A New Material for Balance Springs Gideon Levingston looks at the thermal and magnetic properties of the conventional balance assembly, wheel and spring and suggests a new way of producing long term stability THE ACCURACY of a mechanical watch is These characteristics help to compensate dependent upon the specific frequency of each another. Whereas an increase in the oscillator composed of the balance length is considered normal an increase in wheel and balance spring. When the E is rare in materials, and is thus temperature varies, the thermal expansion considered abnormal. of the balance wheel and balance spring, In summary, when the Fe-Ni balance as well as the variation of the elasticity spring gets hotter, instead of getting less (Young’s Modulus) of the balance spring, elastic it gets more elastic (a positive or change the specific frequency of the abnormal variation in E). This compen- oscillating system, disturbing the accuracy sates for both its dimensional change and of the watch. Approximately three the increasing diameter of the metal quarters of the variation can be attributed balance as it gets hotter and expands. to thermal or magnetically induced Hence the term ‘auto-compensating changes in the balance spring. balance spring’. However this is true only Methods for compensating these 1. A current high-grade COSC-rated balance up to a certain temperature, the Curie variations are based on the consideration and spring in the presence of a child’s toy threshold (named after Pierre Curie) and that the specific frequency depends magnet. concerns the increased dipole activity exclusively upon the relationship between between the elements within the alloy as the torque of the balance spring acting These two terms are not in a linear the threshold is approached. upon the balance wheel and the moment relationship. The work of Charles Edouard of inertia of the balance wheel as is It is necessary that this relationship Guillaume in the development of INVAR indicated in the following relationship should remain as constant as possible (so and other Fe-Ni low expansion alloys was as to keep T constant, i.e. the oscillations a further development of Curie’s investi- are isochronous). gations of magnetism in these alloys that (1) This article describes a way of over- are pivotal to the use of Fe-Ni alloys in coming magnetic and thermal variation in balance springs and balance wheels. T is the period of oscillation, I the moment watches. First the current problem is De-magnetising has long been accepted of inertia of the balance wheel and, G the analysed by re-examining the present state as the solution to this problem, and as torque of the balance spring. of the art. Following this a proposed such is an imperative taught in watch The moment of inertia of the balance solution and a material choice, will be schools. Unfortunately this is neither wheel is a function of its mass M and its examined and demonstrated. practical for every watch owner nor is it radius of gyration r. wholly effective. The torque of the balance spring is a The Current State of the Art What is not widely understood however function of its dimensions: length l, height Ferro nickel (Fe-Ni) metal spring alloys is the relationship between temperature, h, thickness e, and of its Young’s Modulus provide an approximate solution to the magnetism and the useful positive E. The length l of the balance spring problem when the alloy is perfectly de- variation of E in Fe-Ni alloys. It must be (which may be helical or spiral) is the magnetised. However, when the alloy is remembered that the external influences entire length, end to end. The relationship not perfectly demagnetised, the relation- considered here are magnetism and (1) is rewritten: ship is no longer constant: E changes. temperature and their respective effects Balance wheels currently employed in upon the spring and the balance. high grade chronometers are of a gold- If the spring behaves normally, i.e. E is (2) copper or copper-beryllium (GLUCYDUR) negative as in a steel spring, then as the alloys which have similar α (linear temperature increases the system will Temperature variations influence T as a expansion) coefficients lying between +14 require that the workload of the spring is result of expansion and contraction of the and +17 x 10-6/°K. decreased. This is achieved by an inward- balance spring and wheel. Dimensions l, h These balance wheels expand isotrop- bending cut bi-metallic balance wheel and e of the spring and r of the wheel, vary, ically with a rise in temperature as do all where the value of the M multiplied by r2 but M remains constant. metal balance wheels except bi-metallic (equation 2) is decreased. Unfortunately, We know how to compensate for the and ovalising balances which expand aniso- in this Guillaume system both balance and effects of expansion on l, h and e. However tropically. The change in the E value of spring are susceptible to magnetism. the period of oscillation is still subject to the balance spring must therefore With a monometallic balance, when the variations of r and E in keeping with the accommodate this, as is evident from the temperature rises the work load on the relationship expressed by: relationship (3). spring gets greater. The balance wheel The Fe-Ni alloys currently used for radius increases, its gyratory mass shifts balance springs show an increase in both E further from its centre of rotation, and it (3) and l for an increase in temperature across requires greater effort on the part of the the normal ambient temperature range. spring to keep it oscillating at the same Levingston G. Horological Journal July 2004 243 Any watch employing a Fe-Ni balance spring can be stopped by a sufficiently powerful magnet and any exposure to a magnetic field results in the absorption of magnetism in a cumulative manner. After a time the elasticity of the spring changes and isochronism is adversely affected. Magnetic pollution from electric and electro-magnetic sources of all descrip- tions: computers, portable telephones, televisions, electric motors, toys etc, may all cause the alloy to absorb magnetism. In 2. The thickness dimension view ‘e’ (35 a magnetised Fe-Ni alloy the temperature 4. Best chronometer and standard balance microns) of a new high quality chronometer limit for the usefully anomalous behaviour springs under the influence of a magnet. balance spring, at 4000x magnification, showing inclusions from the rolling process of E drops from 40°C to below 30°C, well and indications of the direction rolling. below normal body temperature, and the to retain their reputation in an spring loses its elasticity. environment increasingly subject to When a non compensating mono- magnetic fields from computers, tele- frequency. If the Fe-Ni spring has an metallic balance wheel of GLUCYDUR,or phones and electric circuits as well as the abnormal (+ve) E tendency then it can even gold and copper, expands, its greater earth’s natural varying field forces. compensate for this and all is well. If on gyratory mass cannot be compensated for The solutions must take into account the other hand its elasticity is subject to by the spring. Where the alloy’s physical the external influences of heat, cold and internal dipole changes triggered by a properties require a balance wheel to have magnetism and their inter-relationship. A combination of temperature and magnetic a linear expansion coefficient, α, around non-magnetically sensitive balance spring effects, T will not remain constant and +15×10-6/°K, once beyond the magnetic is one step in the right direction, it must isochronism will be lost. and temperature limits the α coefficient of however be thermally stable or it must be Examination of an Fe-Ni alloy at the the balance intrinsically causes a change compensated by a balance wheel that can microscopic level illustrates just how non- of rate, the balance wheel and balance adjust for the intrinsic thermal character- uniform this material actually is, 2. The spring do not conform to the relationship istics of the spring. difficulties of producing finely alloyed in (2) and the system is no longer metals to the very high specifications isochronous. The watch, depending on the A Solution required in this field should not be balance amplitude, will either gain or lose The non magnetic solution which I have underestimated. My examination and significantly. In fact a wristwatch been developing allows for the effect of analysis of a high-grade balance spring chronometer subject to this effect may magnetism to be ruled out completely at shows how foreign matter can become have as much as ± 10 seconds per day the same time that the material’s impregnated in the processing of such variation. The COSC certificate requires a remarkable thermal properties, very materials to the detriment of the perform- tolerance of +5 to –7 seconds/day. stable and slight modulation of E and very ance. The batch quality of the material is Furthermore, if a low positive α low creep, are exploited. dependant upon its purity. Each batch is coefficient balance is coupled with the Fe- The internal friction of the material as tested empirically and graded into a Ni spring this will neither compensate for known to Watch Timers (Regleurs) is statistical spread of qualities. the magnetised or non-magnetised another physical property very worthy of Analysis using a scanning electron condition of the spring nor for the thermal consideration as it has a consequence microscope, 3, has shown that similar changes intrinsic to metal alloy springs in regarding balance amplitude in particular.