Analysis of the loaded transmission error proved that the actual contact ratio and the effective contact ratios are the valid indices. In order to calculate the loaded transmission error, deformations of a pair of teeth are estimated using Hertzian formulas for the approach deformation and approximate formulas based on the FEM for the bending deflection. The actual contact ratio εr is defined using the rotational angle during which a tooth pair is actually in contact with each other. εr increases with the increase of applied loads. The effective contact ratio, εn, is determined geometrically by gear dimensions and modified tooth surfaces based on the path of contact. Adopting these ratios, the following characteristics are derived. 1) The loaded transmission error correlates to εr when it is smaller than εn and correlates to εn when εr exceeds εn. 2) Loaded transmission errors have their minimums and maximums at the same values of εr. 3) No load transmission error is the largest among the maximums. 4) Gear pairs with higher values of εn show lower loaded transmission error.
Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair
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Umeyama, M., Kato, M., and Inoue, K. (March 1, 1998). "Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair." ASME. J. Mech. Des. March 1998; 120(1): 119–125. https://doi.org/10.1115/1.2826663
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