Noname manuscript No. (will be inserted by the editor) Modiﬁed geometry of spur gear drives for compensation of shaft deﬂections Ignacio Gonzalez-Perez · Victor Roda-Casanova · Alfonso Fuentes Received: date / Accepted: date Abstract One of the greatest concern of spur gears is the edge contact of tooth surfaces that is caused by misalignment of the gear drive. Such a misalignment is caused partially by the deﬂections of the shafts where the gears are mounted. As a result of the edge contact a non favorable condition of bearing contact is achieved, providing a high level of contact and bending stresses. An intensive research and many practical solutions have been directed to modify the gear tooth surfaces in or- der to avoid edge contact. An innovative procedure is proposed here for: (i) determination of the errors of alignment at the gear drive caused by shaft deﬂections, (ii) incorporation of such errors of alignment in the gen- eration process of spur gears for compensation of shaft deﬂections, and (iii), determination of a favorable func- tion of transmission errors for the design load. A ﬁnite element model of a spur gear drive including pinion and wheel shafts is used for the determination of the errors of alignment along the cycle of meshing. Com- pensation of misalignments in gear generation is then accomplished by modiﬁcation of pinion tooth surfaces whereas the wheel tooth surfaces are kept unmodiﬁed. Additional modiﬁcations of pinion tooth surfaces may Ignacio Gonzalez-Perez Polytechnic Universtiy of Cartagena Department of Mechanical Engineering Campus Muralla, Dr. Fleming s/n, 30202 Cartagena Murcia, Spain Tel.: +34-968326429 Fax: +34-968326449 E-mail: ignacio.gonzalez@upct.es Victor Roda-Casanova Universitat Jaume I, Castellon, Spain Alfonso Fuentes Polytechnic University of Cartagena, Spain be required for the obtention of a favorable function of transmission errors. The eﬀect of several misalign- ment compensations in the reduction of contact stresses has been investigated. Postprocessing of load intensity functions and loaded transmission errors is included. The developed approach is illustrated with numerical examples. Keywords gear geometry · tooth contact analysis · ﬁnite element analysis · loaded transmission errors · shaft deﬂections 1 Introduction Spur gear drives are widely applied in the industry and have been a focus of intensive research to improve the load capacity and the conditions of meshing of invo- lute proﬁles. First modiﬁcations on involute proﬁles, proposed in [1], were directed to remove some mate- rial from the borders of the tooth surfaces in order to minimize transmission errors for the design load. Many contributions in this area have been done [2, 3, 4, 5, 6] looking for gear drives with reduced noise and vibra- tion. Substitution of involute proﬁle by other types of proﬁles has been another topic of intensive research. A pair of circular proﬁles for the generating cutters was proposed in [7] and mismatch of the circular proﬁles of the cutters was proposed for localization of the bear- ing contact in [8]. Modiﬁcation of pinion tooth surfaces by application of parabolic proﬁles instead of straight proﬁles of the cutters has been proposed in [9] for the localization of the bearing contact. Localization of the bearing contact by the application of mismatched pro- ﬁles of the cutters makes the contact less sensitive to the errors of alignment but, at the same time, increase contact and bending stresses, and transmission errors.