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Blog: Invar Balances

Copyright © David Boettcher 2005 - 2024 all rights reserved.

First published: 2 May 2024, last updated 22 May 2024.

I make additions and corrections to this web site frequently but, because they are buried somewhere on one of the pages, the changes are not very noticeable. I decided to create this blog to highlight new material.

The article below is part of the page about Temperature Effects.

As always, if you have any comments or questions, please don't hesitate to get in touch via my Contact Me page. I would be interested to get your feedback on this article, about how it reads and if there are any mistakes!


B. W. Raymond Invar Balances

A statement that sounds self contradictory or paradoxical is that “Invar balances contain no Invar”. But it's true, and here is the explanation.

Elgin B W Raymond
Elgin B W Raymond: Click image to enlarge
Elgin B W Raymond Balance
Elgin B W Raymond Balance: Click image to enlarge

Watches like the one shown in the photos here were introduced by the Elgin National Watch Company of Elgin, Illinois, in 1923 under the name “B. W. Raymond”. Benjamin W. Raymond was the Elgin National Watch Company’s first president. These watches were aimed at railway workers and have the features expected in a Railroad Grade watch, with a clear and easy to read dial and lever setting to avoid accidentally changing the time.

The movement is very high quality, with 21 jewels, a fine adjustment Ball type regulator and a special type of compensation balance. The photo of the face of the watch shows within the seconds track that Elgin called this an “Invar Balance”.

The second photo is a close up of the balance. It has a cut bimetallic rim with brass on the outside and a silvery coloured metal on the inside. This metal is a nickel-steel alloy, but it is not Invar. Invar is strictly the name used for the nickel steel alloy with the lowest rate of thermal expansion, which has around 36% nickel. The nickel steel alloy in this balance has a different ratio of nickel to steel and therefore is not Invar.

Unlike brass and steel compensation balances, the rims of which are cut close to the arms, the rims of this balance are cut at an angle of about 30° to the arms. This creates a long and a short section on either side of each arm. Each of these sections carries gold screws for poising the balance and adjusting the compensation. In this balance, the shorter sections carry one screw. These short sections are the sign that the balance is not an ordinary brass and steel compensation balance.

Invar is the name given to a nickel-steel alloy that has very low thermal expansion, meaning that it hardly expands or contracts with changes in temperature. Invar was discovered in 1896 by Dr Charles Guillaume of the International Bureau of Weights and Measures, the BIPM, in Sèvres. It has a nickel content of nominally 36% by weight and a coefficient of thermal expansion of around \(0.8 \times 10^{-6}\) per degree Celsius, which can be further reduced by heat treatment. The name Invar was suggested by Professor Marc Thury because of its lack of thermal expansion and almost invariable dimensions. All other nickel-steel alloys have greater thermal expansion than Invar.

The use of a nickel-steel alloy in compensation balances stems from the problem of the middle temperature error and was the result of the research at the end of the nineteenth century into nickel-steel alloys by Dr Guillaume. In 1899, Guillaume realised that one of alloys he had been studying could be used to resolve the problem of middle temperature error.

Middle temperature error arises because the modulus of elasticity of a steel balance spring does not decrease in direct proportion, or linearly, with increasing temperature, but instead follows a downward curve. A brass and steel compensation balance eliminates most of this effect by reducing its own effective diameter as the temperature increases. However, the compensation provided by a brass and steel compensation balance varies linearly, which means that it can only exactly compensate for the non-linear changes in the modulus of elasticity of a steel spring at either one middle temperature, or at two points equally distributed about the middle temperature. To get the best overall rate, watch and chronometer makers chose the second of these, making the rate correct at two temperatures. The watch would then gain at temperatures between these two points, the middle temperature error, and lose at temperatures outside them.

The reason that the compensation provided by a brass and steel compensation balance varies linearly with temperature is due to a curious coincidence in the rates of thermal expansion of brass and steel. When a piece of metal is heated or cooled by \(\pm \theta\) degrees, its length at the new temperature can be calculated using this expression,

\[ L_\theta = L_0 ( 1 + \alpha \theta + \beta \theta^2 ) \]

where \(L_0\) is the length at the initial temperature, \(\theta\) is the change in temperature and \(L_\theta\) is the length at the new temperature.

Inside the brackets, the \(\alpha\) and \(\beta\) symbols are the coefficients of thermal expansion. Frequently, only the first term with \(\alpha\) is used, but for watches greater accuracy is required so the second term with \(\beta\) is added. If only the first term is used, the result is that the calculated length changes in direct proportion, that is in a straight line or linearly, with changes in temperature. When the second term is added, this introduces a curve or non-linearity into the change in length with temperature, because it is calculated using the square of the change in temperature.

Nickel Steels alpha and beta coefficients
Nickel Steels alpha and beta coefficients: Click image to enlarge

The \(\alpha\) coefficient is called the linear coefficient of thermal expansion. The \(\beta\) coefficient is called the non-linear coefficient, or the quadratic coefficient, because it involves the square of the temperature change.

The curious coincidence that causes the compensation provided by a brass and steel compensation balance to be linear is that the \(\beta\) coefficients of brass and steel are virtually the same, \(5.5 \times 10^{-9}\) and \(5.2 \times 10^{-9}\) respectively. This means that as the brass and steel in the rims of a compensation balance expand when the temperature rises, only their different linear rates of thermal expansion cause the rims to bend, so they move in direct proportion to the change in temperature.

The plot here shows the \(\alpha\) and \(\beta\) coefficients for the nickel steels. The alloy with the lowest \(\alpha\) coefficient occurs at 35.6% nickel and exhibits almost no change in length as its temperature is increased, for which reason it is named Invar. The lowest point of the continuous curve is at \(0.8 \times 10^{-6}\) per degree Celsius, but a short section of curve below that indicates that the coefficient can be reduced further by heat treatment and become negative, so that the material actually contracts with increases in temperature.

The red vertical line through Invar crosses the curve of the \(\beta\) coefficients at the point labelled C, exactly at zero; the zero line is highlighted in red. Between points C and B, the \(\beta\) coefficients are below zero, that is they are negative. This is very unusual, the vast majority of metals have positive \(\beta\) coefficients and expand at an increasing rate as the temperature increases.

The non-linear coefficient of thermal expansion of brass is shown on the figure as the brass-coloured line at \(5.5 \times 10^{-6}\) The non-linear coefficient of thermal expansion of steel lies immediately below it, where the dotted line crosses the y axis at 0% nickel.

One evening in the spring of 1899, Guillaume realised that if the inner steel lamina of a compensation balance was replaced by something that had a rate of non-linear thermal expansion lower than that of steel, the non-linear expansion of the brass would come into play because it was no longer be nullified. The rate of compensation would increase as the temperature increased to more closely match the rate of decrease in the modulus of elasticity of a steel spring, and the middle temperature error would be reduced.

An obvious candidate was Invar, which has a non-linear coefficient of thermal expansion of zero. If Invar was used instead of steel, the non-linear expansion of the brass would make the rate of change of the compensation non-linear. This would reduce the middle temperature error by about 1 second in 24 hours, not enough to eliminate the full error of around 2½ seconds. This is the reason that Invar is not used in compensation balances; it would only partially correct the middle temperature error, and another nickel-steel alloy is much better.

The amount of non-linear compensation is determined by the difference between the non-linear coefficients of the two parts of the bimetallic rims. The non-linear coefficient of Invar is zero and Guillaume realised that the difference would be increased by using one of the nickel-steels that has a negative non-linear coefficient, one of the alloys between the points C and B on the graph. Referring to the graph, it is easy to see how much further away from the non-linear coefficient of thermal expansion of brass the alloys between points C and B become.

Guillaume calculated that an alloy with 44% nickel would virtually eliminate the middle temperature error. He called this alloy Anibal, from “acier nickel pour balanciers” (nickel-steel for balances).

The first compensation balances with Anibal instead of steel were made by James Vaucher, a balance manufacturer in Travers. When fitted to a Nardin chronometer, the middle temperature error was reduced by about 90%. Guillaume then undertook further experimental work in conjunction with the Société des Fabriques de Spiraux Réunies to reduce the error still further. As a result of this, the nickel content of Anibal was reduced from 44% to 42%. The invention of the balance had cost Guillaume only a few calculations, but the experiments were quite expensive and consequently the results were kept secret until revealed in the early 1920s.

Looking at the plot of the \(\alpha\) and \(\beta\) coefficients for the nickel steels, the lowest point on the curve of the \(\beta\) coefficients is at around 38% nickel. Using this alloy instead of Anibal would produce too much non-linear compensation. It would cause a new middle temperature error in the opposite direction to the previous one.

Compensation Balance Non-linear Effects
Compensation Balance Non-linear Effects: Click image to enlarge

The difference between the linear coefficients of the two metals in the bimetallic rims of a compensation balance causes the rims to move in a way directly related to a change in temperature. The different metals being discussed here that could be used with brass to form a compensation balance have different linear coefficients of thermal expansion, which cause would cause different amounts of movement for a given temperature change. However, this is not important to the analysis of the non-linear effects because the compensations screws or masses can be moved along the rim to make the change in moment of inertia the same.

It is the difference between the non-linear coefficients that reduces middle temperature error, by making the compensation follow a similar curve to the changes in the modulus of elasticity of a steel spring. The effect is very small in comparison to the linear effects. The middle temperature error of a steel balance spring with a brass and steel compensation balance is about 2½ seconds per day in the middle of a 30° temperature range, whereas the change in rate due to an uncompensated steel spring over the same temperature range would be 330 seconds per day. In order to see the non-linear effects on a graph, the linear effects have to be stripped out.

The plot here called Compensation Balance Non-linear Effects shows the effects of only the non-linear coefficients of the different combinations in a bimetallic strip of brass with steel, Invar, Anibal with 44% nickel and 42% nickel, and nickel-steel with 38% nickel. One thing that is very noticeable is how flat the curve of brass with steel is almost completely flat and it is easy to see that it doesn't compensate in any way for the non-linear reduction in the modulus of elasticity of the spring. The combination of brass and Anibal with 42% nickel gives the best compensation for the non-linear changes in the stiffness of the balance spring.

Various names were used for brass and Anibal compensation balances. In 1912, Guillaume was moved to write a letter to the Journal Suisse d’Horlogerie about this. He said

The balance that I described for the first time in this journal is quite generally, in French-speaking countries, designated by the name of its author. In Hamburg, it is called Nickelstahlunruhe, an incomplete denomination, since nickel-steel constitutes only a part of it, while in Kew, it is called an Invar-balance, a decidedly erroneous name, Invar not entering into the composition of the balance.

After this, it became more common to refer to them as “Guillaume balances”, although some in England continued to refer to them as Invar balances. This was most likely simply due to a lack of familiarity with them. English chronometer makers used palladium alloy balance springs which had much less middle temperature error than steel springs and were corrosion resistant, so better for marine chronometers, and English watchmakers were not disposed to using highly priced foreign balances, whatever their name.

This is the answer to the apparently paradoxical assertion that Invar balances contain no Invar. The balances in Elgin B. W. Raymond watches are actually Guillaume balances, with the inner layer of the rim made of Anibal. It is not known why Elgin called them Invar balances, but it might have been after the earlier use at Kew and by some in the English trade, or possibly because the name Invar was well known and associated with precision metrology and timekeeping. Whether Elgin made them in-house or bought them from Switzerland is not known.

If you have any comments or questions, please don't hesitate to get in touch via my Contact Me page.

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Copyright © David Boettcher 2005 - 2024 all rights reserved. This page updated May 2024. W3CMVS. Back to the top of the page.