[Paper Review] A novel nonlinear amplitude-modulation gyroscope incorporating internal resonance

S. Amir Mousavi Lajimi, Navid Noori+3 more|arXiv (Cornell University)|Jan 7, 2017

Geophysics and Sensor Technology8 references3 citations

TL;DR

This paper proposes a novel nonlinear amplitude-modulation gyroscope using two-to-one internal resonance between a drive mode (second structural mode) and a sense mode (fundamental mode), achieving enhanced bandwidth and sensitivity. By exploiting nonlinear modal coupling via a double-H or T-shaped design, the system exhibits saturation behavior that stabilizes the sense response and improves noise resilience, enabling higher performance in open-loop operation without complex closed-loop control.

ABSTRACT

We are presenting the design and the preliminary numerical and experimental analyses of two mismatched Coriolis vibratory gyroscopes incorporating nonlinear modal interaction. A novel double-H design includes two clamped-clamped beams and a suspended mass in the middle connected to the base beams via four short cantilevers. Another design is a T-shaped gyro including a primary doubly-clamped beam and a secondary sense beam. A combination of analytical, finite element, and experimental analyses are employed to study the characteristics of the nonlinear gyro. The drive mode matches the structure's second mode, while the sense mode matches the fundamental mode of the structure. Our preliminary study indicates that the bandwidth and the sensitivity of the rotation rate sensor are improved by employing the nonlinear modal interaction.

Motivation & Objective

• To overcome the limited sensitivity and narrow bandwidth of conventional amplitude-modulation Coriolis vibratory gyroscopes.
• To leverage nonlinear modal interactions through internal resonance to enhance sensor performance.
• To design and validate a double-H and T-shaped MEMS gyroscope with frequency-matched 2:1 internal resonance between drive and sense modes.
• To demonstrate improved stability and noise resilience via saturation phenomena in the sense response.
• To provide a pathway for high-performance, low-complexity open-loop gyroscopes using nonlinear dynamics.

Proposed method

• Designing a double-H and T-shaped MEMS structure where the drive mode operates at the second mode frequency and the sense mode at the fundamental mode, creating a 2:1 internal resonance.
• Employing finite element analysis (Ansys Mechanical APDL) for static, modal, harmonic, and transient response simulations of the micro-scale T-gyro.
• Fabricating prototypes using SOIMUMPs process and validating with SEM imaging and macro-scale testing on a rate table.
• Developing a lumped-mass model with coupled nonlinear equations of motion to describe the system dynamics, including Coriolis and nonlinear stiffness terms.
• Using direct numerical integration and a two-variable perturbation method to solve the nonlinear equations and predict saturation behavior.
• Conducting experimental frequency-response measurements on a macro-scale T-gyro using piezoelectric actuators, laser displacement sensors, and MATLAB/Simulink control for data acquisition.

Experimental results

Research questions

• RQ1 Can internal resonance in a mismatched beam-mass system enhance the sensitivity and bandwidth of an amplitude-modulation gyroscope?
• RQ2 How does nonlinear coupling between a second-mode drive and fundamental-mode sense response affect the dynamic stability and signal-to-noise ratio?
• RQ3 To what extent does the saturation phenomenon in the sense mode improve measurement stability under varying excitation amplitudes?
• RQ4 Can a 2:1 internal resonance configuration reduce the need for complex closed-loop control in open-loop gyroscopes?
• RQ5 How do the frequency-response curves of the sense beam change with increasing excitation amplitude, and what does this imply for operational bandwidth?

Key findings

• The T-shaped macro-scale gyroscope exhibited a measurable increase in bandwidth and sense amplitude across multiple excitation amplitudes, with a flat region in the frequency-response curve indicating stable operation.
• Numerical simulations showed that the sense mode amplitude grows significantly after a threshold excitation amplitude, demonstrating nonlinear saturation behavior.
• FFT analysis confirmed that the drive mode’s second harmonic (excitation frequency) transfers energy to the sense mode via internal resonance and Coriolis coupling, producing a primary response at the sense mode’s fundamental frequency.
• The system achieved a high-amplitude, wideband response in the sense direction due to internal resonance, improving signal detectability and reducing sensitivity to frequency drift.
• The use of a 2:1 frequency ratio allowed filtering of noise near the sense mode’s natural frequency, enhancing long-term stability and reducing electronic noise impact.
• The double-H design successfully amplified the sense signal through added mass, and both designs demonstrated feasibility for nonlinear amplitude-modulation gyroscope applications.