Showing papers on "Critical speed published in 2017"

Experimental and empirical investigations of traffic flow instability

Abstract: Traffic instability is an important but undesirable feature of traffic flow. This paper reports our experimental and empirical studies on traffic flow instability. We have carried out a large scale experiment to study the car-following behavior in a 51-car-platoon. The experiment has reproduced the phenomena and confirmed the findings in our previous 25-car-platoon experiment, i.e., standard deviation of vehicle speeds increases in a concave way along the platoon. Based on our experimental results, we argue that traffic speed rather than vehicle spacing (or density) might be a better indicator of traffic instability, because vehicles can have different spacing under the same speed. For these drivers, there exists a critical speed between 30 km/h and 40 km/h, above which the standard deviation of car velocity is almost saturated (flat) along the 51-car-platoon, indicating that the traffic flow is likely to be stable. In contrast, below this critical speed, traffic flow is unstable and can lead to the formation of traffic jams. Traffic data from the Nanjing Airport Highway support the experimental observation of existence of a critical speed. Based on these findings, we propose an alternative mechanism of traffic instability: the competition between stochastic factors and the so-called speed adaptation effect, which can better explain the concave growth of speed standard deviation in traffic flow.

Nonlocal Thermo-Electro-Mechanical coupling vibrations of axially moving piezoelectric nanobeams

Abstract: This work is concerned with the thermo-electro-mechanical coupling transverse vibrations of axially moving piezoelectric nanobeams which reveal potential applications in self-powered components of biomedical nano-robot. The nonlocal theory and Euler piezoelectric beam model are employed to develop the governing partial differential equations of the mathematical model for axially moving piezoelectric nanobeams. The natural frequencies of nanobeams under simply supported and fully clamped boundary constraints are numerically determined based on the eigenvalue method. Subsequently, some detailed parametric studies are presented and it is shown that the nonlocal nanoscale effect and axial motion effect contribute to reduce the bending rigidity of axially moving piezoelectric nanobeam and hence its natural frequency decreases within the framework of nonlocal elasticity. Moreover, the natural frequency decreases with increasing the positive external voltage, axial compressive force and change of temperature, while increases with increasing the axial tensile force. The critical speed and critical axial compressive force are determined and the dynamical buckling behaviors of axially moving piezoelectric nanobeams are indicated. It is concluded the nonlocal nanoscale parameter plays a remarkable role in the size-dependent natural frequency, critical speed and critical axial compressive force.

Critical speed and free vibration analysis of spinning 3D single-walled carbon nanotubes resting on elastic foundations

Abstract: In this article, the influences of critical speed on the free vibration behavior of spinning 3D single-walled carbon nanotubes (SWCNT) are investigated using modified couple stress theory (MCST). Moreover, the surrounding elastic medium of SWCNT has been considered as a model of Winkler, characterized by the spring. Taking into consideration the first-order shear deformation theory (FSDT), the rotating SWCNT is modeled and its equations of motion are derived using the Hamilton principle. The formulations include Coriolis, centrifugal and initial hoop tension effects due to rotation of the SWCNT. The accuracy of the presented model is validated by some cases in the literature. The novelty of this study is considering the effects of rotation and MCST, in addition to considering the various boundary conditions of SWCNT. The generalized differential quadrature method (GDQM) is used to discretize the model and to approximate the equation of motion. Then investigation has been made on critical speed and natural frequency of the rotating SWCNT due to the influence of initial hoop tension, material length scale parameter, constant of spring, frequency mode number, angular velocity, length-to-radius ratio, radius-to-thickness ratio and boundary conditions.

The influence of soil nonlinear properties on the track/ground vibration induced by trains running on soft ground

Abstract: The deflections of the track under a moving train depend on the stiffness of the underlying soil as well as the properties of the track and the train. In many situations, small-strain linear properties can be assumed for the soil. However, particularly for soft soil, as the load speed approaches the speed of Rayleigh waves in the ground, the deflections increase considerably. In such situations the use of the small-strain soil stiffness may lead to inaccuracies in the estimates of track deflections or of the critical speed. A finite element model of the track and ground has been developed to study the deflections induced by trains running on soft ground. Soil nonlinearity is introduced through a user-defined subroutine. The nonlinearity is specified in terms of the shear modulus reduction as a function of octahedral shear strain, which can be based on data obtained from laboratory tests on soil samples. The model is applied to the soft soil site at Ledsgard in Sweden, from which extensive measurements are available from the late 1990s. It is shown that the use of a linear model based on the small-strain soil parameters leads to an underestimation of the track displacements when the train speed approaches the critical speed, whereas the nonlinear model gives improved agreement with measurements. In addition, an equivalent linear model is considered, in which the equivalent soil modulus is derived from the laboratory curve of shear modulus reduction using an ‘effective’ shear strain. For this approach it is shown that the predictions in this specific case are improved by using a value of 20% of the maximum strain as the effective strain rather than the value of 65% commonly used in earthquake studies.

Critical rotational speed, critical velocity of fluid flow and free vibration analysis of a spinning SWCNT conveying viscous fluid

Abstract: In this article, the influences of rotational speed and velocity of viscous fluid flow on free vibration behavior of spinning single-walled carbon nanotubes (SWCNTs) are investigated using the modified couple stress theory (MCST). Taking attention to the first-order shear deformation theory, the modeled rotating SWCNT and its equations of motion are derived using Hamilton’s principle. The formulations include Coriolis, centrifugal and initial hoop tension effects due to rotation of the SWCNT. This system is conveying viscous fluid, and the related force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. The accuracy of the presented model is validated with some cases in the literatures. Novelty of this study is considering the effects of spinning, conveying viscous flow and MCST in addition to considering the various boundary conditions of the SWCNT. Generalized differential quadrature method is used to approximately discretize the model and to approximate the equations of motion. Then, influence of material length scale parameter, velocity of viscous fluid flow, angular velocity, length, length-to-radius ratio, radius-to-thickness ratio and boundary conditions on critical speed, critical velocity and natural frequency of the rotating SWCNT conveying viscous fluid flow are investigated.

Whirl frequencies and critical speeds of a rotor-bearing system with a cracked functionally graded shaft – Finite element analysis

Abstract: Finite element (FE) formulations have been developed for dynamic analysis of a functionally graded (FG) shaft having a transverse crack. Two nodded Timoshenko beam element with four degrees of freedom (DOFs) per node has been used where effects of translational and rotary inertia, transverse shear deformations, and gyroscopic moments are considered. Local flexibility coefficients (LFCs) of the cracked FG shaft are determined analytically as a function of crack size, power-law gradient index (k), and temperature using the Castigliano's theorem and Paris's equations which are used to compute the stiffness matrix in the FE analysis. Temperature dependent thermo-elastic material properties of the FG shaft are considered graded in the radial direction following power-law gradation. Using the present formulations, an FG shaft composed of zirconia (ZrO2) and stainless steel (SS) is considered and the forward and backward whirl frequencies and critical speeds are determined. Influences of crack size, power-law gradient index, slenderness ratio, and temperature gradient on the dynamic characteristics of the rotor-bearing system with an FG shaft have been studied. Results show that the power-law gradient index has significant influence on the whirl frequencies and critical speed both for cracked and un-cracked FG shaft and could be judiciously chosen in designing FG shafts.

Experimental Investigations of Resonance Vibration Control for Noncollocated AMB Flexible Rotor Systems

Abstract: The resonance vibration control of active magnetic bearing (AMB) supported flexible rotors is a challenging topic in the industrial applications. This work addresses the two issues on the noncollocated AMB flexible rotor systems while passing through the critical speed. A modal separation scheme is established to enhance the observability of the bending mode, and a damping optimization procedure of the electromagnetic force is proposed to provide the maximum control efficiency. First, the rotor imbalance analysis is carried out, and several possible approaches to minimize the vibration of the flexible rotor are presented. Then, the detailed descriptions of the bending mode extraction scheme using notch filters and phase-lead compensators are discussed for a noncollocated flexible rotor system. The root locii of the closed-loop AMB-rotor system with and without additional phase-lead compensator are also performed. A solution to determining the phase angles between the measured rotor displacements to the bearing forces is established using the physical modeling and experimental identification. Finally, simulation and experimental results on a 10 kW magnetically suspended centrifugal compressor show the effectiveness of the proposed methods.

Sommerfeld effect in a gyroscopic overhung rotor-disk system

Abstract: Deflection of a rotor-disk at the free end of a flexible overhung rotor-shaft causes rotation about diametral axis and consequently leads to a strong gyroscopic coupling in a spinning overhung rotor system. When the rotor is spun up about its axis, the unbalance in the rotor-disk causes transverse and rotational vibrations to increase as the spin speed approaches the critical speed of the rotor. These transverse and rotational vibrations dissipate a lot of energy, and if the rotor is driven through a non-ideal drive, i.e., a motor which can supply a limited amount of power, then the entire motor power may be spent to account for the energy dissipation. As a result, the rotor speed may get stuck in resonance at the critical speed or jump through the critical speed to a much higher speed with lower transverse and rotational vibration levels. These symptoms, normally referred to as the Sommerfeld effect, occur due to the intrinsic energetic coupling between the drive and the driven systems and are important design considerations for development of various rotating machinery with flexible rotor-shafts or supports (bearings). Sommerfeld effect in a strongly gyroscopic rotor dynamic system is studied in this article. The dynamics of an overhung rotor system near the regimes of Sommerfeld effect is studied by using a discrete and a continuous shaft-rotor model coupled with the model of the non-ideal motor drive. The models are developed using multi-energy domain modeling approach in bond graph model form. A steady-state analysis of power transfer mechanism is used to postulate the ideal characteristics of Sommerfeld effect in the neighborhood of the critical speed, and thereafter, full transient analysis is performed with aid of the bond graph model-generated coupled equations of motion to validate the postulated characteristics of the Sommerfeld effect.

The Influence of Shaft’s Bending on the Coupling Vibration of a Flexible Blade-Rotor System

Abstract: The influence of shaft bending on the coupling vibration of rotor-blades system is nonignorable. Therefore, this paper analyzed the influence of shaft bending on the coupling vibration of rotor-blades system. The vibration mode function of shaft under elastic supporting condition was also derived to ensure accuracy of the model as well. The influence of the number of blades, the position of disk, and the support stiffness of shaft on critical speed of system was analyzed. The numerical results show that there were two categories of coupling mode shapes which belong to a set where the blade’s first two modes predominate in the system: shaft-blade (SB) mode and interblade (BB) mode due to the coupling between blade and shaft. The BB mode was of repeated frequencies of () multiplicity for number blades, and the SB mode was of repeated frequencies of () multiplicity for number blades. What is more, with the increase of the number of blades, natural frequency of rotor was decreasing linearly, that of BB mode was constant, and that of SB mode was increasing linearly. Natural frequency of BB mode was not affected while that of rotor and SB mode was affected (changed symmetrically with the center of shaft) by the position of disk. In the end, vibration characteristics of coupling mode shapes were analyzed.

Design optimization of rotor-bearing system considering critical speed using Taguchi method:

Abstract: The purpose of this study is to utilize Taguchi method, which can prove to be a handy and effective tool for determining minimum vibration response of rotor-bearing system set to avoid running at critical speed. In the study, three test cases considering different coupling type (elastic, jaw, and solid) and disc location (disc location A, B, and C) were conducted to observe behavioral changes of the shaft system considering vibration signatures. Each test case was conducted for three different shaft running speeds of 12, 18, and 24 Hz. To find the minimum peak amplitude values by experimenting different combinations of the rotor-bearing system set needs a lot of experiments for reaching solution. Moreover, the solution proves costly because of the time consumed in doing many experiments. This fact depicts the importance of an efficient optimization method to be used. Taguchi method can determine the design parameters, which have the greatest influence on the solution through a very limited number of exper...

Online control of critical speed vibrations of a single-span rotor by a rotor dynamic vibration absorber at different installation positions

Abstract: The serious vibration of rotors around the critical speed is a problem in rotor systems To overcome this problem, a single-span twodisk rotor bench was built to simulate the starting process of a rotor A new Rotor dynamic vibration absorber (RDVA) was designed and installed in the middle of the rotor A on-off control method based on speed was applied to control the on-off position of the electromagnet in RDVA Therefore, the natural frequencies between two selected values could be changed The principles for the vibration control of the rotor system were studied The vibration suppression performance of an RDVA is a function of its location The location of the RDVA is subject to several constraints due to the compact structure of the rotor system As a result, RDVA cannot always be installed at the optimal location of vibration suppression Accordingly, a study was performed to observe the effect of RDVA location on the vibration suppression performance Results showed that installing RDVA with on-off control between the two disks not only suppressed the violent vibrations of the rotor at critical speed during the starting process but also avoided the two resonance peaks generated by the traditional absorber RDVA maintained the vibration of the rotor at a low level in the entire speed range Furthermore, the vibrations of the rotor system decreased by 20 % when RDVA was installed near the rotor support

Sliding down an arbitrary curve in the presence of friction

Abstract: The motion of a block sliding on a curve is a well studied problem for flat and circular surfaces, but the necessary conditions for the block to leave the surface deserve a deeper treatment. In this article, we generalize this problem to an arbitrary surface, including the effects of friction, and provide a general expression to determine under what conditions a particle will leave the surface. An explicit integral form for the speed is given, which is analytically integrable for some cases. We demonstrate general criteria to determine the critical speed at which the particle immediately leaves the surface. Three curves, a circle, a cycloid, and a catenary, are analyzed in detail, revealing several interesting features.

The generation of gravity–capillary solitary waves by a pressure source moving at a trans-critical speed

Abstract: The unsteady response of a water free surface to a localized pressure source moving at constant speed in the range , where is the minimum phase speed of linear gravity–capillary waves in deep water, is investigated through experiments and numerical simulations. This unsteady response state, which consists of a V-shaped pattern behind the source, and features periodic shedding of pairs of depressions from the tips of the V, was first observed qualitatively by Diorio et al. (Phys. Rev. Lett., vol. 103, 2009, 214502) and called state III. In the present investigation, cinematic shadowgraph and refraction-based techniques are utilized to measure the temporal evolution of the free-surface deformation pattern downstream of the source as it moves along a towing tank, while numerical simulations of the model equation described by Cho et al. (J. Fluid Mech., vol. 672, 2011, pp. 288–306) are used to extend the experimental results over longer times than are possible in the experiments. From the experiments, it is found that the speed–amplitude characteristics and the shape of the depressions are nearly the same as those of the freely propagating gravity–capillary lumps of inviscid potential theory. The decay rate of the depressions is measured from their height–time characteristics, which are well fitted by an exponential decay law with an order one decay constant. It is found that the shedding period of the depression pairs decreases with increasing source strength and speed. As the source speed approaches , this period tends to approximately 1 s for all source magnitudes. At the low-speed boundary of state III, a new response with unsteady asymmetric shedding of depressions is found. This response is also predicted by the model equation.

Vibration analysis of functionally graded nanocomposite plate moving in two directions

Abstract: In the present study, vibration analysis of functionally graded carbon nanotube reinforced composite (FGCNTRC) plate moving in two directions is investigated. Various types of shear deformation theories are utilized to obtain more accurate and simplest theory. Single-walled carbon nanotubes (SWCNTs) are selected as a reinforcement of composite face sheets inside Poly methyl methacrylate (PMMA) matrix. Moreover, different kinds of distributions of CNTs are considered. Based on extended rule of mixture, the structural properties of composite face sheets are considered. Motion equations are obtained by Hamilton's principle and solved analytically. Influences of various parameters such as moving speed in x and y directions, volume fraction and distribution of CNTs, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of composite plate on the vibration characteristics of moving system are discussed in details. The results indicated that thenatural frequency or stability of FGCNTRC plate is strongly dependent on axially moving speed. Moreover, a better configuration of the nanotube embedded in plate can be used to increase the critical speed, as a result, the stability is improved. The results of this investigation can be used in design and manufacturing of marine vessels and aircrafts.

Suppressing Wind-Induced Oscillations of Prismatic Structures by Dynamic Vibration Absorbers

Abstract: The suppression of oscillations of an elastically mounted prism under galloping by a dynamic vibration absorber (DVA) with linear damping and stiffness is investigated. A model considering the dynamic coupling of the prism and the DVA is constructed, with the aerodynamic loads acting on the system represented by a quasi-steady approximation. Based on the coupled nonlinear governing equations of motion, a linear analysis is first conducted to explore the coupled frequency and damping, and the onset speed of galloping in the presence of the DVA. Subsequently, the normal form of the Hopf bifurcation for the coupled system near the onset of galloping is derived to characterize the type of instability (supercritical or subcritical), while evaluating the effects of the DVA parameters. The results show that with appropriate parametric values, the DVA has great impact on the onset speed of galloping and can significantly alleviate the oscillation amplitude of the prism.

Modeling of the effects of phase shift on cutting performance in elliptical vibration cutting

Abstract: In the elliptical vibration cutting process, the elliptical locus is considered to be a vital factor that affects cutting performance. Besides the cutting speed and vibration amplitudes, the phase shift (i.e., the phase difference between the two-directional output harmonic vibrations forming the elliptical locus) is an intrinsic parameter that determines the shape and inclination of the elliptical locus with respect to the cutting direction. In this paper, a numerical recursive search method is proposed to investigate the effect of phase shift in elliptical vibration cutting. It has been shown that the critical speed ratio for considerably improving the cutting performance has a sinusoidal correlation with the phase shift. For elliptical loci with arbitrary shapes, the developed model theoretically predicts the maximal influential thickness of cut, surface roughness, and the tool-workpiece contact ratio as a function of phase shifts. Experiments were conducted to validate the developed model through the evaluation of the machined surface profile, roughness, and dynamic cutting force. The obtained results offer a method to determine the proper machining variables in cutting hard and brittle materials during the elliptical vibration cutting process with an arbitrary locus.

Vibration characteristic analysis and numerical confirmation of an axially moving plate with viscous damping

Abstract: In this paper, the vibration characteristics of axially moving plates with viscous damping are analyzed. A partial differential linear equation of motion with four simply supported edges is presented. The effects of two different viscous damping models are highlighted, while both of them have been introduced in previous studies. The investigation into the two different viscous damping models is interesting in itself. It is noteworthy that which model is closer to the fact, for which there are no systematic techniques of investigation to deal with this problem. In order to give a reference for possible verification in experiment, the difference of the two different viscous damping models in theory was proposed. The complex frequencies and its corresponding complex modes are studied by the complex mode approach. As other parameters are fixed, the effect of some parameters, such as viscous damping coefficients, axial speeds, aspect ratios, stiffness ratios, and support stiffness parameters, on the frequencie...

Critical rotating speed of rotor cup in an air suction open-end spinning machine

Abstract: Simulation of three-dimensional turbulent flow in a rotor spinning machine is carried out, and the flow structure and behavior in the rotor cup are analyzed. The governing equations are the steady three-dimensional Navier–Stokes equations and the Spalart–Allmaras turbulence model. The results show that the rotating speed has great influence on the flow behavior in the rotor cup. It is found that there is a critical speed of the rotor cup beyond which the pressure and velocity on the slip surface is not changed anymore regardless of the magnitude of the rotating speed. When the rotating speed is larger than this critical speed, the flow structure becomes unstable with the increasing of the rotating speed. The mechanism of this phenomenon is that the airflow in the rotor groove passes about 180 degrees from two sides along the rotor wall and a pressure balance is achieved. When the rotating speed is larger than the critical speed, the balance will break down. When the rotor speed is low, the flow characteri...

Ride, eigenvalue and stability analysis of three-wheel vehicle using Lagrangian dynamics

Abstract: This research paper studies the ride behaviour of coupled vertical-lateral 9 degree of freedom model of a three wheel vehicle formulated using Lagrangian dynamics. The mathematical model is validated by simulating PSD vertical and lateral acceleration of three-wheel vehicle sprung mass and comparing the same obtained from actual testing results. The natural frequencies, i.e., eigenvalues of main rigid bodies, i.e., sprung mass, front wheel steering arm and rear unsprung mass of the system are determined through MATLAB simulations. Critical speed of the vehicle is also determined in order to investigate the dynamic stability, and parameters which influence the critical speed are analysed.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate

Abstract: The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.

Dynamic Behaviour Analysis of a Commercial Roll-Tensioned Circular Sawblade

Abstract: A commercial woodcutting circular sawblade was analysed in this work. The lateral stiffness on the periphery was measured, and the natural frequencies were determined by modal analyses. The sawblade was modelled by the finite element method, where the influence of the internal stresses caused by roll-tensioning of the sawblade was considered. The roll-tensioning force was determined based on the measurement of the sawblade rolling profile, where it was established that the sawblade had been rolled with a force of 7800 N. The analysis showed that at the aforementioned force, the lateral stiffness was a maximum; here, the calculated and measured stiffnesses were 81 and 60 N/mm, respectively. The calculated natural frequencies agree well with the measured ones, where in the most important vibrational modes there is only a 7% difference. The maximum rotational speed for the sawblade was determined to be 85% of the critical speed. Because the sawblade was clamped with a ratio of clamping of only 0.25, the maximum rotational speed was amounted to 6630 rpm. Increasing the rolling force would increase the critical speed but greatly reduce the lateral stiffness.

Shock-Resistance Rotor Design of A High-Speed PMSM for Integrated Pulsed Power System

Abstract: This paper provides stress analytical models for a variable-speed simplified rotor of the surface-mounted permanent magnet synchronous motor (PMSM) The impact developed by alternator discharge on the prime motor rotor was analyzed Parameters, such as interference fits between sleeve and magnets, rotor core and shaft, sleeve thickness, rotor heating have significant influences on the design of the shock-resistance rotor Then the stress distribution of the actual rotor was verified by a 3-D finite element analysis model, and the critical speed of the integrated rotor was computed