Critical Rotational Speed Research Articles

Analysis of particle dynamics in a rotating dish

Although the rotating dishes are widely used in industrial processes, there are not many studies regarding the behavior of granular flow in this type of device. It is reported that the particle dynamics directly influences the dish performance in relation to its applications, e.g., in the granulation process. This work provides an experimental study about the effect of the main variables (rotational speed, angle of inclination, and physical properties of particles) on the behavior of particle dynamics in a rotating dish. The conditions, under which transitions between the flows regimes (rolling, cascading, cataracting, and centrifuging) occurred, were identified and the effects of the studied variables were quantified. The increase in the rotational speed and filling degree and the decrease in the angle of inclination caused a decrease in the angle of departure of the particles and anticipated the transition between flow regimes, demonstrating that both responses are correlated. Correlations proposed in the literature for predictions of the critical rotational speed related to the centrifuging regime were analyzed. A new equation was proposed, which reduced the average percentage deviation from 52.83% to 14.27% when compared to experimental data. • The particle dynamic behavior in a dish granulator was investigated. • The influence of relevant variables was quantified. • The transitions between the characteristic flow regimes were identified. • A new equation to predict the critical rotational speed was proposed.

Development of the design and technology of extrusion of metal-polymer mixtures for the production of feedstocks

The paper is devoted to the development of new equipment for the production of metal-polymer thread. 3D printing with metal-polymer thread is one of the advanced directions in the technology of manufacturing metal parts of complex shape. The proposed technology is an alternative to the currently existing metal injection molding (MIM) technology and selective laser melting printing technology. An important step in this work was to conduct computational experiments to determine the effect of screw rotation on the process pressure parameter and the design of the main assembly of the screw extruder. As a result of the research, the pressures on the metal-polymer composition were determined depending on the rotation speed of the screw. With a rotation of 30 rpm, the pressure reached 0.05 Pa and the maximum pressure was 0.18 MPa. The experiments were carried out in the CradelSFlow program. The computer calculation showed a margin of the screw strength coefficient k=1.8, and a maximum deflection of 2.8∙10–4 m, which meets the condition of static rigidity. To determine the correct value of the gap δ between the screw ridge and the extruder walls, an analysis of the rotor dynamics was carried out. The result of this study is the critical extruder rotation speed of 60 rpm at which the phenomenon of precession may occur. Amplitude-frequency characteristics ydin=7∙10–4 m. According to the results of the dynamic calculation, the screw dimensions were adjusted, the geometry was reduced by ∆=0.5 mm. The experiments made it possible to verify the optimal parameters of the technological process of metal-polymer mixture extrusion. The data obtained are important for the improvement and development of 3D printing technology for metal parts of complex geometric shape.

A Predictive Analysis Method of Shafting Vibration for the Hydraulic-Turbine Generator Unit

The shafting vibration for the Hydraulic-Turbine Generator Unit (HGU) inevitably affects the safe and stable operation of the Units. Excessive shafting vibration could cause fatigue damage of materials, which eventually leads to malfunction of HGU and even results in damage accidents in serious cases. Generally speaking, the vibration is mainly generated from the high-speed rotation of the shafting, and mechanical, hydraulic, and electrical factors as the vibration exciting sources may be coupled all to cause a vibration of the HGU, so it is necessary to take the whole shafting as a specific object of study. In recent years, many scholars have conducted much research on them and their results are focused more on how to control the influence of external excitation sources of vibration, but still lack consideration of the shafting’s internal mechanism of vibration. In this paper, a predictive analysis method is proposed to reveal the internal mechanism of vibration. Starting from the analysis of natural vibration characteristics of the shafting, this study establishes the finite element calculation model of the shafting of the HGU based on the finite element analysis method. By selecting appropriate research methods and calculation procedures, the modal analysis of the dynamic characteristics of the shafting structure is carried out. Finally, the first ten-order natural vibration characteristics and critical rotational speed of the shafting structure are successfully calculated, and the results conform to the basic laws of shafting vibration. In addition, by comparing the relationship between rotational frequency such as the rated speed, runaway speed, and critical speed of the shafting, the possibility of resonance of the HGU is analyzed and predicted, and then some suggestions for optimization design such as increasing the shafting’s stiffness and balancing its mass distribution are proposed. Therefore, this study provides a basis for guiding the structural design and optimization of the shaft system in engineering, and avoids the resonance caused by the excitation source such as rotational frequency, thereby ensuring the safe and stable operation of the HGU.

Displacement flows in rotating pipes

<h2>Abstract</h2> Displacement flows frequently occur in natural phenomena and industrial applications, e.g., in lung airways, oil well cementing, coating and cleaning of processing machinery. We study experimentally and numerically the effects of a pipe axial rotation on buoyant miscible flows in inclined pipes, while considering three cases of progressively increasing complexity: (i) Newtonian exchange flows (Lyu et al., 2020), (ii) Newtonian displacement flows (Lyu & Taghavi, 2018), and (iii) viscoplastic displacement flows (Lyu & Taghavi, 2020). We show how the flow dynamics is governed by an elegant balance among the characteristic velocities of the flow. We demonstrate that increasing the pipe rotation speed induces transverse mixing and results in a complete removal of the displaced fluid by the displacing fluid, above a critical rotation speed. Our findings offer insights on how to improve displacement efficiency using rotational motion.

Simulation analysis of dynamic coefficients for high-speed water-lubricated bearing-rotor system of satellite

With the development of space technology, the traditional aerospace cooling technology is hard to meet the constantly developing requirements of heat dissipation. In order to address the problem of temperature control for aerospace systems, the pump-driven fluid loop system has been often adopted. In the pump-driven fluid loop system, the rotor system is needed to be analyzed. In this paper, the rotor coupling system of the canned pump with multiple journal bearings has been studied based on the bearing data, lumped parameter method, Reynolds equation and finite element method. By solving the Reynolds equation, parameters of each bearing have been solved, and a database file has been formed. The bearing data have been addressed by linear interpolation. In this study, the static indeterminate problem has been combined to analyze the bearing force, and the bearing characteristic parameters under the steady-state condition have been solved based on the iterative method. The results indicated that the influences of clearance ratio and rotational speed on the natural frequency, critical rotational speed and unbalanced response of the rotor show certain regularity. The study provides a theoretical basis for the stable operation of the whole rotor system.

Influence of machine variables on the microstructure and mechanical properties of AA6061/TiO2 friction stir welds

ABSTRACT The present work explicates the joining of TiO2 (rutile) particles reinforced aluminium matrix composites (AMCs) through the friction stir welding (FSW) technique. Joining of AMCs using conventional fusion welding techniques faces a lot of challenges, which can be overcome by the FSW process. The effect of the two most critical process variables, welding speed, and tool rotational speed on the grain structure of the joint and on the mechanical behaviours was evaluated. The study revealed that machine variables regulate the quantity of heat input, heat exposure duration, and rate of cooling, thereby, significantly altering the grain size in the weld region and mechanical behaviour of the joint. The tool rotational speed had a substantial impact on the joint strength, whereas tool traverse speed facilitates homogeneous dispersion of reinforced particles in the matrix. The ‘W’-shaped hardness variation profile was observed across the weld zone, showing the highest hardness in the weld stir zone. The UTS of the welded specimen, measured across the joint was almost equal to the parent material with fracture occurring at the interface of the heat-affected and the thermo-mechanically affected zone which was the weakest point in the weld region.

Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed

We study the existence and stability of standing waves associated with the Cauchy problem for the nonlinear Schrödinger equation (NLS) with a critical rotational speed and an axially symmetric harmonic potential. This equation arises as an effective model describing the attractive Bose–Einstein condensation in a magnetic trap rotating with an angular velocity. By viewing the equation as NLS with a constant magnetic field and with (or without) a partial harmonic confinement, we establish the existence and orbital stability of prescribed mass standing waves for the equation with mass-subcritical, mass-critical, and mass-supercritical nonlinearities. Our result extends a recent work of Bellazzini et al. (Commun Math Phys 353(1):229–251, 2017), where the existence and stability of standing waves for the supercritical NLS with a partial confinement were established.

Structural FEM Analyses of a Landing Gear Testing Machine

The “Electro-mechanical Landing gear system Integration for Small Aircraft” (E-LISA) research project has the objective of developing an innovative “iron bird”, a testing facility dedicated to executing tests on an innovative landing gear of a small aircraft. This document presents the structural analyses of this complex testing machine performed with the Finite Element Method (FEM). Key purposes of these numerical simulations were the quantifications of the stress and displacement fields under the loading conditions foreseen for the machine. A modal analysis was performed with the aim of calculating eigenvalues and eigenvectors useful to provide an assessment of the structural dynamic response. The most critical mode shapes and the related frequencies were calculated, and the potentially critical rotational speeds were quantified. Finally, the Peak Stress Method (PSM) was adopted to quantify the fatigue resistance of the most critical weldments and an infinite fatigue life was assessed for the most critical one. The design of the machine, which is currently under manufacturing, was validated by the structural analyses presented here.

Post-resonance backward whirl analysis in cracked overhung rotors

Overhung rotors usually exhibit recurrent transitions through critical whirl rotational speeds during startup and coast down operations, which significantly differ from their steady-state whirl responses. The presence of angular acceleration results in a linear-time-varying (LTV) system, which, although technically linear, still presents complexities often evinced by a nonlinear system. In general, backward whirl zones can either precede the critical forward whirl speed (termed as pre-resonance backward whirl, Pr-BW), or immediately follow the critical forward whirl speed (termed as post-resonance backward whirl, Po-BW). The Po-BW in the whirl response of a cracked overhung rotor with a breathing crack is studied here as distinct from that of geometrically symmetric configurations of other rotor systems. The equations of motion from the finite element (FE) model of an overhung rotor system with a breathing crack are numerically integrated to obtain the whirl response. The transient whirl responses with different bearing conditions are thoroughly investigated for excitation of Po-BW. The Po-BW zones of rotational speeds are determined via the wavelet transform method and full spectrum analysis (FSA) and applied to signals with added noise. The results of this work confirm the excitation of the Po-BW in cracked overhung rotors and confirm the robustness of the employed methods.

Coupled bending torsional vibrations of viscoelastic rotors with fractional damper

The behavior of a Jeffcott rotor with lateral-torsional coupling is investigated in the presence of internal and external damping and eccentricity. The governing equations are derived based on the Lagrange method. Also, the Laplace method and linearization is used to solve the governing equations for free vibrations analysis. For a rotor with unbalance, the instability occurs when the real part of eigenvalues has positive values, and at the same time, it is the intersection point between the lines of natural frequencies. The instability speed increases with increasing the external damping, yet dependent on the internal damping and unbalance. Also, it is demonstrated that the rotor critical speed is affected by the order of fractional derivatives.

Mixed Convective Transport around Counter Rotating Tandem Cylinders at Low Reynolds Number

Rotating an object in a flowing fluid brings stability to the flow around the object. Consequently, an inherently unsteady flow may be degenerated into a steady pattern. On the contrary, cross thermal buoyancy brings instability to the flow causing triggering of vortex shedding even at relatively low Reynolds numbers. Hence, rotation and cross buoyancy produces opposing effects in this context. Furthermore, multiple objects in a flowing fluid develop intriguing wake dynamics following their interference effects. When tandem cylinders are placed in a flowing stream, depending on the gap between them, the vortex shedding may get triggered. These physical behaviors are coupled in this work to understand the simultaneous effect of rotation, cross thermal buoyancy (Richardson number, 0–1) and cylinder gap spacing (0.2–3) on the wake dynamics around tandem circular cylinders at Reynolds number 100 and Prandtl number 0.71. It is observed that at a critical rotational speed, the unsteady periodic flow is transfigured to a steady pattern. At smaller gap spacings (0.2, 0.7), a higher rotational speed is required particularly at higher strengths of buoyancy (0.5, 1) to control the flow instabilities and suppress the vortex shedding. The critical rotational speed is maximum at gap spacing of 0.2 for the highest buoyancy strength. Furthermore, the critical rotational speed reduces as the gap spacing increases.

Analysis of Nonlinear Vibration Characteristics of the Concentric Face-Gear Split-Torque Transmission System

The concentric face-gear split-torque transmission system (CFGSTTS) is a new type of transmission that has significant applications in helicopter main gearboxes. To study the influence of various parameters on the dynamic characteristics of the CFGSTTS, a 23-degree-of-freedom translation-torsion nonlinear dynamic model was established based on the lumped parameter theory. The model includes tooth backlash, error excitation, time-varying meshing stiffness with meshing phase difference, meshing damping, and elastic support deformation. The excitation conditions for the time-varying meshing stiffness of face-gear pairs were calculated based on the strain energy theory. The bifurcation characteristics of the system with different parameters were obtained by the nonlinear dynamics numerical analysis method. The research shows that the system exhibits rich vibration response characteristics at different rotating speeds. The amplitude of the vibration displacement in the system bifurcation diagram increases significantly with the increase of the tooth backlash and input torque, whereas the amplitude decreases constantly with the increase of the meshing damping. The critical rotational speed at which chaotic motion occurs increases significantly with increasing input torque and damping ratio but decreases with increasing tooth backlash. The bearing clearance has a weak influence on the vibration displacement amplitude of the system and the speed range of chaotic motion.

The vibration modal characteristics of drillstring in compound drilling

The compound drilling plays an important role in improving borehole quality. The modal analysis model of drillstring is established to analyze the modal of longitudinal vibration, lateral vibration and torsional vibration, respectively. Compared with longitudinal and torsional vibrations, the intrinsic frequency range of lateral vibration are smaller, and it is harder to prevent resonance by adjusting critical rotation speed in case of lateral vibration. The intrinsic frequency of drillstring decreases as drillstring length increases. The longer drillstring is, the larger the increase and the smaller the interval range between the intrinsic frequencies of orders will be. It is easier to cause resonance when the frequency of exciting forces changes. As the number of order increases, the intrinsic frequency of the three vibrations increases and their increase amplitude is: longitudinal vibration > torsional vibration > lateral vibration. The results are benefit for the drillstring design and improving the wellbore quality.

Water modelling on particle dispersion during KR desulphurization process

ABSTRACT In the current study, a 1:7 scaled water model was established to investigate the dispersion of desulphurizer particles during the Kanbara Reactor (KR) desulphurization process. The concentration, movement, and dispersion of the particle in the liquid were visualized and analysed. The influence of the impeller rotation speed, immersion depth, particle density and addition amount, and ladle wall baffle on the particle dispersion were systematically studied. The minimum critical rotation speed at which particles began to disperse into the liquid under different parameters was obtained. A regression equation for the influence of the impeller immersion depth and particle mass proportion on the critical rotation speed was proposed. Particles were easier to be driven into the liquid by the stirring impeller due to the higher particle additions. The area proportion of dispersed particles using the baffle was increased by three times compared with the case without the baffle.

Investigation of the direct utilization possibility of methane fermentation residue sludge as liquid fertilizer by micronization

ABSTRACT For establishing a sustainable society, it is crucial to reuse the organic waste as a material resource. Therefore, herein, we aim to pulverize the methane fermentation residue sludge by ball milling and high-speed agitation to directly utilize it as a liquid fertilizer. The solid particles in the sludge can be below 100 µm, corresponding to the nozzle diameter of the boom sprayer by both ball milling and high-speed agitation; when ball milling was carried out for at least 1 h, the ratio of coarse particles larger than 100 µm decreased by less than 10%. In addition, the phosphate-ion concentration in the sludge increased with a decrease in the particle size of solid in the sludge mainly due to increase in its specific surface area. Furthermore, we investigated the effects of various experimental conditions for ball milling on the pulverization efficiency. Results suggests that for grinding the soft solid particles in the sludge by ball milling, the volume ratio of the total medium balls and sludge, total volumes of the balls and sludge, and inner pot volume should be larger, while the ratio of the rotation speed to the critical rotation speed should be almost the same as those reported previously in the reports on grinding of inorganic particles to attain an effective pulverization.

A CFD- RSM study of cuttings transport in non-Newtonian drilling fluids: Impact of operational parameters

Cuttings removal out of the wellbore represents a real barrier for successful drilling operations. The performance of hole cleaning is determined by several factors. The current article provides a theoretical study of the impact of three operational parameters on cuttings transport in non-Newtonian drilling fluids. Computational fluid dynamics (CFD) is used to study the effect of drill pipe rotation speed (from 0 to 200 rpm), inclination angle (0–90⁰), and pipe eccentricity (0–0.8) on the cuttings transport ratio (CTR), cuttings volume concentration (CVT), and pressure drop. Response surface methodology (RSM) is employed to explore the two-factor interactions and to optimize the parameters by minimizing the CVT while maximizing the CTR. RSM is also used to generate statistical models to correlate the impact of the aforementioned three factors to the hole cleaning performance (represented by CVT, CTR, and pressure drop). Results revealed that many interactions exist between the tested operational parameters. The drill pipe rotation has the dominant effect on the performance of cuttings transportation, with the effect are more pronounced for highly deviated and horizontal wells. The results indicate that there are only a few cases of inadequate hole cleaning that drill-pipe rotation cannot control, and those cases are associated with the operation in vertical wellbore sections. Less effective cuttings transportation (i.e lower CTR) was observed when the hole angle deviated from the vertical. In addition, a significantly higher CVT (up to 73%) was recorded for eccentric pipes as compared to the concentric cases, primarily due to the reduced fluid velocity in the narrow gap of the eccentric annulus. As far as the pressure drop is concerned, lower pressure loss was obtained at lower rotation speeds and higher angles of inclination from the vertical. As the drill pipe rotational speed increased, the pressure drop decreased slightly until a critical rotatory speed was reached, thereafter, the pressure drop increased markedly. This trend was similar for all pipe eccentricities at any inclination angles, however, the critical rotational speed at which the pressure loss started to increase was found to be dependent on both the inclination angle and eccentricity. Operating at low drill pipe rotation speeds in a concentric annulus is recommended for vertical wells while higher speeds are favorable for more effective cuttings transport in horizontal wells. The CFD simulation results have been validated against experimental measurements for single and multiphase flow for different cases with/without drill pipe rotation at various inclination angles for both Newtonian and Non-Newtonian fluids.

Vortex fluidic induced mass transfer across immiscible phases.

Mixing immiscible liquids typically requires the use of auxiliary substances including phase transfer catalysts, microgels, surfactants, complex polymers and nano-particles and/or micromixers. Centrifugally separated immiscible liquids of different densities in a 45° tilted rotating tube offer scope for avoiding their use. Micron to submicron size topological flow regimes in the thin films induce high inter-phase mass transfer depending on the nature of the two liquids. A hemispherical base tube creates a Coriolis force as a ‘spinning top’ (ST) topological fluid flow in the less dense liquid which penetrates the denser layer of liquid, delivering liquid from the upper layer through the lower layer to the surface of the tube with the thickness of the layers determined using neutron imaging. Similarly, double helical (DH) topological flow in the less dense liquid, arising from Faraday wave eddy currents twisted by Coriolis forces, impact through the less dense liquid onto the surface of the tube. The lateral dimensions of these topological flows have been determined using ‘molecular drilling’ impacting on a thin layer of polysulfone on the surface of the tube and self-assembly of nanoparticles at the interface of the two liquids. At high rotation speeds, DH flow also occurs in the denser layer, with a critical rotational speed reached resulting in rapid phase demixing of preformed emulsions of two immiscible liquids. ST flow is perturbed relative to double helical flow by changing the shape of the base of the tube while maintaining high mass transfer between phases as demonstrated by circumventing the need for phase transfer catalysts. The findings presented here have implications for overcoming mass transfer limitations at interfaces of liquids, and provide new methods for extractions and separation science, and avoiding the formation of emulsions.

SENSITIVITY OF STRENGTH, RIGID AND DYNAMIC CHARACTERISTICS OF THE CONSOLE ROTOR TO VARIATION OF DESIGN PARAMETERS

The analysis sensitivity of strength, rigid and dynamic characteristics of the console rotor to variation of design parameters in paper describes The speed of rotation of the shaft, the material of the impeller vary. The dependences of radial and axial displacements on the angular velocities of rotation and the modulus of elasticity of the impeller material are established. For objects of the type of rotary systems with a cantilever arrangement of the impeller, not one, but a set of criteria has been introduced into consideration, which should be taken into account in the research of this type of objects. The tendencies of change of the first and second critical rotational speeds from the modulus of elasticity, rotor rotational frequencies and density of the impeller material are also determined. On this basis, recommendations have been developed for determining the design parameters of the rotor part of the air blower with a cantilevered impeller. Keywords: air blower; critical rotation speed; natural vibration frequency; rotary system; stress-strain state

Damage analysis of rotation speed on corrosion film of 3Cr steel in the CO2 environment with silty sand

The 3Cr steel used as the tubing has serious corrosion damage in a flowing CO2 environment with silty sand. Hence, the investigation for the influence of flow velocity on the corrosion behavior of 3Cr steel has an important and practical significance. It could not only unveil the corrosion damage mechanism of the steel under dynamic conditions, but also provide a theoretical basis for the corrosion protection of the tubing. In this paper, the effect of flow velocity on the corrosion film of 3Cr steel in a CO2 environment with silty sand was investigated by adjusting rotation speed. The results revealed that the corrosion resistance of 3Cr steel was first reduced, followed by enhancing and then reduced as the rotation speed increased. There was a critical rotation speed for the transformation of corrosion mechanism of 3Cr steel, i.e., 600 r/min. When the rotation speed was lower than the critical speed, the mass transfer process of corrosive medium dominated the corrosion resistance of 3Cr steel, and silty sand participated in the formation of corrosion film. The increasing rotation speed accelerated the mass transfer process, which first reduced and then improved the corrosion resistance. When the rotation speed was higher than the critical speed, the shear stress of silty sand played a predominant role. At the same time, silty sand impinged on the corrosion film, and then destroyed the stability of the film, leading to a significant decrease of the corrosion resistance. Silty sand changed from participating in the corrosion film to destroying the corrosion film with increasing rotation speed.

Balancing high-speed rotors at low speed using optimized parametric excitation and tuned nonlinear feedback

The paper presents an improved slow-speed mass balancing procedure capable of reducing high-speed related imbalance. Parametric excitation is used to project the small imbalance forces onto a chosen mode of vibration, corresponding to a high critical rotation speed. The method employs two kinds of parametric excitation leading to combination and principal parametric resonances. The former projects the imbalance forces onto a selected vibration mode, and the latter significantly amplifies the dynamic response due to imbalance. In addition to the parametric excitations, specially tuned nonlinear feedback forces are applied to limit the response to desired vibration levels and achieve a pseudo-linear behavior. In situ proper tuning of the nonlinear terms, and parametric excitations, enables to increase both amplification and sensitivity to the imbalance forces without having to compromise between the two. The latter includes digital, nonlinear feedback that enhances the sensitivity to imbalance forces, while limiting the level of vibration. This method allows to identify the projection of the imbalance on any desired mode, and therefore to cancel them by adding or removing mass. An experimental realization of the method validates the theory with good accuracy.