Chapter VI: The Train.
53. The first requirement for the watch train is to make it as large as the diameter of the movement permits. The very limited area allowed by the dominant taste for a portable timekeeper is an obstacle to reaching a higher degree of perfection in gearing; if it is possible to manufacture the wheels and pinions of a pendulum clock with satisfying accuracy then it will be increasingly difficult to do this as the space in which we have to build the watch decreases. If we had simpler means to examine the accuracy of the division and the cutting of small pinions, even of the best manufacturers, then we would soon arrive at the conclusion that these qualities necessarily decline with the size of the pinion. The inequalities and deformations caused by grinding and polishing are nearly the same with large pinions as with small, but small pinions suffer relatively much more from them. This refers only to the production of pinions; but before a pinion runs in the train it goes through the hands of the pinion turner. First he has to determine whether it runs completely true and then to set it true if necessary. With all operations of this kind the worker has to rely on his eye to determine if the condition of the piece is satisfactory. The eye however, like all human senses, is reliable only within certain limits, and if a good worker says a pinion is round then we must not understand this mathematically; it only indicates that an experienced eye cannot see any deviation from the round. There are thus small errors which escape the sharpest eye and their absolute size is approximately the same for large pieces as for small. For example, if a careful worker turns a pinion of 3 mm diameter he cannot tell if it is out of round by less than a hundredth of this size, 0.03 mm. This error is the smallest that can be differentiated by the eye, and with pinions of 1 mm diameter it will be not one hundredth but three hundredths of the diameter; and therefore it is relatively of three-times greater importance with small pinions. The same argument can be extended to the accuracy of wheels and it is clear that it is of the greatest importance to have as large a train as the diameter of the watch allows.
54. Another matter of great importance is the even transmission of power from the barrel to the escapement by the train. This uniformity can only be obtained by good gearing, and there is sufficient evidence that gears with pinions of high leaf numbers are more perfect; it is advisable that centre pinions are never given less than 12 leaves, 3rd and 4th pinions 10 and escape pinions should have at least 7 leaves. The difference this has on production costs is so insignificant that it should be no problem to use pinions with highest possible number of teeth in inferior watches. (5)
The centre pinion will then have more fragile teeth and be more exposed to damage from sudden impacts, which come from the mainspring breaking or the pressure of rough winding. The teeth of the barrel, which must also be thinner, will be more exposed to buckling from the same causes; but these dangers are partly remedied by the circumstance that almost two leaves of pinions of 12 work into two teeth of the barrel at the same time, while in pinions of smaller count only one tooth leads with a larger movement angle. Consequently, the force of any sudden impact from the barrel will be distributed over two teeth of a pinion with a high leaf number, significantly reducing the apparent danger of breakage. Besides, there is a better transmission of power with fine teeth and so a weaker mainspring can be used, with which there is a less violent impact if it breaks.
55. One of the chief requirements for good and even transmission of power is a correct and suitable form for the teeth of wheels, and it is amazing to see in what an indifferent way this important matter is treated by many people. It is a well-known fact that wheel teeth, in order to work appropriately, must have an epicyclic form, and no machine-maker would accept any other for his spur wheels. About a century ago Berthoud treated this matter in the most detailed way, and Reid and others also explained the principles of the design of wheel teeth in the clearest manner; but in vain. It seems that most of our professional colleagues decided to regard the form of their teeth as a matter of taste. The wheels of most English and other watches have, with very few exceptions, teeth which scorn the rules of Berthoud, Reid and other masters; a form of which nothing can be said other than that it looks quite good in the eyes of the makers and users. When the late Adolph Lange had the courage, at the beginning of his production, to give the teeth of his wheels the theoretically correct form it was met with hostility in Germany and ridiculed on all sides. I knew a watchmaker who did not want to buy his watches because they had this "horrible" tooth profile. It is difficult to argue against such reasons and I heard a respectable and good watchmaker explain that he could not understand epicyclic teeth. Fortunately times are now different; in particular, thanks to our specialised journals, there are among our watchmakers a proper recognition and a striving to achieve the best possible, and there is now hardly a watchmaker who would not know what a well-formed tooth should look like.
56. The reciprocal ratios of the train wheels should also have a certain harmony, which can be attained by a regular distribution of the wheel diameters and the fineness of the teeth.
57. With regards to the escape wheel pinion for larger watches, I would recommend at least 8 leaves with a 4th wheel of 75 teeth and an escape wheel of 16 teeth. The last gearing, which is the most sensitive to any irregularities of transmission, will be significantly improved.
58. The following are the sizes of a train for a watch of 43 mm or 19 Swiss lines, which would correspond exactly, in my view, to the above conditions:
| Diameter of the Barrel = 43.0 x 0.485 =(See note 6) | 20.85 mm |
| Centre wheel | 15.40 |
| 3rd wheel | 15.40 |
| 4th wheel | 11.80 |
The tooth numbers for this are:
| Barrel | 90 | Centre pinion | 12 |
| Centre wheel | 80 | 3rd pinion | 10 |
| 3rd wheel | 75 | 4th pinion | 10 |
| 4th wheel | 75 | Escape pinion | 8 |
| Escape wheel | 16 |
| Barrel | 0.345 mm |
| Centre wheel | 0.300 mm |
| 3rd wheel | 0.270 mm |
| 4th wheel | 0.240 mm |
It is easy to see that this distribution is quite regular.
For watches 43 mm or larger in diameter a train with 12-leaf pinions is excellent, but provided that the gears are planted and laid out with the greatest care. Then the train will be:
| Barrel | 105 | Centre Pinion | 14 |
| Centre Wheel | 96 | 3rd Pinion | 12 |
| 3rd Wheel | 90 | 4th Pinion | 12 |
| 4th Wheel | 80 | Escape Pinion | 8 |
| Escape Wheel | 15 |
...from which the following tooth pitches result:
| Barrel | 0.300 mm |
| Centre wheel | 0.240 mm |
| 3rd wheel | 0.220 mm |
| 4th wheel | 0.216 mm |
59. The train should be laid out in such a way that the seconds circle comes on a suitable part of the dial. This circle must be as large as possible to have clear divisions, but not so large that it completely covers the VI of the hour circle. A good arrangement I can recommend is to set the centre of the seconds circle exactly half way between the centre of the dial and its edge. If this rule was generally observed it would be a decided step towards regularity of construction; it would make things much easier for dial manufacturers and dealers, and would make dial replacement much simpler for the repairer.
A still larger seconds circle could be obtained by shifting its centre nearer the centre of the dial, but this minor advantage would be too expensive and detrimental to the layout of the train.
60. The length of the arbors should only be limited by the height of the frame. The larger the distance between the bearings of a pinion the better for its safe guidance and operation. The same quantity of side shake necessary for free movement will affect the depthing of a long pinion less than a short one.
The generally accepted construction rules for machines cannot be used for the diameters of pivots in watch work, because if we tried to set their size by theoretical relationship to the power which they must handle, then we would get pivots so small that they would be very difficult to manufacture; and the cross section of such a pivot might come into a disadvantageous relationship with the molecular structure of steel. Besides, we must always remember that the pivots of the train must not only be proportioned to handle the mainspring force with safety, but also the violent force which comes from breaking a mainspring or rough winding. Consequently, very few can object to the diameters of pivots which are normally used in pocket watches.
61. It remains to say a few words about a new improvement. It has been mentioned (Art. 54) that the centre pinion and the barrel are in continual danger of having their teeth bent or broken by the sudden impact of a breaking mainspring.
These accidents are so annoying that a number of small inventions have been made in order to avoid them. It will not be redundant to say a little and express my views about them in order to find whether they actually do what they promise.
62. One of these safety mechanisms consists of a kind of flexible transmission on the 3rd wheel. This wheel a (see Fig. 20) sits loosely on the arbor which carries a disk riveted onto the pinion. On this smooth disk a spring c is fastened with a vertical pin d which projects into the space between the spokes of the 3rd wheel. In this way it turns the wheel while the watch is going. The end of the pin has a chamfer and it is assumed that, if the mainspring breaks, the force of the impact slides the tapered end over the wheel spoke. I could not advise the use of this safety device because I believe that it will be made ineffective by the inertia of the parts lying between the 3rd wheel and the mainspring. The destruction caused by a sudden jerk will be completed before the power of it reaches the 3rd wheel; in the same way that explosive powder, in a hole bored into hard rock and stopped up with loam, will burst the rock by its sudden effect before it has time to remove the soft loam plug.
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Figures 20 and 21.
Safety mechanism on the third wheel for mainspring breakage. The 3rd wheel a is loose on the arbor and is turned by the pin "d." The arrow indicates the direction of rotation of the wheels.
This mechanism, if it is to have any chance of success, must presuppose an exact adjustment of the mainspring so that it does not give way to the force of the mainspring when fully wound, but a force beyond that causes it to slide. If this is not the case, then the safety of the centre pinion is not ensured and an excessive force from rough winding, when the stopwork comes into effect, will probably overcome the spring c and thus cause the hands to advance. I am of the opinion that the watch owner would regard such an irregularity in its rate as a serious defect, rather than a random accident unconnected with its time keeping and which cannot be eliminated by the watchmaker, however careful he is.
63. Another invention promises more, because the controlling resistance lies in the centre pinion. This has a rather large hole and is fitted onto the arbor on which the wheel is riveted. The pinion is held on the arbor by a nut and a spring washer. When the pinion is set in motion it works like a one-piece pinion because of the friction which holds it on the arbor and which is a little more than the force which is exerted by the mainspring. However, an increase of this force causes the pinion to rotate on the arbor and so absorb the power without damage to other working parts.
It is easily understood that this arrangement protects the centre pinion and barrel teeth, not just against the sudden impacts of a breaking mainspring, but also against excessive force when winding; and without causing a change in the time indicated by the watch (Art. 62).
However, this invention also has its disadvantages. The centre pinion with its large hole, particularly if it has less than 12 leaves, has too little space between this hole and the base of its teeth, and thus the durability of it is endangered. This mechanism can be used in a watch whose hands are set from the front, but it appears questionable for the hollow centre arbors which are used in watches whose hands are set from the rear.
64. I recently had in my hands a somewhat similar safety centre pinion of English work; it had an arbor onto which the pinion was screwed by three turns. This thread was cut into the hole of the pinion and into the arbor, and it has to be a right-hand thread if the centre wheel is over the pinion (a left-hand thread is required in the other case). While the watch is running this screw thread is tightened by the mainspring. If, however, an impact in the opposite direction occurs, then it unscrews itself and so avoids the harmful effects. This method, although it appears very effective, is also subject to serious doubts. The greater force at the end of winding is not avoided and will, in fact, screw the pinion on more firmly; so that it may not unscrew or it may break, considering that it is rather fragile because of the large hole. By the way, and this is the main objection, we cannot be sure in which direction the impact of a breaking mainspring will take place. If the mainspring breaks close to its outside end then the impact will take place in the direction of normal rotation and this safety device will be of no use at all; on the contrary, the pinion, weakened by the large hole, will be endangered. The device will be effective only in the case that the mainspring breaks at its inner end.
65. It is a general need to secure the centre pinion against accidents, and all thinking manufacturers should seriously consider this matter. It seems that up to now no good solution has been found. The best method is the pinion fitted onto a round but slightly conical arbor and held by a nut and a spring washer, but the decreased strength of the pinion is a problem.
66. Nevertheless, I have never attached such a safety pinion to a watch of my manufacture because I believe that I can obtain the same purpose in much simpler way. Firstly, a substantial step in this direction can be attained if the above-mentioned principles concerning the barrel and the train are observed, and a mainspring of comparatively greater length and smaller strength is used. In the case of a break the impact which follows is less harmful; and when winding the stop of the stopwork is more easily noticed than with an excessively strong mainspring. Also a thin and long mainspring which develops more than 6 turns, of which only 4 are used, is much less likely to break.
Briefly, I consider it very desirable and practically easy to strengthen the teeth of the centre pinion and the barrel by giving them a more suitable form. If one of these teeth is found broken then, without exception, the break took place at the base where the tooth is thinnest and has two sharp corners (as the taste of the majority of watchmakers require it). A change of this form, from the dotted line at a in Fig. 22, would approximately double the strength of the tooth without any disadvantage resulting. I feel convinced that the general use of this form for the teeth of the barrel, centre pinion and centre wheel would fulfil the discussed purpose very well, although we cannot be assured that complete safety from breakages would result from it. However in this respect the other mechanisms are at least equally dubious.
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Figure 22.
Wheel and pinion with round bases, which better resist the shock of a breaking mainspring.
notes:
5 Or small watches. Grossmann uses "geringen" for two purposes. Usually he means "small", but sometimes he means "inferior" or "lesser grade". A few instances are ambiguous and I have footnoted these. [Trans]
6 See Art. 25.
