FE prediction method for tooth variation in hot forging of spur bevel gears

Abstract Tooth variations in spur bevel gears have significant effects on the transmission performance, noise, and vibration and directly affect the reliability and stationarity of equipment. The hot forging process is the principal method used for the mass production of spur bevel gears owing to its high efficiency and high quality of products. However, hot forging of spur bevel gears is a high-pressure, high-temperature, and instantaneous forming process; hence, the evolution of tooth variations is extremely difficult to predict and measure. An accurate prediction of tooth variations in the hot forging process of spur bevel gears is an important precondition for tooth variation control to improve tooth accuracy. In this study, a new finite element (FE) analysis strategy of tooth variation prediction in the hot forging of spur bevel gears is proposed according to transitive relations of stress, strain, and temperature. Following this new strategy, a series of FE models are developed, so that the positional and shape variations on the tooth surface caused by die shrink-fitting (DSF), die elastic deformation (DED), die thermal expansion (DTE), gear elastic recovery (GER), and nonuniform cooling shrinkage of gear (NCSG) are comprehensively investigated. To verify the reliability of this FE analysis strategy, a hot forging experiment of a spur bevel gear was carried out, and the tooth variations of the tooth die and hot forged gear were measured using a gear-measuring machine. The results show that the factors causing the positional variation in order of importance from highest to lowest are DSF, DED, GER, NCSG, and DTE, and those for shape variation are DSF, DED, GER, DTE, and NCSG. Moreover, the shape variation of the final hot forged gear increases in the tooth profile direction and decreases in the tooth lengthwise direction. Finally, the simulation results closely agree with the experimental results, confirming the reliability of the FE analysis strategy proposed in this study.