Grooved Resonator Arm Dimensions for Lower CI and Stable Q
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Solution Overview
Problem
Existing resonator elements, such as those described in JP-A-2013-229733, lack an optimal value for the width of the land (main surfaces across the groove) to enhance the Q value or decrease the CI value, which affects vibration characteristics and efficiency.
Innovation Solution
A resonator element with a vibrating arm having a wide part with a specific width range (30 μm≤Wa≤75 μm) and a thickness range (110 μm≤T≤150 μm), where the depth of the grooves and the width of the surfaces across the grooves are optimized to satisfy 0.884≤(t1+t2)/T≤0.990 and 0.0056≤Wb/T≤0.0326, improving electric field efficiency and reducing unnecessary vibrations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the groove depth is optimized to increase Q value, then vibration quality improves, but the width of land (main surfaces across the groove) remains unoptimized affecting overall performance
Solution Approach 1:
The patent applies parameter changes by establishing specific numerical ranges for multiple dimensions: arm part width (30-75 μm), thickness (110-150 μm), groove depths (0.884≤(t1+t2)/T≤0.990), and land width (0.0056≤Wb/T≤0.0326). This systematic parameter optimization resolves the contradiction by providing concrete dimensional specifications that simultaneously improve Q value while managing device complexity through defined ranges rather than isolated adjustments.
2Reliability
If the arm part width is increased to improve vibration characteristics, then Q value increases, but the device size increases
Solution Approach 1:
The patent resolves this contradiction through parameter changes by defining a specific width range for the arm part (30-75 μm) that optimizes Q value while controlling device size. This is combined with optimizing other parameters such as thickness (110-150 μm) and groove dimensions to achieve high vibration quality within a compact form factor, demonstrating that isolated parameter adjustment is insufficient and comprehensive dimensional optimization is required.
3Stability of the object's composition
If the thickness of the arm part is increased to secure rigidity, then structural stability improves, but the device size and mass increase
Solution Approach 1:
The patent applies parameter changes by specifying a thickness range (110-150 μm) that provides sufficient rigidity while minimizing device volume. This thickness optimization works in conjunction with optimized groove depths (0.884≤(t1+t2)/T≤0.990) and arm part width (30-75 μm) to achieve the desired rigidity-to-volume ratio, demonstrating that thickness cannot be optimized in isolation but requires coordinated adjustment with other dimensional parameters.
4Reliability
If multiple parameters are optimized simultaneously to improve vibration efficiency, then Q value and CI value improve, but the manufacturing complexity increases
Solution Approach 1:
The patent addresses this contradiction through systematic parameter changes by defining interrelated dimensional ranges that can be manufactured within standard tolerances. The specified ranges for arm part width (30-75 μm), thickness (110-150 μm), and groove dimensions provide a manufacturable design space that achieves high vibration efficiency (improved Q and CI values) without requiring ultra-precision manufacturing, balancing performance improvement with manufacturing feasibility.
Data Source
AI summary
A resonator element includes a base part and a vibrating arm. The vibrating arm includes an arm part and a wide part whose width is larger than that of the arm part. In the arm part, a first groove is formed on the first surface side, and a second groove is formed on the second surface side. 30 μm≤Wa≤75 μm, in which a width of the arm part is Wa, a thickness T between the first surface and the second surface of the arm part satisfies 110 μm≤T≤150 μm. 0.884≤(t1+t2)/T≤0.990, in which a depth of the first groove is t1, and a depth of the second groove is t2. 0.0056≤Wb/T≤0.0326, in which a width of the first surface arranged across the first groove and a width of the second surface arranged across the second groove are Wb. A length L1 of the vibrating arm satisfies L1≤1000 μm.