Self-excited Motion Research Articles

Self-Sustained Oscillation of Electrothermally Responsive Liquid Crystal Elastomer Film in Steady-State Circuits.

Self-excited oscillations have the advantages of absorbing energy from a stable environment and Self-control; therefore, Self-excited motion patterns have broader applications in micro devices, autonomous robots, sensors and energy-generating devices. In this paper, a Self-sustained curling liquid crystal elastomer (LCE) film-mass system is proposed on the basis of electrothermally responsive materials, which can realize Self-oscillation under a steady-state current. Based on the contact model and dynamic LCE model, a nonlinear dynamics model of LCE film in steady-state circuits is developed and numerical calculations are carried out using the Runge-Kutta method. Through numerical calculations, it is demonstrated that LCE film-mass systems have two motion patterns in steady-state circuits: namely, a Self-oscillation pattern and a stationary pattern. Self-sustained curling of LCE film originates from the fact that the energy absorbed by the system exceeds the energy dissipated due to the damping effect. In addition, the critical conditions for triggering Self-oscillation and the effects of several key dimensionless system parameters on the amplitude and period of Self-oscillation are investigated in detail. Calculation results show that the height of electrolyte solution, gravitational acceleration, elastic modulus of LCE film, limit temperature, curvature coefficient, thermal shrinkage coefficient and damping factor all have a modulating effect on the amplitude and period of Self-oscillation. This research may deepen the understanding of Self-excited oscillation, with promising applications in energy harvesting, power generation, monitoring, soft robotics, medical devices, and micro and nano devices.

Self-oscillating floating of a spherical liquid crystal elastomer balloon under steady illumination

Self-oscillations have the advantages of direct energy harvest from the constant environment, autonomy, and portability of the equipment, and it is desired to develop a wealth of new self-excited motion modes for greatly expanding the application of active machines. In this paper, a self-oscillating floating balloon is creatively constructed, which consists of an optically-responsive liquid crystal elastomer (LCE) spherical balloon under steady layered illumination. A theoretical model is developed based on the well-established dynamic LCE model and the ideal gas model, and dynamics of the self-floating balloon is calculated numerically. The results show that the LCE balloon can self-float continuously up and down by the steady layered illumination, which is elucidated to arise from the coupling between the process-related buoyancy and the constant gravity. The self-floating of the LCE balloon can be maintained by the energy of the constant illumination, which compensates for the damping dissipation of the system. Furthermore, the effects of the system parameters on the triggering condition, amplitude and equilibrium position of the self-floating are extensively investigated. The self-floating balloon constructed in this paper will expand the application scope of self-oscillations, and its simple operation and accurate control will enjoy great application prospects in the fields of soft robotics, targeted therapy, military monitoring and environmental measurement.

Thermally driven self-oscillation of an elastomer fiber with a hanging weight

Self-excited motion has been recently extensively explored for various applications ranging from autonomous systems to energy harvesting devices. Our recent experiment has discovered that an ultrathin thermally responsive liquid crystal elastomer (LCE) fiber with a hanging weight can self-oscillate in a steady temperature field. Compared to many systems previously studied, which can generate self-excited motions when subjected to time-invariant stimuli such as light and humidity, the LCE fiber–mass system is simple and its heat-driven self-oscillation is very robust. During the self-oscillation, the LCE fiber continuously converts thermal energy to mechanical work, making it capable of harvesting low-grade waste heat. In this paper, we formulate a nonlinear dynamic theory for the system to understand its heat driven self-oscillation behavior. We have further obtained asymptotic solutions of the system with a few assumptions.

Self-excited air flow passage changing device for periodic pressurization of soft robot

Recently pneumatic-driven soft robots have been widely developed. Usually, the operating principle of this robot is the inflation and deflation of elastic inflatable chambers by air pressure. Some soft robots need rapid and periodic inflation and deflation of their air chambers to generate continuous motion such as progress motion or rotational motion. However, if the soft robot needs to operate far from the air pressure source, long air tubes are required to supply air pressure to its air chambers. As a result, there is a large delay in supplying air pressure to the air chamber, and the motion of the robot slows down. In this paper, we propose a compact device that changes its airflow passages by self-excited motion generated by a supply of continuous airflow. The diameter and the length of the device are 20 and 50 mm, respectively, and can be driven in a small pipe. Our proposed in-pipe mobile robot is connected to the device and can move in a small pipe by dragging the device into it. To apply the device widely to other soft robots, we also discuss a method of adjusting the output pressure and motion frequency.

Light-powered self-excited motion of a liquid crystal elastomer rotator

Self-excited motions have the advantages of directly harvesting energy from the environment, autonomy, and portability of the equipment, and consequently, the development of a wealth of new self-excited motion modes can greatly expand the application of active machines. In this paper, a rotator capable of self-excited movement is proposed, which consists of a liquid crystal elastomer (LCE) bar and a regular bar with an axle. Based on the dynamic LCE model, through theoretical modeling and numerical calculation, it is found that the LCE rotator has three motion modes, namely static mode, oscillation mode and rotation mode. The detailed dynamical process reveals the mechanism of self-excited oscillation and rotation. In this paper, the effects of parameters such as light intensity, damping coefficient, dimensionless gravitational acceleration, length ratio, illumination region and initial angular velocity on the self-excited oscillation and rotation are further studied systematically, and the corresponding limit cycles are given by various cases. The results show that the light intensity, damping coefficient and length ratio have important influence on the motion mode, while the initial angular velocity does not affect the motion mode. The influence of various parameters including light intensity and illumination region on the amplitude and frequency of self-excited oscillation is also studied. It is found that the amplitude mainly depends on light intensity and damping. This study can deepen people's understanding of non-equilibrium self-excited motions and provide promising applications in the fields of energy harvest, power generation, monitoring, soft robotics, medical devices and micro–nano-devices.

Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

The nonlinear behavior of a rigid rotor supported by herringbone grooved journal gas bearings (HGJBs) was investigated in this study. The two-dimensional narrow groove theory (2D-NGT) was adopted to model the HGJBs. A set of integrated rotor-bearing state equations were built by coupling the rotor motion equations and the bearing Reynolds equation. An implicit integrator with adaptive time step method was used to solve those state equations continuously. Two low-stability HGJBs were implemented to experimentally demonstrate and analyze the appearance of self-excitation motions. The theoretical model was successfully validated by the experimental data on predicting the onset speed of the sub-synchronous vibration of the HGJB-rotor system and the whirl frequency ratio. The predicted limit cycle amplitude increases as the speed increases until the rotor contacts with the bearing surface, which leads to a bearing failure. Forward conical mode dominates the self-excited motion during the whole speed range of self-excited motion. The prediction shows that the HGJB-rotor system can still operate in a stable, even though the rotor is installed vertically, i.e., without static load on the bearings. This is a distinct advantage in comparison to plain bearings. As the static load applies on the bearings increases, the onset speed of sub-synchronous vibration increases as well. For the investigated rotor-bearing system, an increase of the onset speed of sub-synchronous vibration from 36 krpm to 75 krpm is predicted as the static load increases from 0 to 4 times of the rotor weight. This indicates an increased HGJB stability with increased static load. The rotor orbits show complex shapes when the imbalance excitation is considered in the simulation. Both synchronous frequency and whirl frequency are shown in the spectral analysis. Moreover, the speed range of self-excited motion reduces from [38,48] krpm to [40,42] krpm as the imbalance increases from 0 to 40 mgmm.

Post-critical behavior of an auto-parametric aero-elastic system with two degrees of freedom

A generalized two-degree-of-freedom non-linear mathematical system with non-linear gyroscopic and non-conservative terms was used to set up a model for heave and pitch self-excited motion. The stability conditions for a girder with a bluff cross-section in wind flow were identified and presented. The analysis, based on the Routh–Hurwitz conditions and a numerical evaluation of the model, comprises both the self-excited case and an assumption of a harmonic load. The boundaries between different response types that depend on the frequencies of two principal aero-elastic modes are shown. The properties of the response located at these limits and the tendencies of the response in their neighborhood are discussed. The results can be used to explain several experimentally observed effects.

Leakage, Drag Power, and Rotordynamic Force Coefficients of an Air in Oil (Wet) Annular Seal

Wet gas compression systems and multiphase pumps are enabling technologies for the deep sea oil and gas industry. This extreme environment determines both machine types have to handle mixtures with a gas in liquid volume fraction (GVF) varying over a wide range (0–1). The gas (or liquid) content affects the system pumping (or compression) efficiency and reliability, and places a penalty in leakage and rotordynamic performance in secondary flow components, namely seals. In 2015, tests were conducted with a short length smooth surface annular seal (L/D = 0.36, radial clearance = 0.127 mm) operating with an oil in air mixture whose liquid volume fraction (LVF) varied to 4%. The test results with a stationary journal show the dramatic effect of a few droplets of liquid on the production of large damping coefficients. This paper presents further measurements and predictions of leakage, drag power, and rotordynamic force coefficients conducted with the same test seal and a rotating journal. The seal is supplied with a mixture (air in ISO VG 10 oil), varying from a pure liquid to an inlet GVF = 0.9 (mostly gas), a typical range in multiphase pumps. For operation with a supply pressure (Ps) up to 3.5 bar(a), discharge pressure (Pa) = 1 bar(a), and various shaft speed (Ω) to 3.5 krpm (ΩR = 23.3 m/s), the flow is laminar with either a pure oil or a mixture. As the inlet GVF increases to 0.9 the mass flow rate and drag power decrease monotonically by 25% and 85% when compared to the pure liquid case, respectively. For operation with Ps = 2.5 bar(a) and Ω to 3.5 krpm, dynamic load tests with frequency 0 < ω < 110 Hz are conducted to procure rotordynamic force coefficients. A direct stiffness (K), an added mass (M), and a viscous damping coefficient (C) represent well the seal lubricated with a pure oil. For tests with a mixture (GVFmax = 0.9), the seal dynamic complex stiffness Re(H) increases with whirl frequency (ω); that is, Re(H) differs from (K−ω2M). Both the seal cross coupled stiffnesses (KXY and −KYX) and direct damping coefficients (CXX and CYY) decrease by approximately 75% as the inlet GVF increases to 0.9. The finding reveals that the frequency at which the effective damping coefficient (CXXeff = CXX − KXY/ω) changes from negative to positive (i.e., a crossover frequency) drops from 50% of the rotor speed (ω = 1/2 Ω) for a seal with pure oil to a lesser magnitude for operation with a mixture. Predictions for leakage and drag power based on a homogeneous bulk flow model match well the test data for operation with inlet GVF up to 0.9. Predicted force coefficients correlate well with the test data for mixtures with GVF up to 0.6. For a mixture with a larger GVF, the model under predicts the direct damping coefficients by as much as 40%. The tests also reveal the appearance of a self-excited seal motion with a low frequency; its amplitude and broad band frequency (centered at around ∼12 Hz) persist and increase as the gas content in the mixture increase. The test results show that an accurate quantification of wet seals dynamic force response is necessary for the design of robust subsea flow assurance systems.

Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding.

We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.

Galloping instability and control of a rigid pendulum in a flowing soap film

A pendulum suspended in a fast flowing soap film may show sustained oscillations. The conditions necessary for self-excited motion to occur are outlined: a flow velocity above a threshold value along with geometrical constraints. The role of vortex shedding is discussed, and the observed instability is shown to be well-described by the galloping instability. Experimental results are supported by numerical simulations. Furthermore, we observe that the instability may be suppressed by attaching a long enough filament to the rear of the pendulum.

Comparison Vibration Amplitude for Magnetic Damping in Turning of Stainless Steel AISI 304

This paper presents the improvement in chatter vibration damping using different types and arrangements of magnets, as well as comparison with normal cutting conditions in turning of stainless steel AISI 304. Chatter is defined as the self-excited violent relative motion between the cutting tool and work-piece. It is the common vibration problem that limits the productivity of machining processes, since it leads to shortened tool life, poor surface finish, breakage and premature damage of cutting tool, as well as mechanical deterioration. The occurrence of chatter during metal cutting process also causes instability of the machine tool system. Though there has been a large number of works on identifying the causes of chatter and its behavior, there is still no consensus among researchers on this very vital issue of machining. Previously, the incidence of chatter was thought to be due to forced vibration, BUE formation, cutting speed, and cracking during chip formation. Different ways to overcome this problem have been investigated, such as using piezoelectric inertia actuators, feed-forward neural network controllers, and work-piece preheating methods. In this research, permanent magnets with different size, strength, and composition are mounted around the cutting tool. A vibration sensor (accelerometer) is placed at the bottom of the tool to record the suppression of chatter amplitude in turning operation. It is shown that magnetic force can modify the frequency response function of the cutting tool resulting in improved cutting stability in turning operations. Chatter can then be effectively suppressed due to increased cutting stability.

Development of Mathematical Model for Chip Serration Frequency in Turning of Stainless Steel with Magnetic Damping from Tool Side

Chatter, the self-excited and violent oscillatory motion between the tool and the work-piece, is detrimental to all machining operations, especially turning. It can lead to poor surface topography, reduced productivity, excessive tool wear, and damaged machine-tool components. Several theories have been introduced to explain chatter, but their predictions have not always been reliable. Therefore, chatter avoidance has relied on inefficient techniques like limiting material removal rates or expensive setups such as actuators and ultrasonic vibration damping systems. However, a deeper investigation into chatter formation reveals that chip morphology and segmentation play a significant role during incidence of machining chatter. The novel Resonance theory of chatter combines the concept of mode coupling of the machining setup and serrated chip formation, to explain the incidence of chatter. To validate the postulates of this theory, models for chip serration frequency are essential. At the same time, a reliable and economical chatter control method is required. To this end, the current research work developed an empirical mathematical model of chip serration frequency in turning of stainless steel AISI 304 using Response Surface Methodology (RSM). Also, it investigated the influence of damping provided by magnetic field from a permanent magnet. The developed chip serration model shows good agreement with experimental data.

Response types and general stability conditions of linear aero-elastic system with two degrees-of-freedom

The unified linear variant of the general mathematical description of stability conditions for a girder with a bluff cross-section under the influence of wind flow is presented. A double degree-of-freedom model for the heave and pitch self-excited motion is used. The properties of the response located at the stability limits and the tendencies of the response in their vicinity are analyzed by means of the Routh–Hurwitz theorem. The respective stability conditions are depicted in the frequency plane delimited by the frequencies of two principal aero-elastic modes. Conditions for flutter onset and divergence are identified as special cases of the general theory. The results can be used as an explanation of several experimentally observed effects. The application of this method to real bridges is presented and compared with existing results from other approaches.

Recirculation zone dynamics of a transversely excited swirl flow and flame

This work investigates the response of the vortex breakdown region of a swirling, annular jet to transverse acoustic excitation for both non-reacting and reacting flows. This swirling flow field consists of a central vortex breakdown region, two shear layers, and an annular fluid jet. The vortex breakdown bubble, a region of highly turbulent recirculating flow in the center of the flowfield, is the result of a global instability of the swirling jet. Additionally, the two shear layers originating from the inner and outer edge of the annular nozzle are convectively unstable and rollup due to the Kelvin-Helmholtz instability. Unlike the convectively unstable shear layers that respond in a monotonic manner to acoustic forcing, the recirculation zone exhibits a range of response characteristics, ranging from minimal response to exhibiting abrupt bifurcations at large forcing amplitudes. In this study, the response of the time-average and fluctuating recirculation zone is measured as a function of forcing frequency, amplitude, and symmetry. The time-average flow field is shown to exhibit both monotonically varying and abrupt bifurcation features as acoustic forcing amplitude is increased. The unsteady motion in the recirculation zone is dominated by the low frequency precession of the vortex breakdown bubble. In the unforced flow, the azimuthal m = −2 and m = −1 modes (i.e., disturbances rotating in the same direction as the swirl flow) dominate the velocity disturbance field. These modes correspond to large scale deformation of the jet column and two small-scale precessing vortical structures in the recirculation zone, respectively. The presence of high amplitude acoustic forcing changes the relative amplitude of these two modes, as well as the character of the self-excited motion. For the reacting flow problem, we argue that the direct effect of these recirculation zone fluctuations on the flame response to flow forcing is not significant. Rather, flame wrinkling in response to flow forcing is dominated by shear layer disturbances. Recirculation zone dynamics primarily influence the time-average flame features (such as spreading angle). These influences on the flame response are indirect, as they control the transfer function relating shear layer fluctuations and the resulting flame response.

Identification of the nonlinear excitation force acting on a bowed string using the dynamical responses at remote locations

For achieving realistic numerical simulations of bowed string instruments, based on physical modeling, a good understanding of the actual friction interaction phenomena is of great importance. Most work published in the field including our own has assumed that bow/string frictional forces behave according to the classical Coulomb stick–slip model, with an empirical velocity-dependent sliding friction coefficient. Indeed, the basic self-excited string motions (such as the Helmholtz regime) are well captured using such friction model. However, recent work has shown that the tribological behavior of the bow/string rosin interface is rather complex, therefore the basic velocity-dependent Coulomb model may be an over-simplistic representation of the friction force. More specifically, it was suggested that a more accurate model of the interaction force can be achieved by coupling the system dynamical equations with a thermal model which encapsulates the complex interface phenomena. In spite of the interesting work performed by Askenfelt [32], a direct measurement of the actual dynamical friction forces without disturbing the string motion is quite difficult. Therefore, in this work we develop a modal-based identification technique making use of inverse methods and optimization techniques, which enables the identification of the interface force, as well as the string self-excited motion, from the dynamical reactions measured at the string end supports. The method gives convincing results using simulated data originated from nonlinear computations of a bowed string. Furthermore, in cases where the force identifications are very sensitive to errors in the transfer function modal parameters, we suggest a method to improve the modal frequencies used for the identifications. Preliminary experimental results obtained using a basic bowing device, by which the string is excited with the stick of the bow, are then presented. Our identifications, from the two dynamical string reactions, are consistent as attested by the comparison of the two available versions of the string dynamical motion and of the friction force. Furthermore, the method seems adequate to investigate the interface force for the bowed string.

Bifurcation Analysis of Ultrashort Self-Acting Gas Journal Bearings for MEMS

The development of microrotational devices in microelectromechanical systems (MEMS) has introduced a kind of ultrashort self-acting gas journal bearing with low length-to-diameter ratios. The bifurcation of ultrashort self-acting gas journal bearing-rotor systems is studied in this paper. The system is modeled as a rigid rotor supported by bearing forces as a result of gas viscosity and rotational speed. The spectral collection method is employed to discretize the nonlinear Reynolds equation describing the pressure distribution of the working fluid of the bearing. A system of nonlinear partial differential equations, which couples the fluid equation and the equations of the rotor motion, is presented and solved using the Runge-Kutta method. The bifurcation diagram, rotor center orbits, phase portraits, frequency spectra, and Poincare maps are utilized to analyze the dynamic characteristics of the rotor-bearing system for different operating conditions. The effects of the rotational speed and length-to-diameter ratio on the system dynamic behaviors are investigated with both low and high initial eccentricity ratios. The analyses show that the system exhibits complicated behaviors at low eccentricity ratios as a result of the self-excited whirl motion. For high eccentricity ratios, the bearing behavior comprises synchronous and subharmonic motions. A further understanding of the nonlinear dynamics of gas journal bearing in MEMS is given by the analysis results.

Effect of vertical high-frequency parametric excitation on self-excited motion in a delayed van der Pol oscillator

We investigate the interaction effect of fast vertical parametric excitation and time delay on self-oscillation in a van der Pol oscillator. We use the method of direct partition of motion to derive the main autonomous equation governing the slow dynamic and then we apply the averaging technique on this slow dynamic to derive a slow flow. In particular we analyze the slow flow to analytically approximate regions where self-excited vibrations can be eliminated. Numerical integration is performed and compared to the analytical results showing a good agreement for small time delay. It was shown that vertical parametric excitation, in the presence of delay, can suppress self-excited vibrations. These vibrations, however, persist for all values of the excitation frequency in the case of a fast vertical parametric excitation without delay [Bourkha R, Belhaq M. Effect of fast harmonic excitation on a self-excited motion in van der Pol oscillator. Chaos, Solitons & Fractals, 2007;34(2):621–7.].

Linear Stability Analysis of a Tilting-Pad Journal Bearing System

This paper describes a mathematical model to study the linear stability of a tilting-pad journal bearing system. By employing the Newton-Raphson method and the pad assembly technique, the full dynamic coefficients involving the shaft degrees of freedom as well as the pad degrees of freedom are determined. Based on these dynamic coefficients, the perturbation equations including self-excited motion of the rotor and rotational motion of the pads are derived. The complex eigenvalues of the equations are computed and the pad critical mass identified by eigenvalues can be used to determine the stability zone of the system. The results show that some factors, such as the preload coefficient, the pivot position, and the rotor speed, significantly affect the stability of tilting-pad journal bearing system. Correctly adjusting those parameter values can enhance the stability of the system. Furthermore, various stability charts for the system can be plotted.

Effect of fast harmonic excitation on a self-excited motion in Van der Pol oscillator

Abstract This paper studies the effect of horizontal and vertical fast harmonic parametric excitation on periodic self-excited motion in Van der Pol pendulum. The method of direct partition of motion is first applied to derive the equation governing the slow motion of the oscillator which is the main equation of vibrational mechanics. Then, a perturbation method is used on the slow motion equation to obtain analytical approximation for the periodic solution and its frequency in the slow dynamic. A relationship between the frequency of the limit cycle and the frequency of the fast harmonic excitation is derived. It is shown that in the case where the point of suspension of the pendulum is subjected to horizontal fast harmonic excitation, the periodic self-excitation can disappear. In contrast, this periodic solution persists in the case of the vertical fast harmonic excitation. Numerical simulations on the slow flow and on the original equation confirms the analytical prediction.

Lund’s Contribution to Rotor Stability: The Indispensable and Fundamental Basis of Modern Compressor Design

In the early design of compressors and turbines, it was of importance to locate the rotor critical speeds so as to insure that a turbo rotor would not be operating at a critical speed. As compressor and turbine design became more sophisticated, a more detailed analysis of the rotor damped critical speeds and rotor log decrements was necessary. With compressors and turbines operating at higher speeds, under high power levels, and at multiples of the first critical speed, the problem of stability or self-excited whirling is of paramount importance. The onset of self-excited motion may lead to large amplitudes of motion with possible destructions of the rotor or the inability of the compressor to operate at peak power levels. Encountering this phenomenon with a compressor on an off-shore oil platform can mean millions of dollars of lost production. Self-excited whirling can be caused by fluid-film bearings, seals, Alford-type cross-coupling forces, or internal shaft friction, to name a few of the excitation mechanisms. The problem of computing the approximate values of the rotor log decrement under full speed and loading conditions requires the solution of a complex eigenvalue problem. The computation of the rotor complex roots is an order of magnitude more difficult than the problem of undamped critical speed calculations. J. W. Lund presented the first practical numerical procedure for computing turbo-rotor log decrements. The mathematical transfer matrix method pioneered by Lund has allowed industry to develop and stabilize a vast array of rotating machinery leading to the savings to industry of millions of dollars. Without the procedures of Lund, for example, it would not have been possible to resolve stability problems encountered with both the hydrogen and oxygen space shuttle pumps. This paper briefly presents some of the attributes of the Lund stability procedure and its unique characteristics.