Figure 1: Exploded view of an assembled balance wheel
Figure 2: Plan of a screw balance wheel
General description
The balance wheel and the hairspring of a watch together form its regulating organ. The balance wheel is an inertia wheel made up of an annular mass called the felly, supported by arms (generally two or three) (Figure 2). To ensure the best possible accuracy of the watch while consuming minimal energy, the balance wheel should ideally have the greatest possible moment of inertia and the smallest possible mass.
Moment of inertia
Formulas
(for the balance)
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I = moment of inertia of the balance (kg·m²)
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m = mass of the balance (kg)
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r = radius of gyration of the balance (m)
(for the hairspring)
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C = stiffness of the hairspring (N·m/rad)
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f = frequency (Hz)
Plain balance wheels
There are many types and designs of balance wheels. Today, balance wheels can be divided into two main categories. Plain balance wheels are the most important group. They are generally made of beryllium copper, beryllium bronze, or Glucydur (similar types of alloys). They offer a very good ratio between mass and moment of inertia, as well as an excellent thermal expansion coefficient. Plain balance wheels may have two or three arms (Figure 3).
The daily rate adjustment of movements fitted with plain balance wheels is generally carried out by modifying the active length of the hairspring and therefore requires the presence of an index regulator. As for their (static or dynamic) poising (see ” Timing adjustment operations“), it is usually performed by machining (one or more cuts) under the balance wheel felly (see “Timing adjustment operations”).
Variable-inertia balance wheels
As their name suggests, the moment of inertia of such balance wheels can be adjusted by the watchmaker during the initial start-up of the movement or during servicing (overhauls). This type of balance wheel is more expensive and complex to produce than plain balance wheels, but it offers greater flexibility and precision in adjustment. They are now found in most higher-quality watches. Although many designs and constructions exist, two main categories of variable-inertia balance wheels can be distinguished today.
Screw balances
This is the oldest and most traditional form of variable-inertia balance wheels. The circumference of the balance wheel felly carries a variable number of screws (generally between 16 and 18). The screws are arranged in pairs (positioned 180° apart around the felly) (Figure 4).
The poising (static and dynamic) of such balance wheels is generally carried out by slightly machining the head of the screw located at the heavy point (see “Timing adjustment operations”). To modify the balance wheel’s moment of inertia, thin washers are inserted or removed between the screw(s) and the balance wheel felly. In this way, the poising can be corrected while also modifying the moment of inertia and therefore acting on the frequency of the regulating organ.
The frequency and daily rate of watches fitted with such balance wheels can therefore be adjusted exclusively by modifying the balance wheel’s moment of inertia, without necessarily requiring an index regulator (i.e., without adjusting the rate via the active length of the hairspring).
“Masselotte” or collet-type balances
Appearing more recently, this type of balance wheels offers the same advantages as screw balance wheels while providing better aerodynamic performance and simplifying adjustment. Collets (split timing weights) are fitted on the balance wheel felly by being press-fitted (friction-fitted) onto a stud (Figure 5).
It is therefore easy to rotate one or more collets (timing weights) around their respective axes. This makes it possible to carry out both static and dynamic poising of the balance wheel, as well as to modify its moment of inertia and thus the frequency of the regulating organ.
By moving the slots of the collets (timing weights) toward the inside of the balance wheel, the moment of inertia increases, the frequency decreases, and the watch runs slower. Conversely, by moving the slots toward the outside, the balance wheel’s moment of inertia decreases, the frequency increases, and the watch runs faster (Figure 6).
Christian Huygens, a Dutch mathematician, astronomer, and physicist, contemporary with Galileo, with whom he shared certain subjects of study (astronomy, pendulum), discovered in December 1659 the theory of the isochronism of the cycloid. According to this theory, the period of a pendulum is constant, regardless of its amplitude, when the end of the pendulum moves in a cycloidal path. This theory still governs all calculations related to the regulation and precision of clocks and watches to this day. Huygens is also known for being the first (or one of the first) to associate a flat hairspring with a rimmed balance wheel. An invention that allowed the development of travel clocks (marine chronometers) and later wristwatches.
Although many attempts and research have been made to imagine more efficient mechanical oscillators (in precision, frequency, etc.), Huygens’ invention remains unbeatable to this day.
Watchmakers quickly understood that two of the factors most disrupting the accuracy of a watch are gravity and temperature differences. To compensate for the effects of gravity Abraham-Louis Breguet invented the tourbillon in 1801. To combat expansion due to temperature changes, watchmakers devised split bimetallic balance wheels. The expansion of the first metal being mechanically opposed to that of the second metal results in thermal compensation, with a minimally modified moment of inertia of the balance wheel. This type of balance wheel disappeared in the 20th century following the invention of the Invar alloy in 1907 by Charles-Edouard Guillaume. This iron and nickel alloy has an extremely low expansion coefficient. It found numerous applications (metrology, cryogenics, watchmaking, etc.) and even contributed to the invention of television, earning Guillaume the Nobel Prize in Physics in 1920.
Balance wheels made of this 64% iron and 36% nickel alloy undergo such negligible thermal influence that they will revert to a monometallic composition and a rimmed shape. Since the early 21st century, new materials have appeared and are sometimes found in the composition of balance wheels.
The inertia of a balance wheel must be located as much as possible at its periphery, while its centre must be as light as possible. Therefore, one may find balance wheels made of titanium (non-magnetic, robust, lightweight, and low-expansion metal) with gold masses on their felloes.
A balance wheel consists of two components: its inertia wheel and its staff. The staff is made of steel and can be readily produced on a watchmaker’s lathe and a manual pivoting lathe. The manufacture of the balance wheel itself is more delicate due to the precision it requires. Nevertheless, a balance wheel can be made artisanally through various turning and milling operations, although today most independent craftsmen prefer to rely on the industrial solution of Swiss-type turning (décolletage), which is also well suited to small series or unique pieces.
On an industrial scale, the rim of the balance wheel and its staff are generally machined by an automatic lathe. In addition to the turning operations inherent in these two components, milling of the arms can also be performed on the same machine. In this way, all turning and milling operations are perfectly concentric, and the balance wheel is better balanced. The methods chosen for finishing, decoration, assembly, and balancing operations are then selected based on the watch’s range (hand polishing or drum polishing, hand or machine rolling, etc.). As with each manufacturing method, the balance wheel is calibrated upstream and downstream of each assembly operation.