REGULATING ORGAN (balance wheel – hairspring system)
Figure 1: Exploded view of the regulating organ
Figure 2: Plan of the assembled regulating organ (screw balance, flat hairspring)
Definition
The regulating organ is the oscillating device that sets the rate of a timepiece. In portable watches (pocket or wrist), the regulating organ is generally the balance wheel and hairspring assembly, which forms a harmonic oscillator whose period regularity determines the watch’s accuracy. It converts the energy stored in the mainspring into a succession of regular oscillations, thereby governing the regularity of timekeeping.
Different regulating organs
| Type of timekeeping instrument | Regulating organ | Frequency | Accuracy |
|---|---|---|---|
| Clocks | Pendulum | 0.5–1 Hz | – |
| Mechanical watches / clocks | Balance-spring | 2.5–5 Hz | approx. 5-10 s/day |
| Electronic watches | Tuning fork | 300–720 Hz | approx. 5-10 s/month |
| Electronic watches | Quartz crystal | 32,000 Hz | approx. 1 s/month |
| Atomic clocks | Atoms (various types) | 429,228,004,229,873.2 Hz | approx. 1 s/13 billion years |
The pendulum
This is the oldest mechanical oscillator. It consists of a rod with a suspended mass whose height is generally adjustable. It is found in most clocks and pendulum clocks. At the beginning of the 17th century, Galileo observed that the period of a pendulum is constant regardless of its amplitude (the theory of isochronism). This theory was later refined by Christiaan Huygens, who subsequently invented the balance wheel – hairspring. Pendulums can achieve excellent chronometric results. Unfortunately, they cannot be moved while operating and therefore are not suitable for portable timepieces. Pendulums generally oscillate at frequencies between 0.5 Hz and 1 Hz. Motion, shocks, and temperature variations influence the accuracy of pendulum-regulated clocks.
The balance spring (balance wheel and hairspring)
This is the regulating organ of most portable mechanical watches. The balance spring was invented in 1675 by Christiaan Huygens. This major breakthrough made it possible to transport timekeeping instruments (marine chronometers, pocket watches, then wristwatches) while they were running. It consists of an inertia wheel (the balance wheel) and a thin spiral spring (the hairspring). The oscillation frequency of a balance spring is generally between 2.5 Hz and 5 Hz. This is the type of regulating organ detailed in this chapter.
The tuning fork
This is a type of regulating organ used in electronic (battery-powered) watches. It consists of a steel blade shaped like a tuning fork. An electromagnet maintains the oscillations of the fork’s prongs through the piezoelectric effect. Such an oscillator operates in a range between about 300 Hz and 720 Hz. The vibrations of the tuning fork actuate index fingers that drive the seconds wheel. As a result, the seconds hand of a tuning-fork-regulated watch makes 300 to 720 steps per second and appears to move continuously. This type of oscillator was briefly used in the early 1970s before being surpassed by quartz technology. Because of their technology and the audible frequency range of the tuning fork, watches equipped with such a resonator emit a characteristic continuous high-pitched sound.
Quartz
The principle of quartz is similar to that of the tuning fork. A direct electric current causes a quartz crystal, cut in the shape of a tuning fork, to vibrate. Through the piezoelectric effect, the quartz oscillates at a frequency of 32,000 Hz (32 kHz). The quartz converts the direct current it receives into an alternating current at this same frequency. The electronic circuit of the movement reduces this frequency down to 1 Hz in order to regularly drive the watch’s stepper motor.
Cesium, rubidium, and strontium atoms
The principle of such regulating organs is to induce energy-state transitions in cesium-133 or rubidium atoms. These transitions generate electromagnetic radiation from the atom’s electrons at a very high and extremely stable frequency. The oscillation frequency of cesium-133 atoms is 9,192,631,770 Hz, and the latest optical atomic clocks can excite strontium electrons at a frequency of 429,228,004,229,873.2 Hz. The accuracy drift of such clocks is about one second over 13 billion years (roughly the age of the universe). Beyond time measurement, such clocks are used in astronomy, science, and physics (nuclear research, satellite guidance, navigation systems, etc.).
The balance wheel–hairspring system
Description and components
The regulating organ of mechanical watches consists mainly of an inertia wheel called the balance wheel and a spring in the form of an Archimedean spiral called the hairspring. The balance wheel is riveted onto its staff. On this same staff, the inner end of the hairspring is fixed by means of the collet (Figures 2 & 3).
The outer end of the hairspring is fixed to the balance cock by means of the stud (Figures 2 & 4).
At an angle α generally between 60° and 70° from the stud (Figure 5, point 1), the terminal curve of the hairspring passes between the two regulator pins (Figure 5, point 2). The regulator pins are press-fitted into the regulator index (Figure 5, point 3), which pivots with slight friction concentrically to the balance wheel axis.
Important:
The presence or construction of the various components of the regulating organ may vary from one movement to another (e.g., optional presence of a regulator index or a movable stud holder).
Balance–hairspring motions
During the operation of the watch, the hairspring oscillates concentrically about its axis on either side of its equilibrium position, also called the equilibrium position or “dead point” (Figure 7). When the balance wheel is pushed beyond its equilibrium position (during an impulse; see escapement), the hairspring is wound.
When the impulse is delivered in one direction, the spring is tensioned in extension (Figure 6), and when the impulse is delivered in the other direction, the spring is tensioned in contraction (Figure 8). In both cases, a restoring torque (elastic torque) is created that brings the balance wheel back to its equilibrium position (dead point) (Figures 6 to 8).
Mathematical relationship:
The mathematical relationship between the balance wheel and the hairspring is as follows (see: Pairing up the balance wheel and hairspring):
T = Period (s)
I = Moment of inertia of the balance about its axis (kg·m²)
C = Elastic torque (stiffness) of the hairspring (N·m/rad)
