BALANCE SPRING / HAIRSPRING
Figure 1: Exploded view of an assembled balance wheel
Figure 2: Plan of a flat hairspring
Description
The hairspring is a metallic, silicon, or even carbon-nanotube blade with a rectangular cross-section. It is wound onto itself in a spiral shape and generally has between 12 and 15 turns (Figure 2). Combined with the balance wheel, it forms the regulating organ of mechanical watches.
Role
The hairspring has the same function for a watch balance wheel as gravity does for a clock pendulum. Its role is to constantly return the oscillator (balance wheel or pendulum) to the midpoint of each of its vibrations: the dead point (or equilibrium position) (so called because it is the position occupied by the oscillator when it no longer receives energy and comes to rest).
The inner end of the hairspring is fixed to the balance wheel staff by means of a collet (a movable attachment). The outer end of the hairspring is fixed to the balance wheel cock by means of a stud (a fixed point).
When the lever transmits its impulse to the balance wheel, the balance wheel begins its free vibration. The hairspring develops in contraction, slows the balance wheel until it stops, and brings it back to the dead point. The balance wheel then receives an impulse that starts an opposite vibration. The hairspring then develops in expansion and again brings the balance wheel back to the dead point.
The hairspring is responsible for accuracy. Whether the energy of the impulses transmitted to the balance wheel is high or low, and whatever angle the balance wheel travels (amplitude), each vibration must have exactly the same duration (period). This is isochronism. The active length of the hairspring determines the precision of the watch’s regulation. If the hairspring is too short, the watch runs fast; if it is too long, the watch runs slow.
Constructions and materials
Watches fitted with an index regulator allow the active length of the hairspring to be adjusted, in this case determined by the position of the two regulator pins. Since the hairspring does not develop perfectly concentrically to the balance wheel axis, it creates poising defects in vertical positions. Based on this observation, some watchmakers developed modified outer coils. By raising the outer coil so that it returns above the horizontal plane of the hairspring and attaching it to the cock in this position, the concentric development of the hairspring in operation is greatly improved (Breguet overcoil, Phillips terminal curve).
Cylindrical (helical) and spherical hairsprings with double terminal curves allow a nearly concentric development of the hairspring. Their complex manufacture and the space they require limit their use in wristwatches to a few exceptional timepieces.
Traditionally, hairsprings are made from an alloy called Elinvar. This alloy, invented in 1920 by Charles-Édouard Guillaume, offers an excellent elastic modulus, a low thermal expansion coefficient, and relative resistance to magnetic fields (compared to conventional steels). Manufacturing Elinvar hairsprings requires great expertise and extremely high precision. As a result, only a small number of firms master their production (see the industrial methods section below).
Appearing in the early 2000s, silicon hairsprings offer a better elastic modulus than steel and are completely amagnetic. Their production cost is relatively low, and their manufacturing technology (DRIE) allows novel geometries. However, they are very brittle and any shape correction is impossible (see the high-tech methods section below). The use of silicon hairsprings is now becoming widespread.
Characteristics
Hairspring stiffness
C = Elastic constant of the hairspring (N·mm/rad)
E = Elastic modulus of the strip (MPa)
h = Height of the hairspring (mm)
e = Thickness of the hairspring (mm)
L = Length of the hairspring (mm)
CGS number of the hairspring
The CGS number of a hairspring is a standardized reference that characterizes the mechanical properties of the hairspring, enabling consistent selection and replacement.
K = Calculated CGS number (N·mm³/rad)
C = Elastic constant of the hairspring (N·mm/rad)
D = Outer diameter of the hairspring (mm)
d = Inner diameter of the hairspring (collet diameter) (mm)
p = Pitch (mm)
Proportionality factor
This is the ratio between the outer diameter of the hairspring and the diameter of the balance wheel. It depends on the frequency of the regulating organ. When replacing a hairspring, this factor makes it possible to calculate the CGS number of the hairspring based on a trial hairspring.
= Outer diameter of the hairspring (mm)
= Diameter of the balance wheel (mm)
= Proportionality factor
Calculation of the CGS number from a trial hairspring
The following formula makes it possible to determine an approximate CGS number of an unknown hairspring based on the known CGS number of a trial hairspring and its outer diameter measured after counting. The required hairspring diameter depends on the balance wheel diameter and the proportionality factor (see above).
K = CGS number of the unknown hairspring (N·mm³/rad)
K′ = CGS number of the trial hairspring (N·mm³/rad)
D = Required outer diameter of the hairspring (mm)
D′ = Diameter of the trial hairspring at the counting point (mm)
Variation of the hairspring length as a function of the daily rate
ΔL = Variation of the hairspring length as a function of the daily rate (mm)
= Hairspring length at the counting point (mm)
μ = Daily rate (s/day)
In 1675, Christiaan Huygens, who had discovered the theory of the pendulum (isochronism) twenty years earlier—probably aided by the preliminary work of Abbé de Hautefeuille in France and Dr. Robert Hooke in England—had the first watch regulated by a balance spring made. Portable clocks (travel clocks), navigation timekeepers (marine chronometers), and watches could then exist, providing mechanical watchmaking with the foundations of its technical principles. These principles have continually been improved through knowledge and technological advances but remain fundamentally unchanged to this day.
Watchmakers adopted Huygens’ principle and quickly realized that the influence of temperature variations and poise (concentric development of the hairspring) was significant. In 1766, John Harrison devised a thermal compensation system. A bimetallic strip controlled the index regulator’s movement to correct the active length of the hairspring as it expanded or contracted. Prestigious watchmakers such as Ferdinand Berthoud, Pierre Le Roy, and A.-L. Breguet refined Harrison’s work or developed their own thermal compensation solutions (bimetallic balances, etc.). In 1782, John Arnold patented a cylindrical hairspring. Unlike Huygens’ flat hairspring, it develops concentrically to the balance axis. This type of hairspring provides exceptional chronometry, particularly when paired with a detent escapement. Chronometry, navigation, and thus exploration greatly benefited from this true revolution. However, the cylindrical hairspring requires far more manufacturing steps and expertise than a flat hairspring and demands a volume that can significantly increase movement thickness. This is why its use in portable watches is limited to a few exceptional timepieces.
It was not until 1919 that Charles-Édouard Guillaume, who had invented Invar twenty-five years earlier, developed Elinvar (elastic and invariable). This alloy revolutionized hairsprings thanks to its low thermal expansion coefficient, ideal elastic modulus, and low sensitivity to magnetic fields. Together with his work on Invar, it earned Guillaume the Nobel Prize in Physics in 1920 and it remains the alloy used in the traditional manufacture of hairsprings.
Since 2000, the application of DRIE silicon production technology has revolutionized the world of hairsprings. This manufacturing method requires advanced and costly technology, but the process itself is relatively straightforward to master and allows high-quality mass production. The material (silicon) offers excellent elasticity, is non-magnetic, and has remarkable resistance to wear and corrosion. This production method has been experiencing continuous growth ever since.
Introduced into watchmaking around the year 2000, silicon has literally revolutionized the production of many components, and the hairspring in particular. Although the production technology (DRIE) is complex, production costs are low and allow durable repeatability with absolute precision. This is the same method used to manufacture integrated circuits.
The principle consists of etching a silicon plate (the wafer) of a given thickness (generally that of the finished component) using a photolithographic process. This method makes it possible to produce highly complex profiles with micrometer-level precision. Depending on the size of the components to be made, several hundred parts can be produced simultaneously on a single wafer.
The most complex shapes can be achieved without the limitations imposed by the radius of a milling tool or even the wire of an EDM machine. Since this process applies no mechanical stress, it is possible to manufacture very thin components (such as springs) or to skeletonize them to reduce weight. Silicon is a material with hardness greater than steel, an excellent elastic modulus, and amagnetic properties. The progress and success of this technology make it increasingly attractive in terms of production costs, and it is becoming more widely used for manufacturing many components (notably for the escapement and the regulating organ).
Emerging in watchmaking since the year 2000, silicon has truly revolutionized the production of many components, especially the hairspring. While the production technology is complex, the process requires much less expertise and often involves only one automated step. This method is used for the fabrication of integrated circuits. The principle involves cutting a silicon wafer to a given thickness (generally that of the finished component) using a photolithographic process. This method can achieve the most complex profiles with precision reaching the micron. Depending on the size of the components to be produced, several hundred pieces can be made simultaneously on the same substrate wafer. The most complex profiles can be obtained without the drawback of the radii of a milling tool or even the wire of an EDM machine. This process exerts no mechanical stress, allowing for the creation of very thin components (springs, etc.) or perforating them to reduce weight. Silicon is harder than steel, has an excellent elasticity module, and is non-magnetic. Advances in this technology and its success make it increasingly attractive in terms of production costs and tend to become widespread for the production of many components (especially for the escapement and regulating organ).