1st Edition

Direct Gear Design

ISBN 9781439876183
Published March 22, 2013 by CRC Press
324 Pages 318 B/W Illustrations

USD $160.00

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Book Description

Over the last several decades, gearing development has focused on improvements in materials, manufacturing technology and tooling, thermal treatment, and coatings and lubricants. In contrast, gear design methods have remained frozen in time, as the vast majority of gears are designed with standard tooth proportions. This over-standardization significantly limits the potential performance of custom gear drives, especially in demanding aerospace or automotive applications. Direct Gear Design introduces an alternate gear design approach to maximize gear drive performance in custom gear applications.

Developed by the author, the Direct Gear Design® method has been successfully implemented in a wide variety of custom gear transmissions over the past 30 years. The results are maximized gear drive performance, increased transmission load capacity and efficiency, and reduced size and weight. This book explains the method clearly, making it easy to apply to actual gear design.

  • Describes the origin and theoretical foundations of the Direct Gear Design approach as well as some of its applications—and its limits
  • Details the optimization techniques and the specifics of Direct Gear Design
  • Discusses how this approach can be used with asymmetric gears to further improve performance
  • Describes tolerance selection, manufacturing technologies, and measurement methods of custom gears
  • Compares Direct Gear Design with traditional gear design from both an analytical and an experimental perspective
  • Illustrates the applicability and benefits of this gear design approach with implementation examples

Written by an engineer for engineers, this book presents a unique alternative to traditional gear design. It inspires readers to explore ways of improving gear transmission performance in custom gear applications, from higher transmission load capacity, efficiency, and reliability to lower size, weight, and cost.

Table of Contents

Historical Overview
Direct Gear Design® Origin
Gear Design Based on Rack Generating Technology
Gear Design without Rack Generation
Gears with Asymmetric Teeth

Macrogeometry of Involute Gears
Involute Tooth Parameters
Gear Mesh Characteristics
Pitch Factor Analysis
Application of Direct Gear Design for Different Types of Involute Gears

Area of Existence of Involute Gears
Area of Existence of Symmetric Gears
Area of Existence of Asymmetric Gears
Area of Existence and Pitch Factors
Application of Area of Existence

Involute Gearing Limits
Number of Teeth
Pressure Angle
Contact Ratio
Practical Range of Involute Gear Parameters

Tooth Geometry Optimization
Involute Profile Optimization
Tooth Modeling and Bending Stress Calculation
Root Fillet Optimization
Bending Strength Balance
Final Stress Definition

Gear Design Details
Gear Transmission Density Maximization
High Gear Ratio Planetary Drives
Self-Locking Gears
Plastic Gear Design Specifics
Gear Tooth Profile Modeling

Tolerancing and Tolerance Analysis
Gear Specification
Accuracy Selection
Tolerance Analysis

Gear Fabrication Technologies and Tooling
Gear Machining
Gear Forming

Gear Measurement
Measurement over (between) Balls or Pins
Span Measurement
Composite Gear Inspection
Elemental Gear Inspection

Comparison of Traditional and Direct Gear Design®
Comparable Geometry and Stress Analysis
Gear Testing Results Comparison
Design Method Selection

Implementation Examples
Speed Boat Gearbox
Turboprop Engine Gearbox
Seed Planter Gearboxes


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Dr. Alexander L. Kapelevich is a gear design consultant at AKGears, LLC. He holds a master’s degree in mechanical engineering at Moscow Aviation Institute and a Ph.D. degree in mechanical engineering at Moscow State Technical University. Dr. Kapelevich has more than 30 years of custom gear transmission research and design experience. He began his career working in the Russian aviation industry, where he was involved in R&D, software development, testing, and failure investigation for aerospace gear transmissions. Living in the United States since 1994, he developed the Direct Gear Design® methodology for custom gear transmissions that have been implemented in various fields, such as aerospace, automotive, agriculture, defense, robotics, racing, and many others. His specialties are the gear drive architecture, planetary systems, gear tooth macrogeometry optimization, gears with asymmetric teeth, and gear transmission performance maximization. Dr. Kapelevich is a member of American Gear Manufacturers Association.

Featured Author Profiles

Author - Alexander L.  Kapelevich

Alexander L. Kapelevich

Owner/President, AKGears, LLC
Shoreview, Minnesota, USA

Learn more about Alexander L. Kapelevich »


"This book was written by [an] engineer for engineers, to show an alternative to the traditional way of gear design."
Wonderpedia, Today's Featured Article 03.10.2014

"Direct Gear Design is a must-have book for the modern gear specialist. To be competitive, the world is looking for alternative methods to make new products. The gear production industry is not an exception. Finite element analysis, digital simulation tools, computer-controlled machining, [and] new materials demand the development of new approaches to design gears. Direct Gear Design by Alexander L. Kapelevich is exactly the book that established or new generation engineers should look for. It is practical; informative; includes recommendations, useful charts, diagrams, and tables; provides valuable information on gear geometry limitations; and brings implementation examples of different gearbox applications. The book introduces a new vision of gear design while addressing the old gear design challenges of reducing the stress level and increasing reliability of the gear trains."
—Mr. Yuriy Gmirya, Sikorsky Aircraft Corporation, USA

"… a useful tool for gear and transmission designers to come up with optimum gear design. Today we are forced to increase load carrying capacity, reduce transmission weight, and fulfill noise requirements without increasing manufacturing costs. The described new method, Direct Gear Design, and asymmetric gear design are helpful to reach this target."
—Dr. Franz J. Joachim, ZF Friedrichshafen AG, Germany

"A modern description of how gears should be designed today when we have computer tools that allow us to optimize our gear designs far beyond what the standards allow us."
—Dr. Anders Flodin, Höganäs AB, Sweden

"Finally, a new book that deals with gear macrogeometry! While many papers are being published on microgeometry/gear corrections, only little work is published on the more important issue of gear macrogeometry optimization. This book opens up a new window of opportunity for the gear designer, and it deals with one of the few gear geometry types not yet fully utilized, asymmetric gears. This is most welcome, as it will encourage designers to think ‘outside the box’. And with today’s gear-cutting technologies (e.g., direct machining), the manufacturing of non-standard gears displaying superior performance is feasible at little cost increase. Furthermore, the book covers a wide area of gear types and gives practical hints on how to balance gear strength, how to design high addendum gears, and how to achieve unusually high ratios."
—Mr. Hanspeter Dinner, EES Gear GmbH, Switzerland