Entwicklung eines Auslegungs- und Berechnungsverfahrens für reduzierte Planetenkoppelgetriebe mit beliebiger Leistungsführung
Final Report Abstract
Complex-compound planetary gear transmissions can feature particular and significant advantages in comparison to standard planetary gears or spur gear trains. However, analysis and synthesis of complex-compound planetary gear transmissions are rather complex. Hence, the question of which structure matches an intended application the best and how this structure behaves in terms of its power loss performance is difficult to answer. This study is dedicated to the calculation of kinematics and statics for loss-free conditions and operating conditions with power losses as well as to the structure synthesis of complex-compound planetary gears during the early design phases. It is shown that the well-established representation method known as ‘Wolf symbols’ can be used for efficiency computations. By means of Wolf symbols, planetary gears are converted into substitution figures. Feasible substitution figures are either kinematically-equivalent or functionally-equivalent. Kinematically-equivalent substitution figures allow a correct determination of speeds and torques for loss-free operating conditions. More-over, functionally-equivalent substitution figures feature correct torques in consideration of power losses. Substitution figures offer a clear view of the transmission structure while reducing the number of parameters to be determined. However, the Wolf symbol representation is not unique for complex-compound planetary gear sets. In general, multiple functionally-equivalent substitution figures are available as a function of the given structure and the present operating conditions. Furthermore, an efficiency approximation method is derived. Only limited information about the transmission is needed by taking into account a global basic train efficiency instead of individual values for each basic train. Without knowledge of the exact structure, the efficiency is approximated quite accurately with regard to a structure synthesis. Planetary gear transmissions can feature very high as well as very low efficiency values. Self-locking is an extreme case occurring for special designs and operating conditions. As for complex-compound planetary gear transmissions, self-locking can also occur only apparently for unfavorably chosen boundary conditions. A procedure is proposed revealing if an operating condition and central shaft respectively is self-locking or not. Planetary gear synthesis is a major problem in the face of the diversity of available structures and possible combinations. Many developers build all solutions within a certain range by means of combinatorics and check their applicability subsequently. At this, useless solutions are also produced. A universal structure synthesis method for complex-compound planetary gear transmissions is proposed within this study. This method takes advantage of a lever analogy, which is detached from design aspects and used to define desired operating conditions. A simple and clear lever model is derived from these operating conditions. The lever is specified furthermore by means of the efficiency approximation method mentioned above in order to diminish the number of resulting solutions in advance. In addition, a reference transmission structure is to be defined indicating the most complicated structure to be considered. Hereby, the number of solutions is likewise decreased and impractical solutions are avoided. A systematic matching process combining the lever model and the reference transmission generates definite transmission structures. In sum, only feasible structures satisfying the desired operating conditions are created. The lever analogy being used is qualified for transmissions with a basic structure featuring a kinematic degree of freedom of two. For the synthesis of different and more complex structures a more general approach is required. By now numerous examples of systems being composed with the aid of graph theory can be found which focus on limited types of gear trains. A comprehensive and general approach is missing. For more complex transmissions current combinatorial approaches are limited by the explosion of viable possibilities. For this purpose, the requirements regarding a new transmission application are to be formulated as (linear) target functions and edge conditions limiting the solution space. Then, an efficient algorithm can be used to generate solutions without combinatorics. It is believed that this approach would present the most promising potential for an as universal as possible synthesis method.
Publications
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Efficiency Determination and Synthesis of Complex-Compound Planetary Gear Transmissions, Dissertation TU München, 2012, ISBN 9783843907897
Kurth, F.
