Notes on the design of machine elements
NOTES ON THE DESIGN OF MACHINE ELEMENTS
BY JOHN H. BARR,
Professor of Machine Design, Sibley College, Cornell University
ITHACA, NEW YORK, 1901.
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Notes on the design of machine elements
PREFACE.
These notes were prepared to accompany Professor W. C. Unwin's Elements of Machine Design, Part I. Taken in connection with this text-book, they form an outline of the course in the Design of Machine Elements as given to the Junior class of Sibley College, Cornell University.
The arrangement of the topics indicates the order in which the subjects are discussed, so that these notes serve as a syllabus of the lectures as well as a commentary on the text-book. In order that this double function may be fulfilled, numerous headings of articles are inserted accompanied simply by references to Professor Unwin's book. When it has seemed desirable to supplement or qualify the statements of the text-book, comments follow the appropriate references. The treatment of certain topics is quite independent of the text-book, and references to the authorities used are generally given in connection with the discussion of such subjects.
A short list of Reference Books is added to suggest the sources of fuller information and data. These books are arranged in classes, as an indication of their general scope, but the3' overlap to a considerable degree.
The preparation of these Notes has extended over a period of two or three years, advanced sheets having been printed and distributed to the classes from time to time. The conditions under which they have been issued has necessarily resulted in errors and imperfections, and many of these are apparent.
I desire to acknowledge my great obligation to the numerous writers and investigators consulted. I am especially indebted to Professor Dexter S. Kimball and Mr. William N. Barnard for their helpful criticism and careful reading of the manuscript and proof.
STRAINING ACTIONS IN MACHINES.
Nature of Straining Actions - The character of the straining action and of the stress which results from a given load depends upon the direction and point of application of the load force, (or forces), and upon the form, the position, and the arrangement of the supports, of the member. A given load may produce tension, compression, shearing, flexure, or torsion; or a combination of these. Of course tension and compression cannot both exist at the same time between any pair of molecules, or particles. Flexure is a combination of tensile and compressive stresses between different sets of molecules; or, as it is often expressed, in different fibres, of the same body. Torsion is a special form of shearing stress. Owing to the frequent occurrence of flexure and torsion it is convenient to treat these as elementary forms of stress.
The stresses due to tension, compression and flexure are essentially molecular actions normal to the planes separating adjacent sets of interacting molecules: that is, the stresses increase or de- crease the distances between these molecules along lines connecting them.
The primary straining effect in shearing and torsional actions is displacement of adjacent molecules, between which the stress acts, tangentially to the planes separating such molecules. In uniform shear, the interacting molecules move, relatively, with a rectilinear translation. In torsional. action, the adjacent molecules, each side of the plane of stress, have a relative rotation about an axis.
General Idea of the Factor of Safety - The working stress in a member must be less than the ultimate strength of the material, because:
(a) Members of structures and machines are not made to be broken in ordinary service.
(b) Materials employed in engineering usually take a permanent deformation, or set, before rupture occurs.
(c) There is always liability of defects in the material and imperfections in workmanship.
(d) In many cases there is danger of stress greater than the normal working stress from an occasional excess of load, or from accidents which are not foreseen or computed in advance of their occurrence
It is generally essential that a part be not only strong enough to avoid breaking under the regular maximum working load, but also that it shall not receive a permanent set; for a machine member ordinarily becomes useless if it takes such set after having been given the required form. In many cases a temporary strain, even considerably below the elastic limit, would seriously impair the accuracy of operation, and in such cases the members often require great excess of strength to secure sufficient rigidity. It follows from these considerations that the working stress should always be below the elastic limit and it must often be much lower than the elastic strength
The elastic strength of many of the common materials of construction is not much above one- half the ultimate strength, and the proper allowance for defects, overloading and other contingencies depends upon the conditions of the particular case. It thus appears that the working stress should never be as great as one-half, and it should seldom exceed one-third, of the working strength of the material In structures liable to little variation of load and to no shock, the working stress may be from one-third to one fourth the ultimate strength, with such comparatively homogeneous and ductile materials as wrought iron, mild steel, etc. With brittle materials, as cast iron, hard steel, etc. (which are more subject to hidden defects and are less reliable generally), a greater margin is required for safety. If the conditions are such that the material is apt to deteriorate seriously, a suitable decrease of computed working stress should be made.
The effect of a suddenly applied load (shock or impact) is to produce a stress in excess of that due to the same load applied gradually, and where such impulsive application of the load is to be expected, an appropriate reduction of the ordinary working stress should be made to provide for this action. Experience and experiment have shown that the repeated variation or reversal of stress affects the endurance of a material, sometimes causing a piece to break under a load which it has often previously sustained. The theory of this gradual deterioration is not very completely developed as yet; but enough has been learned to show that the working stress must be reduced as the magnitude of the variations of stress and the number of such variations increases.
Resilience - If a material is distorted by a straining action, it is capable of doing a certain amount of work as it recovers its original form. If the deformation does not exceed the elastic strain, this amount of work is equal to the work done upon the material in producing such deformation. If the material is strained beyond the elastic limit, it only returns work equal to that expended in producing elastic deformation; and the energy required to cause the plastic deformation, or set, is not recovered, as it is not stored but has been expended in producing such permanent change of form. Ordinary springs illustrates the first case ; the shaping of ductile metals by forging, rolling, wire-drawing, etc , are processes in which nearly all of the energy is expended in producing set.
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Notes on the design of machine elements
The stresses due to tension, compression and flexure are essentially molecular actions normal to the planes separating adjacent sets of interacting molecules: that is, the stresses increase or de- crease the distances between these molecules along lines connecting them.
The primary straining effect in shearing and torsional actions is displacement of adjacent molecules, between which the stress acts, tangentially to the planes separating such molecules. In uniform shear, the interacting molecules move, relatively, with a rectilinear translation. In torsional. action, the adjacent molecules, each side of the plane of stress, have a relative rotation about an axis.
General Idea of the Factor of Safety - The working stress in a member must be less than the ultimate strength of the material, because:
(a) Members of structures and machines are not made to be broken in ordinary service.
(b) Materials employed in engineering usually take a permanent deformation, or set, before rupture occurs.
(c) There is always liability of defects in the material and imperfections in workmanship.
(d) In many cases there is danger of stress greater than the normal working stress from an occasional excess of load, or from accidents which are not foreseen or computed in advance of their occurrence
It is generally essential that a part be not only strong enough to avoid breaking under the regular maximum working load, but also that it shall not receive a permanent set; for a machine member ordinarily becomes useless if it takes such set after having been given the required form. In many cases a temporary strain, even considerably below the elastic limit, would seriously impair the accuracy of operation, and in such cases the members often require great excess of strength to secure sufficient rigidity. It follows from these considerations that the working stress should always be below the elastic limit and it must often be much lower than the elastic strength
The elastic strength of many of the common materials of construction is not much above one- half the ultimate strength, and the proper allowance for defects, overloading and other contingencies depends upon the conditions of the particular case. It thus appears that the working stress should never be as great as one-half, and it should seldom exceed one-third, of the working strength of the material In structures liable to little variation of load and to no shock, the working stress may be from one-third to one fourth the ultimate strength, with such comparatively homogeneous and ductile materials as wrought iron, mild steel, etc. With brittle materials, as cast iron, hard steel, etc. (which are more subject to hidden defects and are less reliable generally), a greater margin is required for safety. If the conditions are such that the material is apt to deteriorate seriously, a suitable decrease of computed working stress should be made.
The effect of a suddenly applied load (shock or impact) is to produce a stress in excess of that due to the same load applied gradually, and where such impulsive application of the load is to be expected, an appropriate reduction of the ordinary working stress should be made to provide for this action. Experience and experiment have shown that the repeated variation or reversal of stress affects the endurance of a material, sometimes causing a piece to break under a load which it has often previously sustained. The theory of this gradual deterioration is not very completely developed as yet; but enough has been learned to show that the working stress must be reduced as the magnitude of the variations of stress and the number of such variations increases.
Resilience - If a material is distorted by a straining action, it is capable of doing a certain amount of work as it recovers its original form. If the deformation does not exceed the elastic strain, this amount of work is equal to the work done upon the material in producing such deformation. If the material is strained beyond the elastic limit, it only returns work equal to that expended in producing elastic deformation; and the energy required to cause the plastic deformation, or set, is not recovered, as it is not stored but has been expended in producing such permanent change of form. Ordinary springs illustrates the first case ; the shaping of ductile metals by forging, rolling, wire-drawing, etc , are processes in which nearly all of the energy is expended in producing set.
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Notes on the design of machine elements
