Resonator Tapered Portion Geometry for Q Factor Stability
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Solution Overview
Problem
Existing resonator elements with tapered portions often experience a decrease in the Q factor due to thermoelastic loss, which can be exacerbated by the shape of the tapered portion, leading to instability in vibration mode and potential damage from impacts or environmental factors.
Innovation Solution
The resonator element's tapered portion is designed with controlled taper length and width occupancies (η and ξ) to suppress thermoelastic loss, with specific ranges for these parameters to maintain or increase the Q factor, and the shape can be formed by straight lines or curved lines to disperse stress and reduce distortion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a tapered portion is provided in the connection portion between the resonating arm and the base portion, then vibration leakage is suppressed and the Q factor is increased, but the Q factor is often decreased due to thermoelastic loss from the shape of the tapered portion
Solution Approach 1:
The patent applies parameter changes by precisely controlling the geometric parameters of the tapered portion. Specifically, the taper length occupancy ratio (Lt/L) is set to 0.003 to 0.03 and the taper width occupancy ratio (Wt/W) is set to 0.006 to 0.06. By optimizing these dimensional parameters, the design suppresses thermoelastic loss while maintaining the benefits of vibration leakage suppression, thereby increasing the Q factor.
2Reliability
If the tapered portion shape is not optimized, then manufacturing is simpler, but the Q factor decreases due to excessive thermoelastic loss
Solution Approach 1:
The patent establishes specific parameter ranges for the tapered portion: taper length occupancy ratio (Lt/L) of 0.003 to 0.03 and taper width occupancy ratio (Wt/W) of 0.006 to 0.06. These quantified parameters provide clear manufacturing guidelines that balance ease of fabrication with optimal Q factor performance, making the design both manufacturable and high-performance.
3Strength
If a tapered portion is provided to suppress vibration leakage, then the resonator is protected from impacts and vibration mode deterioration, but thermoelastic loss increases and reduces the Q factor
Solution Approach 1:
The patent optimizes the tapered portion dimensions with taper length occupancy ratio (Lt/L) of 0.003 to 0.03 and taper width occupancy ratio (Wt/W) of 0.006 to 0.06. This precise parameter control ensures the tapered portion provides adequate impact protection and vibration mode stability while minimizing thermoelastic loss through optimized geometry.
Solution Approach 2:
The patent applies local quality by creating a tapered portion with specific geometric properties at the connection region between the resonating arm and base portion. The taper width and length are locally optimized to provide both mechanical protection (impact resistance) and acoustic performance (minimized thermoelastic loss), with the tapered geometry concentrating the protective function where needed while controlling energy loss.
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 a stable vibration mode with an increased Q factor, reducing thermoelastic loss and protecting the resonator from impacts, while also allowing for easier handling and protection against environmental factors by housing the element in a vacuum package.
Implementation Method 1
the Q factor is often decreased depending on the shape of the tapered portion. Presumably, this is because a thermoelastic loss resulting from the shape of the tapered portion exceeds an increase in the Q factor resulting from a suppression effect of vibration leakage by providing the tapered portion
Implementation Method 2
at least one resonating arm which performs flexural vibration
Data Source
AI summary
A resonator element includes: at least one resonating arm which performs flexural vibration; a base portion connected to an end of the resonating arm; and a tapered portion which is axisymmetrical with respect to a centerline which bisects the width of the resonating arm, and which has a width increasing toward a portion of the tapered portion connected to the base portion from a portion of the tapered portion connected to the resonating arm, wherein assuming that the length and width of the resonating arm are L and W and the length and width of the tapered portion are Lt and Wt, the shape of the tapered portion is controlled to satisfy a taper length occupancy η=Lt/L and a taper width occupancy ξ=2 Wt/W.