400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 SAE TECHNICAL PAPER SERIES 1999-01-1050 Static Load Sharing Characteristics of Transmission Planetary Gear Sets: Model and Experiment Ahmet Kahraman General Motors Corporation Reprinted From: 1999 Transmission and Driveline Systems Symposium (SP-1440) International Congress and Exposition Detroit, Michigan March 1-4, 1999Downloaded from SAE International by American Univ of Beirut, Monday, July 30, 2018The appearance of this ISSN code at the bottom of this page indicates SAE’s consent that copies of the paper may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay a $7.00 per article copy fee through the Copyright Clearance Center, Inc.Operations Center, 222 Rosewood Drive, Danvers, MA 01923 for copying beyond that permitted by Sec-tions 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying such ascopying for general distribution, for advertising or promotional purposes, for creating new collective works,or for resale. SAE routinely stocks printed papers for a period of three years following date of publication. Direct your orders to SAE Customer Sales and Satisfaction Department. Quantity reprint rates can be obtained from the Customer Sales and Satisfaction Department.To request permission to reprint a technical paper or permission to use copyrighted SAE publications in other works, contact the SAE Publications Group. No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior wr itten permission of the publisher. ISSN 0148-7191 Copyright 1999 Society of Automotive Engineers, Inc. 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 the paper. A process is available by which discussions will be printed with the paper if it is p ublished in SAE Transactions. For permission to publish this paper in full or in part, contact the SAE Publications Group. Persons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 3 00 word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE. Printed in USAAll SAE papers, standards, and selected books are abstracted and indexed in the Global Mobility DatabaseDownloaded from SAE International by American Univ of Beirut, Monday, July 30, 20181 1999-01-1050 Static Load Sharing Characteristics of Transmission Planetary Gear Sets: Model and Experiment Ahmet Kahraman General Motors Corporation Copyright © 1999 Society of Automotive Engineers, Inc. ABSTRACT One of the most common applications of planetary (epi- cyclic) gear sets is found in automotive transmissions. Aplanetary gear set typically total torque applied to beshared by multiple planets making a higher power densitypossible. This advantage of the planetary gear setsrelies heavily on the assumption that each pinion carriesan equal share of the total torque applied. However, inproduction, gear manufacturing and assembly variationsalong with certain design parameters may prevent equalload sharing among the planets. Here, a generalizedmathematical model of a single-stage planetary gear sethaving n planets is developed to predict load shared by each planet under quasi-static conditions. The modeltakes into account effects of two most common errorsincluding pinion carrier errors and gear run-out errors.Results of an experimental test program are used to val-idate the predictions of the model. Generalized guide-lines for equal load sharing are also presented. INTRODUCTION Planetary gear trains, also known as epicyclic geardrives, are widely used in many automotive, aerospaceand marine applications. They have numerous advan-tages over counter-shaft gear drives including high