Abstract/Details

Point de reference, rigidite d'engrenement et dynamique des engrenages

Brousseau, Jean.   Universite Laval (Canada) ProQuest Dissertations Publishing,  1994. NN97784.

Abstract (summary)

En fonctionnement, les roues dentees subissent des mouvements de corps rigide et des mouvements locaux crees par la presence d'ondes elastiques. Les modeles Disques Rigides et Dents Flexibles (DR-DF) tentent de predire les mouvements de corps rigide; un ressort simule le comportement elastique de l'engrenement. Pour calculer la flexibilite des dents, on mesure les deplacements par rapport a un point de reference. Si la question du point de reference est resolue pour l'aspect statique, elle ne l'est pas pour l'aspect dynamique.

La problematique etudiee dans ce travail est la suivante: comment doit-on calculer la rigidite d'engrenement pour que les predictions faites avec un modele DR-DF soient les meilleures possibles? Sous-jacentes a cette problematique, il y a les questions du point de reference et de la flexibilite du corps de l'engrenage.

Du cote theorique, une methode est proposee pour deriver la matrice de couplage des modeles DR-DF. Elle est exprimee par le produit matriciel K$\sb{coup}$ = A$\sp{\rm{\bf T}}$LA. ou A et K sont les matrices de projection et de rigidite. Pour l'evaluation des points de reference, l'etude se base sur le raisonnement suivant: si la rigidite d'un modele DR-DF est bien choisie, on doit trouver une correspondance entre les frequences naturelles des modeles DR-DF et elements finis d'un engrenage en prise. Nous presentons des resultats pour les engrenages droits (massifs, semi-massifs et a jante mince) et spiro-coniques.

Entre le rayon d'alesage et un point appele "point de depart", la ligne radiale passant par le centre d'une dent chargee se deforme de facon lineaire; a partir du point de depart, cette ligne radiale flechit dans la direction de la charge. Les resultats pour les engrenages droits montrent que le point de depart permet d'obtenir une tres bonne correspondance entre les frequences naturelles des deux types de modeles. Plus le corps d'un engrenage est flexible et plus il importe de tenir compte de sa flexibilite.

Pour les engrenages spiro-coniques, le vecteur normal a une composante axiale qui influence les comportements statique et dynamique. Plus la flexibilite du corps et la composante axiale du vecteur normal sont grandes, moins le corps se deforme de facon lineaire et moins la correspondance obtenue avec le point de depart est bonne.

Alternate abstract:

You are viewing a machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer

In operation, gear wheels undergo rigid body motions and local motions created by the presence of elastic waves. The Rigid Discs and Flexible Teeth (DR-DF) models attempt to predict rigid body motions; a spring simulates the elastic behavior of the mesh. To calculate the flexibility of the teeth, the displacements are measured with respect to a reference point. If the question of the reference point is resolved for the static aspect, it is not for the dynamic aspect.

The problem studied in this work is the following: how should we calculate the mesh stiffness so that the predictions made with a DR-DF model are the best possible? Underlying this issue are the issues of the reference point and the flexibility of the gear body.

On the theoretical side, a method is proposed to derive the coupling matrix of the DR-DF models. It is expressed by the matrix product K$\sb{coup}$ = A$\sp{\rm{\bf T}}$LA. where A and K are the projection and stiffness matrices. For the evaluation of the reference points, the study is based on the following reasoning: if the rigidity of a DR-DF model is well chosen, a correspondence must be found between the natural frequencies of the DR-DF models and finite elements of a meshing gear. We present results for spur gears (solid, semi-solid, and thin-rim) and spiral-bevel gears.

Between the bore radius and a point called the "starting point", the radial line passing through the center of a loaded tooth deforms in a linear fashion; from the starting point, this radial line bends in the direction of the load. The results for the spur gears show that the starting point makes it possible to obtain a very good correspondence between the natural frequencies of the two types of models. The more flexible the body of a gear, the more important it is to consider its flexibility.

For spiral bevel gears, the normal vector has an axial component that influences static and dynamic behavior. The greater the flexibility of the body and the axial component of the normal vector, the less the body deforms linearly and the poorer the correspondence obtained with the starting point.

Indexing (details)


Subject
Mechanical engineering
Classification
0548: Mechanical engineering
Identifier / keyword
Applied sciences; French text; flexible tooth gears; gears; rigidity
Title
Point de reference, rigidite d'engrenement et dynamique des engrenages
Alternate title
Reference point, mesh stiffness and gear dynamics
Author
Brousseau, Jean
Number of pages
291
Publication year
1994
Degree date
1994
School code
0726
Source
DAI-B 56/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
978-0-315-97784-6
Advisor
Gosselin, Claude
University/institution
Universite Laval (Canada)
University location
Canada -- Quebec, CA
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
French
Document type
Dissertation/Thesis
Dissertation/thesis number
NN97784
ProQuest document ID
304163872
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304163872