Meander Flexural Resonator Balancing for High Q Stability

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Solution Overview

Problem

Existing resonators, particularly those made from quartz crystals, suffer from symmetry defects due to chemical engraving processes, leading to poor dynamic balancing, energy loss, and degradation of quality factor and frequency stability, which affects their performance in timekeeping and force sensing applications.

Innovation Solution

The resonator design includes a vibrant portion with a median plane of symmetry and an orthogonal symmetry plane, featuring longitudinal slits that form meanders, which compensates for movement components parallel to the median axis, reducing energy losses and enhancing the quality factor.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If chemical etching is used to manufacture quartz resonators, then manufacturing precision is improved, but symmetry defects are generated due to crystalline orientation

Engineering Contradiction:

Improveetching precisionVSAvoidsymmetry

Core Design Contradiction:

Manufacturing precisionVSStability of the object's composition

Solution Approach 1:

The patent intentionally introduces asymmetry through a compensation mass to counterbalance the unwanted symmetry defects caused by chemical etching. The compensation mass is strategically positioned to restore dynamic balance to the resonator, thereby resolving the contradiction between manufacturing precision and symmetry stability.

Inventive Principle:

Principle #4Asymmetry

2Ease of manufacture

If simple electrode configurations are used on wafer faces, then ease of manufacture is improved, but manufacturing precision deteriorates due to difficulty in generating effective bending

Engineering Contradiction:

Improveelectrode configuration simplicityVSAvoidbending generation effectiveness

Core Design Contradiction:

Ease of manufactureVSManufacturing precision

Solution Approach 1:

The patent introduces an intermediate compensation mass as a mediator between the simple electrode configuration and the desired bending effect. This compensation mass enables the simple electrode configuration to effectively generate the required bending vibrations while maintaining ease of manufacture.

Inventive Principle:

Principle #24Intermediary (Mediator)

3Productivity

If resonator beams are chemically etched with NH4F-HF mixture, then productivity is improved due to high etching speed, but symmetry is broken causing energy loss

Engineering Contradiction:

Improveetching speedVSAvoidvibration energy loss

Core Design Contradiction:

ProductivityVSLoss of energy

Solution Approach 1:

The patent converts the harmful symmetry-breaking effect of chemical etching into a beneficial solution by introducing a compensation mass. This compensation mass transforms the energy loss caused by asymmetry into a controlled parameter that can be optimized, thereby maintaining high productivity while reducing vibration energy loss.

Inventive Principle:

Principle #22Blessing in disguise (Convert harm into benefit)

4Device complexity

If symmetry breaking occurs in resonator, then manufacturing simplicity is maintained, but quality factor deteriorates due to poor dynamic balancing

Engineering Contradiction:

Improveresonator structure simplicityVSAvoidquality factor

Core Design Contradiction:

Device complexityVSReliability

Solution Approach 1:

The patent employs a compensation mass as a counterweight to offset the dynamic imbalance caused by symmetry breaking in the resonator structure. This allows the resonator to maintain its structural simplicity while achieving the required dynamic balance for high quality factor performance.

Inventive Principle:

Principle #8Anti-weight (Counterweight)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This design achieves reduced vibration energy losses, leading to a higher quality factor and improved frequency stability, while also maintaining symmetry and reducing parasitic mechanical coupling in gyrometers.

Implementation Method 1

the piezoelectric tensor of trigonal class crystals offers an optimal coupling for the Syy deformation, i.e. along the beam axis, with an Exx electric field. For this, the bending vibration of the beam is excited by direct piezoelectric effect using electrodes which are located along the beam in order to generate the electric field Exx, and to detect the deformations Syy via electric charges which are generated by indirect piezoelectric effect on these same electrodes.

Methodology Applied

Scientific EffectPiezoelectric effect: Piezoelectric Effect

Implementation Method 2

Methodology Applied

Scientific EffectVibration energy loss reduction through symmetry compensation:

Data Source

PatentEP4305752B1Flexural vibration mode resonator with high quality factor for the realization of time references, force sensors or gyrometers

Publication Date: 2025.05.07 OFFICE NAT DETUDES & DE RECH AEROSPATIALES

Figure 1a~1b
Figure 2a~2b
Figure 3a~3c

AI summary

A resonator is suitable for reducing or decreasing to zero a force that is or would otherwise be transmitted by a vibrating portion of the resonator to a bearing part (Pf). To this end, the vibrating portion comprises two extensions (P1, P2) that are each meander shaped so that two segments of each extension have respective speed components that are oriented in inverse directions. Such a resonator, which is balanced, may advantageously be used within a gyrometer or a force sensor.