Amit Dolev

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

Abstract 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.

A Parametric Amplifier for Weak, Low-Frequency Forces

The present work introduces a tunable parametric amplifier (PA) with a hardening, Duffing-type nonlinearity. By introducing a multi-frequency parametric excitation, one is able to achieve both: (i) High amplification of the weak, low-frequency external excitation (ii) Projection of the low frequency on any natural frequency of the system, thus transforming the low frequency excitation to a frequency band where signal levels are considerably higher. Having developed multiple-scales based expressions for the response of such systems, it is demonstrated that (a) The analytical analysis agrees well with numerically obtained simulations. (b) Both the phase, magnitude and spatial projection of this force on any system’s eigenvector can be retrieved by appropriate selection of parameters, with superior signal to noise levels.Closed form analytic expressions for the sensitivity and gain are derived and analyzed. Additionally, some practical applications envisaged for the proposed method will be outlined.Copyright

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.

Dual frequency parametric excitation of a nonlinear, multi degree of freedom mechanical amplifier with electronically modified topology

Abstract 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.

Balancing High-Speed Rotors at Low Rotation Speeds Using Parametric Excitation

Presented is a novel method allowing to perform mass balancing of flexible vibration modes, while rotating at low speeds. Through special external excitation, the projection of imbalance forces on vibration modes corresponding to high rotation speed can be found. The main merit of this method is that it uses measurements taken at low speeds, which anticipate the imbalance effects at considerably higher speeds. Standard mass balancing procedures of flexible bending modes, require the rotor to be rotated up to its operating speed. High speed rotors such as small jet engines and turbochargers cannot be rotated to such high speeds at laboratory conditions, and therefore are usually balanced using commercial balancing machines that are limited to low speeds. At low speeds it is impossible to detect the projection of imbalance forces on high frequency modes and thus low-speed balancing can worsen vibrations once the system is operational.

Experimental travelling waves identification in mechanical structures

Vibrations are often represented as a sum of standing waves in space, i.e. normal modes of vibration. While this can be mathematically accurate, the representation as travelling waves can be compact and more appropriate from a physical point of view, in particular when the energy flux along the structure is meaningful. The quantification of travelling waves assists in computing the energy being transferred and propagated along a structure. It can provide local as well as global information about the structure through which the mechanical energy flows. Presented in this paper is a new method to quantify the fraction of mechanical power being transmitted in a vibration cycle at a specific direction in space using measured data. It is shown that the method can detect local defects causing slight non-uniformity of the energy flux. Equivalence is being made with the electrical power factor and electromagnetic standing waves ratio, commonly employed in such cases. Other methods to perform experiment based wave identification in one-dimension are compared with the power flow based identification. Including a signal processing approach that fits an ellipse to the complex amplitude curve and Hilbert transform for obtaining the local phase and amplitude. A new representation of the active and reactive power flow is developed and its relationship to standing waves ratio is demonstrated analytically and experimentally.