【発明の詳細な説明】
本発明は屈曲モードと捩りモード振動が結合し
た結合水晶振動子の切断角度に関する。本発明は
屈曲、捩り水晶振動子の周波数温度特性に優れた
新カツト角を提案するものである。腕時計用振動
子として音叉型屈曲水晶振動子が一般的に使用さ
れている。しかし、このタイプの振動子は周波数
温度特性が２次曲線で表わされるため広い温度範
囲に互つて零温度係数を与えることが出来ず、時
間精度に限界があつた。そこで、最近は特開昭55
−75326で見られるように、屈曲モードに捩りモ
ードを結合させ、屈曲モードの周波数温度特性を
改善し、優れた周波数温度特性を得ている。そし
て、この優れた周波数温度特性を与えるカツト角
は音叉の辺比によつて若干異なるが約−10゜付近
が使用されている。本発明はこれら従来の屈曲、
捩れ振動子の研究する中で、上記カツト角以外に
も周波数温度特性に優れた新カツト角が存在する
ことを見い出した。以下、本発明について詳細に
説明する。DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a cutting angle of a coupled crystal resonator in which bending mode and torsional mode vibration are coupled. The present invention proposes a new cut angle that has excellent frequency-temperature characteristics for bent and torsion crystal resonators. A tuning fork type bent crystal resonator is generally used as a resonator for a wristwatch. However, since the frequency-temperature characteristic of this type of vibrator is represented by a quadratic curve, it is not possible to provide a zero temperature coefficient over a wide temperature range, and there is a limit to the time accuracy. Therefore, recently, JP-A-55
As seen in -75326, the torsional mode is combined with the bending mode to improve the frequency-temperature characteristics of the bending mode, resulting in excellent frequency-temperature characteristics. The cut angle that provides this excellent frequency-temperature characteristic varies slightly depending on the side ratio of the tuning fork, but a cut angle of around -10° is used. The present invention is directed to these conventional bending methods.
While researching torsional oscillators, we discovered that there is a new cut angle other than the above cut angle that has excellent frequency-temperature characteristics. The present invention will be explained in detail below.
水晶振動子、特に、屈曲モードに捩りモードを
結合させ、この周波数温度特性の挙動を理論的に
解析する試みは未だ行なわれていない。そこで、
本発明は屈曲モードと捩りモードの結合した屈
曲、捩り水晶振動子について理論解析を行ない、
特に、振動子の寸法、カツト角に対する周波数温
度特性の関係を調査した。今、屈曲モードの共振
周波数をF、捩りモードの共振周波数をTとする
と屈曲モードに捩りモード振動が結合して得られ
る共振周波数は次式のようになる。2
＝１／2y（2 F＋2 T±√（2 F−2 T）2
−4c2 F 2 T） −(1)
但し、ｙは無次元の値、ｃは弾性結合因子
本発明は(1)式より、共振周波数のテイラー展
開により、一次、二次、三次温度係数を求めてい
る。第１図は本発明の音叉型屈曲捩りモード水晶
振動子の結晶軸との関係を示し、音叉型形状はＺ
板から形成され、同図に示すように音叉腕の長さ
ｌはｙ軸方向からなり、Ｘ軸と一致した腕幅Ｗ、
板厚ｔとからなつている。又、Ｘ軸のまわりの回
転は反時計方向を正とし、時計方向を負とする。
第２図は理論解析によつて得られた結果で、Ｗ＝
0.35mm、ｌ＝0.95mmで厚みｔを最適値にしたとき
の一次温度係数αが零となる、カツト角θによる
二次温度係数βの関係を示し、カツト角−10゜付
近でα、βともに零になり、これが従来見い出さ
れ使用されているカツト角であり、第２図から明
らかなように、カツト角が−50゜付近にもα、β
が同時に零となるカツト角が存在することが分か
る。又、このカツト角は振動子の寸法等によつて
若干変化するが、本発明では、たとえ寸法を変え
ても、カツト角が−40゜〜−60゜の範囲内であれば
α、βを常に零にすることが出来る。以上、述べ
たように、本発明は屈曲モードと捩りモード振動
の結合した結合水晶振動子について理論解析を行
ない。その結果、周波数温度特性に優れた水晶振
動子を提供できる、新カツト角を見い出した。 No attempt has yet been made to theoretically analyze the behavior of the frequency-temperature characteristics of a crystal resonator, especially by coupling the torsional mode to the bending mode. Therefore,
The present invention performs a theoretical analysis of a bent and torsion crystal resonator in which a bending mode and a torsion mode are combined.
In particular, we investigated the relationship between frequency and temperature characteristics with respect to the dimensions of the vibrator and the cut angle. Now, if the resonant frequency of the bending mode is F and the resonant frequency of the torsional mode is T , then the resonant frequency obtained by coupling the torsional mode vibration to the bending mode is as follows. 2 = 1/2y( 2 F + 2 T ±√( 2 F − 2 T ) 2 −4c 2 F 2 T ) −(1) However, y is a dimensionless value and c is an elastic coupling factor. From equation 1), the first-order, second-order, and third-order temperature coefficients are obtained by Taylor expansion of the resonance frequency. Figure 1 shows the relationship between the crystal axis and the tuning fork type bending torsion mode crystal resonator of the present invention, and the tuning fork type shape is Z.
It is formed from a plate, and as shown in the figure, the length l of the tuning fork arm is in the y-axis direction, and the arm width W, which coincides with the x-axis, is
It consists of plate thickness t. Further, regarding rotation around the X axis, counterclockwise direction is positive and clockwise direction is negative.
Figure 2 shows the results obtained by theoretical analysis, where W=
The relationship between the secondary temperature coefficient β depending on the cut angle θ is shown, where the first temperature coefficient α becomes zero when the thickness t is set to the optimum value at 0.35 mm and l = 0.95 mm. Both become zero, and this is the cut angle that has been found and used in the past.As is clear from Figure 2, even when the cut angle is around -50°, α and β
It can be seen that there exists a cut angle for which both are zero at the same time. Also, this cut angle varies slightly depending on the dimensions of the vibrator, etc., but in the present invention, even if the dimensions are changed, α and β can be maintained as long as the cut angle is within the range of -40° to -60°. It can always be set to zero. As described above, the present invention performs a theoretical analysis of a coupled crystal resonator in which bending mode and torsional mode vibrations are coupled. As a result, we discovered a new cut angle that can provide a crystal resonator with excellent frequency-temperature characteristics.
【図面の簡単な説明】[Brief explanation of the drawing]
第１図は音叉型水晶振動子と結晶軸との関係を
示す。第２図は一次温度係数αが零のときのカツ
ト角θと二次温度係数βとの関係を示す。
ｌ＝音叉腕長さ、Ｗ＝音叉腕幅、ｔ＝音叉板
厚。
FIG. 1 shows the relationship between a tuning fork type crystal resonator and the crystal axis. FIG. 2 shows the relationship between the cut angle θ and the secondary temperature coefficient β when the primary temperature coefficient α is zero. l = tuning fork arm length, W = tuning fork arm width, t = tuning fork plate thickness.