Wen-Ming Zhang

Nonlinear Dynamic Analysis of Electrostatically Actuated Resonant MEMS Sensors Under Parametric Excitation

Electrostatically actuated resonant microelectromechanical systems (MEMS) sensors have gotten significant attention due to their geometric simplicity and broad applicability. In this paper, nonlinear responses and dynamics of the electrostatically actuated MEMS resonant sensors under two-frequency parametric and external excitations are presented. The presented model and methodology enable simulation of the steady-state dynamics of electrostatic MEMS undergoing small motions. Response and dynamics of the MEMS resonator to a combination resonance are studied. The responses of the system at steady-state conditions and their stability are investigated using the method of multiple scales. The results showing the effect of varying the dc bias, the squeeze film damping, cubic stiffness, and ac excitation amplitude on the frequency response curves, resonant frequencies and nonlinear dynamic characteristics are given in detail. Frequency response, resonant frequency and peak amplitude are examined for variation of the dynamic parameters involved. This investigation provides an understanding of the nonlinear dynamic characteristics of microbeam-based resonant sensors in MEMS

Polynomial Chirplet Transform With Application to Instantaneous Frequency Estimation

In this paper, a new time-frequency analysis method known as the polynomial chirplet transform (PCT) is developed by extending the conventional chirplet transform (CT). By using a polynomial function instead of the linear chirp kernel in the CT, the PCT can produce a time-frequency distribution with excellent concentration for a wide range of signals with a continuous instantaneous frequency (IF). In addition, an effective IF estimation algorithm is proposed based on the PCT, and the effectiveness of this algorithm is validated by applying it to estimate the IF of a signal with a nonlinear chirp component and seriously contaminated by a Gaussian noise and a vibration signal collected from a rotor test rig.

Electrostatic micromotor and its reliability

Abstract Research and development in microelectromechanical systems (MEMS) have made remarkable progress since the advent of the first electrostatic micromotor in 1987. Considerable efforts have been directed to the investigation of the failure mechanisms and reliability of electrostatic micromotors. This paper provides a brief overview of failure modes and mechanisms and solving methods in electrostatic micromotors that are commonly met. It focuses on the introduction of the failure modes and mechanisms with numerical and experimental methods as well as the recent methods for reducing the failures and the development in future. In addition, the paper illustrates our investigation on the contact dynamics between the rotor and bearing hub and the effects of gas-lubricated bearing which decrease the possibility of friction, contact, and wear in electrostatic micromotors.

Spline-Kernelled Chirplet Transform for the Analysis of Signals With Time-Varying Frequency and Its Application

The conventional time-frequency analysis (TFA) methods, including continuous wavelet transform, short-time Fourier transform, and Wigner-Ville distribution, have played important roles in analyzing nonstationary signals. However, they often show less capability in dealing with nonstationary signals with time-varying frequency due to the bad energy concentration in the time-frequency plane. On the other hand, by introducing an extra transform kernel that matches the instantaneous frequency of the signal, parameterized TFA methods show powerful ability in characterizing time-frequency patterns of nonstationary signals with time-varying frequency. In this paper, a novel time-frequency transform, called spline-kernelled chirplet transform (SCT), is proposed. By introducing a frequency-rotate operator and a frequency-shift operator constructed with spline kernel function, the SCT is particularly powerful for the strongly nonlinear frequency-modulated signals. In addition, an effective algorithm is developed to estimate the parameters of transform kernel in the SCT. The capabilities of the SCT and parameter estimation algorithm are validated by their applications for numerical signals and a set of vibration signal collected from a rotor test rig.

General Parameterized Time-Frequency Transform

Interest in parameterized time-frequency analysis for non-stationary signal processing is increasing steadily. An important advantage of such analysis is to provide highly concentrated time-frequency representation with signal-dependent resolution. In this paper, a general scheme, named as general parameterized time-frequency transform (GPTF transform), is proposed for carrying out parameterized time-frequency analysis. The GPTF transform is defined by applying generalized kernel based rotation operator and shift operator. It provides the availability of a single generalized time-frequency transform for applications on signals of different natures. Furthermore, by replacing kernel function, it facilitates the implementation of various parameterized time - frequency transforms from the same standpoint. The desirable properties and the dual definition in the frequency domain of GPTF transform are also described in this paper. One of the advantages of the GPTF transform is that the generalized kernel can be customized to characterize the time - frequency signature of non-stationary signal. As different kernel formulation has bias toward the signal to be analyzed, a proper kernel is vital to the GPTF. Thus, several potential kernels are provided and discussed in this paper to develop the desired parameterized time - frequency transforms. In real applications, it is desired to identify proper kernel with respect to the considered signal. This motivates us to propose an effective method to identify the kernel for the GPTF.

Tunable Micro- and Nanomechanical Resonators

Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.

Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects

In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.

Component Extraction for Non-Stationary Multi-Component Signal Using Parameterized De-chirping and Band-Pass Filter

In most applications, component extraction is important when components of non-stationary multi-component signal are key features to be monitored and analyzed. Existing methods are either sensitive to noise or forced to select a proper time-frequency representation for the considered signal. In this paper, we present a novel component extraction method for non-stationary multi-component signal. The proposed method combines parameterized de-chirping and band-pass filter to obtain components of multi-component signal, which avoids dealing with time-frequency representation of the signal and works well under heavy noise. In addition, it is able to analyze the multi-component signal whose components have intersected instantaneous frequency trajectories. Simulation results show that the proposed method is promising in analyzing complicated multi-component signals. Moreover, it works effective in a high noise environment in terms of improving the output signal-to-noise rate for the interested component.

Application of Parameterized Time-Frequency Analysis on Multicomponent Frequency Modulated Signals

Parameterized time-frequency (TF) transforms, with signal-dependent kernel parameters, have been proposed to analyze multicomponent frequency modulated (FM) signals. Usually, the kernel parameters are estimated through recursive approximation of TF representation (TFR) ridge when instantaneous frequency models of the components have the same parameter settings. However, it will be inapplicable if the components have the different FM sources. In this paper, we introduce a novel method that enables the parameterized TF transform to generate the well-concentrated TFR for both the monocomponent signal and a wide class of multicomponent FM signals, whose components are modulated by either the same or the different sources. The proposed method contains two aspects: 1) estimating kernel parameters based on spectrum concentration index and 2) separating components and assembling the parameterized TFRs of the separated components. An advantage of the proposed method is that it avoids the dependence of the TFR while estimating the parameters. Moreover, it is effective at low signal-to-noise rate. The validity and practical utility of the proposed method are demonstrated by both the simulated and real signals. The results show that it outperforms the traditional TF methods in providing the TFR of the improved concentration for various multicomponent FM signals.

Characteristics analysis and dynamic responses of micro-gas-lubricated journal bearings with a new slip model

In this paper, a new slip model based on kinetic theory of gases for gas-lubricated journal bearings in micro-electro-mechanical systems (MEMS) is applied using a physical approach. The corresponding modified governing equation and mathematic model are presented and the flow rate is plotted versus the inverse Knudsen number. Pressure distributions along the gas bearing at various Knudsen numbers and bearing numbers are plotted and the load carrying capacities are also obtained. A numerical analysis of a rigid rotor supported by gas-lubricated journal bearings is presented for dynamic behaviour. The slip flow effect on the properties, including pressure distribution, load carrying capacity and dynamic coefficients, of the micro-gas-lubricated journal bearings and dynamic responses of the micro rotor-bearing system are estimated and analysed in detail. It is shown that the dynamic coefficients increase with increasing bearing number except for two damping coefficients and the rotor-bearing system runs at a much higher rotating speed to keep stable when slip flow occurs. Moreover, the oscillation period of the rotor operating with the slip model is longer than that with the continuum flow. In addition, the whirl frequency is reduced from 0.422 to 0.079 under the slip effect. Therefore, the results of this study contribute to a further understanding of the characteristics and nonlinear dynamics of gas-film rotor-bearing systems in MEMS.