Measurement of Tooth Pair Deflections With Ultra High Resolution Encoders and Prediction of Transmission Error Under Load in High Precision

The purpose of this research is to predict transmission error under loading conditions in high accuracy. Transmission error is very important information in the evaluation of gear engagement and the prediction of vibration and noise from gear boxes. In some experiments, measurement of transmission error is sometimes performed to grasp an actual situation of gear static engagement. However, it is impossible to measure all of gear pairs in mass production for actual transmission manufacturers. The prediction of transmission error by the simulation in high accuracy should be powerful and effective means in application. The most important and indispensable information to simulate accurate transmission error under load is the deflection of a gear tooth and the displacement in tooth pair contact. One of conventional approaches is to predict bending deflections with FEM analysis. However it is very difficult to calculate the deflections in high accuracy by FEM because of less grid density, inadequate constraint conditions, the lack of information of actual loading conditions, and so on. To overcome the difficulty, the authors try to measure tooth pair deflections directly by experiments using a couple of ultra high precision encoders. The measurement strategy is to obtain the deflection of only single tooth pair during a whole period of tooth engagement. It can be achieved by use of a specially manufactured gear which has large and intentional pitch deviations. Experimental formulas of gear tooth pair deflections are derived from measured results. Putting assumption that tooth deflections with respect to applied loads can be expressed approximately as a curve of the second order, the stiffness of single-tooth engagement is evaluated. Transmission error is simulated with the obtained formula of the tooth stiffness and the result is compared with the measured transmission error and discussed.© 2007 ASME