Citation: Civan, S.E.; Demir, C. Load Distribution and Dynamic Response in Torque Split Applications. Machines 2022, 10, 1218. https:// doi.org/10.3390/machines10121218 Academic Editor: Davide Astolfi Received: 12 November 2022 Accepted: 12 December 2022 Published: 15 December 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). machines Article Load Distribution and Dynamic Response in Torque Split Applications Süleyman Emre Civan 1,2, * and Cihan Demir 1 1 Department of Mechanical Engineering, Yildiz Technical University, Barbaros Bulvari, 34349 Istanbul, Turkey 2 Tusas Engine Industries, Inc. (TEI), Esentepe Mahallesi Cevreyolu Bulvari No. 356, 26210 Eskisehir, Turkey * Correspondence: suleymancivan@gmail.com or suleymanemre.civan@tei.com.tr Abstract: This study consists of constructing and analyzing gear mathematical models of torque split systems for contact pressure distribution and dynamic transmission error at different gear positions concerning phase angles. According to the method specified in the AGMA 927 standard, load distribution is calculated by considering shaft torsion and bending deformations. Partial contact loss may occur as a result of shaft bending with asymmetric gear positioning on a long shaft. The contact separation can be decreased by reaction force balancing if the driven gears are in the opposite position with respect to the drive gear. In the calculation of the dynamic transmission error of the torque split model, a parametric phase difference for the gear positions is proposed using gear geometry parameters. The variation of the dynamic response according to the change in the parametric phase angle in the torque split system is analyzed for the same values of each gear. Small changes in the phase values change the system response significantly. To obtain lower dynamic transmission error amplitude, the phase difference and gear positions are examined. The contact pressure distribution is validated by the finite element method, and the dynamic transmission error is compared with the experimental study in the literature. Keywords: spur gear; phase difference; torque split; nonlinear gear dynamics; shaft bending 1. Introduction The gear system is a key element of power transmission systems in aerospace, auto- motive, and rail applications in terms of achieving the required speed and torque ratio from input to output. Gear vibration has an important place in drivetrain systems due to noise and durability issues. Gear systems generate dynamic forces that are much higher than static forces in the gear pair under operating conditions. These high-frequency dy- namic forces are transmitted through the bearings, producing noise in the system. In addition, variable forces reduce the fatigue life of transmission elements. For this reason, gear dynamics are important in the design of a quiet and durable gear system. Most studies in the literature have been performed on gear pairs. However, the effects of systems such as torque split and idler gear in torque-transferred gear mechanisms should also be considered. Some studies involving the load distribution and gear pair stiffness for the gear pair can be given as follows; Eritenel and Parker [1] investigated the force and torque distribution, which is non-uniformly distributed along the gear width, in helical gear pairs, taking into account the partial tooth contact loss. Elastic deformation components in the system are not formulated in this study. Yuan et al. [2] used the Timoshenko beam theory to find shaft bending along the width of the gear. The displacements at the gear pair contact are investigated by considering the gear width in slices. The linear and time-dependent gear pair stiffness modeling method finds the dynamic transmission error. Yuan et al. [3] worked on a hybrid model with lumped mass parameters with loaded tooth contact analysis in cylindrical gears. In addition to the effect of the error along the face width on the loading, the effects of damping and helix angle in the gear pair are investigated. Wang et al. [4] considered the gear in slices along the width, and the variation Machines 2022, 10, 1218. https://doi.org/10.3390/machines10121218 https://www.mdpi.com/journal/machines