# Elements of machine design - Kimball

ELEMENTS OF MACHINE DESIGN

BY DEXTER S. KIMBALL, A.B.
Professor of Machine Design and Construction, Sibley College, Cornell University,

AND

JOHN H. BARR, M.S., M.M.E.
Manager, Smith Premier Works. Formerly Professor of Machine Design, Sibley College, Cornell University

NEW YORK, JOHN WILEY & SONS, 1909

Elements of machine design

PREFACE

This book is the outgrowth of the experience of the authors in teaching Machine Design to engineering students in Sibley College, Cornell University. It presupposes a knowledge of Mechanism and Mechanics of Engineering. While the former subject is a logical part of Machine Design, it may be, and usually is, for convenience, treated separately and in advance of that portion of the subject which treats of the proportioning of machine parts so that they will withstand the loads applied. The same logical order is usually followed in actual designing, as it is, ordinarily, necessary and convenient to outline the mechanism before proportioning the various members.

With the mechanism determined, the remainder of the work of designing a machine consists of two distinct parts:

(a) Consideration of the energy changes in the machine, and the maximum forces resulting therefrom.

(b) Proportioning the various parts to withstand these forces. This logical procedure, and the fundamental principles underlying the first part (a), are seldom made clear to the student, in works of this character; and such information as is given on energy transformation in machines is, in general, that relating to special cases or types. A thorough understanding of these general principles is, however, in most cases, essential to successful design, since a consideration of the machine as a whole necessarily precedes consideration of details. A very brief discussion of typical energy and force problems is given, therefore, in Chapter II, in the hope of making this important matter somewhat clearer to the beginner.

While the treatment presented presupposes a knowledge of Mechanics of Materials, a brief discussion of the more important straining actions is given in Chapter III, partly to make the application of the various formulae to engineering problems somewhat more definite, and partly to present such rational theory as is of assistance in selecting working stresses and factors of safety. This discussion serves also to show why certain equations have been selected in preference to others, and also to collect in concise form the more important equations relating to stress and strain with which the designer needs to be familiar.

The general principles of lubrication and efficiency are discussed in Chapter IV. Both of these are of prime importance to the engineer; and while the discussion is necessarily brief it is believed that the fundamental principles are fully covered.

The remainder of the book is devoted to the discussion of some of the more important machine details, with a view of showing how the theoretical considerations and equations discussed in the first part of the work are applied and modified in practice. The treatise is, in no sense, a hand-book, neither is it a manual for the drafting room, but is a discussion of the fundamental principles of design, and only such practical data have been collected as are needed to verify or modify logical theory. It is hoped that the illustrative numerical examples which are introduced throughout the work may, in conjunction with the analytical methods given, suggest proper treatment of practical problems in design. The treatment of all topics is necessarily brief, as it was desired to obtain a text-book which could be conveniently covered in one college year and yet present the salient features of the subject needed by the student as a preparation and basis for more advanced work. While intended primarily for engineering students it is hoped that it may also prove of some interest to the practicing designer. It has been the endeavor in the preparation of the book not only to develop rational analytical treatment, with due regard to constructive considerations and other practical limitations, but to reduce the analysis to such forms and terms that definite numerical results can be obtained in concrete problems.

Considerable of the matter contained in the book has already been published, specially for the use of students in Sibley College, under the tide of “Special Topics on the Design of Machine Elements,” by John H. Barr, and also in “Elements of Machine Design,” Part I, by the Authors. The writers have availed themselves freely of the work of many others in the field, for which due credit is given in the text.

CONTENTS

- Introductory. Definitions and Fundamental Principles
- The Energy and Force Problem. Consideration of Machines AS A Means of Modifying Energy
- Straining Actions in Machine Elements. Fundamental Formulas for Strength and Stiffness
- Friction, Lubrication, and Efficiency
- Springs
- Riveted Fastenings
- Screws and Screw Fastenings
- Keys, Cotters, and Force Fits
- Tubes, Pipes, Flues, and Thin Plates
- Constraining Surfaces, Sliding Surfaces, Journals, Bearings, Roller and Ball Bearings
- Axles, Shafting, and Couplings
- Belt, Rope, and Chain Transmission
- Applications of Friction. Friction Wheels, Friction Brakes, and Clutches, 350
- Toothed Gearing, Spur, Bevel and Screw Gears
- Flywheels, Pulleys and Rotating Discs
- Machine Frames and Attachments

The purpose of machinery is to transform energy obtained directly or indirectly from natural sources into useful work for human needs. Useful work involves both motion said force, hence the basis of Machine Design is the laws that govern motion and force.

The term useful work carries with it the idea of definite motion and definite force, for work itself is always of a definite or measurable character. An examination of any machine will show that its parts arc so put together as to give definite constrained motion suitable for the work to be done. The constrainment of motion is determined by the moving parts, the stationary frame and the nature of the connections between them.

Mechanics is the science which treats of the relative motions of bodies, solid, liquid, or gaseous, and of the forces acting upon them.

Mechanics of Machinery is that portion of pure mechanics which is involved in the design, construction, and operation of machinery. It has been noted that the consideration of a machine involves constrained motion, hence that portion of pure mechanics is mostly needed in Machine Design which deals with stationary structures and constrained motion. While the laws of Mechanics of Machinery give us the underlying principles on which machine action rests, their practical application brings in many modifying conditions.

Machine Design therefore may be defined as the practical application of Mechanics of Machinery to the design and construction of machines.

A Mechanism is a combination of material bodies so connected that motion of any member involves definite, relative, constrained motion of the other members. A mechanism or combination of mechanisms which is constructed not only for modifying motion but also for the transmission of definite forces and for the performance of useful work is called a machine. A machine consists of one or more mechanisms; a mechanism, however, is not necessarily a machine. Many mechanisms transmit no energy except that required to overcome their own frictional resistance, and are used only to modify motion as in the case of most engineering instruments, watches, models, etc.

A brief reflection will show that the same mechanism will serve for different machines (see any treatise on Kinematics) and within limits the design of the mechanism for a given machine may usually be carried out, so far as motion is concerned, with little regard to the amount of energy to be transmitted. This, of course, does not apply to such mechanisms as centrifugal governors, or in general where inertia or other kinetic actions affect constrainment of motion. Except for the limitations of such cases as those just noted, the design of any machine may be di- vided into two main parts:

(1) Design of the mechanism to give the required motion.

(2) Proportioning of the parts so that they will carry the necessary loads due to transmitting the energy, without undue distortion or practical departure from the required constrained motion.

(1) The design or selection of the mechanism for a machine is governed by the manner in which the energy is supplied and the character of the work to be done; for energy may be supplied in one form of motion and the work may have to be done with quite a different one. If mechanisms already exist which will accomplish the desired result the problem is one of selection and arrangement of parts. But if a new type of machine is to be built, or a new mechanism is desired, the solution of the motion problem borders on or may indeed be of the nature of invention. While it is true that in most cases the mechanism and the relative proportions of its parts can be designed to suit the work to be done without reference to the energy transmitted, in general it is necessary to know something about the energy transmitted before any definite dimensions of the parts of the mechanism can be fixed, and frequently before the nature of the mechanism is determined. Furthermore, the methods and available facilities of construction control the design to a large extent. Thus in designing a steam engine the size of the cylinder must be first fixed before the length of crank and connecting-rod can be fixed, and in general while the mechanism can be treated apart from the energy problem it is necessary to keep the latter constantly in mind.

(2) The problem of proportioning the various parts of a machine so that they will carry their loads without excessive or undue deformation may conveniently be divided into two parts:

(a) Solution as a whole, of the energy and force problem in the mechanism.

(b) Assigning of dimensions to the various parts based on the forces acting upon them.

(a) When the type and proportions of the mechanism have been fixed the relative velocity of any point in the mechanism may be found. If then the energy which the mechanism must transmit is known, it is possible, in general, to find the forces acting at any point since the law of Conservation of Energy underlies all machines; or the product of velocity multiplied by force is constant throughout the train. If the forces acting on a machine member and the manner in which. it is connected are known, these may serve as a basis for the assigning of definite dimensions to the part. A fuller discussion of this important principle is given in Chapter III.

(b) If the forces acting on a machine member can be deter- mined it would seem easy to choose the material and assign proportions to it based on the laws of Mechanics, and such is the case when the stresses are simple and the conditions fully known. Thus a machine member subjected to simple tension within known limits, can be intelligently proportioned in this manner. But in many cases the forces acting are very complex, the theoretical design is not always clear, and our knowledge of materials and their laws is limited in many respects. Recourse must there- fore often be made to judgment or to empirical data, the result of experience. Even when the conditions are clear, theoretical de- sign must always be tempered with practical modification and by constructive considerations, etc. The logical method of proportioning machine elements where theory is applicable is, therefore, as follows:

(a) Make as close an analysis as possible of all forces acting and proportion parts according to theoretical principles.

(b) Modify such design by judgment and a consideration of the practical production of the part.

In the case of details and unimportant parts, judgment and empirical data are commonly the best guides.

Summing up then, the logical steps in the design of a machine are as follows:

(I) Selection of the mechanism.
(II) Solution of the energy and force problem.
(III) Design of the various machine members so they will not unduly distort or break under the loads carried.
(IV) Specification and Drawing.

The last step, Specification and Drawing, is a necessary and important adjunct to the process of design; it is a powerful aid to the designer's mental process and is the best way of showing the workman what is to be done to construct the machine in question, and also of making a record of what has actually been done. It is not machine design of itself, however, as machines may be designed and built without any drawings. It is, nevertheless, an indispensable part of the designer's equipment. Very often written specifications accompanying the drawings are not only useful but necessary. In fact the highest skill on the part of the designer is often needed to clearly and fully specify in writing just what is to be done, as the writing of specifications presupposes the most intimate knowledge of theory of design, and selection of materials.

From the foregoing it is seen that the part of Machine Design included in Mechanism can be and generally is for convenience taught as a separate subject, and the student is expected to have a knowledge of Mechanism, Mechanical Drawing, Mechanics of Engineering, and Materials of Engineering as a preparation for the work contained in this book. The chapters that follow deal therefore with the solution of the Energy and Force Problem, and the Design of Machine Elements.