Rotational Vibration of a Spur Gear Pair Having Tooth Helix Deviation: Effect of Lead Modifications

Lead form modification has been used to avoid detrimental effects of tooth helix deviation caused by manufacturing error or misalignment of a gear pair from the viewpoint of tooth strength on gear design. Hence parabolic crowning, elliptic crowning and end relief are adopted conventionally as a typical modified lead form. However the effect of both the shape and the amount of the lead modification on dynamic characteristics of the gear pair has not been made clear enough yet. Using the simulator which was developed by authors and is capable of analyzing vibration response of a pair of spur gear considering tooth surface deviation, the present paper shows that the effect of a proper lead crowning is to maintain the designed dynamic behavior even when tooth helix slope deviation exists, or that is equivalent to misalignment. An optimum form of end relief approximated to that of crowning is determined by the least square method. In addition, since the amplitude of gear vibration is sensitive to the tooth profile error, importance of considering tip relief is presented.