Abstract In our previous study, the Matsumoto equation was modified by introducing the directivity of machining marks on the tooth surfaces (directional parameter), and it was adapted to estimate the gear friction coefficient with various finishing processes. However, this new estimation equation has been applied only to gear pairs with the same finishing process and under manual transmission fluid (MTF) lubricated conditions. Thus, this study extends its application to a gear pair with different finishing processes and the case under automatic transmission fluid (ATF) lubricated conditions. Herein, efficiency tests were performed using gears with four different finishing processes (grinding, barreling, honing, and small-angle honing), and friction values obtained experimentally were compared with the values estimated from the unmodified and modified Matsumoto equations. Consequently, the correlations between the experimental and estimated friction values were significantly improved.
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