Dynamics Of Early 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".

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.

While the basic working principle and the mechanical construction of automatic transmissions has not changed significantly, increased requirements for performance, fuel economy, and drivability, as well as the increasing number of gears has made it more challenging to design the systems that control modern automatic transmissions. New types of transmissions—continuously variable transmissions (CVT), dual clutch transmissions (DCT), and hybrid powertrains—have presented added challenges. Gear shifting in today’s automatic transmissions is a dynamic process that involves synchronized torque transfer from one clutch to another, smooth engine speed change, engine torque management, and minimization of output torque disturbance. Dynamic analysis helps to understand gear shifting mechanics and supports creation of the best design for gear shift control systems in passenger cars, trucks, buses, and commercial vehicles. Based on the authors’ graduate-level teaching material, this well-illustrated book relays how the fundamental principles of hydraulics and control systems are applied to today’s automatic transmissions. It opens with coverage of basic automatic transmission mechanics and then details dynamics and controls associated with modern automatic transmissions. Topics covered include: gear shifting mechanics and controls, dynamic models of planetary automatic transmissions, design of hydraulic control systems, learning algorithms for achieving consistent shift quality, torque converter clutch controls, centrifugal pendulum vibration absorbers, friction launch controls, shift scheduling and integrated powertrain controls, continuously variable transmission ratio controls, dual-clutch transmission controls, and more. The book includes many equations and clearly explained examples. Sample Simulink models of various transmission mechanical, hydraulic and control subsystems are also provided. Chapter Two, which covers planetary gear automatic transmissions, includes homework questions, making it ideal for classroom use. In addition to students, new engineers will find the book helpful because it provides the basics of transmission dynamics and control. More experienced engineers will appreciate the theoretical discussions that will help elevate the reader’s knowledge. Although many automatic transmission-related books have been published, most focus on mechanical construction, operation principles, and control hardware. None tie the dynamic analysis, control system design, and analytic investigation of the mechanical, hydraulic, and electronic controls as does this book.

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

These two volumes constitute the refereed proceedings of the First International Conference on Intelligent Robotics and Applications, ICIRA 2008, held in Wuhan, China, in October 2008. The 265 revised full papers presented were thoroughly reviewed and selected from 552 submissions; they are devoted but not limited to robot motion planning and manipulation; robot control; cognitive robotics; rehabilitation robotics; health care and artificial limb; robot learning; robot vision; human-machine interaction & coordination; mobile robotics; micro/nano mechanical systems; manufacturing automation; multi-axis surface machining; realworld applications.