Worm with wrong thread angle?

5 05 2009

Just lately, I was  pleased with myself at having acquired and restored a rather corroded Heath and Co sextant. The last act was to have been to lubricate the rack, and a good way of distributing the oil to where is is needed is to wind the index arm the full length of the rack. On this occasion, as I did so, I noticed a slight periodic roughness each time the micrometer read around 55 minutes. Sometimes this happens when the worm shaft is slightly bent and the micrometer drum rubs against its index periodically, but in this instance, all was well in that area. I decided to have a very close look at the worm.

In Heath micrometer sextants, the worm shaft rotates between conical and adjustable centres that rest in conical holes in the ends of the shaft. This is a very good way to ensure concentricity of the worm, as the shaft rotates on the same centres that were used to produce it, and it is possible by careful adjustment to eliminate all backlash. To remove the worm shaft together with the micrometer drum, it is necessary to undo the locking nuts and back off both centres, when it is just possible to wiggle the shaft free. If necessary, the micrometer drum can then be removed from the shaft. The next pictures show the removal sequence.

copy-of-100_27481

copy-of-100_2751

I had already examined the worm using magnifying spectacles, but this time I used a stereo microscope. It was then possible to see fine burrs at one point on the crest of the threads and I became curious about how this had come about. I then noticed that the angle of the thread was unusually sharp and that the crests were not truncated as is usually the case.. It is perhaps just possible to see that the thread angle seems wrong in the next photograph. The lower, stainless steel worm is the original and the upper one is a bronze replacement.

100_2738

In screws and nuts generally, it is important that the load is borne on the flanks of the threads and not on the crests. This is even more important in leading screws, and the worm and rack of a micrometer sextant is equivalent to a short screw rotating against a small part of the circumference of a very long nut. While the pitch of a thread is important, it is also important that the flank angles of the screw and nut are the same. The following sketch illustrates what happens when they are not.

worm-thread-angle

In the upper half, the thread angles match and the threads are truncated to remove any possibility of their bearing on their crests. In the lower illustration, however, with mis-matched thread angles, the crest of the worm bears on the bottom of the rack and all wear and damage is likely to be concentrated on the crest of the worm.

At first, I thought that at some time in the past, the worm had been damaged. Someone had made a perfectly competent job of producing another one, except that he had made a wrong guess at the thread angle and had left the crest sharp, so that it bore on the bottom of the rack rather than on the flanks of the teeth. Without rather special measuring gear, it is not easy to measure the thread angle, but I made the assumption that in an English sextant made by a conservative maker around 1967, it was probably of Whitworth form, with an included angle of 55 degrees, but the rack angle seems to be about 60 degrees . I used some of my diminishing stock of drawn phosphor bronze bar to make a new shaft and worm with this angle, seen in the pictures above. The micrometer then moved the index arm with a pleasing smoothness and absence of periodic roughness. It will be interesting to re-calibrate the sextant and compare the results with those of the original certificate, which showed no more than 12 seconds of error.

A few days later, I was able to examine another Heath micrometer sextant and discovered that the thread angle of the worm was just as mine had been, unusually sharp. I conclude that Heath delibertely arranged for the crests of the worm to bear on the flanks of the rack teeth.

In the type of release catch used in this brand of sextant, some post-war Kelvin and Hughes sextants and the USSR SNO-T sextant, the worm is swung out of the plane of the rack to disengage it. The majority of sextants swing  the worm shaft and its bearings in the plane of the rack about a hinge on one end of the chassis (swing arm chassis) on which they are mounted. In the former type, it would be pointless to have a worm that was free of backlash unless the swing arm was also free of backlash. The final photograph shows Heath and Co.’s way of mounting it between centres to achieve this.

100_2752

You can read much more about the fine detail of the nautical sextant in my book The Naked Nautical Sextant and its Intimate Anatomy

Postscript: Together with several other instruments, I calibrated the worm of this sextant on 5th July. You can see the results in the posting “A Worm Turns” (above).

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