Measurement of the Undulation of Large Gears (Part 1)

The Approximate Fundamental Equations on the Tomlinson Undulation Recorder and These Solutions

Abstract

The Tomlinson undulation recorder is widely used measure to the undulations of large gears because of its easy handling. Since the recorded data of this recorder do not show the actual undulation, they need be analysed to obtain the undulation. Only on the sinusoidal undulation, the analyses becomes simple and was utilized up to this time.
But the results of our recent undulation measurements tell us that the undulation shows too complicated forms to be approximated by the simple sine waves and that an analyses applicable in general should be considered.
This paper relates to the analyses of obtaining the undulation from the recorded data in a general case. In this first report, the approximate fundamental equations are obtained in which the gear is regarded as a rack plate. These equation are solved both numerically and graphically.The method of interpolating the obtained points on the curve also shown. Using these analyses, (1) the possible least amplitude of undulation can be estimated in a general case, and (2) the whole undulation can be obtained when the undulation belong to the C-type.