THE THEORY AND PRACTICE OF WORM GEAR DRIVES ILLES DUDAS This page intentionally left blank Series Consultant: Prof KJ Stout, University of Huddersfield, UK THE THEORY AND PRACTICE OF WORM GEAR DRIVES ILLES DUDAS Department of Production Engineering, University of Miskolc, Hungary m PENTON PRESS, LONDON Publisher's note Every possible effort has been made to ensure that the information contained in this book is accurate at the time of going to press, and the publishers cannot ac- cept responsibility for any errors or omissions, however, caused. All liability for loss, disappointment, negligence or other damaged caused by the reliance of the infor- mation contained in this handbook, or in the event of bankruptcy or liquidation or cessation of trade of any company, individual, or firm mentioned, is hereby excluded. Apart from any fair dealing for the purposes of research or private study, or criti- cism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may only be reproduced, stored or transmitted, in any form, or by any means, with the prior permission in writing of the publisher, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers at the undermentioned address: Penton Press Kogan Page Ltd 120 Pentonville Road London Nl 9JN www.uk © Illes Dudas 2000 British Library Cataloguing in Publication Data A CIP record for this book is available from the British Library ISBN 9781 9039 9661 4 Typeset by The Midlands Book Typesetting Company Ltd, Loughborough, Leicestershire, England.
Printed and bound by CPI Antony Rowe, Eastbourne To my wife, three children and parents The author with his early CNC grinding wheel dressing experimental equipment CONTENTS Foreword by Professor EL. Litvin, University of Illinois xi Preface xiii Acknowledgements xvi List of symbols xix 1 Introduction 1 1.1 Classification of worm gear drives 4 2 A short history and review of the literature 7 2.1 A short history of the worm gear drive 7 2.2 Development of tooth cutting theory for spatial drives 13 2.3 Cylindrical worm surfaces 16 2.1 Helicoidal surfaces having arched profile 16 2.2 Cylindrical worm gear drives with ruled surfaces 26 2.4 Conical helicoid surfaces 26 2.5 Surface of tools 29 2.6 General conclusions based on the literature 30 Manufacturing geometry for constant pitch helicoidal surfaces 33 3.1 Development of manufacturing of cylindrical worm gear drives having arched profile 33 3.1 Analysis and equation of helicoidal surface having circular profile in axial section 35 3.2 Analysis of worm manufacturing finishing; an exact solution 42 The Theory and Practice of Worm Gear Drives 3.3 Problems of manufacturing geometry during final machining of worm - determination of grinding wheel profile 44 3.2 Investigation of geometric problems in manufacturing cylindrical helicoidal surfaces having constant lead; general mathematical - kinematic model 61 3.1 Investigation of geometric problems when manufacturing cylindrical helicoid surfaces using general mathematical - kinematic model 64 3.2 Analysis of manufacturing geometry for conical helicoid surfaces 75 3.3 Geometric analysis of hobs for manufacturing worm gears and face-gears mated cylindrical or conical worms 102 3.1 Investigation of cutting tool for manufacturing worm gear mated with worm having arched profile 110 General mathematical model for investigation of hobs suitable for generating cylindrical and conical worms, worm gears and face gear generators 124 4.1 Application of general mathematical - kinematic model to determine surface of helicoidal surface- generating tool for cylindrical thread surfaces 135 4.2 Machining geometry of cylindrical worm gear drive having circular profile in axial section 136 4.3 Machining geometry of spiroid drives 148 4.4 Intersection of cylindrical helicoidal surface having circular profile in axial section (ZTA) and the Archimedian thread face surface as generating curve of back surface 162 4.1 Generation of radial back surface with generator curve 164 4.2 Contact curve of the back surface and the grinding wheel 165 4.5 Manufactured tools for worm gear generation and other tools having helicoidal surfaces 169 4.1 Design and manufacture of worm gear milling cutters 169 IX Contents Grinding wheel profiling devices 182 5.1 Devices operated according to mechanical principle 183 5.2 Advanced version of the wheel-regulating device operating on the mechanical principle 186 5.3 CNGcontrolled grinding wheel profiling equipment for general use 191 Quality control of worms 200 6.1 Checking the geometry of worms 200 6.1 Determination of worm profile deviation 201 6.2 Checking of helicoidal surfaces on 3D measuring machines 204 6.1 Use of 3D measuring machines 206 6.3 Checking of helicoidal surfaces by application of 3D measuring device prepared for general use (without circular table, CNC-controlled) 209 6.4 Results of measurement of helicoidal surfaces 217 Manufacture of helicoidal surfaces in modern intelligent integrated systems 222 7.1 Application of expert systems to the manufacture of helicoidal surfaces 222 7.1 Problems of manufacturing worm gear drives 223 7.2 Structure of the system 224 7.3 The full process 224 7.2 Intelligent automation for design and manufacture of worm gear drives 227 7.1 Conceptual design of helicoidal driving mates 228 7.2 Manufacture of worms and worm gears 245 7.3 Measurement and checking of helicoidal surfaces in an intelligent system 251 7.1 Checking of geometry using coordinate measuring machine 253 7.4 Development of the universal thread-grinding machine 255 7.1 Review of thread surfaces from the point of view of thread-grinding machines 255 7.2 Manufacturing problems of thread surfaces 255 The Theory and Practice of Worm Gear Drives 7.3 Requirements of the thread-grinding machine 257 7.4 Development of a possible version 258 7. Main operating characteristics and quality assessment of worm gear drives 260 8.1 Testing the meshing of the mated elements 260 8.1 Building in the mating elements 261 8.2 Adjustment and position checking of contact area 262 8.2 Checking the important operational characteristics of worm gear drives 271 8.1 Running in of the drives 271 8.2 Determination of optimal oil level 274 8.3 Investigation of warming up of the drives 274 8.4 Investigation of efficiency of drives 277 8.5 Investigation of noise level of drives 280 9 Summary of results of research work 289 References 294 Further reading 303 Index 331 FOREWORD The writing of this Foreword to this book presents me with a won- derful opportunity to recall my visits to Miskolc and my meetings with the distinguished scientists and the friends that I was lucky enough to make there. My friends from Miskolc, Professor Zeno Terplan and Dr Jozsef Drobni, gave me the best present that I could have asked for - they translated in 1972 the Russian edition of my book Theory of Gearing into Hungarian.
I was delighted to find in my conversations with Drs Imre Levai, Zeno Terplan and Illes Dudas a mutual interest in topics such as non-circular gears, planetary trains and worm gear drives. The greatest reward for a scientist is to have a following, and this I found in Hungary. My joy in this could perhaps best be expressed by citing the fa- mous verse 'The Arrow and the Song' by Henry Wadsworth Longfellow: / shot an arrow into the air, It fell to earth, I knew not where; And the song, from beginning to end, I found again in the heart of a friend I hope that this short introduction explains why I am grateful for the opportunity to write a Foreword to this excellent book written by Professor Dudas. The generation and manufacture of worm gear drives and the design of tools (hobs, grinding disks) for worm and worm gear generation is an important area of research.
The application of CNC machines to the manufacture of worms and worm gears, their 1 x" 1 The Theory and Practice of Worm Gear Drives precision testing, and the computerized design of tools have broadened the horizons of research and have required from the researchers a good knowledge of the theory of gearing and specialized topics in differential geometry. In this book Dr Illes Dudas makes a significant contribution to these topics of research; included are the author's summaries of the results of research obtained by himself and other researchers. In addition, Professor Dudas demonstrates the results of his great and wide experience in the design and manufacture of worm gear drives and in neighbouring subject areas. The contents of the book cover the main topics of the design and manufacture of gear drives.
I am familiar with the research per- formed by Professor Dudas whom I was able to meet at International Conferences (in San Diego and Dresden) and at our University, and by exchange of our publications. There is litde doubt that this book will be prove to be a most usefiil work for researchers and engineers in the area of gears. Litvin University of Illinois at Chicago Chicago, USA 1999 PREFACE Automation is playing an ever-increasing role in the development of both product and manufacturing technologies. Automation pro- vides important means of improving quality and increasing productivity as well as making production more flexible, in line with changing needs.
State of art computer control now has a role for machine tools and in manufacturing technology. Design of the prod- uct as well as of manufacturing equipment has been taken over by computer-aided, and sometimes by completely automated, systems. In the increase in efficiency of manufacturing processes and prod- uct quality, the most important element has been computer-aided engineering. Helicoid surfaces are often used in mechanical structures like worm gear drives, power screws, screw pumps and screw compres- sors, machine tools, and generating gear teeth.
Therefore many research and manufacturing organizations are becoming involved with their design, manufacture, quality control and application. Theory and practice in this field are usually treated separately in textbooks. There are significant differences between different ma- chining technologies, and checking methods for helicoidal surfaces are not always designed and manufactured precisely and optimally. I have been particularly fortunate to have been able to work, during the course of my career, in many fields of engineering.
Dur- ing my years as a professional engineer I always felt attached to scientific investigation concerned with the correlation between con- struction and manufacturing technology. Following a short period in industrial practice I worked, for ten years, as a designer. My first assignments were the design of service equipment (for example the DKLM-450 type wire-rope bunch lifter), and later, wire pulling I 1 The Theory and Practice of Worm Gear Drives stages, wire-end sharpeners, etc. The need for an improved worm gear drive arose in the course of this work.
The machine factory at Diosgyor (DIGEP, Hungary) was using wire pulling stages and decided to modernize them, to reduce their noise level, weight and cost along with developing an increase in the efficiency and load-carrying capacity. The modernization was carried out successfully so that the kinematically complicated drive systems were simplified too. The experience gained during tests showed that drive systems ful- filling exacting requirements can only be solved by using special worm gear drives. The technical development of worm gear drives at DIGEP resulted in worm gear drives with different geometries such as convolute helicoids with limited bearing capacity, worm drives with rolling contact elements and helicoidal surfaces curved at their axial section.
Comparing them, it became clear that the development of curved axial section type helicoidal surfaces was called for. Research in the fields of manufacturing technology development, as well as toothing geometry of mated pairs and the overall check- ing and quality control of these drives, are summarized in some of my published works (Dudas, 1973, 1980, 1988b). Worm gear drives designed and manufactured by application of this newly developed method have operated efficiently both in Hungary and abroad in a range of different products.