arXiv subjects

Izhak Bucher

Publications and source records attributed to Izhak Bucher.

12 recordsLinked to original sources

arXiv2023

An identification method for oscillators with response-dependent inertia

This paper is concerned with identifying the instantaneous modal parameters of forced oscillatory systems with response-dependent generalized inertia (mass, inductance, or equivalent) based on their measured dynamics. An identification method is proposed, which is a variation of the "FORCEVIB" method. The method utilizes analytic signal representation and the properties of the Hilbert transform to obtain an analytic relationship between a system's natural frequency and damping coefficient to its response and excitation signals. The proposed method is validated by comparing the identification results to the asymptotic solution of a simple system with response-dependent inertia and is then demonstrated, numerically and experimentally, for other more complicated nonlinear systems.

eess.SY↗

arXiv2023

Iterative Decoupling Method for High-Precision Imaging of Complex Surfaces

Nonlinear systems and interaction forces are pervasive in many scientific fields, such as nanoscale metrology and materials science, but their accurate identification is challenging due to their complex behaviour and inaccessibility of measured domains. This problem intensifies for continuous systems undergoing distributed, coupled interactions, such as in the case of topography measurement systems, measuring narrow and deep grooves. Presented is a method to invert a set of nonlinear coupled equations, which can be functions of unknown distributed physical quantities. The method employs a successive approach to iteratively converge to the exact solution of the set of nonlinear equations. The latter utilizes an approximate yet invertible model providing an inexact solution, which is evaluated using the hard-to-invert exact model of the system. This method is applied to the problem of reconstructing the topography of surface contours using a thin and long vibrating fiber. In nanoscale metrology, measuring inaccessible deep and narrow grooves or steep walls becomes difficult and singular when attempting to extract distributed nonlinear interactions that depend on the topography. We verify our method numerically by simulating the Van der Waals (VdW) interaction forces between a nanofiber and a nanoscale deep groove, and experimentally by exploiting magnetic interactions between a magnetic topography and a vibrating, elastic beam. Our results validate the ability to accurately reconstruct the topography of normally inaccessible regions, making it a possible enhancement for traditional point based AFM measurements, as well as for other nonlinear inverse problems.

eess.SY↗

arXiv2020

Experimental identification of multimode traveling waves in a coupled wave-tube

An essential part of nondestructive testing and experimental modeling of waveguides is the decomposition of propagating wave patterns. The traveling wave ratio is a measure of partial reflections assisting in quantifying the pureness of a single traveling wave from a power flow perspective. This paper expands the notion of traveling wave ratio for multimode systems and outlines several schemes capable of decomposing the waves into their different traveling modes while quantifying their traveling and standing proportions individually. A method to strike an optimal balance between increasing model order and to maintain low uncertainty is proposed. An experimental study performed on an acoustic wave tube, which utilizes the various methods while assessing their accuracy and performance, is reported. The results described here emphasize the importance of including additional propagating modes. In addition, the results illustrate the capability of using the recursive multichannel least-mean-squares method for both a fast decomposition and as a basis to formulate closed-loop schemes controlling the wave's propagation patterns.

physics.app-ph↗

arXiv2019

A new approach to single-tone frequency estimation via linear least squares curve fitting

Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a digital phase locked loop (DPLL) (online) are employed for such an estimate. However, with the linearization approach presented here, one can harness the efficiency of LLS to obtain very good estimates, while experiencing little penalty for linearizing. In this paper, the mathematical basis of this algorithm is described, and the bias and variance are analyzed analytically and numerically. With the batch version of this algorithm, it will be demonstrated that the estimator is just as good as NLS. But because LLS is non recursive, the estimate it produces much more efficiently than from NLS. When the proposed algorithm is implemented online, it will be demonstrated that performance is comparable to a digital phase locked loop, with some stability and tracking range advantages.

eess.SP↗

arXiv2018

Analytical, numerical and experimental investigation of a tunable, nonlinear multi-degree-of-freedom parametrically excited amplifier

A tunable, multi-degree-of-freedom, parametrically excited amplifier is introduced as an apparatus capable of shifting slow, weak signals to higher frequencies, by exploiting the amplifier natural resonances via controlled parametric excitation and nonlinear feedback. This device can find use as a signal amplifier and as a spectrum control device. A tuned dual-frequency signal is created to parametrically excite (pump) the system and produce the desired energy shift. The pump signal is applied by a controlled electromechanical actuator, and is modified in-situ according to the slow frequency signal and the desired response. A three DOF model is introduced, and the governing nonlinear EOM are derived and solved analytically via asymptotic methods and verified with numerical simulations. A parametric design of an experimental rig was carried out, and the importance of experimental calibration and system identification is emphasized. Some preliminary experimental results are provided with favorable agreement with the theory.

physics.app-ph↗

arXiv2018

Balancing rotating structures using slow-speed data via optimized parametric excitation and nonlinear feedback

The paper presents an improved mass balancing procedure for fast rotating machinery, while it is being rotated at speeds considerably slower than the "critical speeds", where dangerously high vibration amplitudes may arise. By utilizing tuned dual frequency parametric excitation along with optimized nonlinear feedback terms, the slow imbalance forces are projected onto a chosen mode of vibration. This allows to identify the imbalance projection on that specific mode, and to cancel these forces by adding or reducing mass. The scheme benefits from two kinds of parametric excitation yielding combination and principal parametric resonances. The former is used to project the imbalance forces onto a selected vibration mode, and the latter significantly amplifies the response. By tuning the parametric excitation and the nonlinear terms in an optimal manner, a pseudo-linear behavior is formed. This behavior enables to increase both amplification and sensitivity to the imbalance forces without having to compromise between the two.

physics.app-ph↗

arXiv2018

Optimizing the dynamical behavior of a dual frequency parametric amplifier with quadratic and cubic nonlinearities

The paper describes a novel parametric excitation scheme that acts as a tunable amplifier by controlling two pumping signals and two nonlinear feedback terms. By modulating the stiffness of a mechanical oscillator with a digital signal processor, low frequency inputs are projected onto a higher resonance frequency, thus exploiting the natural selective filtering of such structures. Described is an optimized dual-term nonlinear stiffness resonator that enhances the input signal level and the sensitivity to changes in both amplitude and phase, while limiting the obtained response to desired levels. This amplifier is geared to cases when the frequency of the input is known or measurable, like in rotating structures, while the amplitude and phase are too weak to be detected without amplification. It is shown that by tuning the cubic and quadratic feedback terms, the amplifier benefits from a nearly linear response behavior, while exploiting the benefits of nonlinear and pumping signal enhancements.

physics.app-ph↗

arXiv2017

Realization of a Contactless Acoustic Levitation Motor via Doublet Mode Control and Autoresonance

This paper demonstrates analytically and experimentally an acoustic levitation motor which has the ability to levitate and rotate an object in the air without mechanical contact. To realize such a device two core methods are applied simultaneously; (i) resonance tracking with an Autoresonance feedback loop, (ii) generation of controlled structural traveling waves. The purpose of the first method is to achieve near-field acoustic levitation, which can levitate an object of a few kilograms. In this research, this is accomplished through high amplitude vibration of an aluminum annulus at ultrasonic frequencies (~30kHz). For high efficiency, the annulus is designed to have a very high Q value, and operating even slightly off resonance ceases levitation. Compounding this is the fact that the natural frequency constantly drifts as ambient conditions and loading change. To accommodate such a drift, and produce stable levitation automatically, a resonance tracking feedback loop is employed here. Simultaneously, the purpose of the second method is to achieve propulsion forces on the levitated object by propagating and controlling traveling waves in the aluminum annulus to create a thin layer of rotating air beneath the levitated body. Even though a single vibration mode can produce only standing waves, an axisymmetric structure possesses two modes per natural frequency, and excitation of a doublet mode pair can generate effective travelling waves. The present paper develops the theory behind the use of the Autoresonance feedback method for achieving constant levitation and propagating travelling waves in co- and counter rotating directions. It will be shown that all this can be accomplished with only single sensor. The result is a stable, repeatable and a highly controllable contactless acoustic levitation motor.

physics.app-ph↗

arXiv2017

Dual frequency parametric excitation of a nonlinear multi degree of freedom amplifier with a digitally modified topology

Mechanical or electromechanical amplifiers can exploit the high-Q and low noise features of mechanical resonance, in particular when parametric excitation is employed. Multi-frequency parametric excitation introduces tunability and is able to project weak input signals on a selected resonance. The present paper addresses multi degree of freedom mechanical amplifiers or resonators whose analysis and features require treatment of the spatial as well as temporal behavior. In some cases, virtual electronic coupling can alter the given topology of the resonator to better amplify specific inputs. An analytical development is followed by a numerical and experimental sensitivity and performance verifications, illustrating the advantages and disadvantages of such topologies.

physics.app-ph↗

arXiv2017

Dynamic balancing of super-critical rotating structures using slow-speed data via parametric excitation

High-speed machinery is often designed to pass several $"$critical$"$ speeds, where vibration levels can be very high. To reduce vibrations, rotors usually undergo a mass balancing process, where the machine is rotated at its full speed range, during which the dynamic response near critical speeds can be measured. High sensitivity, which is required for a successful balancing process, is achieved near the critical speeds, where a single deflection mode shape becomes dominant, and is excited by the projection of the imbalance on it. The requirement to rotate the machine at high speeds is an obstacle in many cases, where it is impossible to perform measurements at high speeds, due to harsh conditions such as high temperatures and inaccessibility (e.g., jet engines). $\\$ This paper proposes a novel balancing method of flexible rotors, which does not require the machine to be rotated at high speeds. With this method, the rotor is spun at low speeds, while subjecting it to a set of externally controlled forces. The external forces comprise a set of tuned, response dependent, parametric excitations, and nonlinear stiffness terms. The parametric excitation can isolate any desired mode, while keeping the response directly linked to the imbalance. A software controlled nonlinear stiffness term limits the response, hence preventing the rotor to become unstable. These forces warrant sufficient sensitivity required to detect the projection of the imbalance on any desired mode without rotating the machine at high speeds. Analytical, numerical and experimental results are shown to validate and demonstrate the method.

physics.app-ph↗

arXiv2016

A rotational traveling wave based levitation device - Modeling, design, and control

Described is a device acting on an acoustically levitated object by manipulating the pressure and flow of a thin layer of air such that its rotation can be precisely controlled without mechanical contact. Virtual work analysis assists in simplifying the multi-actuator control problem into a problem governed by a controllable parameter. Actuation is done with a vibrating ring capable of producing ultrasonic standing and traveling waves, creating the acoustic excitation that affects the pressure in a thin, intermediate layer of gas. A distinctive vibration pattern is required to generate the temporal and spatial pressure field of the squeezed air layer that gives rise to both acoustic levitation force and rotational torque. Described are the physical and design development stages leading to an optimized structure, all followed by verifying and dynamics-calibration experiments. Moreover, by precisely controlling the ratio of standing and traveling waves in a closed-loop, one can affect the shear forces applied by the squeezed air layer, thus creating a non-contacting manipulation mechanism. An over-actuated set-up is converted via an algebraic transformation, into a simplified single control-parameter problem. The transformation ties the standing waves ratio, and hence the rotational torque, to the amplitudes and phases of the actuators. This arrangement leads to an effective closed loop methodology that was implemented experimentally showing good performance and exhibiting rapid angular positioning.

physics.class-ph↗

arXiv2016

Modelling and closed loop control of near-field acoustically levitated objects

The present paper introduces a novel approach for modelling the governing, slow dynamics of near-field acoustically levitated objects. This model is sufficiently simple and concise to enable designing a closed-loop controller, capable of accurate vertical positioning of a carried object. The near-field acoustic levitation phenomenon exploits the compressibility, the nonlinearity and the viscosity of the gas trapped between a rapidly oscillating surface and a freely suspended planar object, to elevate its time averaged pressure above the ambient pressure. By these means, the vertical position of loads weighing up to several kilograms can be varied between dozens and hundreds of micrometers. The simplified model developed in this paper is a second order ordinary differential equation where the height-dependent stiffness and damping terms of the gas layer are derived explicitly. This simplified model replaces a traditional model consisting of the equation of motion of the levitated object, coupled to a nonlinear partial differential equation, accounting for the behavior of the entrapped gas. Due to the relatively simple form of the model developed here, it constitutes a convenient foundation for model based control algorithms, governing the slow dynamics of near-field acoustically levitated objects. Indeed, based on the former, a height dependent, gain scheduled PID controller is developed and verified numerically and experimentally, both providing satisfying results.

physics.flu-dyn↗