An investigation on thermoelastic damping of high-Q ring resonators

Hossain, Syed T.; McWilliam, Stewart; Popov, Atanas A.

doi:10.1016/j.ijmecsci.2015.12.023

Cited by 51 publications

(17 citation statements)

References 29 publications

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“…Thermoelastic damping is particularly important for MEMS resonators, where regions of compression and expansion simultaneously appear. Zener [25,26] was the first to develop the theory of thermoelastic damping for thin rectangular beams under flexural vibrations, and the thermoelastic damping is [21] QTED−1=ΔMω0τ1+false(ω0τfalse)2 where ΔM is the relaxation strength, which only depends on the temperature and material properties and has a value of 2.02×10−4 for crystalline silicon at 298 K [27]. ω0 is the angular frequency of resonators.…”

Section: Energy Loss Analysismentioning

confidence: 99%

“…The key in the low thermoelastic damping design is to maintain the resonator away from the Debye peak [21], where τ≈ω0−1. For the elastic beam with a width of 18 μm, the Debye peak appears at 467 kHz with QTED of 9.5 k. Thus, the working frequency of the proposed DRG, which is 16 kHz, is far away from the Debye peak, and the corresponding QTED is 139 k.…”

Section: Energy Loss Analysismentioning

confidence: 99%

“…The energy loss mechanism of thermoelastic damping is relatively mature and has been used to analyse the DRG [21,22,23]. However, the anchor loss of DRGs, especially considering their structurally asymmetry and fabrication imperfections, lacks careful study.…”

Section: Introductionmentioning

confidence: 99%

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Energy Loss in a MEMS Disk Resonator Gyroscope

2019

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Analysing and minimizing energy loss is crucial for high performance disk resonator gyroscopes (DRGs). Generally, the primary energy loss mechanism for high vacuum packaged microelectromechanical system (MEMS) resonators includes thermoelastic damping, anchor loss, and electronic damping. In this paper, the thermoelastic damping, anchor loss, and electronic damping for our DRG design are calculated by combining finite element analysis and theoretical derivation. Thermoelastic damping is the dominant energy loss mechanism and contributes over 90% of the total dissipated energy. Benefiting from a symmetrical structure, the anchor loss is low and can be neglected. However, the electronic damping determined by the testing circuit contributes 2.6%–9.6% when the bias voltage increases from 10 V to 20 V, which has a considerable impact on the total quality factor (Q). For comparison, the gyroscope is fabricated and seal-packaged with a measured maximum Q range of 141k to 132k when the bias voltage varies. In conclusion, thermoelastic damping and electronic damping essentially determine the Q of the DRG. Thus, optimizing the resonance structure and testing the circuit to reduce energy loss is prioritized for a high-performance DRG design.

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Section: Energy Loss Analysismentioning

confidence: 99%

Section: Energy Loss Analysismentioning

confidence: 99%

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Energy Loss in a MEMS Disk Resonator Gyroscope

2019

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“…The ring resonator is a flexural beamlike geometry under in-plane vibration. Thus, its analytical model of TED is similar to the Zener and LR models [9,[16][17][18][19]. Wong et al [9] studied TED for in-plane ring resonators based on the LR theory and presented an analytical model, which is similar to the LR model of beams.…”

Section: Introductionmentioning

confidence: 99%

Entropy Generation and Thermoelastic Damping in the In-plane Vibration of Microring Resonators

Tai

Zheng

et al. 2019

Entropy

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Thermoelastic damping is a critical issue for designing very high quality factor microresonators. This paper derives the entropy generation, associated with the irreversibility in heat conduction, that is used for ring resonators in in-plane vibration and presents an analytical model of thermoelastic damping according to heat increments calculated by entropy theory. We consider the heat flow only in radial thickness of the ring and obtain a complex temperature field that is out of phase with the mechanical stress. The thermoelastic dissipation is calculated in the perspective of heat increments that appear due to entropy generation. The analytical model is validated by comparing with an LR (Lifshitz and Roukes) model, finite-element method and measurement. The accuracy of the present model is found to be very high for different ambient temperatures and structures. The effects of structure dimensions and vibration frequencies on entropy generation and thermoelastic damping is investigated for ring resonators under in-plane vibration.

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“…Several energy dissipation mechanisms exist, including air damping, surface loss, support loss, electrical damping, and thermoelastic damping (TED) 19–23 . In DRGs encapsulated in high-vacuum packages and working in elliptical modes, TED has been identified as the major energy dissipation mechanism and imposes an upper limit on the attainable Q 8,24 . Therefore, thermoelastic quality factor ( Q TED ) improvement is the main target in optimization of DRGs.…”

Section: Introductionmentioning

confidence: 99%

0.04 degree-per-hour MEMS disk resonator gyroscope with high-quality factor (510 k) and long decaying time constant (74.9 s)

et al. 2018

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The disk resonator gyroscope is an attractive candidate for high-performance MEMS gyroscopes. This gyroscope consists of a sensor and readout electronics, and the characteristics of the sensor directly determine the performance. For the sensor, a high-quality factor and long decaying time constant are the most important characteristics required to achieve high performance. We report a disk resonator gyroscope with a measured quality factor of 510 k and decaying time constant of 74.9 s, which is a record for MEMS silicon disk resonator gyroscopes, to the best of our knowledge. To improve the quality factor of the DRG, the quality factor improvement mechanism is first analyzed, and based on this mechanism two stiffness-mass decoupled methods, i.e., spoke length distribution optimization and lumped mass configuration design, are proposed and demonstrated. A disk resonator gyroscope prototype is fabricated based on these design strategies, and the sensor itself shows an angle random walk as low as 0.001°/√h, demonstrating true potential to achieve navigation-grade performance. The gyroscope with readout electronics shows an angle random walk of 0.01°/√h and a bias instability of 0.04°/h at room temperature without compensation, revealing that the performance of the gyroscope is severely limited by the readout electronics, which should be further improved. We expect that the quality factor improvement methods can be used in the design of other MEMS gyroscopes and that the newly designed DRG can be further improved to achieve navigation-grade performances for high-end industrial, transportation, aerospace, and automotive applications.

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An investigation on thermoelastic damping of high-Q ring resonators

Cited by 51 publications

References 29 publications

Energy Loss in a MEMS Disk Resonator Gyroscope

Energy Loss in a MEMS Disk Resonator Gyroscope

Entropy Generation and Thermoelastic Damping in the In-plane Vibration of Microring Resonators

0.04 degree-per-hour MEMS disk resonator gyroscope with high-quality factor (510 k) and long decaying time constant (74.9 s)

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