Resonator, has balance spring allowed to cooperate with balancer and arranged at angle with respect to Z-axis of crystallographic axes, and crystal provided between specific degrees for pairing balancer with spring

[0001] l'a thermally compensated balance - hairspring matched and more specifically a hairspring formed from single crystal quartz.

[0002] le 1,519 250 the EP document is disclosed making a spiral spring made of single crystal quartz. However, a spiral spring made of single crystal quartz is not easy to be paired in practice.

[0003] le object of the present invention is to overcome all or part the drawbacks mentioned above by providing an improved pairing of a spiral quartz with its balance.

[0004] a this effect, the invention relates to a resonator comprising a hairspring formed in a single crystal quartz crystal crystallographic axes the X, the Y, Z-, the X-axis, being the electrical axis and the Y axis the mechanical axis, and cooperating with a balancer characterized in that the coefficient of expansion of the balance is between + 6 ppm °c.'¹ et + 12 ppm °c.'¹ for a cutting angle of the spiral with respect to the Z axis of the crystal quartz crystal between -5 et + 5 degrees ° for paired in the balance with the balance spring.

[0005] in accordance with other advantageous features of the invention:

- the expansion coefficient of the rocker is substantially equal to + 9 ppm °c.'¹ for a cutting angle of the spiral with respect to the axis Z of said single crystal quartz crystal substantially equal to + 2 degrees;

- the pendulum comprises titanium and/or [...] and/or platinum.

[0006] d'other features and advantages shall become apparent clearly is as made hereinafter, illustratively the least and limiting, reference to the accompanying drawings, in which:

the Figures 1 and 2 represent schematically the cutting angle 9 of a hairspring in single-crystal quartz according to the invention;

fig. 3 schematically depicts a thermally compensated balance - balance spring according to the invention.

[0007] as illustrated in Figure. 3, the invention relates to a resonator type 1 - 3 balance balance spring 5.3 the balance and the hairspring 5 are preferably mounted on the same axis in such a resonator 7.1, the moment of inertia of the balance/3 has the formula:

[...]=the MR(1)

where m is the mass and R the radius of gyration which of course depends on the coefficient of extent AB of the rocker.

[0008] de more, the elastic constant c of the hairspring 5 has the formula:

EHE To?

[...]

VBE1 2 L

(2)

wherein e is the Young's modulus of the hairspring, hr its height, its thickness W and L is its developed length.

[0009] finally, the frequency f of the resonator 1 sprung balance corresponds to the formula:

00 [...] L.

2. π[...]1

- f.

(3)

[0010] of course, it is desired that the frequency variation as a function of temperature of a resonator is substantially zero. The frequency variation as a function of temperature in the case of a resonator spiral substantially follows the following formula:

the I / δ

\∂E1

is the frequency variation as a function of temperature;

[...] ∂]_

'∂ T-I

is the change in Young's modulus as a function of temperature, [...] to say the thermoelastic coefficient (CTEs) of the hairspring;

α -_O the expansion coefficient of the hairspring, expressed in ppm. °c'¹ ;

α -_b. the expansion coefficient of the balance, expressed in ppm. °c'¹ ;

[0011] the oscillations of any resonator for a time base or frequency to be maintained, the temperature dependence also includes an optional contribution maintaining system as, for example, a lever escapement (not shown) Swiss interacts with the pin 9 of the tray 11 also mounted on the spindle 7.

[0012] referring to Figure 1 and 2, the invention relates more particularly to a resonator 1 wherein the balance spring 5 is formed from a single crystal quartz crystallographic axes the X, the Y, Z-, the X-axis, being the electrical axis and the Y axis the mechanical axis. Shown these drawings that the height H of the coils is substantially the same orientation as the crystallographic Z-axis. More precisely the height H shape, with the Z-axis, an angle 8 which may be positive or negative. The modification of this angle θ for varying the characteristics of the hairspring 5 without having to modify the geometry.

[0013] on thus comprises from formulae (1) - (4) that it is possible the hairspring 5 paired with the balance wheel 3 so that the frequency f of the resonator 1 is substantially insensitive to temperature variations. The use of quartz for the manufacture of a hairspring 5 also provides the advantage, in addition to its excellent thermal characteristics, also have excellent mechanical and chemical properties, in particular at the age and very low sensitivity to magnetic fields.

[0014] for a cutting angle θ substantially equal to + 2 degrees, thus it has empirically been found that an expansion coefficient of the balance Aβ 3 were to be substantially equal to + 9 ppm °c.'¹ to obtain a temperature coefficient substantially equal to + 0.06 [...] ' VCs'¹ which is very below conditions equal to [...] 0.6 [...][...] '¹ °C.'¹ .

[0015] more generally, so that the thermal coefficient of resonator 1 remains substantially to + 0.1 [...] '¹ °C.'¹ , [...] to say always under the conditions [...], and for an angle θ cutting of the hairspring 5 with respect to the Z axis of the crystal quartz crystal between -5 et + 5 degrees degrees, the expansion coefficient α_b. the swing arm 3 is between + 6 ppm °c.'¹ et + 12 ppm °c.'¹ .

[0016] to meet these expansion coefficients α_b. , the balance 3 can in particular comprise titanium and/or [...] (symbol in AFNOR: z2nkd 18-09-05) and/or platinum. In addition, advantageously, it should be noted that the [...] can be weakly sensitive to magnetic fields according to its tempering temperature.

[0017] of course, the present invention is not limited to the illustrated example but is susceptible to various variations and modifications apparent to those skilled in the relevant arts. In particular, any other material balance 3 respecting expansion coefficients explained above can be used.