Contents Preface vii... Acknowledgements Vlll Introduction ix 1 Crown wheel and pinion 1 Torque at rear axles 4 Vehicle performance torque 5 Axle torque (from maximum engine torque through the lowest gear ratios) Axle torque - from wheel slip Drive pinion torque Stress determination and scoring resistance Bending stress Contact stress 2 Internal running gear 16 Shaft stressing for size 16 Input shaft 19 Intermediate shaft 19 Output shaft 19 Internal gears 20 Lubrication system 22 Gear engagement 22 Interlock system 26 Reverse gear 27 Differential 27 Bearing arrangement and casing 30 3 Lubrication of gears 33 Principles of gear lubrication 36 Group A 36 Spur gears 36 Helical gears 37 vi Contents Bevel gears 38 Crossed helical gears 38 Group B 39 Worm gears 39 Hypoid gears 40 Tests for lubricating oils 46 4 Gear tooth failures 50 Gear tooth failure 52 Tooth fracture 53 Tooth surface failures 54 5 Crowa wheel and pinion designs 61 Klingelnberg palloid spiral bevel gear calculations 66 Basic conception 66 Terminology 67 Bevel gear calculations 67 ‘0’-bevel gears 80 Bevel gear V drives 82 Tooth profiles 83 Gear blank dimensions 84 Formulae for the determination of the external forces 88 Strength of teeth 96 Rules for the examination of the tooth profile by the graphic method 100 Example of spiral bevel gear design 106 6 Oerlikon cycloid spiral bevel gear calculations 113 Design features 113 Production features 113 Gear calculation with standard En cutters 117 Strength calculation 1 30 7 Gearbox design - rear-engined racing cars 134 Basic aims 134 In-line shaft arrangement 135 Internal gear arrangement 137 Face-dog selectors 137 Bearhg arrangement 139 Crown wheel and pinion layout 141 Differential location and type 143 Transverse-shaft arrangement 148 Selector system 150 Selector interlock system 152 Lubrication method 155 Gearbox casing 157 Materials guide 158 Index 161 Preface This book has been written in an effort to put down on paper some of the experience I have gained during my forty-five years in the transmission design field, thirty-one years of which was designing Formula One gearboxes, and the last five years before retirement with Lotus Engineering as Chief Designer - Transmissions. Knowing of no other book that covered this subject made me more determined to proceed with it. I have attempted to work through the design procedure in the same order used on the many gearbox designs I have been involved with. Alternative types of crown wheel and pinion designs to the widely used Gleason system are covered, that is, Klingelnberg and Oerlikon. Various types of differential are described along with interlock systems which prevent the selection of more than one gear at a time. It contains a wide coverage of gear failures, their causes and requirements to prevent further failures, together with an engineering understanding of lubrication and its application. The book also includes a list of materials along with the heat treatment applied and race-proven in the B.R.M. Formula One Racing Transmissions as a guide to the designer. A. Stokes vii Introduction The purpose of this book is to provide both the student and young professional design engineer with an overall guide to the amount of work involved in the design of a manually operated automotive gearbox, and the problems that can be encoun- tered both during the design stages and in operation. I am unaware of any other book which gives such information and at the same time attempts to provide a methodical system of solving what appears to be a fairly straightforward engineering design problem to the majority of people, but often turns into one requiring great care and dedication. Otherwise the design can develop into a very complex piece of machinery which is both difficult and expensive to produce and proves incapable of achieving the original objectives that were laid down for the transmission. The purpose of any gearbox or transmission is to provide a drive, which often includes a range of selected intermediate gear ratios, between the power unit and the final source of the drive, whether it is to be used in an industrial, marine or automotive application. In the automotive industry this means the provision of a drive between the engine and the road wheels. This drive must be smooth, quiet and efficient and capable of being produced to a strict budget price while proving extremely reliable. With the exception of a transversely mounted engine and gearbox unit, the drive will at some point have to change direction through a 90" angle. Starting with the 90" angle drive, this being one of the following types of gear: (a) a pair of straight bevel gears (b) a pair of spiral bevel gears (c) a pair of hypoid bevel gears and commonly known as the crown wheel and pinion this book will attempt to follow the design sequence used by the author during the design of a manually operated automotive gearbox. Each of the chapters will deal with a-specific problem which is encountered during the design phases and during operation. Chapter 1. This chapter begins with a comparison of the merits of spiral bevel gears and hypoid gears when employed as the final drive in the automotive gearbox, ix x Introduction i.e. the crown wheel and pinion. Then the identification of the hand of spiral of both the spiral and hypoid bevel gears is explained, followed by the recommended hand of spiral. The major portion of the remainder of the chapter gives the details of the ‘Empirical formulae and calculation procedures’ produced by the American Gleason Gear Co. for rear axle or final drive units. These formulae give the following details: (a) torque at rear axles, and vehicle performance torque (b) axle torque, and axle torque from wheel slip (c) drive pinion torque (d) stress determination and scoring resistance The final pages cover the calculation of the crown wheel and pinion ratio and the layout of the initial lines for the gearbox design. These foregoing calculations provide a means of ensuring that the crown wheel and pinion operates satisfactorilyrelative to its specific environment and is designed with adequate strength to cope with the range of torques involved. Chapter 2. This chapter attempts to describe the process of designing the internal running gear, starting with the range of internal ratios, the input shaft, the intermediate shaft and the output shaft. The formulae for stressing these shafts are given, to enable the size of the shafts to be finalized. This is followed by the calculation of the road speed in the various internal ratios, and the selection of the ratios most suited for the particular application. The next pages describe various types of gear engagement systems and the need for an interlock system which prevents more than one internal gear being selected at any given time. The final pages cover the various types of differential that can be used, the choice of bearings and oil seals and finally the type of lubrication system required to suit the application. The closing pages also describe the layout of the gearbox internal running gear and the gearbox casing; the situations that the casing must be able to cope with are also described in some detail. Chapter 3. This chapter is totally dedicated to a complete description of the lubrication of gears. Starting with a brief history of the many dramatic changes that have been made in the lubrication of gears and lubrication in general engineering in the past few years, the various methods used to apply lubricant to gears are listed and explained. The problems of applying lubricant to the various types of gear, with the varying characteristics in the way in which the teeth of the mating gears move relative to each other, are also covered in some detail. This is followed by some advice on the type of lubrication to be chosen from the varying applications relative to the type of gear form and the pitch line speed. Then the loss in efficiency due to excess or inadequate lubrication is analysed. The final pages look at different types of lubricant used in gear drives. Chapter 4.This chapter is dedicated to all the various forms of gear failure that can be encountered by the engineer where gear trains are concerned. In the examination of the failures, the varying reasons or causes of failure, along with suggested remedies, are listed. The failures in any gear train fall into one of two forms, as follows: (a) complete fracture of the gear tooth, usually occurring at the root of the tooth which breaks away in one whole section Introduction xi (b) damage or destruction of the working or mating faces of the gear teeth The factors which either individually or as a combination result in the above failures are listed, before the identification of the failures and their respective remedies. Chapter 5.The different forms of crown wheel and pinion that are available to the designer are discussed in this chapter. The three forms are: (a) the Gleason system, produced by the Gleason Gear Co. of America (b) the Oerlikon system, from the Oerlikon Co. of Switzerland (c) the Klingelnberg system, introduced by the German company, Klingelnberg The differences between the three methods are discussed, together with a general description of the forces created when a pair of spiral bevel gears run together. The movement of the tooth contact pattern as the load applied to the gear increases is also discussed. The final pages of the chapter give a brief description of, and the calculations for, the manufacturing and inspection dimensions for a pair of Klingelnberg palloid spiral bevel gears.