Publication: Accurate Gear Tooth Contact Determination and Sensitivity Computation for Hypoid Bevel Gears
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Accurate Gear Tooth Contact Determination and Sensitivity Computation for Hypoid Bevel Gears

- incollection -
 

Author(s)
Olaf Vogel

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
We investigate a new method for gear tooth contact analysis based on a mathematical model of the generating process. The approach allows the computation of the paths of contact as the solution set of a nonlinear operator equation using a minimally augmented defining system for certain first order singularities. As a byproduct we obtain curvature properties of the gear tooth flanks, the reduced curvatures at the contact points, as well as the boundaries of the paths of contact in a convenient way. Using automatic differentiation, all the geometric quantities are computable with the machine accuracy of the computer. For the first time, we provide analytical sensitivities of the determined contact properties with respect to arbitrary machine tool settings such as additional motion parameters. Thus the systematic optimization of the gear tooth contact as well as the evaluation of the impact of perturbations on the contact pattern become available in a straightforward fashion. In order to obtain the desired sensitivity information, we compute derivative tensors of an implicit function up to order three using the software tool ADOL-C.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Vogel2002AGT,
       author = "Olaf Vogel",
       title = "Accurate Gear Tooth Contact Determination and Sensitivity Computation for Hypoid Bevel
         Gears",
       pages = "197--204",
       chapter = "23",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "We investigate a new method for gear tooth contact analysis based on a mathematical
         model of the generating process. The approach allows the computation of the paths of contact as the
         solution set of a nonlinear operator equation using a minimally augmented defining system for
         certain first order singularities. As a byproduct we obtain curvature properties of the gear tooth
         flanks, the reduced curvatures at the contact points, as well as the boundaries of the paths of
         contact in a convenient way. Using automatic differentiation, all the geometric quantities are
         computable with the machine accuracy of the computer. For the first time, we provide analytical
         sensitivities of the determined contact properties with respect to arbitrary machine tool settings
         such as additional motion parameters. Thus the systematic optimization of the gear tooth contact as
         well as the evaluation of the impact of perturbations on the contact pattern become available in a
         straightforward fashion. In order to obtain the desired sensitivity information, we compute
         derivative tensors of an implicit function up to order three using the software tool ADOL-C."
}


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