# The Balance Wheel of a Watch

The Horologium September 24, 2002 admin

# THE BALANCE WHEEL OF A WATCH

by Walt Odets

The balance and balance spring are the “regulating organs” of the mechanical wristwatch, and it, therefore, seemed appropriate to begin my series of technical essays here–specifically with the balance wheel itself (I will discuss balance springs in a following piece). It is the precise and regular back and forth oscillation of the balance that operates the escape lever (anchor fork) and thus via the escape wheel, fourth wheel, third wheel, “center” wheel, and mainspring barrel regulates the unwinding of the mainspring. The balance and spring are known as a “rotary oscillating system.” Although we impart meaning to a watch–it “shows” the time or even the moon–as a mechanism it is simply a way to regulate the unwinding of a spring. It is the balance wheel (and spring) that ultimately conducts this controlled operation.

Of course, there are many details that significantly complicate this operation if the watch is to be “accurate,” which is to say, unwind its mainspring in some consistent relationship to the rotation of the earth on its axis. Most of these complications originate in the balance spring. The spring is necessary to propel and reverse the balance. Having swung to a fully clockwise position, the balance wheel has “wound” the balance spring, and it is the force of the spring unwinding that reverses the direction of and propels the balance in the opposite direction, to the fully counter-clockwise position. In this position, the wheel has fully unwound the balance spring, and the force of the spring contracting again reverses and propels the wheel.

### A DEFINITION OF TERMS

Each swing of the balance (in one direction) releases one tooth of the escape wheel and thus moves the entire movement (including seconds hand) one “increment.” The terms half-swing and swing are sometimes used interchangeably. Full-swing means from rest to fully counterclockwise, to fully clockwise and then back to rest. Beats per hour always refers to half-swings (or swings), so that an 18,000 bph watch is making 9,000 full swings per hour. Amplitude refers to the number of degrees of rotation of the swing in either direction. Dial up, a watch in good condition is expected to have a swing between approximately 270 and 315 degrees.

### THE ISSUE OF TEMPERATURE

While I will leave the many complicated details of the balance spring aside for the present, it is still necessary to say that conventional steel springs are very sensitive to temperature. Thus, when steel springs were all that were available, it was seen that a rise in temperature caused an increase in the thickness of the balance spring, an increase in the height and length of the spring, and a reduction in the “modulus” (elasticity) of the spring. The total effect of increasing temperature on the spring decreases the rate of the watch (a slower daily rate), largely because of the change in modulus (the other three effects tend to cancel each other).

Because there was no way, until the 1930’s, to control the response of the balance spring to temperature, all balance wheels in watches of any quality were “compensation” balances. A compensation balance compensates for the effects of temperature on the balance spring (and does not, in contrast to common opinion, compensate for temperature effects on the wheel itself). The most common compensation balance is a bimetallic, split balance (as shown in Figure 1), also known as the Earnshaw balance. The rim of the wheel is made of brass on the outside layer, steel on the inside. Because brass expands less with increased temperature than steel does, the rim ends (the “cut” ends) curl inward with a rise in temperature. This effectively smaller diameter of the balance wheel increases its speed, and offsets the temperature effects on the spring. Figure 3 illustrates a compensation balance at high temperatures. Conversely, the cut ends curl outwards with a drop in temperature, increasing the effective diameter of the balance and slowing the watch.

### THE SCREWED BALANCE

Figure 1 shows not only a bimetallic compensation balance, but a screwed balance. These screws around the perimeter of the balance can be moved in and out, can be moved to different holes, and small washers can be placed under them to increase their weight. They are used initially to poise the balance, which is to say, remove heavy spots and balance the balance. When the screws near the cut ends of the rim are moved in or out, they effect the amount of temperature compensation the balance provides. This allows matching the compensation effects of the balance to the temperature error of the particular spring. Adding weight near the cut end of the rim (or moving screws to holes near the cut ends) increases the compensating effect of the balance for both heat and cold.

Figure 2 shows an illustrious variation on the cut, bimetallic screwed balance, the Guillame balance. The Guillame balance is used in observatory trial watches because of its superb accuracy, but is never used in production watches because of its fragility. Made of nickel alloy and brass layers, it expands non-linearly and is the only balance that can compensate for so-called middle temperature error. (When a watch is adjusted for minimum error at temperature extremes, it tends to run fast at moderate temperatures). The Guillame balance is easily recognizable because the rim cuts are further from the balance arms that in the more common Earnshaw balance. The Guillame balance is always used with a plain steel spring and can commonly provide accuracy of 0.02 seconds per day per degree centigrade. This is approximately 15 times the accuracy of the best conventional bimetallic balances.

### THE SELF-COMPENSATION BALANCE SPRING

Around 1930, a number of new alloys (cold-worked and heat treated) became available for balance springs. Ultimately, this was to change the design of balances completely. The most famous of these new alloys was a combination of nickel, chromium, berrylium, titanium, aluminum, and iron and was trade-named the Nivarox. The best grade of Nivarox springs (Nivarox I Highest) provides a temperature error of only about plus or minus 0.3 seconds per degree Centigrade per day.

This development allowed the common use of monometallic balances because the balance no longer needed to provide compensation for the temperature errors of the spring. These new monometallic balances were made with an uncut rim of a single metal, but provided with screws for poising the balance. They look much like a screwed compensation balances, but without the cuts in the rim (and with a rim of a single metal, which is visible under a loupe). Figure 4 illustrates such a balance. The unused screw holes are indicated by the dotted lines.

### THE GLUCYDUR BALANCE

At about the time the Nivarox was being developed, another alloy was being developed for the balance wheel itself. Made of beryllium, copper, and iron (berrylium bronze), this new alloy was trade-named Glucydur. It was exceptionally hard and stable, and very resistant to deformation or damage. R. Lavest, principal of the horological section of the Neuchatel Technical High School said of the Glucydur balance, “This balance, made of a very hard metal, 400 Brinell, non-magnetic, non-corrosive, having a fine lustre, is outstanding for its remarkably brilliant finish and the air of fine workmanship it lends to the movement. For mass-produced as wells as for special movements, the Glucydur Balance is in great demand, appreciated by pivot-makers and adjusters alike. It makes adjustment easier and its discovery means one step further in watchmaking technique.” (Quoted from “The Elements of Watchcraft,” Charles Rohr Publishers, 1949). Today, the Glucydur balance is the standard in fine watches, though other materials are used in some less expensive watches.

For many years, and to some extent today, the Glucydur balance (monometallic, of course, and uncut) continued to be used with adjustment screws, as shown in Figure 4. This allows relatively easy (and reversible) poising adjustments in the field. Perhaps as importantly, watch repairers were very reluctant to give up the familiar adjustment screws, and often felt that their appearance suggested a quality watch. But as experience with the Glucydur balance developed, it became clear that its extreme hardness and stability allowed poising of the balance at the factory and that poise would maintain itself over many years of use–and even abusive handling. Thus, it began to occur to engineers that adjustment screws might not be necessary, and the modern “smooth balance” was born. This smooth Glucydur balance is shown in Figure 5, with its easily recognizable arms of distinctive shape. By 1968, about 90 percent of high quality Swiss watches were using the smooth Glucydur balance, and it is seen in virtually all quality watches today.

Even as the smooth Glucydur balance was gaining widespread favor, there was a concurrent development, which deserves mention. This is the adjustable balance with rotatable weights instead of screws. Only two are in production today, the Gyromax by Patek Philippe and the Microstella by Rolex. Instead of using a balance rim with threaded holes and screws, these two balances use weights that can be rotated on their mounting pins to move the mass of the weight towards the inside or outside of the balance. A Patek Gyromax balance is illustrated in Figure 6. On the Rolex balance weights are at the junction of the four balance arms and rim, and only four weights are used. The most important advantage of the rotatable weight is that a larger diameter balance can be used because the screws are not projecting off the perimeter taking up space in the movement. Additionally, the weights can be used to adjust the daily rate of the watch, thus eliminating the need for a conventional regulator. (The significance of this will be discussed in a later essay). In the Patek design, with the weights set down into the rim, aerodynamic drag and dust snags are both reduced. Judging by its literature on the Gyromax, Patek considers the aerodynamic issue significant.

The rim of the Gyromax balance, with weights, is shown in Figure 7. Because the slot in the weight reduces the mass of the weight at that point, rotation of the weight adjusts the distribution of mass around the balance rim. If a pair of opposing weights are adjusted equally, the daily rate of the watch can be adjusted. More mass towards the outside of the balance (slot towards the center of the balance) increases the effective diameter and slows the daily rate. Weights may also be rotated individually to adjust the poise of the balance.

### THEORETICAL CONSIDERATIONS AND POISING

With high-grade Nivarox temperature-compensating balance springs (and thus elimination of the need to have the balance wheel compensate for spring temperature errors), what is needed of a balance is a perfectly round, perfectly poised rotating body. For consistent (i.e. “accurate”) operation, a balance with as much “rotational inertia” as possible is desirable. In practice, this will be the largest possible diameter balance with its weight concentrated as far on the periphery as possible. Although a smaller diameter balance may be made to have as much rotational inertia as a larger diameter balance by simply increasing its weight, this will result in a balance that is heavier than the larger diameter balance of equivalent rotational inertia. This would place more stress on the pivots, require a stiffer balance spring, and, ultimately, a stiffer mainspring. Thus diameter–and space within the movement to accommodate it–is the defining, critical factor, and one of the most critical decisions made in designing a watch.

Although no balance is perfectly poised and perfectly stable, the high quality, smooth Glucydur balance has come very close to this objective. Though it can be adjusted, it is rarely necessary to adjust it for poise in the field. Screwed and rotatable mass balances, of course, can easily be adjusted in the field, though this practice too is becoming rare as fewer and fewer watchmakers are trained in the timing of watches.

The adjustment of watches for isochronism (consistency of rate as the mainspring unwinds) and for positions (consistency of rate in different positions) involves both the balance wheel and the balance spring. The two are intimately related. As a result, balance wheels are sometimes deliberately put out of poise to compensate for (non-temperature) errors introduced by the spring attachments (inner and outer) or spring overcoil (the last, top curve of the spring before attachment to the stud on the balance bridge). Although this is not an advisable practice, it is often done, particularly for positional adjustments.

A balance is “true” when the rim is perfectly round and the rim rotates perfectly around its pivot (i.e. the pivot is in the exact center of the balance). This check is made before poising of the balance. For poising itself, the balance pivots are held in a pair of calipers (Figure 8) or a special poising tool (Figure 9). The balance is spun and the heavy point of the balance will, of course, stop at the bottom. Instead of slowly coming to a stop in one direction, the out-of-poise balance will also rotate back and forth before coming to rest. This operation is little different from the static balancing of an automobile tire. (Dynamic balancing occurs in conjunction with balance spring adjustments when the watch is actually timed to positions with the balance installed.)

Screwed balances are statically poised by lightening the screw (or screws) at the heavy point. Screws come in different weights, washers may be removed from under screws, and material may be removed from the underside of the screw head. Gyromax-style balances allow removal of the heavy spot by rotating the slot of a weight (or weights) towards the outside of the rim. Smooth Glucydur balances require the chamfering of the underside of the balance rim with the tip of a small rat-tail file.

Springing and timing of the watch will be the subject of a future essay.