THEORETICAL AND EXPERIMENTAL STRESS ANALYSES OP COMMON MECHANISMS IN FARM MACHINERY By SYED AEJAZ ALI A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1952 ACKNOWLEDGMENTS The author wishes to express his thanks and sincere appreciation for the helpful suggestions and timely guidance and encouragement from the following persons who brought this project into existence. Dr. W. M. Carleton, professor in charge of major work. Professor A. W. Farrall, Head of Agricultural Engineering Department. Professor H. F. McColly, Agricultural Engineering De­ partment . The writer is also grateful to Dr. R. T. Hinkle, and Professor Paul DeKoning both of the Mechanical Engineering Department for their cooperation and assistance in making possible the use of electronic instruments. The author also expresses his thanks for the help received from other staff members and persons in charge of the research laboratory in the Agricultural Engineering Department. THEORETICAL AND EXPERIMENTAL STRESS ANALYSES OP COMMON MECHANISMS IN FARM MACHINERY By Syed Aejaz All AN ABSTRACT Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OP PHILOSOPHY Depart of Agricultural Engineering Year 1952 Approved_ Ia/ ) / ) f' - lV SYED AEJAZ ALI - ABSTRACT In the development and manufacturing of the farm im­ plements and machinery, a common practice that had been followed very extensively, and still is followed to a certain extent is to design a machine or its part basing the know­ ledge on the rigorous mathematical theory or derived and empirical formulas plus the previous experience in the ex­ perimental trial and error methods* These analytical solutions were frequently aided by many safety factors assuring the de­ signer that his designed mechanisms were devised with a suf­ ficient margin of safety. These practices which are very much refined and improved in the industrial design by the exhaustive theoretical in­ vestigations supported by the highly developed experimental techniques, have begun to influence the realm of farm equip­ ment design. Experimental methods developed and introduced during the past decade for the amelioration of design and developmental procedures in the industrial work are at present being utilized by a farm machinery design engineer. The photo­ elasticity, X-ray analysis, brittle lacquer method and the electric strain gauges are among the many experimental means made available for the determination and analysis of stresses and strains which form the basis of any design. With these constantly improving trends in the field of machinery design, an attempt was made by the author to use one of the available means, namely the electric strain gauges as - V - SYED AEJAZ ALI - an aid for the experimental stress analysis. ABSTRACT The goal set for the utilization of this experimental technique was to evaluate analytically, the stresses in some of the commonly used mechanisms in farm machinery, to determine the stresses from the experimental work and to compare or correlate the two. For this purpose, an experimental laboratory machine was constructed representing the common mechanisms such as the plunger assembly, the mower assembly, and the belt and gear drives. It was apparent from the experimental results that the magnitudes of stresses in the above mechanisms was in almost every case higher than the theoretically determined values. Moreover, the stress patterns as revealed by the experimental work not only point out the form and types of stresses in the assembly, but also serve as a tremendous aid as a valuable tool for the design engineer in the field of farm machinery. Such factors as the effects of centrifugal forces, the re­ peated stresses, and the variable power requirements influ­ enced the stress pattern in each of the above assemblies. TABLE OP CONTENTS Page INTRODUCTION................... 1 REVIEW OP LITERATURE................................ 4 Progress of Stress Analysis....................... 5 Description of Experimental Methods............... 9 Analogies.............................. ......... 9 Membrane Analogy.............................. 10 Electric Analogy.............................. 15 Hydrodynamical Analogies...................... 15 Photoelasticity................................. 16 Mechanical Strain Gauges and Testing Machines... 25 X-ray Techniques for Stress Analysis........... 27 Brittle Lacquer Method.......................... 51 Electric Strain Gauges and Their Instrumentation................................. 57 PURPOSE OP THE INVESTIGATION........................ 56 Instrumentation of the Project.................... 58 The Brush Analyzer.............................. 59 The Mercury Torquemeter......................... 59 The Stroboscope................................. 64 The Simpson Meter Model 260................... 64 The Electric Dynamometer........................ 65 Experimental............................ 67 - vii Page The Analysis of the Centre-Crank Mechanism..... 70 Flywheel....................................... 70 Connecting Rod................................ 72 Crankshaft.................... 74 The Analysis of the SideCrank Mechanism........ 75 The Gear Drives.............................. 80 The V-belt Drives............................. 8l CONCLUSIONS................................ 84 SUGGESTIONS FOR FURTHER STUDY....................... 86 APPENDIX............................................. 87 SELECTED BIBLIOGRAPHY.................................. 106 LIST OF FIGURES Figure Page 1 Model Under Study in a Plane Polarlscope 2 Localized Stresses in the Fillets of a 20 Gear Tooth................................... 3 Stresscoat Lacquer Selection Chart 4 Stresscoat Pattern on Crankshaft Loaded .. in Bending.................................... 5 22 3^- 36 Three Basic Circuits of Wire Resistance Gauge s ........................................ 4-3 6 Strain Gauge Drawbar Dynamometer............. 47 7 Bonded Wire Gauge Torquemeter................ 48 8 Small Magnetic-coupled Torquemeter........... 50 9 General-purpose Economy Oscillograph Type S 14-C.................................. 55 10 Wiring Diagram Brush Analyzer Model BL 310... 60 11 Detail Drawing of the Mercury Torquemeter.... 62 12 Mercury Torquemeter Mounted on the Main Shaft......................... 63 13 Instruments Used in the Project.............. 66 14 Side View of the Experimental Machine 68 15 Rear Right Side View of the Experimental Machine....................................... 16 69 Graph of Effects of Load Variation on Crankshaft Stresses.......................... 76 - ix Figure 17 Page Strain Recordings of 1/2 inch Gauge at the Pitman Mid-section for Variation Speeds..... 18 78 Dynamic and Static Wiring Circuit for Electric Strain Gauges....................... 102 19 Top View of the Assembly..................... 10j5 20 Side View of the Assembly..................... 104 21 Front View of the Gear Assembly.............. 105 LIST OP TABLES Table I Page Thickness Radiographed with Different Voltages........................................ II Characteristics of Stresscoat Brittle Coatings............................. 29 INTRODUCTION Engineering design has in the past been based mainly on the personal experience of the designer and some mathematically derived or empirical equations. Analytical approaches to design problems, aided by various safety factors, had for some time no appropriate experimental means possible for evaluation of actual loading patterns In machine parts. Current trends in the development of experimental aspect as a vital tool of the design engineer have revolutionized the procedures and practices followed by predecessors. Serviceability of a machine part for a long time based on the idea of designing huge and cumbersome elements has been replaced by refined techniques and more rationalistic methods which determine ex­ perimentally the load distribution in a certain machine under actual operating conditions. Furthermore, the significance of such factors as fatigue, elastic limit, S-N curve, and residual and repeated stresses In relation to design problems has been emphasized by means of experimental tests which re­ veal the influence of the above factors on the actual design. A great achievement made in this field was the experimental study of forces and stresses under dynamic conditions which not only Improved the design fundamentals, but also gave a comparison between the prevailing analytical methods and the more advanced experimental procedures. - 2 Similar to the history of engineering design has been the evolution of agricultural machinery design. Constant changes in this field have brought forth the improved form of modern ploughs through a gradual process of replacement, and a better performing efficient tractor for farm power developed from the primitive prototypes. Like in the industry, in the farm machinery enterprise, most prevalent design practices included judgment of design based on the engineer's experience and field testing of the machines; reinforcing certain parts, if they failed during the previous tests. No specific procedures or simplified and yet accurate means were available to evaluate the actual phenomena taking place in various components of a machine, particularly under dynamic conditions. Experimental aids originally developed and improved for industrial applications have influenced significantly the field of farm machinery design, where crude and bulky machines are steadily and progressively being replaced by efficient ones. With the advent of better experimental design methods, the application of these techniques became more common in farm machinery design. Use of such techniques as photoelasticity, electric strain gauges, and electro-magnetic devices has been responsible for the improvements in present day equipment used in agriculture. Studies on reduction of extra weight, stability of tractors and other equipment, elimination of undesired vibrations transmitted to the supports of a mower or a har­ vesting machine, analysis of indeterminate frame structures of a harrow or a loader, and tests on the force distributions - 3 in a mold/board plough are among the innumerable problems where experimental techniques are being successfully applied for solving conditions which otherwise involved mathematical approach founded on factors which were in many cases impossible to eval­ uate. In certain cases, use of these experimental methods for the design of harvesting machines has resulted in the reduction of undesirable excessive weight up to twenty percent. The object of this study was to apply some of these avail­ able experimental means in the analysis of stress patterns in some mechanisms of farm machines, both under static and dynamic operating conditions, and then drawing a comparison or similarity with the theoretical and analytical methods. For this purpose, certain components, such as a plunger or compressor, a side-crank machine like a mower, and various kinds of drives such as gear and belt drives were isolated and mounted in a compact form. This experimental stress machine made feasible a comparative study and testing of the mechanisms under variable operating conditions. The electric strain gauge method was employed for the testing purpose. Among the main features of this experimentation were such items as the determination of repeated and whipping stresses in connecting rods, evaluation of effects of torsional vibrations in crank­ shafts, torsional and bending stresses in flywheels, gear teeth, and the main shaft. Having evaluated these values, an attempt was made to compare them with the theoretically determined values in order to correlate the two techniques, and to bring out the elements of relatively higher accuracy and simplicity as observed in the former. REVIEW OF LITERATURE In any conventional design work, knowledge of the follow­ ing three elements is of significant importance: 1. Type of loading, 2. Distribution of load. 3. Properties of the material. At present, various techniques are employed in evaluating the applied load pattern. Some of these methods determine the static and average or steady state dynamic loads with reason­ able accuracy. However, two factors usually account for the complication and difficulty in solving for load distribution. Statically indeterminate structures such as frames of many farm implements make mathematical solution impractical. In addition to this, the computation of force distribution in individual members of complex shapes becomes extremely diff­ icult . Two possible approaches are made by the design engineers in evaluating the working stresses in various mechanisms. The first is the usual theoretical design procedure, very often involving calculations based on rigorous mathematical formulae and equations. This is the method where, at the end of the solution, a so-called factor of safety is thrown in. This safety factor usually varies anywhere from two to twenty, de­ pending on the magnitude of the risk involved in the use of - 5 that particular machine, and to overcome the possible errors in assumptions made at various stages of the design. The second commonly used procedure is the trial and error method, which has a very wide application in industrial design works. Elaborating on the use of this method in farm machinery design, a research engineer has said that most new designs of fanri -=> implements are modifications of some previous implement, enough similar to provide the basic design data by virtue of its successful or unsuccessful performance. Many very dependable implements have been developed by building an admittedly in­ adequate pilot model, placing it in the field and reinforcing the part that failed until the revised model performed (19). The method, as compared to the former, is not too impractical, but the main drawback in this type of work is that in most in­ stances, such an approach leads to extra heavy structures which become expensive and uneconomical from the commercial and practical standpoint. Progress of Stress Analysis Stress analyses techniques, whether theoretical or exper­ imental, are concerned with the determination of stresses and strains caused in a structure deformed within the elastic range, and also due to the plastic deformation. Theoretical evalua­ tion of stresses is not flexible enough in that it is limited in application to structural members of certain shapes. The ■S’" theory without the experimental part becomes invaluable from - 6 the standpoint of planning and development in design work. A combination of both the theoretical knowledge and experimental procedure is very much desirable for the execution of success­ ful planning in the field of engineering design. With the evolution of experimental stress analysis techniques to an advanced stage, this link between theory and experimental work has been growing stronger. In the early part of the seventeenth century, Galileo stated several factors responsible for the failure of simple elements: his conclusions mainly derived from experimental work. Realizing that the science of mechanics of materials was hardly known at that time, his contributions, though erroneous, can be referred to as the precedent of modern stress analysis (22). Robert Hooke gave an impetus to the retarded experimental elasticity by stating his well-known Hooke's law where he mentioned that the elongation of an elastic member was proportional to the applied force. Location of the neutral axis of deflected beams was another significant contribution made by Mariotte (22). During the eighteenth century, Bernouli compared the elastic properties of the materials by using their cellular structure. Euler's formula derived from his column theory, Lagrange's and Euler's theory of elastic stability, and Coulomb *s torsion theory were among the outstanding works accomplisher during the latter part of the eighteenth century. It could be stated that during this century, concentration of efforts was more towards the theory of elasticity than on the direct improvement of experimental elasticity. - 7 Young's modulus of elasticity was a significant addition towards furthering the experimental knowledge. Equilibrium equations as given by Navier form the basis of the theory of elasticity. Poisson's work on verification of Navier's equations, and Poisson's ratio, along with Cauchy's analysis of stress at a point by using six components, were the im­ portant works of the earlier nineteenth century. Contributions made by Saint Venant- his famous torsion theory and his Saint Venant principle, Maxwell's works on statically indeterminate structures, and Airy's stress functions marked the progress of theory of elasticity during the latter half of the nineteenth century. David Brewster, F. E. Neumann, and Clerk Maxwell dis­ covered the laws about the double refraction of the deformed isotropic solids, and the stress-optical relationship, which laid the foundation for the modern science of photoelasticity (12). Later on, Wilson and Mesnager attempted some investi­ gations on simple structures by utilizing the same principles. A further contribution made in this field was the treatise on photoelasticity by Coker and Filon in 1951 (7). Use of hydrodynamic-torsion analogies, and membranetorsion analogy are among the several experimental methods, evolved during this century. Kelvin, Tait, and Boussinesq have been the pioneers in the hydrodynamic-torsion analogies work; while the name of Prandtl is mentioned in connection with the membrane-torsion analogy. Dr. L. B. Tuckerman revolutionized mechanical strain gauging technique by developing a mechanical-optical strain gauge of a short gauge length; rugged in construction and of greater accuracy. During the period of 1920 to 19^-0, several mechanical gauges were made available. Among these were the Huggenberger tensometer and the dePorest scratch-type gauge, the latter made flexible for recording static and dynamic strains of rather low frequency. Along with the experimental progress, two significant contributions to the theory were made during the earlier twentieth century. Buckingham's theory of dimensional analysl by means of pi theorem, presented in 1915* and Westgaard's pre sentation of strain rosette equations, added tremendously in analyzing the relationship between the model under study and the prototype, and in graphical and mechanical solutions of various problems. The Brittle lacquer method marks another distinct step towards the progress of experimental stress analysis. Pre­ liminary investigation on this subject was made by Dietrich and Lehr, two German scientists. This study was followed up by the Frenchmen, Portevin and Cymboliste, and later on materialized for a useful practical purpose by dePorest and Ellis. The application of X-Rays technique for evaluation of stresses in machine parts has been a fairly recent addition to the list of experimental means of stress analysis. Also, - 9 the development or high speed photography has found a very wide scope In analyzing loading patterns, travelling Impacts, and other stresses In several mechanisms which need a quick evalu­ ation not possible by any other experimental procedure. Among the latest of these developments, and probably a very highly accurate and practical method, with a very wide application In studies of both the static and dynamic loadings, is the development of the variable resistance electric strain gauge by the ingeneous works of de Forest. With the constant improvements in electronic devices, it can be said that electric strain gauge technique will be extensively adapted in numerous phases of experimental stress analysis work. Description of Experimental Methods Analogies With the advancement of mathematics in applied sciences and engineering, analogic experimental methods in stress analysis became more popular. In general, analogic treatment to a certain problem is desirable in situations where solu­ tions of equations representing a physical system are often too difficult to derive, or the numerical solution becomes a labourious task, and a direct study either on the system or a model Is not quite feasible. Analogical investigations made on electric circuits were correlated for determination of the nature of mechanical vibra­ tions, flow of fluids through tiles and closed or open pipes, - 10 and other problems Involving study of mechanical properties of certain mechanisms. Application of membrane analogy can be cited In cases like the shape of a soap film representing shearing stress In a twisted bar; and the solution of a pro­ blem of slow motions of a viscous fluid In two dimensions representing the solution to a flexure problem of a plate. Various stages that form the basis of an analogic ex­ periment can be briefly stated in the following words. At first, a mathematical analysis or equations are derived for a physical system whose analogue is to be studied. Similar mathematical form is obtained for the analogue of the physical system. An attempt is then made to correlate the two by means of their mathematical expressions. Finally, the physical investigation is conducted on the analogue and the results are transferred to the original physical system. Membrane Analogy. Membrane analogies are used either for a torsion or bending experiment. In such cases, either a soap film, a rubber membrane, or a meniscus surface is the most common kind. Soap film analogy is a very desirable one because of the fact that the unit tension T is automatically uniform throughout. The differential equation of the elevated surface z = f (x,y) assumed for a homogeneous membrane stret­ ched with uniform edge tension T over a contour s bounding an area S of the (x,y) plane and dilated by a uniform pressure p - I l ­ ls ti + (#)g3 ¥§a'- g If If life + t1 + (gf)2l gf* _ [i In a case where + ( H )2 + ^ ( | f )2 ] 4 T no pressure Isexerted against the membrane, the above equation reduces to zero on the right hand side (17). Anthes was the first one to come out with the application of soap film analogy for torsion problems in 1906, He used a rectangular box with a slot in its vertical side through which the film was stretched. The film was inflated by blowing in a measured amount of air displaced from a glass tube. Later on, Griffith and Taylor introduced their apparatus in 1917* which became very widely used for such experiments. The maximum limiting linear dimension for an experimental hole is around 5 inches, in case of circular hole the radius is taken equal to twice the ratio of the area to the perimeter of the circle, so that the average boundary slope of the ex­ perimental hole should equal to the slope at the edge of the cirle. of symmetrical patterns, studies of contours In case on only one half the hole are conducted. The Anthes checkerboard, Griffith and Taylor autocollimeter, Quest collimeter, Relchenbacher's automatic recorder, and Thiel's photogrammetric camera are the instruments developed and used for evaluation of the slope of the pressure soap film in order to determine the stress pattern of the model under study. The first one yields results closer to the theoretical 12 analysis (within 1 to 3^) than any other method. Measurement of volume under the soap film surface is accomplished either by contour method using a vertical micrometer (Taylor and Griffith), the 'black-spot* method, or by the integration of the slopes as determined by the former instruments. Probably the most direct way would be the measurement of the volume of air introduced in forming the soap film membrane. When the zero-pressure soap film is used in a torsion test, the use of function F = - GGx2 is suggested for the building of the boundary wall. The boundary ordinates lie on the surface of a parabolic cylinder z f= kx^ (k a constant), and the shape of actual hole to be cut from a flat plate can be obtained by computing the ordinates. (2kx(f^l+4k2x f ) Here x § represents the x coordinate of the projection of the boundary on the horizontal plane, and x is the corresponding x coordinate on the developed surface. After cutting the hole, the sheet is bent on a cylinder z(= kxp, the edge of the curved plate giving the boundary ordinates. Kopf and Weber have introduced the use of a rubber dia­ phragm, stretched over a cut out surface in a plate and bulged into a mass of paraffin of unit specific gravity by water - 13 pressure. On hardening, the paraffin proves a permanent cast of the bulged diaphragm. This enables getting data on In­ clination of normal stress lines. The advantageous part of this rubber diaphragm is the sizeable reduction of sag due to weight on account of large allowable tension, the permanent nature of the diaphragm, the simplicity of operation, the liesurely evaluation of contours from frozen paraffin, and the allowable accuracy in the measurement of the ordinates and in building of boundary heights. Meniscus surface membrane analogy has been first suggested by Piccard and Baes in 1926. The separation of two immiscible liquids is used in these experiments for torsion analogy. Due to the presence of capillarity, an equivalent constant tension exists on the surface, and the meniscus can be used both for pressure and no-pressure experiments. Electric Analogy. Jacobsen was the first one to perform electric analogy experiments on torsion of axially symmetric shaft for determining stress-concentration factor for circular shafts of two diameters connected by a circular fillet. The results of his experiment checked with the graphical results of Willers (18), but differed from the experimental results of Weigand or the theoretical work of Sonntag. Thum and Bautz have also introduced a method of electric analogy studying the problem of stress-concentration factor in shafts. Their method, in comparison to that of Jacobsen's, does not require measurement of the potential, but drawing of - 14 equipotential lines only. This directly locates the point of maximum stress concentration. Moreover, the 3hape of the model can he easily changed. The differential equation for the distribution of the steady-state potential V in a thin plate of constant thickness can be represented as follows: b2V + d2V . _ o the coordinate plane x,y, is in the same plane as the plate. For the analogy between the above equation and that of torsion problem, the"following relationship is used: 2 V where y,l s & = 0 a function of x and y. To represent similarity between the above differential equation and the case of bending, the differential equation 2 V

is some other function of x and y only. The boundaries of the thin plate used should be of such shape and held at such voltages that V on the boundaries should be similar to those required of <|> and if* by their boundary and single-valuedness conditions. Similar to the above differential equation for steadystate potential V in a thin plate, the equation of steady-state current flow can be stated as follows: 15 or 6 55c ( h_ av) _d_ (h_ av) R dx + dy R dy “ where x and y are cartesian coordinates, R Is the specific resistance of a cube of unit edge, h Is the plate thickness, and axis z is chosen parallel to the thickness of the plate* In connection with electric analogy as a means of solving stress problems experimentally, Kron's analogy of elastic field, Bush*s electric network for pin-connected and rigidjoint structural frames, Mallock's machine for solving simul­ taneous linear equations, hold a very significant place. Hydrodynamical Analogies. Three hydrodynamic analogies on torsional problems have been studied by Thomson and Tait, Boussinesq, and Greenhill (17). A brief account of these is presented in the following: a). The steady-state motion of an irrotaional non-viscous fluid filling an infinite prism of cross-section S, rotating with unit negative angular velocity can be interpreted by -2 over S, C a constant, (commonly taken as Zero) over boundary s. y, is the stream function. b). The steady-state pressure produced laminar axial flow of a viscous fluid in a pipe of cross-section S can also be represented by the above equations, where now the axial velocity. denotes - 16 c). The steady-state motion of an ideal non-viscous fluid circulating with uniform longitudinal vorticity in a foxed prism S is characterized by the equations: Z = (J) + i ^ and 2 V -2 over S, where Z is an analytic function, and (p is the velocity potential represents the stream function. Since the producing of a vorticity of such a nature is difficult, this analogy does not have much of sin experimental significance. Photoelasticity Photoelasticity as a designer's tool has met with a great success in the stress analysis work. Problems not readily solvable analytically by other available techniques have yielded valuable data when the method of photoelasticity was applied. Photoelasticity provides an over-all visual picture of the shearing-stress distribution throughout a specimen. It makes possible the measurement of stresses at a point, thus the regions of high stress gradient can be evaluated. In precision, results obtained in two dimensions by photoelastic methods are comparable to strain gauge measurements. A fairly elaborate pattern of stress distribution can be obtained on irregular shapes of the model used for studying the prototype. Thus stresses at in­ terior points may be evaluated. Sir David Brewster was the first one to publish in 1816 that clear stressed glass when examined in polarized light - 17 exhibited coloured patterns. However, not much practical use was made of these results, and very few applications were made until the turn of that century. Reputed physicists like Neumann, Maxwell, and Wertheim (22), have furthered the pro­ gress of the theory established by Brewster by defining that the optical retardation causing the colour effects is pro­ portional to the difference of the principal stresses existing in the glass. Later, Professor E. G, Coker of the University of London introduced celluloid models and used monochromatic light which made possible m o d e m laboratory photoelastic studies. The development of synthetic plastics and invention of Polaroid for producing large beams of polarized light have greatly assisted the promotion of photoelasticity for labor­ atory techniques, and have significantly reduced the cost factor involved. Works accomplished by Procht, Hetenyi, Drucker, I>olan, Filon and Murray have played a great role in furnishing an adequate tool for modern design engineer. Glass, celluloid, bakelite, and several other synthetic resins under stress refract a beam of light similar to a crystal. This double-refraction, temporary in nature, is like in a wave plate; and the retardation is dependent on the intensity of the stress, the refraction disappearing at the removal of the load. For the cases of plane stresses within the elastic limit, the following laws govern the transc mission of light for photoelastic stress determination. - 18 a.. The light 4s polarized in the directions of the prin­ cipal stress axes and is transmitted only on the planes of principal stress. b. Intensities of the principal stresses in the two planes govern the velocity of transmission of light in each principal plane. Moreover, this transmission obeys the following equations represented in terms of plane stress (8 ). N — — Ng M = M-l - Mg = = AQ*2_ + Both have either a bonded or unbonded form. The non- metallic unbonded gauge has a resistance element so arranged that when one part of the gauge is varied with respect to the other, it causes a change in pressure, which in turn varies the resistance of the element. It consists of a series of car­ bon plates put together in a stack. Any displacement in one part of this stack relative to the other, changes pressure on the stack plate, hence the resistance of the element is altered. The non-metallic bonded gauge has the resistance element bonded directly to the specimen, and the strains in the speci­ men change the pressure or the dimensions of the bonded ele­ ment, thus transforming a displacement into electrical resis­ tance. Bloch prepared a carbon coating to be directly applied to the structure under test. The carbon particles, by moving closer or apart give a variation in resistance similar to that of a microphone. The measuring unit employed by Bloch was an - 4 1 - ordinary two-stage amplifier. Later, Hamilton Standard Divi­ sion of United Aircraft Corporation developed an impregnatedplastic resistor which is used at present in place of carbon coating. Both bonded and unbonded non-metallic gauges have a rather restricted range of applications such as in aircraft propeller tests during flight, displacements, loads and strains in flexible cables, vibrating members, pressure gauges and dynamometers. The main disadvantages are that they are cum­ bersome and less accurate than the wire resistance strain gauges. The unbonded metallic gauge was first devised by R. W. Carlson (5).» and used in detecting strains in concrete struc­ tures. Carlson gauges in their simplest form consisted of three coils of wound wires, one coil being unaffected by the gauge motion, and the other two colls made tension sensitive; one having reduction in tension and the other an increase in its tension whenever the gauge was displaced. Unbonded wire strain gauges having essentially the same principle are made by Statham Laboratories, and are used in several devices such as pressure pick-ups, and force and acceleration recordings. Clark and Datwyler at California Institute of Technology and Professor Ruge at Massachusetts Institute of Technology were the noted men who came out with practical application of the bonded electric wire-reslstance strain gauge directly to the specimen being tested. A resistance wire strain gauge is composed of a fine grid of wire about 0.001 inch in diameter, and cemented between two sheets of treated paper or felt. SR-4 gauges manufactured by the Baldwin Southwark Division, - 42 Baldwin Locomotive Works, are the type of electric strain gauges used extensively in current stress analysis work. In order to obtain better and accurate results by the use of electric strain gauges, the following factors are of im­ portance : The determination of the location for mounting strain gauges, a thorough cleaning of the surfaces on which the gauge is to be applied, a good bond between the gauge and the specimen, sufficient drying period (preventing excessively high temperatures if artificial heat is used), and an open check of the gauge to detect any damage done during the mount­ ing process. Detailed information on mounting procedure is furnished by the gauge manufacturing company or could be ob­ tained from various articles dealing on this topic. Fundamentally, electric wire resistance gauges require four simple circuits for the transformation of the measured mechanical displacement into electrical resistance. The first circuit Includes the source of supply; it could be a d-c battery or an a-c oscillator unit. second part of the main circuit. The gauge circuit Is the This correlates the mechan­ ical displacement to be measured to the potential difference caused due to the displacement. The amplifier circuit, which merely boosts up the signal from the gauge circuit without any warping or distortion, forms the third circuit. The re­ cording or metering circuit is the fourth element of the main circuit. This circuit has two parts, the discriminator and the galvanometer or oscilloscope. Thus It has a double func­ tion, it discriminates the sign of displacement being measured - and then records the signal. 4? - A diagrammatic sketch of the static and dynamic circuits as prepared by H. R. Lissner and C. C. Perry, and used for a resistance wire electric strain gauge is presented in the Appendix. The circuit essentially consists of a simple Wheatstone bridge, the active and dummy gauges usually forming two sides of the bridge. To start with, the bridge is balanced under no load, or for dynamic testing, under static loading conditions. As the active gauge is further stressed, either due to static loading in a static circuit, or due to dynamic stresses in a dynamic cir­ cuit, it unbalances the formerly balanced Wheatstone bridge. The deviation from balanced condition, after being amplified, serves as a measure of mechanical strain in the specimen tested. Gauge factor, very frequently encountered in connection with bonded wire electric gauges, is simply a ratio of change of resistance to change of strain, and is dimensionless. Ex­ pressed by a formula is would be: AR G.F. = R E where G.F. refers to gauge factor, A R is the change in resistance, R is the total change, and E indicates the unit strain. According to F. G. Tatnall (28), three basic types of cir­ cuits are applicable in all types of strain gauge work. A - 44 diagram representing all three forms of the circuits is shown in Figure 5. The first one is for measuring bending, elimin­ ating both tension or compression. Applications of this type can be cited in shop gauges, comparators, and other instru­ ments replacing dial gauges. The second kind of circuit is the one for measuring axial components only by eliminating bending. This circuit is commonly used in determination of load on the work as in a press or power tool, in measuring fluid pressures, in commercial pressure cells, and in engine indicators. The last type of circuit is the one used for measuring torque or twist. This circuit measures both static torque and torsional vibrations. Electric strain gauges have diversified uses. Some of the more unusual and important applications are listed below. These gauges have been used in explosive impact tests, anal­ ysis of hortonsphere, underwater explosions, evaluation of residual and fatigue stresses, and in model studies in super­ sonic wind tunnel tests. In the aircraft Industry they are used for determining Impact loading of the airplane, repeated load Investigations in aircraft components, and In telemetering Impact forces in airplane drop-test. The gauges are applied in ship-building problems, structural evaluation of engine parts, in observing performance of large machinery operating conditions, and in determining vibratory stresses In turbo­ supercharger buckets. They are used in farm machinery as an aid in development and In design, and for determining power - 45 - IDAS FIG. A. MOMENT LOAD l R2 F1G*B« FORCE C AND D OH OPPOSITE SIDS I ■x ‘ I) FIG.C. TORSION Pig. 0. Three Basic Circuits of Wire Resistance Gauges. (29) - 46 and torque distribution under field conditions. As a means of measuring other physical properties, the gauges are used for precision determination of weights, as accelerometers, as velocity meters, as three component force recorders, and used as drawbar dynamometers as shown in Figure 6 . Among the u n ­ usual applications, strain gauges are used for determining mechanical behavior of the skull and its contents when sub­ jected to injuring blows. With so numerous advantages, these strain gauges also have some drawbacks. Exact location of the gauges is a very important factor, its determination sometimes becoming im­ practical. High temperatures or oily conditions can make these gauges defective. Centrifugal forces in rotating parts (where gauges are mounted), tend to break the lead wires away from the gauge, thus ruining the finer gauge wires. Instru­ mentation and careful analysis of the stresses calls for an experienced person with high skill in order to get satisfactory performance and accurate results. In most of the stress analysis work, strain gauges are mounted on rotating parts, and a satisfactory means to make electrical contact between the rotating elements and the sta­ tionary recording and control unit Is highly desirable. devices used for this purpose are called torquemeters. The Figure 7 shows a bonded wire gauge torquemeter designed by A. C. Ruge (26). This is essentially a brush and slip ring assembly where three brushes In parallel are used on each slip ring In Figure 6 . Strain gauge drawbar dynamometer. (i4) Figure 7. Bonded wire gauge torquemeter. - 49 - order to provide continuous contact even under heavy vibrations. However, due to the fact that at times the resistance between the rings and brushes is greater in magnitude than the actual variation in resistance of the strain gauges, this unit be­ comes inefficient and may cause severe error in recordings or readings of actual strains. Also high speeds and oil in the slip rings effect the performance. Another unit using electromagnetic principle for making between stationary instruments and rotating mechanisms is the magnetic-coupled torquemeter constructed by B. P. Langer and K. L. Wommack (2l), as shown in Figure 8. In principle, the torquemeter consists of a magnetic strain gauge where the por­ tion of magnetic circuit carrying the coils remains stationary, and the variable air gaps are mounted on the rotating shaft. The magnetic flux is transmitted from the stator to the rotor through radial air gaps. No slip ring3 and no electric coil3 (which may be damaged due to centrifugal forces) are required. On account of its calibration of the circuit and rather intri­ cate construction, its accuracy is effected, and construction becomes a costly item. A mercury bath collector as constructed by D. E. Burrough (4) has been used on some power and torque determinations. The critical electro-chemical nature of mercury being in contact with metal influences the properties and tends to vary the re­ sistance more than the resistance variation in the body of the gauge itself. The construction details, together with modified torquemeter as designed by the author are discussed in the ex­ perimental part of the thesis. - 50 - - 51 The strain gauge is a fine and tiny resistance element in which slight changes in length or cross-section result in re­ sistance variations of the Wheatstone bridge. The means of measuring and recording the strains, therefore, become essen­ tially a problem of determining these minute resistances. The more important pieces of equipment that go into the strain measuring circuits are power supply units, bridge cir­ cuits, amplifiers, oscillographs and galvanometers. Several strain recording sets have been manufactured, varying mainly in the number of measuring channels, capacity, and power supply units . An entire strain gauge control unit consists of balancing controls for strain gauge bridge, a zero adjuster, sensitivity controls, a vacuum-tube amplifier and an output circuit for coupling amplifier output to the oscillograph. In fact it in­ cludes all the electrical instruments between the strain gauge and the recording oscillograph. Several types of amplifiers can be used in the circuit de­ pending on the frequency requirements of strain measurement, and on the kind of electrical power input. A direct-coupled amplifier responds to both static and dynamic strains, whereas the capacitance-coupled amplifier will respond to dynamic strains only. But the direct-coupled amplifier Is not stable, and runs out of adjustment and balance. A capacitance-coupled amplifier together with a phase-sensitive demodulator or dis­ criminator is more commonly used. This combination eliminates - 52 inter-relationship between zero and sensitivity adjustments. The demodulator prevents the carrier frequency from reaching the galvanometer, but lets strain variations pass through. Also this system enables the current to flow through the gal­ vanometer in one direction for tension and in the opposite direction for compression, and galvanometer current will be zero for zero strain. To avoid drifts (caused by heater and plate voltages variation, and by slower variations in the emission of the cathode surfaces) in the vacuum-tube amplifier, negative feedback principle is used. This merely consists of balancing a part of output voltage against the input voltage. Negative feedback is essentially a resistance voltage divider operating backwards, and even though the gain of amplifier may vary widely, the entire gain with a proper negative feed­ back may change very little so as to be immeasurable. These strain gauge control units have resistance and capacitance balancing controls to permit convenient balancing of the strain gauge bridge. A ten-step attenuator is provided for accurate adjustment of sensitivity from zero to one hundred percent in 1C$ steps. The source of power comprises a 12-volt or 24-volt storage battery, or a llO-volt 60-cycle line, and furnishes accurate and regulated d-c power for the anodes of the vacuum tubes in the control unit and carrier power for the strain gauge cir­ cuits. Indicating and recording devices have a great bearing in their use with strain gauges. Proper selection of these - 55 instruments is necessary in order to assure satisfactory re­ sults. An oscillograph is a high speed recording instrument that records strain variations in a permanent form. The galvanometer and a small rotating mirror and the sensitive moving film are the essential recording elements. The mirror rotates through an angle proportional to galvanometer current and reflects a beam of light onto a moving chart of sensitized paper or film. Sometimes, a combination of galvanometers is used in a single oscillograph so as to record a number of strains simultaneously on the same chart. Following are the essential elements of an oscillograph: 1. Galvanometers with mirrors and moving charts. 2. Chart-drive mechanism and a light source and optical system. 3. Time-recording device. 4. A transmission to select suitable recording speed. 5. Viewing screen for the operator to read deflections. 6. A counting device to record each oscillogram. 7. A length-control device for the recording film. 8. Galvanometer circuit attenuators. 9. Automatic control on oscillograph lamp voltage. Oscillographs can be classified into the following groups 1. Cathode ray oscillograph. 2. Magnetic oscillograph. c. Piezoelectric or crystal oscillograph. - 54 - The first kind of oscillographs are not produced commer­ cially. They are mainly used for high frequencies recording which are too high for magnetic oscillographs. The common forms of magnetic oscillographs are the string type and the moving-coil type. The former is sensitive to frequencies ranging from zero to 8,000 cycles per second, and consists of a single straight conductor whose shadow is projected on a moving photographic film. Moving-coil type has a torsion- ally rotatable coil in a magnetic field with a small mirror reflecting beam of light on a moving film. Its frequency res ponse is from zero to 12,000 cycles per second. These oscill ographs have as many as 24 galvanometers and are multichannel instruments. An illustration of a general-purpose Economy Oscillograph is given in Figure 9 manufactured by the Hatha­ way Instrument Company (15)* an organization of high reputa­ tion for making electronic instruments for electric strain gauges and other devices. This oscillograph is multi-channel instrument having six to twenty-four elements. PURPOSE OF THE INVESTIGATION The science of machine design has been in the past based on theoretical evaluations and certain analytical techniques. With the advancement of the experimental procedures and per­ fection achieved in the application of these experimental methods to the design or redesigning of the machines, an ex­ tensive field of experimental machinery testing has been de­ veloped. In the case of farm machines, bulky and somewhat crude mechanisms, formerly designed on the basis of trial and error method, are being refined and modernized by means of the available experimental aids. The main object of this study was to apply one or several of the available experimental techniques in the evaluation of stresses either in the farm machines already designed or in an experimental machine representing a combination of various common mechanisms. Then an attempt was to be made to compare and correlate the experimental data with the theoretical determination of design analysis on the same machine. With this intent, a preliminary investigation was con­ ducted on a hay baler by stresscoating some of the parts with higher stress concentration determined previously by using the theoretical analysis. However, the circumstances did not favor the study on one specific machine, hence the In­ vestigation was left Incomplete. Later, the work was con­ ducted on the feasibility of such an investigation on several - 57 machines. Therefore, it was necessary either to use a farm machine having all the common mechanisms, or build an exper­ imental machine using a combination of the common mechanisms. Several farm machinery and equipment catalogues were sorted in order to obtain information on the various types of mechanisms employed in different kinds of tillage machines, planting, fertilizing, dusting and spraying equipment, har­ vesting and mowing machinery, and in tractors and stationary power units. A listing of the types of mechanisms revealed the fact that among the most common ones were the three kinds of drive mechanism, namely the belt drive, the gear drive and the chain drive, the reciprocating centre-crank mechanism as a piston connecting rod and crankshaft assembly of an engine, a plunger in a hay baler or a compressor unit, and the recip­ rocating side-crank mechanism such as in a mower, a harvesting machine or a combine. After obtaining this data, it was discovered that there was not any one farm machine as yet designed which had all the above-mentioned mechanisms represented. Therefore, an experimental unit was designed and constructed where an assem­ bly of almost all the above types of mechanisms was represented, and the entire unit was made flexible enough either to operate any one mechanism separately, or to employ testing and running of all different mechanisms at the same time. This study was primarily conducted for the evaluation of forces, loading patterns, torsional and vibratory stresses, traveling impacts, and bending, whipping and centrifugal stresses - 58 in the mechanisms commonly used in farm machines. For this purpose the electric wire resistance strain gauges were to be used and a similarity or comparison were to be drawn between the experimental and analytical procedures. Moreover, it was desired that such an investigation being fundamental in its nature, would assist in designing or redesigning the above mechanisms in any farm machine where the knowledge of opera­ tion and performance characteristics were already known. Due to the fact that the experimental machine was to con­ sist of diversified mechanisms, and no recording instruments » for field conditions were available, it was not practical to test the machine under actual field conditions. Therefore, all the experimental test work and analysis was conducted in the laboratory. Instrumentation of the Project A project involving work of an experimental nature would undoubtedly have some instrumentation in order to facilitate measurement and evaluation of certain desired quantities. The nature of this project being similar, this kind of experimen­ tation demanded instruments for measuring speed of rotating parts, mechanical and electrical loads of transmission and drive mechanisms, and the variation of electric resistance of the fine grid of the wire gauges. Besides, some type of arrange- • ment for the steadyresistance electric contact between rotating parts and the stationary recording instruments was necessary - 59 to transfer* electric signals from the gauges to the pen re­ corder. The Brush Analyzer The type of electronic instrument used to amplify the strain gauge signals and to record them in terms of calibrated strains was the Model BL 310 Brush Analyzer and Oscillograph ( 5 ). This instrument had a frequency range from zero to 120 cycles per second, and was equally applicable for both static and dynamic strain measurement. The type of recording con­ sisted of a magnetic pen motor with a recording pen, and chart speed adjustable to 5 » 25 and 125 mm/second. The wiring dia­ gram for the instrument is given in Figure 10. This clearly indicates the path of the electric signal after it is picked up from the Wheatstone bridge. The functions of the attenuator the discriminator, the oscillator and the amplifiers are the same as stated earlier in connection with the description of instruments for strain gauges in the review of literature. t The Mercury Torquemeter In order to bring the electric signals from the rotating units to the stationary Brush Analyzer, some kind of electric contact device with non-varying resistance was required. In looking through the types of such devices, called torquemeters, It was desirable from the economical and steady electric cont ductance standpoint to construct one based on somewhat similar - 6o - Attenuator Pen Motor A-c Amplifier Oscillator Fig. 10 T£Tscriminator. Wiring diagram Brush Analyzer Model BL 310 principle to that of Burrough's mercury bath collector ( 4) . This unit essentially consisted of a pool of mercury in a stationary Plexiglass housing with a metal ring at the bottom of the pool inside the housing. Passing through the housing was a tube connected to the rotating shaft and on this shaft was mounted a metal disk which served for a contact between the wires from the electric gauges and the mercury pool. Leads were taken out from the metal ring in the mercury pool to the Brush Analyzer. The metal used for the rings was brass and for the disks was copper, but the exposed surfaces Were nickle plated in order to prevent mercury reaction, since mercury was found to react with almost all metals except nickle and plat­ inum. Instead of soldering the wires on to the rotating metal disks, a mechanical connection was made by drilling a hole in the disk and putting the end of wire and riveting the wire to the disk. All the exposed parts of the rivets and the wires were also nickle plated. A thin plastic tubing mounted on the tube between the tube and the tube and the disks served as an insulator. To avoid any electrolysis due to impurities in mercury which could very easily vary the steady resistance of the unit, a drop or two of dilute nitric acid or dilute sul­ phuric acid were added. This stabilized the resistance and enabled procuring strain readings from the wire resistance variation of the gauge only. A self-explanatory drawing of the torquemeter is shown in Figure 11. In Figure 12, the torquemeter is shown mounted at the end of a shaft and used ■v Brass disk 2 " Diameter (nickle-plate A Ball Bearing 7 Brass rin 0 (nickle-plated) Scale Full o\ ro Figure 11 Detail Drawing of the Mercury Torquemeter - Figure 12. 63 - Mercury torquemeter mounted on the main shaft. A - 64 for strain readings of the rosette gauges on the pulley shown in the figure. The Stroboscope The nature of the experimental work demanded for more pre cise measurement of the magnitudes of various quantities. Knowing that the type of drive used would affect the precision desired, no mathematical computations were relied upon to de­ termine various speeds of several drives under varying or con­ stant loading conditions. For a higher precision and greater accuracy, the Strobotac was used. Strobotac was used as an electric timing device to measure rotational speeds. Low and high intensities of speeds could be measured by this Strobelight, although in this particular experiment only the low range was used. The accuracy of this instrument as stated by its manufactures was within + 1 %. The Simpson Meter Model 260 A combination of volt meter, ohm meter and ammeter was used during the experimental work. The ohm meter was used to make open check of the resistance gauges so as to determine whether or not there was any damage done to the gauges while mounting or during the operation of the machine. The steadi­ ness of the resistance in the torquemeter cells was also de­ termined by means of the ohm meter. The volt meter and the ammeter combination was used in measuring the output of the electric motor generator type dynamometer used for loading the gears. - 65 The Electric Dynamometer The power-take-off absorption dynamometer was used for loading the gears. It was necessary to have some kind of fairly uniform load and due to its accessibility and flex­ ibility, the electric motor generator combination dynamometer in the research laboratory was the only possibility that could assure comparatively uniform loading. The experimental machine was driven by a Co-op 4 E tractor, and on one end of the main shaft of the machine a universal Joint wa3 mounted to drive the electric dynamometer; the dynamometer was in turn hooked to an electric resistance load panel consisting of 24 individ­ ual heating elements. This enabled uniformity of loading and some variation in the amount of loading by hooking any number of heating elements desired for any specific run. Figure 13 shows the instruments used for this project. From left to right the instruments are the Brush Analyzer with pen recorder, top right the Strobotac and bottom right the combination unit of the ohm meter, ammeter and volt meter. Figure 15. Instruments used in the project. ^ a\ - 67 Experimental The experimental stress analysis machine constructed for the purpose of the investigation consisted of the following mechanisms all mounted together to form a compact unit and yet each of the mechanisms was independent of the other in its operation, or the entire unit was operated as an assembly: 1. The plunger mechanism consisting of a flywheel, crankshaft, a connecting rod, a plunger. a and a piston used as The chamber or cylinder part was sub­ stituted for by a circular pipe whose inside diameter was equal to the diameter of the plunger. A com­ pression spring was used to load the unit. 2. The mower assembly comprising a flywheel type crank, a steel pitman, and a cutter bar. No load was applied to this assembly, and all the analyses were based on no load conditions. 5. The V-belt drive consisting of pulleys driving the plunger mechanism or the mower assembly. 4. The spur gear drive. In this on the shaft connected to the unit the gear was mounted power-take-off of the tractor, and the pinion was keyed to the main shaft which was driving the electric dynamometer. Figures 14 and 15 show the right side and the rear right side views of the assembly. These pictures were during the testing of the plunger and the mower units; therefore, the torquemeter is shown mounted at the end of the main shaft Figure 14. Side view of the experimental machine. oo Figure 15. Rear right side view of the experimental machine instead of* the universal joint which was replaced in the gear tests for driving the electric dynamometer. Detail drawings of the assembly showing each unit separately are added in the Appendix. The machine was at times driven by an adjustable speed electric motor or by the tractor. The Analysis of the Centre-Crank Mechanism Theoretical analysis of the plunger mechanism was made on the flywheel, the crankshaft, and the connecting rod for the conditions under which the experimental testing was conducted. A further discussion on each of these elements is presented below. Flywheel. Three half inch gauges were mounted on the fly­ wheel, one of them was on the underside of the rim, and two were cemented on either side of one of the arms near the gauge on the rim. The variation of the load on the piston was accomplished by using a compression spring having a spring scale of 31 pounds per inch. This enabled the evaluation of stresses for three different loading conditions. In the first case no load was applied against the piston head and it was allowed to operate free. In the second instance, the compression spring was used, but the spring was not initially loaded. In the third series of the test run, the compression spring was initially loaded by placing an extra tube behind the spring inside the main tube. The intent of this test was to measure the total stresses in the rim and in the arms. On account of the fact that this - 71 particular flywheel was too stiff for the set-up, the bending stress signals of a greater magnitude either from the rim or the arms could not be obtained. However, it was observed that the stresses in the arms were much higher than in the rim. In the case of the arms it was apparent that the experimental stress due to sudden starting was as much as five times higher than the dynamic running stresses both due to the belt tension and the centrifugal forces. This value was higher than the theoretically calculated stress, which itself might have been off due to .the variation in magnitude of certain assemptions that were made. Moreover, the computed theoretical stress was for the point of maximum stress concentration, whereas, due to the flywheel curvature, the gauges could not be mounted directly on the theoretical point of maximum stress. The experimental stress in the flywheel rim was 4.7^ higher than the theoretical stress. The flywheel speed was varied from 52.5 rpm to 450 rpm in order to determine the mag­ nitude of the stress due to the centrifugal force. The nature of the set-up restricted speeds of a greater magnitude. Al­ though the values of the stresses in both the rim and the arms were not very high, a significant upward trend was noticeable. However, the increase did not quite follow the high increase in the magnitude obtained from the theoretical analysis. was not the primary intent to run the mechanism at higher speeds, for it was supposed to represent conditions for a plunger of a baler, or a low speed compressor. It - 72 One thing was very significant from the data on the two gauges mounted on the arms. In case of the gauge mounted a— head of the other in the direction of rotation, the belt ten­ sion seemed to add to the existing stresses thus giving a higher stress value than the other gauge recordings which had a somewhat cancellation effect between their compressive and tensile stresses acting at the same point. This was in accord­ ance with the theoretical analysis of the situation. Connecting Rod. Three gauges were mounted at different locations on the connecting rod. One 1/8" gauge was mounted directly above the centre line of the wrist pin and oriented in the direction of the travel of the piston. The second 1/2" gauge was mounted on the middle of the connecting rod between the centre lines of the wrist pin and the crankshaft. The third gauge was cemented directly above the centre line of the crankshaft. The last two gauges were oriented in the same direction as the first gauge. The intent of tests on the connecting rod was to determine the effects and relative magnitudes of repeated compressive and tensil stresses, whipping stresses due to inertia forces, and the vibrating stresses due to impact. Test readings were taken from all three gauges for no load, spring load, and the loaded spring conditions, and for a speed range of 52.5 rpm to 4^0 rpm. A comparison between the theoretical and experimental values of the total stress was made and it was found that the average stress values - 73 (averaged for the three gauges) were about 2-1/2 times higher than the calculated stresses from Bach's and Gordon's Formulas (27). The maximum stress for the same run was far greater in value than the theoretical stress. The stresses, however, in­ creased as the load was applied on the piston head from a no load to loaded spring condition. It was found that for the 1/8" gauge the stress for loaded spring condition was as high as 1200 psi in comparison to the theoretical stress of 541 psi. The stress distribution pattern was also determined from the experimental values, and it was found that the maximum total stress was nearer to the piston end of the connecting rod and decreased slightly from the wrist pin end to about half the length of the connecting rod, but decreased to almost 1/3 at a point directly above the crank pin centre. An effort to Isolate and evaluate the vibratory stresses did not prove successful. It could have been due to two rea­ sons, either the speed of 430 rpm was not high enough to cause any vibratory stress or that the recording instrument which had a maximum frequency range of about 100 cycles per second was not capable of picking up the higher frequency vibratory and travelling impact signals. According to the author's be­ lief, most probably the latter case was true. By studying the graphs from the charts for all the three gauges, it was apparent that for no load condition, the 1/8" gauge recorded maximum stress at an angle of about five degrees between the connecting rod front end and the horizontal. The - 74 - application or load increased this angle until the point of maximum stress was attained at around 15 degrees ahead of the dead centre for the loaded spring condition. For the 1/2" gauge on the mid—section of the connecting rod, it was ob­ served that the maximum stress point was reached ahead of the dead centre. No much variation was noticeable between the no load and the loaded conditions. The other l/2n gauge strain patterns were not sufficiently clear to conclude any results from their graphs. Crankshaft. A 1/8" gauge was mounted on the crankshaft fillet where the crank pin and the crank were jointed, and it was oriented along the centre line of the crank pin. Realizing the fact that most crankshaft failures occur due to repeated bending or reversed torsional stresses, the object of this part of the experiment was to determine experimentally and theoretically the total stress caused by the torsional and bending stresses in the crankshaft caused due to the forces acting against the piston, and due to the inertia forces. Although many approximate methods are available for eval­ uating the stresses theoretically, none of these methods seem to give a decent approximation for any general condition where the stresses in the crankshaft are to be measured. In the project work, it was not feasible to evaluate the torsional and bending stresses separately, but an attempt was made to obtain the total stress. A glance at the comparative magni­ tudes of the theoretical and experimental values presented in - 75 the Appendix distinctly reveals that the experimentally de­ termined stresses were far greater than the calculated values. The experimental chart revealed also that the compressive stresses were two to four times higher than the tensile stresses. Another interesting thing observed from the stress pattern of the graph was that the total stress did not change sharply from the compressive to the tensile stress, but the compressive stress decreased with one slope at first, then the slope changed around 75° of the connecting rod angle with the horizontal be­ fore a high point of tensile stress was reached. This fact in­ dicated that at the point of slope change, impact forces are prevalent, and these forces suddenly vary the load exerted by the connecting rod on the crank pin. An oscilloscope would have been desirable for evaluating the impact frequency. A chart showing the effect of load variation on crank­ shaft stresses is presented in Figure 16. The Analysis of the Side Crank Mechanism The mower assembly was rather similar to the distribution and types of stresses determined earlier in the plunger mechan­ ism. In this experiment, a steel pitman Instead of a wooden pitman was used so as to give a true picture of the stresses with possible dampening effect. The mower was used with no load due to the lack of feasibility of the loading operation in the laboratory. - 76 Fig. 16 G r a p h of e f f o c t s of load variation on c r a n k s h a f t stresses. - - 77 The stresses evaluated experimentally were mainly in various sections of the pitman and in the driving pulley for the mechanism. In this section only the pitman stresses are discussed and the stresses in the pulley are presented in the section of stresses in v-belt drives. Three gauges were mounted at three different locations on the pitman. All gauges used were 1/2 inch In size. One gauge was used directly on the fillet of the socket of the pin Join­ ing the pitman and the cutter bar. The second gauge was mounted at the mid-section of the pitman. The third one was mounted on the fillet directly under the socket of the crank pin. All three gauges were oriented In the direction of travel of the pitman. The unit was run from a speed of 175 r.p.m. to about 1020 r.p.m. The main purpose of this study was to eval­ uate whipping stresses, compressive or tensile stresses, and if possible, the vibratory stresses due to impact. The theoretical analysis was made for the whipping stress and the compressive or tensile stress due to the load. These two added together gave the total average stress in the pitman. The analysis of the experimental data yielded the total stress. The picture of recordings ranging from the minimum speed of 175 r.p.m. to higher speeds showed a considerable increase in the magnitude of the stress with the speed, indicating the effect of whipping stress becoming more pronounced as the speed was increased. A chart of the experimental strain curve for the 1/2 Inch gauge at the mid-section of the pitman is pre­ sented in Figure 17 t for a speed range of 175 r.p.m. to 615 Fig. 17 Strain recordings of inch, gauge at the pitman mid-section for various speeds. - 79 r.p.m., showing that an increase in speed of about 3.5 times resulted in an increase of about 200 percent in the magnitude of the total stress. Furthermore, the chart revealed the fact that the tensile stress at that particular point devel­ oped from about 150 psi to 1500 psi for a speed range of 175 r.p.m. to 615 r.p.m. The compressive stress for the same speed range increased from 1500 psi to almost 3000 psi. This experimental increase of the stress with an increase in the speed checked fairly well with the theoretical relationship obtained from Bach's formula (26) for whipping stresses. A similar trend was apparent in the case of the other two gauges, but the magnitudes of stresses were not quite as high. The stress pattern gave the information that the maxi­ mum stress was somewhere near the mid-section of the pitman and that the stresses at crank end were of a greater magnitude than the stresses at the cutter bar end of the pitman. It is certain that when the load is applied on the cutter bar, the stress pattern may not remain the same. Probably the cutter bar end of the pitman will then show higher stresses. It Is of question whether the stresses at the mid-section will still be the critical stresses in the design of the pitman. Again, comparing the values of the theoretical and experimental stresses it was apparent that the latter were of greater mag­ nitude . The vibratory stresses could not be evaluated experimentally, due to the inability of the instruments to pick up high fre­ quency signals. - 80 The Gear Drives. Gear drives were recognized as a common mode of power transmission in various farm machines. Spur gears, helical gears and bevel gears are very frequently used for transmitting greater load or for chaning the direction of motion of the transmitted load. Any machine from the tillage equipment to a combine will have at least some kind of gear drive. Noticing that gears were very common among the mechan­ isms used in farm machinery, a study on an experimental level was conducted in evaluating stresses and the stress patterns i in the gear teeth. For the purpose of the investigation, a pair of spur gears of a diametral pitch of 5 were used. The pinion was made of steel and had a pitch diameter of four inches. The gear was made of cast iron and with a pitch diameter of eight inches. Two l/l6 inch gauges were mounted on one particular tooth of the pinion and two more l/l6 inch gauges were mounted on the tooth of the gear mating with the tooth of the pinion with the gauges. The locations for mounting the gauges were chosen from the photo elastic tests on mating of spur gears conducted by Boor and Stitz (2). One gauge was mounted directly at the root of the tooth and the direction was oriented such that its centre line made an angle of 90° with the tooth profile. This was to approximate the stresses at the point of the tooth base where the stresses were supposed to be very great. Another gauge was mounted at the point of contact of the tooth and direction oriented approximately along the pitch diameter. - 81 An electric generator load was used for loading the gear and the pinion. The gear was used as the driver and the pinion was the driven one. The load applied was actually a panel of 24 electrical heating elements each of 660 watts and 115 volts. Some variation of the load was accomplished by hooking or un­ hooking the heating elements in the circuit. The maximum stress due to starting load was also sought. The analysis of the stresses both for the theoretical and experimental points of view were made, and the latter were found to be slightly higher. The stress values for one par­ ticular load and speed conditions mentioned in the Appendix were as much as 26.5 percent higher for the experimental anal­ ysis in comparison to the calculated value. Also, it was significant that the stress for the sudden starting was almost 1.5 times higher than the running stress. Moreover, a signal indicating a higher stress than the running stress was recorded when the generator started operating. The effect of the variable power demand of the generator was appar­ ent from the fluctuations of the strain curve. This could mean that the input and thus the output of the generator was rather unsteady, a factor which would not be too desirable. The V-belt Drives. Centrifugal forces and the forces due to net belt tension are usually responsible for the total stresses acting on the rim of a pulley. For the experimental and theoretical analysis of the stress, a rosette of l/l6 inch gauges was made on a point on the rim of the pulley. - 82 Later*, due to the damage done to two of the gauges in the rosette, these were replaced by 1/8 inch gauges. This in­ fluenced the approximate point concept to a certain extent by increasing the area of contact over which the gauges measured the stresses. A rosette was used on a six inches diameter v-belt pulley used for driving the mower mechanism. The idea was not only to evaluate experimentally the magnitudes of the total stresses, but also to determine approximately the direction in which the maximum stress was acting. The results obtained aided in meeting the above goal. The axis of maximum stress was along the perpendicular to the horizontal centre line of the pulley. The values obtained in the test consistently revealed that according to the orienta­ tion of the gauges, the gauge mounted at 45° with the horizon­ tal and to the left of the perpendicular gauge showed a stress of about one-half of the stress recorded by the perpendicular gauge. The gauge to the right of the perpendicular gauge and at 45° with the horizontal gave a recorded value of about a third of the stress in the perpendicular gauge. The effect of speed increase was also pronounced in all gauges on the development of higher stresses. The tests were made while using the pulley as a driver for the mower assembly. The observation of various forms of the strain graphs for the gauges was also interesting and in­ formative. The two gauges at 45° with the horizontal had apparently the same general stress pattern, whereas the per­ pendicular gauge had a pattern of its own. The strain re­ cording for the perpendicular gauge was of a sinusoidal nature showing smoothness of the stress variations. The other two gauge patterns distinctly revealed the temporary discontinuity and a sudden large stress showing the mower effects transmitted back to the pulley. The values obtained by calculation were much lower than the experimental values. between the two. Therefore, no comparison was drawn The lower theoretical values could be attri­ buted to either one or both of the following two reasons. Either the net belt tension was far greater than the one approx imated by the theoretical calculations, or the centrifugal forces were higher in magnitude than the ones determined theoretically. CONCLUSIONS From the results obtained in the various mechanisms, and from the discussion presented in the experimental part, the following conclusions can be derived: The theoretical stress analysis furnishes stress values only on an average basis which in many instances are not the maximum stresses prevailing in a machine part. A flywheel with a heavy rim has greater stresses in the arms than in the rim since the arms carry a greater share of the load. Sudden starting or stopping stresses in the arms may be about 2 to 4 times higher than the running dynamic stresses depending on the set-up. The connecting rod has its maximum stress concentration in the area near the wrist pin, and the value of the stress decreases as points are chosen nearer to the crankshaft. The effect of whipping stress gets pronounced at speeds even as low as 400 r.p.m. The stress pattern varies and suddenly increases with the application of load against the piston, showing a significant increase in the compressive stresses. The stresses in the crankshaft fillet at the Juncture of the crank web and the crank pin are higher in magnitude than the ones theoretically evaluated for bending or torsional - 85 effects combined.. These stress build up tremendously with an increase in load or speed. The pitman stresses for no load conditions are maximum near the mid-section of the pitman, with a greater stress value at the cutter bar end than at the crank end. The stress pattern in the pitman is controlled by the in­ ertia and impact forces and most probably by the loading char­ acteristics that cause variations or yield unsmooth curves for strains. The experimental values of the gear analysis are at some points and certain speeds as much as 26 percent higher than the theoretical values within the speed range of this experi­ ment. The power requirement of the generator was unsteady which constantly varied the stress pattern of the gear tooth. The stresses in the pulley rim are at a maximum at a point on the centre of the rim perpendicular to the centre line of rotation of the pulley. The stress pattern is very distinctly dictated by the type of mechanism the pulley is driving. In the test work the variation of force requirements of the mower influenced the stress patterns of the gauges on the pulley. SUGGESTIONS FOR FURTHER STUDY With the introduction of electric strain gauges, a prac­ tically new field of experimental stress analysis has come forward with bright prospects. It was the Intent of the author to Initiate such type of work in application to farm machinery. Immense opportunities exist for persons Interested in this field. Detail and thorough analysis of even one of the mechan­ isms used by the author could in Itself turn out to be an in­ terestingly extensive project requiring exhaustive research on various factors governing the stress pattern and magnitude and Influencing the operation of the mechanism. Further investigation could be continued in order to re­ fine the design of farm machines. It would be desirable not to restrict to strain gauges only, but to use other experi­ mental methods such as photoelasticity, optical methods and high speed photography, and stress coat. Furthermore, a fundamental research on the development of a versatile torquemeter for field applications would also be of very significant importance. APPENDIX Sample Calculations 1. Centre Crank Mechanism A. The Flywheel, a. Rim The stresses in the flywheel rim are made up of two eompanents, the stresses due to centrifugal forces and the stresses due to bending caused by the flywheel arm re­ straints. In terms of formulas, these stresses are: S = vs P &l TTT4- g (II) and s2 = i Ag D jtL 2 where v denotes the velocity in feet per second of on p a point the mean diameter of the flywheel. is thespecific weight of the flywheel inpounds per cubic feet. L represents the distance in feet along the arc of the mean periphery between flywheel arms. D represents the flywheel diameter t is the rim g = 52.2 ft.per (second)2 . thickness In inches, In Inches, - 88 The resultant stress In the rim is usually taken as 0.75 of S-^, plus 0.25 of the stress Sg. The specific data for the flywheel is asfollows: Wt. of the flywheel = 22 pounds. 8p. w t . of cast iron = 450 poundsper cubic ft. Mean diameter = 15 inches. Velocity of a point on mean diameter = 4.12 ft. per second to 55.5 ft. per second. No. of arms = 5 Arc length between arms = O .785 ft. Rim thickness = 1.575 inches. Prom the above data, for the maximum linear velocity of the flywheel: q _ si - (35.5 )2 450 144 x 52.2 si = 121 psi q _ 2(35.3 )2 (0.785 )2 2 - 52.2 x 15 x 1.375 S 2 = 2.3 psi The resultant stress S = 91 psi Prom the chart, the recorded strain was 8 micro inches per inch fi Modulus of Elasticity of cast iron = 12 x 10 psi The stress = 96 psi which is almost 4.7^ higher than the computed theo­ retical stress. - 89 b. Arms Stresses in flywheel arms consist of three kinds of stresses, namely the bending due to speed variation, bending due to the belt tension since the flywheel was used as a pulley, and the tensile stress due to the centrifugal force. Equations with the explanation of notations are given below. s 1 = T (D - a) 1 Z D (23) s 2 =