400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-0790 Web: www.sae.org SAE TECHNICAL PAPER SERIES 2007-01-2245 Gear Mesh Excitation Models for Assessing Gear Rattle and Gear Whine of Torque Transmission Systems with Planetary Gear Sets Jeffrey A. Morgan and Maruthi R. Dhulipudi General Motors Corporation Refaat Y. Yakoub and Alan D. Lewis LMS International Noise and Vibration Conference and Exhibition St. Charles, Illinois May 15-17, 2007Downloaded from SAE International by Purdue University, Sunday, August 19, 2018The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAE's peer review process under th e supervision of the session organi zer. This process requires a minimum of three (3) reviews by industry experts. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. For permission and licensing requests contact: SAE Permissions 400 Commonwealth DriveWarrendale, PA 15096-0001-USAEmail: permissions@sae.orgTel: 724-772-4028 Fax: 724-776-3036 For multiple print copies contact: SAE Customer Service Tel: 877-606-7323 (inside USA and Canada)Tel: 724-776-4970 (outside USA)Fax: 724-776-0790Email: CustomerService@sae.org ISSN 0148-7191 Copyright  2007 SAE International Positions and opinions advanced in this paper are those of the author(s ) and not necessarily those of SAE. The author is solely responsible for the content of th e paper. A process is available by which discussions will be printed with the pap er if it is publishe d in SAE Transactions. Persons wishing to submit papers to be considered for presentation or publicat ion by SAE should send the manuscript or a 300 word abstract to Secretary, Engineering Meetings Board, SAE. Printed in USADownloaded from SAE International by Purdue University, Sunday, August 19, 2018ABSTRACT This paper presents four methodologies for modeling gear mesh excitations in simple and compound planetary gearsets. The gear mesh excitations use simplified repre- sentations of the gear mesh contact phenomenon so thatthey can be implemented in a numerically efficient man-ner. This allows the gear mesh excitations to be includedin transmission system-level, multibody dynamic models for the assessment of operating noise and vibration lev-els. After presenting the four approaches, a descriptionis made regarding how they have been implemented in software. Finally, example models are used to do a com-parison between the methods INTRODUCTION The ability to predict the noise and vibration (N&V) per- formance of a transmission design is critical in achiev-ing first-time-capable designs. This topic has attractedmany engineers and researchers (see e.g. Ariga et al.[1], Campbell et al. [3], Chung et al. [4], Donley et al.[6], Kanda and Miyauchi [16], Krishnaswami et al. [18,19], Y akoub et al. [32]) 1who used experimental and nu- merical methods to analyze the N&V performance of in-dustrial transmission systems. The experimental methodsare used to understand the frequency signature of trans-mission N&V issues. The experimental methods are notdiscussed in this paper. The numerical methods demon-strated the use of different approaches with complexityvaried from simple lumped models to large scale modelswith many degrees of freedom. The numerical methodsare the subject of this paper. The choice of the appropriate numerical method depends 1The references cited in this paper are just for example and not for exact count.on the specific N&V phenomena to be predicted. In other words, time-domain integrations are usually used to pre- dict gear rattle [17, 23, 32] to capture the transient ef-fects cause by teeth impact. Alternatively, frequency do-main methods are employed to linearize and transform thenonlinear time-domain d