PSI - Issue 12

Andrea Mura et al. / Procedia Structural Integrity 12 (2018) 52–57 Mura et Al. / Structural Integrity Procedia 00 (2018) 000 – 000

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1. Introduction

Rotating shafts are usually supported by bearings that act as low friction connection between the rotating parts and the case of the machine. Therefore, bearings work with loads generated by the rotating parts, mainly depending on the transmitted torque and the components weight. When two rotating shafts are connected by crowned teeth spline couplings, a certain misalignment between hub and shaft is allowed (Alfares et al. 2006) to compensate manufacturing or assembly errors and movements generated by the working conditions (Curà et Al. 2013; Tjernberg 2001). When spline couplings work in misaligned conditions, some unwanted overloads are generated (Elkholy and Alfares 2002; Medina and Olver 2002; Cuffaro et Al. 2014), such as the tilting moment. This overload is generated because of not uniform teeth engaging that brings to not uniform load distribution between engaging teeth (Tjernberg 2001; Leen et Al. 2000; Barrot et Al. 2006; Margineanu et Al. 2012). Tilting moment is balanced by bearings reaction forces that overload the bearings themself and may cause bearings failure. Therefore, uneven loads have to be considered during the transmission design in order to properly design bearings against misalignment overloads (Guo et Al. 2016). Spline couplings are classified according to the tooth shape and the tooth modifications. In particular, concerning tilting moment behavior it is interesting to compare straight teeth and crowned teeth spline couplings as they work in a totally different way when misaligned (Curà and Mura 2013). In particular straight teeth spline couplings show a contact pressure distribution following the punch model while crowned teeth have Hertzian like contact pressure distribution (Curà and Mura 2014). Crowned teeth spline couplings are more suitable to be applied in misaligned conditions as their tooth shape avoid pressure peach and both pressure and contact conditions are better respect to those obtained by straight teeth splines. In the literature, just few works are related to the investigation about tilting moment. In particular some works are related to in straight teeth spline couplings (Elkholy and Alfares 2002), (Curà and Mura 2014). Even less works are available about this phenomenon related to crowned teeth spline couplings (Curà and Mura 2018), nevertheless this kind of spline couplings are the most suitable for working in misaligned conditions. In this work titling moment generated in crowned teeth spline couplings has been investigated by means of numerical simulations performed by a commercial code (Romax designer), focusing on the contact pressure distribution. Numerical results in terms of tilting moment have been compared to those obtained by a theoretical model available in the literature (Curà and Mura 2018).

Nomenclature Cr

crowing radius i-th tooth pair tangential force

i

Ft

Mt total tilting moment M y,TOT y axis tilting moment M z,TOT z axis tilting moment Z teeth number  misalignment angle

2. Theoretical model

Theoretical values of tilting moment have been calculated by a model by Curà et. Al. This model considers the tilting moment M t as the resultant of two moments (M y,TOT and M z,TOT ) about the two main axis perpendicular to the rotating axis (Fig. 1):