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Epicyclic Load Sharing Map - Application as a Design Tool
One of the main advantages of planetary transmissions is that the input torque is split into a number of parallel paths. However, equal load sharing between the planets is possible only in the ideal case due to the presence of positional type manufacturing errors, equal load sharing is not realized, and the degree of inequality in load sharing has major implications for gear system sizing, tolerancing schemes, and torque ratings.
The sensitivity of load sharing to torque, tolerance level, directionality of error, system flexibility, number of planets, and amount of float in the system have all been studied. However, a physical understanding of the true mechanism that leads to the load sharing phenomenon was lacking.
In a recent paper, the author has proposed a physical mechanism that explains all known load sharing behavior. The physical explanation leads to simple expressions that seem to completely describe the complex load sharing behavior. Comparisons to computational models and experimental results have shown excellent correlation.
The proposed physical explanation leads to the concept of an epicyclic load sharing map (ELSM). The ELSM is a plot of the load ratio (or % of input torque) versus a non dimensional parameter Xe. The non-dimensional parameter is a function of combined system stiffness, tolerance level, and operating torque. The ELSM contains curves for 3, 4, 5, 6 and 7 (and more) planet systems. Once a gear set is located on the ELSM, its behavior under any load and error condition can be quickly predicted. Also, the advantages of adding extra planets can be accurately estimated.
The use of the ELSM as a design tool for the general case when there are errors on the position of every carrier pin-hole are illustrated. Statistical simulations are performed for a given manufacturing error distribution for 3 to 7 planet systems
ISBN: 978-1-61481-004-9 Pages: 25
Author: A. Singh
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