This project has been assigned by SwePart Transmissions AB. It is about calculation and dimensioning, of the elements in a cycloid stage of a speed reducer. Their idea is to use the results from this project and go into production of such reducer to cover another segment of the market. The company is interested in supplying transmissions for robust systems and for various industrial purposes, where large ratios of speed reduction are needed. The company has given the necessary input data for the model. They have also provided a real cyclo-drive reducer for further analyses. To obtain the dimensions and forming the geometry of the gears, some parts of Professor Ognyan Alipiev’s Phd work have been used. Professor Alipiev is head of “Theory of Mechanisms and Machines” department in University of Ruse “Angel Kunchev”, Bulgaria. For the determination of forces on the elements, models and drawings has been used Solidworks (SW) CAD software and SW simulation environment. The resultant calculation process can be used for designing the geometry and determination of the properties regarding the cycloid reducer. / Design of a Planetary-Cyclo-Drive Speed Reducer

Shaft mounted speed reducers are used in material handling applications, such as conveyor systems for transporting ore out of mine shafts. A subbase joins the reducer with an electric motor, and serves to limit the misalignment between the motor shaft and the reducer input shaft. The entire assembly is supported at two points: the axis of rotation of the reducer output shaft, which is fixed, and a clevis-pin joint under the motor, which prevents rotation of the assembly about the reducer output shaft axis. In an effort to reduce the production and material costs of subbases that support shaft mounted reducers, Rexnord Corp. is implementing subbase designs that are lighter weight and easier to manufacture than current designs. Impeding the implementation of lower cost designs is the lack of an equation to properly choose subbase dimensions for acceptable values of shaft misalignment. Trial and error in subbase construction may provide designs that give acceptable results for misalignment. Given an equation, however, the weight could be minimized while still limiting misalignment at the coupling location. The project goal is to provide equations that give shaft misalignment as a function of three subbase parameters: tube thickness, mounting strap width, and end cap thickness. Developing design equations by analytical methods is investigated first. Next, finite element models are used to check the analytical results for accuracy. Finally, finite element models are used to perform design sensitivity studies where needed. The final equations for misalignment are given as functions of the three design variables. / Master of Science

Ce travail vise à prédire le comportement dynamique de transmissions par engrenages supportées par des paliers hydrodynamiques, semblables à celles utilisées dans le domaine de la propulsion navale. Un modèle couplé de transmission mécanique est présenté ; il traite la plupart des interactions possibles entre les engrenages, les arbres et les paliers. Un élément d’engrenages à dentures larges, avec raideur non linéaire et dépendante du temps, est combiné à des éléments finis de poutre alors que la contribution des paliers est introduite par la résolution directe de l’équation de REYNOLDS et d’un model thermique simplifié. A cause des jeux de fonctionnement des paliers, une attention particulière a été portée à la définition de l’état de référence et des degrés de liberté. La réponse du système est calculée par la combinaison d’un schéma d’intégration temporelle, d’une méthode de NEWTON-RAPHSON et d’un algorithme de contact normal unilatéral de manière à ce que les conditions de contact aux paliers et entre les dents soient simultanément traitées. Les résultats de simulation sont comparés à des mesures réalisées sur un banc d’essai de haute précision possédant un train simple étage en dentures droites et hélicoïdales, supporté par des paliers lisses de type hydrodynamique. Les comparaisons fournissent un bon accord et aboutissent à la validation du modèle de couplage tant sur les aspects globaux que locaux. Bon nombre de résultats sont également présentés, qui montrent que certains paramètres, bien souvent ignorés dans les modèles de la littérature, tels que la position de la zone d’alimentation des paliers, la température de lubrifiant dans les paliers, les accouplements avec l’environnement extérieur peuvent fortement modifier l’équilibre statique et le comportement dynamique du système, jusqu’aux contacts entre les dents. / The present work is aimed at predicting the dynamic behaviour of geared transmissions supported by hydrodynamic journal bearings, similar to those used in naval propulsion. A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts and hydrodynamic journal bearings. A specific element for wide-faced gears with non linear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements whereas the bearing contributions are introduced based on the direct solution of REYNOLDS’ equation and a simple thermal model. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time-step integration scheme, a NEWTON-RAPHSON method and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. The simulation results are compared with the measurement obtained on a high-precision test rig with single stage spur and helical gears supported by hydrodynamic journal bearings. The experimental and simulation results compare well thus validating the simulation strategy both at the global and local scales. A number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings and external couplings with mechanical parts can be influential on the static and dynamic behaviour of the system.