Rotational Damping Research Articles

Theoretical study of a novel resettable‐inertia damper: Dynamic modeling, equivalent linearization, and performance assessment

AbstractTo passively achieve an inertial device with unidirectional force transmission similar to Bang Bang control, this study introduces a novel energy dissipation device known as the resettable‐inertia damper (RID). The ingenious motion principles of the RID, encompassing a rack‐and‐pinion, bevel gear commutation system, speed transmission, and eddy current damping, are elucidated in detail. In particular, a unidirectional rotational flywheel within the device selectively engages when the primary structure reciprocates. The physical mass of the flywheel undergoes conversion into an amplified inertia through the rack‐and‐pinion mechanism, which enables the enhancement of damping effects coupling the flywheel rotation and eddy current configuration. A coupled multibody dynamic model, combining the clutching effect, the flywheel inertia, and the rotational damping, is formulated to analyze the system with RID (RIDS). Currently, an analysis of the hysteretic behaviors of RID is carried out. To facilitate the design and evaluation of the performance of RIDS, an equivalent linearization method is proposed for RIDS. The feasibility of this simplified method is validated under harmonic excitation. Additionally, the study examines the performance of equivalent linear systems (ELSs) and RIDS under natural ground motions and stochastic stationary excitation in peak and variance responses levels, respectively. Comparison of RID with traditional inerter shows that RID can achieve a more pronounced control with less force transferred to the structure and with the potential to recover vibration energy, highlighting its unique advantages.

Dynamic performance of structures with clutching inertia‐damping system: Theoretical study

AbstractThis paper addresses performance limitations in passive clutching inertia devices due to the absence of flywheel deceleration damping. A solution introducing viscous damping to serve as the flywheel deceleration mechanism is proposed, thus forming the “CIDS” (Clutching Inertia‐Damping System). The study establishes a multi‐body motion analysis model for the CIDS within a single‐degree‐of‐freedom structure. Simulations investigate the impact of control force model parameters on the computation. The impact of additional damping on structural dynamic responses and the system's relative motion is thoroughly elucidated and revealed through dynamic simulations and multi‐body motion decomposition. The “ELS” (Equivalent Linear System) is introduced for the simplified performance assessment of CIDS. Expressions for equivalent damping and inertance are derived based on the equivalence of vibration period and energy in sinusoidal steady‐state vibration. The feasibility and accuracy of ELS for assessing CIDS's performance are validated through response analyses under harmonic and seismic excitations. Notably, displacement indicators exhibit higher precision than acceleration. When subjected to seismic excitation, selecting a more suitable excitation frequency to determine the corresponding equivalent damping can enhance the accuracy of ELS. Considering the frequency dependence of equivalent damping, a frequency‐domain‐based random response evaluation method is proposed. The influence of additional rotational damping, flywheel inertia, and structural natural period on random response is evaluated and analyzed. In CIDS with similar rotational damping and inertia, its control effect is related to the excitation. In summary, this study offers a structured framework for comprehending and evaluating the performance of CIDS, offering valuable insights into its potential engineering design, applications, and analysis.

Field oriented controlled permanent magnet synchronous motor drive for an electric vehicle

<span lang="EN-US">The paper describes field oriented control strategy with space vector pulse width modulation technique of permanent magnet synchronous motor drive system for an electric vehicle. At first, mathematical models of the motor and the drive system for electric vehicle are presented. In order to obtain high performance drive and maximum motor torque, field oriented control strategy and space vector pulse width modulation technique method are applied to drive system in next section. Speed controller design utilizing the popular zero-pole elimination approach causes large integral constant time in case of small rotational damping constant. The desired-transient-response-based approach is employed to overcome the problem. Performance indices include overshoot, undershoot, steady-state speed error, and total harmonic distortion of stator current, are employed to assess the drive systems with two speed controller design methods. Theoretical assumptions are confirmed via simulations and criteria in MATLAB/Simulink environment.</span>

Hydraulic performance of the rotational damping sprinkler: Analysis of the force acting on diffuser tooth I

AbstractImproving water distribution uniformity is crucial for the development of high‐performance irrigation sprinklers, and the diffuser's tooth length greatly influences water distribution. Five diffusers with varying tooth I lengths were designed and researched. The expressions for the force acting on tooth I, the hydraulic performance of the sprinkler and the combination uniformity were obtained analytically and experimentally. The results showed that the tooth I force is affected by the working pressure, the ratio between the plate outlet area and the riser pipe flow area, tooth width, entry water depth, trajectory angle and tooth I slope surface angle. Moreover, the components of the tooth I force acting in the vertical, radial and circumferential directions increase with the tooth I length and working pressure. The necessary condition for normal diffuser operation is that the force in the aforementioned three directions should be greater than 0.37, 0.57 and 0.28 N, respectively. Furthermore, when the working pressure is increased by 50 kPa, hereby reducing the rotation time by 10 min and the tooth I length by 1 mm, its water distribution and combination uniformity are optimal. This study provides a basis for designing and operating diffusers and improving sprinkler hydraulic performance.

Analysis of the effects of nonlinear damping on a multiple-degree-of-freedom quasi-zero-stiffness vibration isolator

In the present paper the effect of nonlinear damping on a multi-directional, Quasi-Zero-Stiffness (QZS) vibration isolator is assessed. A two degree-of-freedom vibration isolator is considered, the design consisting of an X arrangement of two struts comprising concentric magnets known to exhibit quasi-zero-stiffness. Nonlinear damping was accounted for in the system through rotational friction at the joints and damping in line with the struts themselves. The equations of motion were derived for each degree of freedom separately, namely transverse and twist motions, using the Energy method and Lagrange-Euler equations. The equations of motion were solved analytically using the Harmonic Balance method and numerically via Simulink. The numerical results validated the analytical predictions for both degrees of freedom. Absolute transmissibility was used to compare the performance of the system with both linear and nonlinear damping. Damping coefficients were found for optimal performance in each degree of freedom of the isolator. The transmissibility curves were optimised with no linear damping, and low strut and rotational damping coefficients. Complex attributes of the response were identified and discussed including a shift in the time averaged response and non-periodic motion in the response under certain conditions. These complexities can be reduced through a careful selection of linear and nonlinear damping coefficients. The research supports the hypothesis that nonlinear damping can improve the performance of quasi-zero-stiffness vibration isolators and identifies complex behaviours that must be considered in the isolator design.

CRACK INITIATION AT GRAIN BOUNDARY WITH A VARIABLE MISORIENTATION VECTOR

A model is proposed for the initiation of cracks at “knife” grain boundaries, i.e., rectilinear, broken boundaries of deformation origin, oriented along the tension axis, arising as a result of rotational incompatibility in the form of a disclination dump at the stage of pre-fracture of the material. The disorientation of the “knife” boundary decreases down to the breaking point in the body of the grain, and its decrease (rotational instability damping) occurs not continuously, but discretely through the branching of secondary low- and high-angle boundaries. In this case, along the “knife” boundary, at the points of its branching, linear mesodefects of the rotational type arise-wedge disclinations of the same sign. A model of crack initiation in an elastic field of a chain of negative disclinations that create tensile elastic stresses is proposed. When analyzing the conditions for crack initiation, a combined criterion was used, according to which the simultaneous fulfillment of force and energy conditions was required for crack initiation. Within the framework of this model, the critical values of the total value of the Frank vector of disclinations located on the “knife” boundary and the average gradient of its misorientation are calculated, upon reaching which the criterion of crack initiation is satisfied. The dependences of these quantities on the length of the “knife” boundary and the effective screening radius of the elastic field of disclinations are calculated. It is shown that the appearance of cracks is most likely at the boundaries with the largest misorientation gradient (exceeding 8–20 deg/?m, depending on the length of the boundary).

Vibration Characteristics of Rotor System with Loose Disc Caused by the Insufficient Interference Force

The rotating parts looseness is one of the common failures in rotating machinery. The current researches of looseness fault mainly focus on non-rotating components. However, the looseness fault of disc-shaft system, which is the main work part in the rotor system, is almost ignored. Here, a dynamic model of the rotor system with loose disc caused by the insufficient interference force is proposed based on the contact model of disc-shaft system with the microscopic surface topography, the vibration characteristics of the system are analyzed and discussed by the number simulation, and verified by the experiment. The results show that the speed of the shaft, the contact stiffness, the clearance between the disc and shaft, the damping of the disc and the rotational damping have an influence on the rotation state of the disc. When the rotation speed of the disc and the shaft are same, the collision frequency is mainly composed of one frequency multiplication component and very weak high frequency multiplication components. When the rotation speed of the disc and the shaft is close, the vibration of the disc occurs a beat vibration phenomenon in the horizontal direction. Simultaneously, a periodical similar beat vibration phenomenon also occurs in the waveform of the disc-shaft displacement difference. The collision frequency is mainly composed of a low frequency and a weak high frequency component. When the rotation speed of the disc and the shaft has great difference, the collision frequency is mainly composed of one frequency multiplication, a few weak high frequency multiplication components and a few low frequency multiplication component. With the reduction of the relative speed of the disc, the trajectory of the disc changes from circle-shape to inner eight-shape, and then to circle-shape. In the inner eight-shape, the inner ring first gradually becomes smaller and then gradually becomes larger, and the outer ring is still getting smaller. The obtained research results in this paper has important theoretical value for the diagnosis of the rotor system with the loose disc.

Dynamics Modeling and Hydrodynamic Coefficients Identification of the Wave Glider

The wave glider is an ocean-wave-propelled autonomous marine vehicle with unique dual-body architecture, which can converse the energy obtained from the ocean wave into the forward thrust. In this paper, the dynamic models of the submerged glider based on dynamic characteristics of tandem hydrofoils and the surface float were separately established. The pitching angles of the hydrofoils and the submerged glider and the angle of attack between hydrofoils and relative current were considered for dynamic models and hydrodynamic coefficients. The translational hydrodynamic coefficient term for high-angle-of-attack passive motion of the submerged glider was calculated from static test simulations by using Computational Fluid Dynamics (CFD). Moreover, the rotational damping coefficients and added mass coefficients varying with the pitching angle of hydrofoils were analyzed by the simulation of the vertical planar motion mechanism (VPMM) tests. Furthermore, the numerical simulation of longitudinal motion with the computed hydrodynamic coefficients was performed, and the simulation results were compared with the sea trial data. The analysis was performed, and conclusions were drawn, which would provide a theoretical reference for the design of the wave glider.

Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Large Initial Displacements

AbstractFor large initial rectilinear displacements, we investigate free response of a linear oscillator inertially coupled to a rotational nonlinear energy sink (NES). Absent direct rectilinear damping, two ranges of orbitally stable solutions are accessible, in contrast to one range at lower, intermediate energies (2021, J. Appl. Mech. 88, 121009). As at lower initial energies, fractal and riddled basins of attraction are identified for both previously considered numerical combinations of the two dimensionless parameters (characterizing rotational damping, and coupling of rotational to rectilinear motion). In this case, however, the final amplitude, in addition to the final angular orientation, displays initial-condition sensitivity. For one parameter combination, most motionless initial conditions (MICs, with the masses of the linear oscillator and NES both initially at rest) lead to a discrete set of “special” orbitally stable solutions with one of two amplitudes, and no MICs lead to complete dissipation of initial energy. For the other combination, the results are similar to those at intermediate initial energies, with no MICs leading to special solutions, and many leading to complete dissipation. Results for both parameter combinations strongly suggest that no qualitatively new behavior occurs for initial energies beyond those considered here, with nonrotating asymptotic special-amplitude solutions having larger rectilinear amplitude either not existing or existing in only very small parts of the MIC space. With direct damping of rectilinear motion, transient chaos leads to initial-condition sensitivity of settling time, with the case of no direct rectilinear damping providing good guidance to damped-case behavior.

Tilting-Pad Journal Bearings—Frequency-Dependent Dynamic Coefficients and Pivot Flexibility Effects

Tribologists have generally accepted that the dynamic modeling of tilting-pad journal bearings (TPJB) must consider the frequency dependency of the dynamic properties. Industrial compressors, turbines, and other rotating machines are subjected to instability drivers, such as blades, impellers, and seals, leading to dominant vibratory frequencies that are generally quite different from rotational frequency. Though the literature has provided related methods and numerical results, full understanding of the physics of TPJB frequency dependency is not generally available to the design community, and theorists and experimentalists are often not in agreement. This investigation hinges on a single-pad, two degree-of-freedom model that creates a basis for understanding the various geometries and operating conditions related to frequency dependency for a full bearing. The analytical results indicate that both stiffness and damping coefficients show frequency dependency, and that the dependency is primarily associated with the pad rotational damping and the flexibility of the pivot contact region that provides support for the pad. Understanding the role of pivot flexibility in combination with the fluid film provides a key to improving agreement between theory and experiment. This article is a revised and expanded version of the paper presented at the ASME 2019 Turbo Expo in Phoenix, Arizona from 17 to 21 June. The paper number was GT2019-90195 and it was titled “On the Frequency Dependency of Tilting-Pad Journal Bearings”.

A finite micro-rotation material point method for micropolar solid and fluid dynamics with three-dimensional evolving contacts and free surfaces

This paper introduces an explicit material point method designed specifically for simulating the micropolar continuum dynamics in the finite deformation and finite microrotation regime. The material point method enables us to simulate large deformation problems while circumventing the potential mesh distortion without remeshing. To eliminate rotational motion damping and loss of angular momentum during the projection, we introduce the mapping for microinertia and angular momentum between particles and grids through the affine particle-in-cell approach. The microrotation and the curvature at each particle are updated through zero-order forward integration of the microgyration and its spatial gradient. We show that the microinertia and the angular momentum are conserved during the projections between particles and grids in our formulation. We verify the formulation and implementation by comparing with the analytical dispersion relation of micropolar waves under the small strain and small microrotation, as well as the analytical soliton solution for solids undergoing large deformation and large microrotation. We also demonstrate the capacity of the proposed computational framework to handle a wide spectrum of simulations that exhibit size effects in the geometrical nonlinear regime through three representative numerical examples, i.e., a cantilever beam torsion problem, a fragment-impact penetration problem, and a micropolar fluid discharging problem.

Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Intermediate Initial Displacements

AbstractFree response of a rotational nonlinear energy sink (NES) inertially coupled to a linear oscillator is investigated for dimensionless initial rectilinear displacements ranging from just above the smallest amplitude at which nonrotating, harmonically rectilinear motion is unstable absent direct rectilinear damping, up to the next-largest amplitude at which such motion is orbitally stable. With motionless initial conditions (MICs), i.e., initial velocity of the primary mass and initial angular velocity of the NES mass both zero, predicted behavior for two previously investigated combinations of the dimensionless parameters (characterizing rotational damping, and coupling of rectilinear and rotational motions) differs strongly from that found at smaller initial displacements (Ding and Pearlstein, 2021, “Free Response of a Rotational Nonlinear Energy Sink: Complete Dissipation of Initial Energy for Small Initial Rectilinear Displacements,” J. Appl. Mech., 88(1), p. 011005). For both combinations, a wide range of MICs leads to solutions displaying transient chaos and depending sensitively on initial conditions, giving rise to fractality and riddling in the relationship between initial conditions and asymptotic solutions. Absent direct rectilinear damping of the linear oscillator, for one combination of parameters there exists a wide range of MICs with trajectories leading to time-harmonic, orbitally stable “special” solutions with a single amplitude, but no MICs are found for which all initial energy is dissipated. For the other combination, no such special solutions are found, but there exist MICs for which all initial energy is dissipated. With direct rectilinear damping, sensitivity extends to a measure of settling time, which can be extremely sensitive to initial conditions. A statistical approach to this sensitivity is discussed, along with implications for design and implementation.

Heterogeneous Inertia Estimation for Power Systems with High Penetration of Converter-Interfaced Generation

The increasing and fast deployment of distributed generation is posing challenges to the operation and control of power systems due to the resulting reduction in the overall system rotational inertia and damping. Therefore, it becomes quite crucial for the transmission system operator to monitor the varying system inertia and damping in order to take proper actions to maintain the system stability. This paper presents an inertia estimation algorithm for low-inertia systems to estimate the inertia (both mechanical and virtual) and damping of systems with mixed generation resources and/or the resource itself. Moreover, the effect of high penetration of distributed energy resources and the resulting heterogeneous distribution of inertia on the overall system inertia estimation is investigated. A comprehensive set of case studies and scenarios of the IEEE 39-bus system provides results to demonstrate the performance of the proposed estimator.

Stability Analysis of Articulated Bus in Straight-ahead Running Manoeuvre

A comprehensive study on the stability of a planar linearized single-track model of a two-section pusher articulated bus is presented with the aid of a complete set of stability maps. The two sections of the vehicle model are connected at the hitch point by a revolute joint; an equivalent visco-elastic characteristic function describes its rotational visco-elastic properties, playing a major role in stability control and therefore in passive safety. The equations of motion are derived in analytical form, allowing easy implementation of the non-linear model (eventually including a non-linear viscoelastic characteristic functions of the joint). Stability of the linearized model is then studied in equilibrium configurations by means of sensitivity analysis with respect to the model’s governing parameters. Stability maps are drawn on the basis of sets of parameter values related to straight-ahead running, steady-state manoeuvres. The most important parameters controlling the onset of unstable motions are identified, paying attention to the role played by the equivalent rotational damping coefficient and the equivalent torsional stiffness characterizing the connection joint, with the aim of finding criteria for its design.

Stability analysis and control of a flywheel energy storage rotor with rotational damping and nonsynchronous damping

Based on the principle of Lagrange mechanics, especially considering the effects of rotation damping and nonsynchronous damping, a radial 4-dimensional dynamic model of the flywheel bearing rotor system is proposed. Applying the Laplace eigenvalue method, the stability effects of rotational damping, nonsynchronous damping, and their coupling effects are investigated by means of root locus method. Under the control of the linear quadratic regulator, dynamical characteristics of the flywheel bearing rotor system with varied rotational damping and nonsynchronous damping are also studied. The results show that the rotation damping, nonsynchronous damping, and their coupling effects have vast and complex instability effects on high-speed flywheel bearing rotor system. However, there are three exceptions. The tiny proportional rotational damping, remaining below 12%, and the minuscule proportional co-nonsynchronous damping; the product of the nonsynchronous damping and the speed ratio below 5% both can enhance the stability of the system. Furthermore, in the situation that the counter-nonsynchronous damping is coupled with the large proportion of rotational damping, the stability of the system can also be boosted distinctly. On the other hand, the numerical experimental results show that the rotational damping and nonsynchronous damping have a beneficial effect on the flywheel system controlled by linear quadratic regulator. In addition, under the control of linear quadratic regulator, the transient dynamical behavior of the flywheel rotor system with rotational damping or co-nonsynchronous damping performed better than the flywheel rotor system with the coupled damping. The numerical simulations of the transient response of the flywheel rotor system under active control are consistent with some of the derived stability analysis results. The results about the stability analysis and the performance in vibration control give the suggestions for the instability control and fault detection of the system.

Coupling Dynamic Analysis of Fracturing Truck Frame during Operation

In order to study the effect of vibration of the engine and fracturing pump on the truck frame during the fracturing operation, lumped parameter method and state-space method were used to build multi-body dynamics coupling model between the balanced suspension, tires, engine, fracturing pump and the frame. Based on this model, the MATLAB/Simulink software was applied to simulate the characteristic of rotational speed, stiffness, and damping of the 2500 fracturing truck during the fracturing operation. The results show that the maximum intensity of vertical vibration is hundreds of times that of pitch motion. The vibration frequency range of 0∼10 Hz affects vibration most evidently; the variation of stiffness of the rear suspension and the damping of the front and central suspension has a great influence on amplitude, while the variation of damping of rear suspension and the stiffness of the front and central suspension have a great influence on frequency of peak.

Improving Dynamic Performance of Low-Inertia Systems Through Eigensensitivity Optimization

An increasing penetration of renewable generation has led to reduced levels of rotational inertia and damping in the power network. The consequences are higher vulnerability to disturbances and deterioration of the dynamic response of the system. To overcome these challenges, novel converter control schemes that provide virtual inertia and damping have been introduced, which raises the question of optimal distribution of such devices throughout the network. This paper presents a comprehensive framework for performance-based allocation of virtual inertia and damping to the converter-interfaced generators in a detailed low-inertia system. This is achieved through an iterative, eigensensitivity-based optimization algorithm that determines the optimal controller gains while simultaneously preserving small-signal stability and ensuring that the damping ratio and frequency response after disturbances are kept within acceptable limits. Two conceptually different problem formulations are presented and validated on a modified version of the well known Kundur's two-area system as well as a larger 59-bus South-East Australian network.

Longtime behavior for an extensible beam equation with rotational inertia and structural nonlinear damping

The paper investigates the well-posedness, regularity and longtime behavior of solutions for an extensible beam equation with fractional rotational inertia and structural nonlinear damping: (1+(−Δ)θ)utt+Δ2u−M(‖∇u‖2)Δu+N(‖∇u‖2)(−Δ)αut+f(u)=g, with dissipative index α∈(0,1] and rotational index θ∈[0,α). We find a new critical exponent pθα≡N+2(2α−θ)(N−4)+(>p⁎=N(N−4)+) depending on both θ and α and show that when the growth exponent p of the nonlinearity f(u) is up to the range: 1≤p<pθα, the well-posedness, regularity and longtime behavior of the solutions are like parabolic, in the concrete, (i) the IBVP of the equation admits a unique strong solution while its initial data is in weaker energy space; (ii) the related solution semigroup has a strong global attractor and a strong exponential attractor for each θ∈[0,α), where the “strong” means that the compactness, the attractiveness and the finiteness of the fractal dimension of the attractors are all in the topology of the strong solution space; (iii) the family of strong global attractors {Aθ}θ∈[0,α) is upper-semicontinuous on the perturbed index θ at any point θ0∈[0,α). These results improve and extend those in recent literatures [17,24].

Dynamic behavior of multilayer suspension equipment and adjacent post insulators with elastic‐viscous connections

In an electrical substation or converter station, suspension equipment is connected to an adjacent post insulator by a rigid busbar or flexible conductors if the horizontal displacement is significant. In order to investigate the coupling effect between suspension and post equipment connected by a rigid busbar, a scaled-down model based on a multilayer suspended thyristor valve and an adjacent post insulator was tested. Additionally, an analytical model, which took into account the out-of-plane and torsional motion, was established. The test results showed that the damping of the suspended valve approximated to stiffness-proportional damping. The rigid busbar significantly reduced the seismic responses of both the valve and the post insulator by changing the vibration modes and increasing the damping ratio. Based on the analytical model, the rigid busbar connection is recommended for stiff insulators with a low fundamental frequency. A hard soil site, chain connection, low damping ratio, and an appropriate layout all contribute to the advantages of a rigid busbar. A telescopic busbar using additional rotational and axial damping also can improve the system's seismic performance. Rather than automatically installing flexible conductors, it is recommended that equipment parameters be used to determine an appropriate connection type between suspension equipment and an adjacent post insulator.

Effect of the Turret’s Rotational Damping on the Heading Stability of a Turret-Moored FPSO

Effect of the Turret’s Rotational Damping on the Heading Stability of a Turret-Moored FPSO