文档介绍：Available online at hanism
and
Machine Theory
Mechanism and Machine Theory 43 (2008) 80–94
ate/mechmt
Performance assessment of solution methods
for load distribution problem of gear teeth
Carlos Henrique Wink a,*, Alberto Luiz Serpa b
a Eaton Corporation – ponents, 13100 E. Michigan Avenue, Galesburg, MI 49053, USA
b Department putational Mechanics, Faculty of Mechanical Engineering, State University of Campinas, Campinas,
Sa˜o Paulo 13083-970, Brazil
Received 3 May 2006; received in revised form 21 November 2006; accepted 22 December 2006
Available online 20 February 2007
Abstract
In this paper three different procedures to solve load distribution problems of gear teeth for static transmission error
(TE) calculation of gear pairs are presented. Performance assessment was carried out with the three procedures in static
TE calculation of a helical gear pair under load with global tooth contact analysis. The procedures pared in terms
putational effort to solve the load distribution problem and the accuracy of the solution. An incremental procedure
with gradual and iterative load application was assessed for solving the full load distribution problem and calculating TE.
Then the full load distribution problem was replaced by a reduced, but equivalent, problem through a method called
pseudo-interference. The reduced problem was solved using the other two proposed procedures, a linear programming
solution based on an interior-point algorithm and a direct matrix solver based on Cholesky factorisation. This latter pro-
cedure showed to be highly efficient in solving load distribution problems of gear teeth.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Gear transmission error; Gear load distribution; Tooth contact; Mathematical programming
1. Introduction
Gear dynamics and gear noise have been widely studied for five decades [1–3]. The prediction of gear noise
remains as a concern for gear engineers in the design phase. The increa