As demand for the performance improvement of automotive transmission gears increases, gear design is required that achieves high strength, low noise and high efficiency simultaneously. In addition, for high performance it is important not only to select good gear dimensions, but also to improve the tooth contact load distribution which depends on the tooth flank shape and assembly error of the gear pair. Traditional analysis methods calculate the tooth contact load distribution with integral equations that consist of the effect function of bending deflection and that of compressive deformation caused by the contact of gear teeth. However, the complicated integral equations make it difficult to instantly obtain proper results for some tooth flanks distorted by heat treatment and repetition calculation may not converge especially in light load conditions. This paper proposes a new composite analysis method which quickly calculates the tooth contact load distribution of designed or manufactured tooth flanks of helical gears in any load condition. The analytical process consists of three stages: (1) for each flank shape of a gear pair, the three-dimensional relative tooth flank shape is calculated from the actual tooth flank shape and assembly error, and the equivalent tooth profile error of the three-dimensional relative tooth flank shape is obtained by the static deflection which depends on input torque, (2) the static deflection distribution and share load on each line of contact are calculated with the obtained equivalent tooth profile error and the variable stiffness of the involute tooth pair, (3) an integral equation that consists of bending deflection and compressive contact deformation of the gear teeth is solved to obtain the tooth contact load distribution. In practical applications, the tooth contact load distribution is used to output the tooth contact pattern, tooth contact and root bending stresses, and transmission error. The prediction of tooth contact stress and transmission error contributes to the improvement of the pitting strength and gear noise of several transmissions.

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