Time-varying Rotation Rates Research Articles

Vibrational Suspension of Two Cylinders in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

Vibrational Suspension of Two Cylinders in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

Rotational Inertial Physics in Non-Classical Thermoviscous Fluent Continua Incorporating Internal Rotation Rates

In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor; (ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity (complete basis). It is shown that the mathematical model consisting of the conservation and balance laws and constitutive theories presented in this paper has closure. Influence of new physics in the conservation and balance laws on compressible and incompressible thermoviscous fluent continua is demonstrated due to presence of angular velocities and angular accelerations arising from time varying rotation rates when the deforming fluent continua offer rotational inertial resistance. The fluent continua are considered homogeneous and isotropic. Model problem studies are considered in a follow-up paper.

Theory of arbitrary rigid object motion autofocus for non‐uniform target rotation and translation

Moving targets in synthetic aperture radar (SAR) imagery often yield signatures that are smeared beyond recognition. One mitigation strategy is to attempt to refocus such smears as if the corresponding targets were stationary. This problem is especially difficult for cases in which the target executes time-varying rotation rates for roll, pitch and yaw, as well as for simultaneous non-linear target translational motion. The current analysis develops an arbitrary rigid object motion autofocus (AROMA) for performing automatic refocus of such targets having non-uniform rotation and translation profiles. AROMA uses a maximum likelihood signal-theoretic analysis of the physical rotation angles and translation distances arising from the unknown rigid object motions in order to generate refocused target imagery. The efficacy of this methodology is demonstrated via the injection of a simulated rotating and translating target comprised of multiple scattering centres into a cluttered background of measured Ku-band SAR data. Furthermore, the application of AROMA to an input defocused smear corresponding to a ‘target-of-opportunity’ vehicle in measured Ka-band SAR imagery yields significant improvement in the target focus, thus further validating the underlying theoretical analysis developed herein.

Lift Force Acting on a Heavy Solid in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

The dynamics of a heavy cylindrical body in a liquid-filled horizontal cylindrical cavity with a time-varying rotation rate is experimentally investigated. The body is near the cavity boundary under a centrifugal force and undergoes solid-body rotation together with the liquid and the cavity at a fixed rotation rate. The dependence of the body dynamics on the amplitude and frequency of modulation of the rotation rate is investigated. It is found that at a critical amplitude of modulation (at definite frequency), the heavy body repulses from the cavity boundary and comes into a steady state at some distance from the wall. It is found that the average lift force (repulsive one) is generated by the azimuthal oscillation of the body in the rotating frame of reference and manifests itself at a distance comparable to the thickness of the viscous boundary layer. In the experiments, we observed azimuthal drift of the body due to asymmetric azimuthal oscillations of the body. In the limit of high frequency of the rotation rate modulation, the dependence of the lift force coefficient on the gap between the body and the wall is determined.

Lift Force Acting on a Heavy Solid in a Liquid-Filled Rotating Cavity with a Time-Varying Rotation Rate

Lift Force Acting on a Heavy Solid in a Liquid-Filled Rotating Cavity with a Time-Varying Rotation Rate

Oscillation-induced sand dunes in a liquid-filled rotating cylinder.

The dynamics of granular medium in a liquid-filled horizontal cylinder with a time-varying rotation rate is experimentally studied. When the cylinder is purely rotated, the granular medium develops an annular layer near the cylindrical wall. The interface between fluid and sand is smooth and axisymmetric. The time variation of the rotation rate initiates the azimuthal oscillation of the liquid in the cylinder's frame of reference and provokes the onset of quasisteady relief in the form of regular dunes. The stability of the axisymmetric sand surface and dynamics of regular dunes are examined. It is found that the ripple formation is provoked by the quasisteady instability of the Stokes boundary layer. In the range of high Reynolds numbers, the ripple formation occurs at a constant critical Shields number θ_{c}≃0.05. The spatial period of the relief is not sensitive to the fluid viscosity and granule diameter; it is determined by the amplitude of oscillation and ratio between the oscillation frequency and mean rotation rate. Long-term experiments show that there are forward and backward azimuthal drifts of dunes. An initial analysis of the issues related to the dune migration is provided.

Rotation rate estimation in parametrically excited micro gyroscopes

This paper reports the estimation of angular velocity in micro gyroscopes with parametric excitation. The identification procedure is done into two consecutive steps: In the first step, the physical parameters of the gyroscope (stiffness, damping, and actuator parameters) are estimated via continuous time Extended and Unscented Kalman filter. In the second step, a separate Kalman filter is dedicated to estimate the time varying rotation rate, using the output of the first step. Using numerical simulations, it is found that by introducing an artificial noise in the observer equations and tuning its variance, arbitrary temporal variation of angular velocity can be well tracked by the proposed observer.

A Continuously Operating, Flux Locked, Superfluid Interferometer

We report the characteristics of a flux locked, superfluid 4He interferometer that can continuously measure time-varying rotation rates. We describe the principles underlying the interferometer, including the dynamics of a superfluid chemical potential battery used to obtain continuous operation. We also discuss noise and drift issues and their possible amelioration.

On Control System Design for the Conventional Mode of Operation of Vibrational Gyroscopes

This paper presents a novel control circuitry design for both vibrating axes (drive and sense) of vibrational gyroscopes, and a new sensing method for time-varying rotation rates. The control design is motivated to address the challenges posed by manufacturing imperfection and environment vibrations that are particularly pronounced in microelectromechanical systems (MEMS) gyroscopes. The method of choice is active disturbance rejection control that, unlike most existing control design methods, does not depend on an accurate model of the plant. The task of control design is simplified when the internal dynamics, such as mechanical cross coupling between the drive and sense axes, and external vibrating forces are estimated and cancelled in real time. In both simulation and hardware tests on a vibrational piezoelectric beam gyroscope, the proposed controller proves to be robust against structural uncertainties; it also facilitates accurate sensing of time-varying rotation rates. The results demonstrate a simple, economic, control solution for compensating the manufacturing imperfections and improving sensing performance of the MEMS gyroscopes.

S.20.04 Lithium responsive behavioural models: a tool for understanding atypical antipsychotic action in bipolar depression and mania

This paper reports the estimation of angular velocity in micro gyroscopes with parametric excitation. The identification procedure is done into two consecutive steps: In the first step, the physical parameters of the gyroscope (stiffness, damping, and actuator parameters) are estimated via continuous time Extended and Unscented Kalman filter. In the second step, a separate Kalman filter is dedicated to estimate the time varying rotation rate, using the output of the first step. Using numerical simulations, it is found that by introducing an artificial noise in the observer equations and tuning its variance, arbitrary temporal variation of angular velocity can be well tracked by the proposed observer.

A disturbance rejection-based control system design for Z-axis vibratory rate gyroscopes

The current paper presents a new control strategy known as active disturbance rejection control (ADRC) for controlling the sense axis of a vibrational microelectromechanical system (MEMS) gyroscope and detecting time-varying rotation rates. In the ADRC framework, the generalized disturbance, which is referred to as the combination of the internal dynamics and external disturbances, is estimated and compensated for in real time. It is assumed that the drive axis outputs an ideal sinusoidal signal. A force-to-rebalance mode of operation is applied to the sense axis of the gyroscope. Under this mode, the output of the sense axis is continuously monitored and driven to zero by ADRC and the rotation rate is estimated by employing the demodulation technique. Simulation results and performance analysis demonstrate the effectiveness and robustness of the ADRC against parameter variations and noises.