquid in the ring if the condition of its sufficiency is met.

Gas-Expanded Lubricant Performance and Effects on Rotor Stability in Turbomachinery

Gas-expanded lubricants (GELs) are tunable mixtures of synthetic oil and carbon dioxide that enable dynamic control of lubricant viscosity during bearing operation. This control can help reduce bearing power loss and operating temperatures while also providing direct control over bearing stiffness and damping, which can enhance rotordynamic performance. In this work, the bearing and rotordynamic performance of two representative high-speed machines was evaluated when different lubricants, including GELs, were supplied to the machine bearings. The machines chosen for this analysis, an eight-stage centrifugal compressor and a steam turbine-generator system, represent a wide range of speed and loading conditions encountered in modern turbomachinery. The fluids compared for machine performance were standard petroleum-based lubricants, polyol ester (POE) synthetic oils, and POE-based GELs. The performance simulations were carried out using a thermoelastohydrodynamic bearing model, which provided bearing stiffness and damping coefficients as inputs to finite element rotordynamic models. Several bearing performance metrics were evaluated including power loss, operating temperature, film thickness, eccentricity, and stiffness and damping coefficients. The rotordynamic analysis included an evaluation of rotor critical speeds, unbalance response, and stability. Bearing performance results for the compressor showed a 40% reduction in power loss at operating speed when comparing the GEL to the petroleum-based lubricant. The GEL-lubricated compressor also exhibited lower operating temperatures with minimal effects on film thickness. GELs were also predicted to produce lower bearing stiffness when compared to standard fluids in the compressor. Rotordynamic results for the compressor showed that the fluid properties had only minor effects on the unbalance response, while GELs were found to increase the stability margin by 43% when compared with standard fluids. The results from the turbine-generator system also demonstrated increases in low-speed bearing efficiency with the use of GELs, though at higher speeds the onset of turbulent flow in the GEL case offset these efficiency gains. Rotordynamic results for this system showed a contrast with the compressor results, with the GELs producing lower stability margins for a majority of the modes predicted due to increased bearing stiffness in the high-speed turbine bearings and negative stiffness in the lightly loaded, low-speed pinion bearings. These results suggest that GELs could be beneficial in providing control over a wide range of machine designs and operating conditions and that some machines are especially well suited for the tunability that these fluids impart.

Nonsynchronous vibrations of rotor system induced by oil-block inside the rotating drum

Lubrication oil in a rotor system guarantees the rotating components working smoothly and protects the system from being damaged due to friction. A volume of lubrication oil, however, sometimes leaks into the inner cavity of shaft and drums of rotor system and forms an oil-block during rotating operation. The oil-block usually induces abnormal vibration of the rotating machine, which is often observed in practical cases, such as in aero-engine. The work in this paper studies the nonsynchronous vibration (NSV) induced by an oil-block in a rotating drum of a Jeffcott rotor system, which consists of a shaft, a drum and two supporting isotropic bearings. The additional effect due to an oil-block rotating on the inner wall of the drum is included into rotor system differential equations considering the Coriolis acceleration and friction interaction between the oil-block and the drum. Numerical simulations are carried out under two rotating speeds conditions: a lower one and a higher one than the first critical rotor speed, which are defined as rigid rotor case and flexible rotor case. Numerical results states the transverse vibrations by bifurcation diagrams, shaft center trajectories, frequency spectra and Poincare diagrams, which reveal multi-periodic, quasi-periodic and other complex motions due to the existing of oil-block. The internal friction coefficient and mass of the oil-block are found to have a significant effect on the generation and development of NSV. As the oil-block case is very common in practice, the investigation of NSV caused by oil-block in rotor system would benefit the understanding of complex phenomena and contribute to fault detection and diagnosis of rotating machine.