By James D. Smith

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This gives a very reliable answer with an accuracy of a fraction of a micron and can give major clues if anything is going badly wrong. However, at the design stage it is desirable to have an idea of what the reaction of the design will be to the inevitable manufacturing errors, as far as noise and stress are concerned. Conversely, if an existing box is tested, it is an advantage to know what errors might have produced a given (undesirable) result. , which should be better than 1 um uncertainty.

A model to check this does not necessarily have to be extremely accurate, perhaps within a few percent, but it should be able to give a quick, cheap comparative assessment of different designs with realistic assumptions. There are full 3-D finite element programs which take a gear tooth and calculate the deflections when it meshes with another gear tooth but such models are extremely complex. Since there can easily be of the order of 10,000 node points in a realistic model with perhaps 1000 boundary points defining a tooth shape, the calculations are large and, equally important, there is a large technical effort required each time to enter each set of boundary conditions.

Palmer, D. , Burton on Trent. K. A. Hofrnann. Dept. K. G. Munro. University Eng. K. Derek Smith. , Mech. Eng. , Columbus, Ohio, 43210-1107. Prof D. R. Houser. INS A de Lyon, Villeurbane, Cedex, France. Mr D. Remond. University of New South Wales, Australia. B. Randall. Tech. Univ. of Ostrava, CZ - 703 88 Ostrava, Czech Republic. Mr. Jiri Tuma. 1 Elastic deflections of gears The basic geometric theory for spur gears assumes the "unwrapping string" generation of a perfect involute. We can then replace the two mating involute curves with a string unwrapping from one base circle and coiling onto the other base circle as in Fig.

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