Dynamics Of Planetary Gear Trains

A method to analyze the static and dynamic loads in a planetary gear train was developed. A variable-variable mesh stiffness (VVMS) model was used to simulate the external and internal spur gear mesh behavior, and an equivalent conventional gear train concept was adapted for the dynamic studies. The analysis can be applied either involute or noninvolute spur gearing. By utilizing the equivalent gear train concept, the developed method may be extended for use for all types of epicyclic gearing. The method is incorporated into a computer program so that the static and dynamic behavior of individual components can be examined. Items considered in the analysis are: (1) static and dynamic load sharing among the planets; (2) floating or fixed Sun gear; (3) actual tooth geometry, including errors and modifications; (4) positioning errors of the planet gears; (5) torque variations due to noninvolute gear action. A mathematical model comprised of power source, load, and planetary transmission is used to determine the instantaneous loads to which the components are subjected. It considers fluctuating output torque, elastic behavior in the system, and loss of contact between gear teeth. The dynamic model has nine degrees of freedom resulting in a set of simultaneous second order differential equations with time varying coefficients, which are solved numerically. The computer program was used to determine the effect of manufacturing errors, damping and component stiffness, and transmitted load on dynamic behavior. It is indicated that this methodology offers the designer/analyst a comprehensive tool with which planetary drives may be quickly and effectively evaluated.

This book provides comprehensive information for various planetary gear trains, with practical applications and comprehensive references to technical articles. In the text's chapters, readers can find all the information needed for various types of gear trains, with illustrations and examples. The authors help gear designers to creatively understand the design of gears, as well as master the mechanical calculations needed. Planetary Gear Trains is the most comprehensive and up-to-date work available in this key technical area. The book reflects not only teaching, but also the practical experience of the authors. It was developed under the motto "From practice to practice".

This book provides comprehensive information for various planetary gear trains, with practical applications and comprehensive references to technical articles. In the text's chapters, readers can find all the information needed for various types of gear trains, with illustrations and examples. The authors help gear designers to creatively understand the design of gears, as well as master the mechanical calculations needed. Planetary Gear Trains is the most comprehensive and up-to-date work available in this key technical area. The book reflects not only teaching, but also the practical experience of the authors. It was developed under the motto "From practice to practice".

Gears are essential parts of many precision power transmitting machines such as automobiles. The major functions of a gearbox are to transform speed and torque in a given ratio and to change the axis of rotation. Planetary gears yield several advantages over conventional parallel shaft gear systems: They produce high speed reductions in compact spaces, a greater load sharing, a higher torque to weight ratio, diminished bearing loads, and reduced noise and vibration. They are used in automobiles, helicopters, aircraft engines, heavy machinery, and a variety of other applications. Despite their advantages, the noise induced by the vibration of planetary gear systems remains a key concern. Planetary gears have received considerably less research attention than single mesh gear pairs. There is a particular scarcity of analysis of two planetary gear systems and their dynamic response. Hence, this book focuses on the study of two PGTs with different phasing (angular positions) while every individual set remains unchanged.

Machinery Dynamics includes recent advancements in this quickly evolving area, while also analyzing real applications, analyzing integrated systems, and including further discussions on each mechanical component. The book treats mechanisms separately, with different methods depending on the level of accuracy required. The contents of this book is made to suit the needs of MsC and PhD students, researchers and engineers in the areas of design of high speed machinery, condition monitoring of machine operation, and vibration. Addresses theoretical backgrounds on topics, including vibration and elastodynamics Introduces rigid and elastic dynamics of various mechanisms, including linkages, cams, gears and planetary gear trains Features relevant application examples

Understanding how gears are formed and how they interact or ‘mesh’ with each other is essential when designing equipment that uses gears or gear trains. The way in which gear teeth are formed and how they mesh is determined by their geometry and kinematics, which is the topic of this book. Gears and Gear Drives provides the reader with comprehensive coverage of gears and gear drives. Spur, helical, bevel, worm and planetary gears are all covered, with consideration given to their classification, geometry, kinematics, accuracy control, load capacity and manufacturing. Cylindrical gear geometry is the basis for dealing with any gear drives, so this is covered in detail. Key features: Contains hundreds of 2D and 3D figures to illustrate all types of gears and gear drives, including planetary and worm gears Includes fundamental derivations and explanations of formulae Enables the reader to know how to carry out accuracy control and load capacity checks for any gear drive Includes directions for the practical design of gears and gear drives Covers DIN and ISO standards in the area Gears and Gear Drives is a comprehensive reference for gears and gear drive professionals and graduate students in mechanical engineering departments and covers everything important to know how to design, control and manufacture gear drives.

Gears are essential parts of many precision power transmitting machines such as automobiles. The major functions of a gearbox are to transform speed and torque in a given ratio and to change the axis of rotation. Planetary gears yield several advantages over conventional parallel shaft gear systems: They produce high speed reductions in compact spaces, a greater load sharing, a higher torque to weight ratio, diminished bearing loads, and reduced noise and vibration. They are used in automobiles, helicopters, aircraft engines, heavy machinery, and a variety of other applications. Despite their advantages, the noise induced by the vibration of planetary gear systems remains a key concern. Planetary gears have received considerably less research attention than single mesh gear pairs. There is a particular scarcity of analysis of two planetary gear systems and their dynamic response. Hence, this book focuses on the study of two PGTs with different phasing (angular positions) while every individual set remains unchanged.