The traditional gear strength theory[1~3], which has been used up to now, thinks that the effect of the sliding friction hetween teeth on the tooth root bending fatigue stresses of gears can be neglected.The author of this article has made overall analysis and research on the forcing condition of the great gear in the machine tool increasinq speed gearing, and derived the formulas for calculating the tooth root bending fatigue stress of the great gear subjected to the actual outside loads including the sliding friction between teeth. It has been Proved by researches that the effect of the sliding friction between teeth on the tooth root bending fatigue strength of the great gear of the machine tool increasing speed gearing should not be negligible.