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Failure Analysis， Dimensional Determination And Analysis， Applications Of Cams INTRODUCTION It is absolutely essential that a design engineer know how and why parts fail so that reliable machines t hat require minimum maintenance can be designed． Sometimes a failure can be serious， such as when a tire blows out on an automobile traveling at high speed． On the other hand， a failure may be no more t han a nuisance． An example is the loosening of the radiator hose in an automobile cooling system． The consequence of this latter failure is usually the loss of some radiator coolant， a condition that is readily detected and corrected． The type of load a part absorbs is just as significant as the magnitude． Generally speaking， dynamic loa ds with direction reversals cause greater difficulty than static loads， and therefore， fatigue strength must be considered． Another concern is whether the material is ductile or brittle． For example， brittle material s are considered to be unacceptable where fatigue is involved． Many people mistakingly interpret the word failure to mean the actual breakage of a part． However， a d esign engineer must consider a broader understanding of what appreciable deformation occurs． A ductile material， however will deform a large amount prior to rupture． Excessive deformation， without fracture， may cause a machine to fail because the deformed part interferes with a moving second part． Therefore， a part fails(even if it has not physically broken)whenever it no longer fulfills its required function． Somet imes failure may be due to abnormal friction or vibration between two mating parts． Failure also may be due to a phenomenon called creep， which is the plastic flow of a material under load at elevated tempe ratures． In addition， the actual shape of a part may be responsible for failure． For example， stress conc entrations due to sudden changes in contour must be taken into account． Evaluation of stress consideratio ns is especially important when there are dynamic loads with direction reversals and the material is not very ductile． In general， the design engineer must consider all possible modes of failure， which include the following． —— Stress —— Deformation —— Wear —— Corrosion —— Vibration —— Environmental damage —— Loosening of fastening devices The part sizes and shapes selected also must take into account many dimensional factors that produce ext ernal load effects， such as geometric discontinuities， residual stresses due to forming of desired contours， and the application of interference fit joints． Cams are among the most versatile mechanisms available． A cam is a simple two-member device． The i nput member is the cam itself， while the output member is called the follower． Through the use of cams， a simple input motion can be modified into almost any conceivable output motion that is desired． Some of the common applications of cams are —— Camshaft and distributor shaft of automotive engine —— Production machine tools —— Automatic record players —— Printing machines —— Automatic washing machines —— Automatic dishwashers The contour of high-speed cams (cam speed in excess of 1000 rpm) must be determined mathematicall y． However， the vast majority of cams operate at low speeds(less than 500 rpm) or medium-speed cams can be determined graphically using a large-scale layout． In general， the greater the cam speed and outp ut load， the greater must be the precision with which the cam contour is machined． DESIGN PROPERTIES OF MATERIALS The following design properties of materials are defined as they relate to the tensile test． Figure 2.7 Static Strength． The strength of a part is the maximum stress that the part can sustain without losing i ts ability to perform its required function． Thus the static strength may be considered to be approximatel y equal to the proportional limit， since no plastic deformation takes place and no damage theoretically is done to the material． Stiffness． Stiffness is the deformation-resisting property of a material． The slope of the modulus line an d， hence， the modulus of elasticity are measures of the stiffness of a material． Resilience． Resilience is the property of a material that permits it to absorb energy without permanent d eformation． The amount of energy absorbed is represented by the area underneath the stress-strain diagra m within the elastic region． Toughness． Resilience and toughness are similar properties． However， toughness is the ability to absorb energy without rupture． Thus toughness is represented by the total area underneath the stress-strain diagr am， as depicted in Figure 2． 8b． Obviously， the toughness and resilience of brittle materials are very l ow and are approximately equal． Brittleness． A brittle material is one that ruptures before any appreciable plastic deformation takes plac e． Brittle materials are generally considered undesirable for machine components because they are unable to yield locally at locations of high stress because of geometric stress raisers such as shoulders， holes， n otches， or keyways． Ductility． A ductility material exhibits a large amount of plastic deformation prior to rupture． Ductility is measured by the percent of area and percent elongation of a part loaded to rupture． A 5%elongation a t rupture is considered to be the dividing line between ductile and brittle materials． Malleability． Malleability is essentially a measure of the compressive ductility of a material and， as suc h， is an important characteristic of metals that are to be rolled into sheets． Figure 2.8 Hardness． The hardness of a material is its ability to resist indentation or scratching． Generally speakin g， the harder a material， the more brittle it is and， hence， the less resilient． Also， the ultimate strength of a material is roughly proportional to its hardness． Machinability． Machinability is a measure of the relative ease with which a material can be machined． I n general， the harder the material， the more difficult it is to machine． COMPRESSION AND SHEAR STATIC STRENGTH In addition to the tensile tests， there are other types of static load testing that provide valuable informati on． Compression Testing． Most ductile materials have approximately the same properties in compression as in tension． The ultimate strength， however， can not be evaluated for compression． As a ductile specime n flows plastically in compression， the material bulges out， but there is no physical rupture as is the cas e in tension． Therefore， a ductile material fails in compression as a result of deformation， not stress． Shear Testing． Shafts， bolts， rivets， and welds are located in such a way that shear stresses are produ ced． A plot of the tensile test． The ultimate shearing strength is defined as the stress at which failure oc curs． The ultimate strength in shear， however， does not equal the ultimate strength in tension． For exam ple， in the case of steel， the ultimate shear strength is approximately 75% of the ultimate strength in ten sion． This difference must be taken into account when shear stresses are encountered in machine compon ents． DYNAMIC LOADS An applied force that does not vary in any manner is called a static or steady load． It is also common practice to consider applied forces that seldom vary to be static loads． The force that is gradually applied during a tensile test is therefore a static load． On the other hand， forces that vary frequently in magnitude and direction are called dynamic loads． Dyn amic loads can be subdivided to the following three categories． Varying Load． With varying loads， the magnitude changes， but the direction does not． For example， t he load may produce high and low tensile stresses but no compressive stresses． Reversing Load． In this case， both the magnitude and direction change． These load reversals produce a lternately varying tensile and compressive stresses that are commonly referred to as stress reversals． Shock Load． This type of load is due to impact． One example is an elevator dropping on a nest of sp rings at the bottom of a chute． The resulting maximum spring force can be many times greater than the weight of the elevator， The same type of shock load occurs in automobile springs when a tire hits a bu mp or hole in the road． FATIGUE FAILURE-THE ENDURANCE LIMIT DIAGRAM The test specimen in Figure 2.10a．， after a given number of stress reversals will experience a crack at the outer surface where the stress is greatest． The initial crack starts where the stress exceeds the strengt h of the grain on which it acts． This is usually where there is a small surface defect， such as a materia l flaw or a tiny scratch． As the number of cycles increases， the initial crack begins to propagate into a continuous series of cracks all around the periphery of the shaft． The conception of the initial crack is it self a stress concentration that accelerates the crack propagation phenomenon． Once the entire periphery b ecomes cracked， the cracks start to move toward the center of the shaft． Finally， when the remaining so lid inner area becomes small enough， the stress exceeds the ultimate strength and the shaft suddenly brea ks． Inspection of the break reveals a very interesting pattern， as shown in Figure 2.13． The outer annula r area is relatively smooth because mating cracked surfaces had rubbed against each other． However， the center portion is rough， indicating a sudden rupture similar to that experienced with the fracture of brittle materials． This brings out an interesting fact． When actual machine parts fail as a result of static loads， they norma lly deform appreciably because of the ductility of the material． Figure 2.13 Thus many static failures can be avoided by making frequent visual observations and replacing all defor med parts． However， fatigue failures give to warning． Fatigue fail mated that over 90% of broken autom obile parts have failed through fatigue． The fatigue strength of a material is its ability to resist the propagation of cracks under stress reversal s． Endurance limit is a parameter used to measure the fatigue strength of a material． By definition， the endurance limit is the stress value below which an infinite number of cycles will not cause failure． Let us return our attention to the fatigue testing machine in Figure 2.9． The test is run as follows： A s mall weight is inserted and the motor is turned on． At failure of the test specimen， the counter registers the number of cycles N， and the corresponding maximum bending stress is calculated from Equation 2. 5． The broken specimen is then replaced by an identical one， and an additional weight is inserted to inc rease the load． A new value of stress is calculated， and the procedure is repeated until failure requires o nly one complete cycle． A plot is then made of stress versus number of cycles to failure． Figure 2.14a shows the plot， which is called the endurance limit or S-N curve． Since it would take forever to achieve an infinite number of cycles， 1 million cycles is used as a reference． Hence the endurance limit can be found from Figure 2.14a by noting that it is the stress level below which the material can sustain 1 mil lion cycles without failure． The relationship depicted in Figure 2.14 is typical for steel， because the curve becomes horizontal as N a pproaches a very large number． Thus the endurance limit equals the stress level where the curve approac hes a horizontal tangent． Owing to the large number of cycles involved， N is usually plotted on a logari thmic scale， as shown in Figure 2.14b． When this is done， the endurance limit value can be readily det ected by the horizontal straight line． For steel， the endurance limit equals approximately 50% of the ulti mate strength． However， if the surface finish is not of polished equality， the value of the endurance limi t will be lower． For example， for steel parts with a machined surface finish of 63 microinches ( μin． )， the percentage drops to about 40%． For rough surfaces (300μin． or greater)， the percentage may be as l ow as 25%． The most common type of fatigue is that due to bending． The next most frequent is torsion failure， whe reas fatigue due to axial loads occurs very seldom． Spring materials are usually tested by applying variab le shear stresses that alternate from zero to a maximum value， simulating the actual stress patterns． In the case of some nonferrous metals， the fatigue curve does not level off as the number of cycles bec omes very large． This continuing toward zero stress means that a large number of stress reversals will ca use failure regardless of how small the value of stress is． Such a material is said to have no endurance l imit． For most nonferrous metals having an endurance limit， the value is about 25% of the ultimate stre ngth． EFFECTS OF TEMPERATURE ON YIELD STRENGTH AND MODULUS OF ELASTICITY Generally speaking， when stating that a material possesses specified values of properties such as modulus of elasticity and yield strength， it is implied that these values exist at room temperature． At low or elev ated temperatures， the properties of materials may be drastically different． For example， many metals are more brittle at low temperatures． In addition， the modulus of elasticity and yield strength deteriorate as the temperature increases． Figure 2.23 shows that the yield strength for mild steel is reduced by about 7 0% in going from room temperature to 1000oF． Figure 2.24 shows the reduction in the modulus of elasticity E for mild steel as the temperature increase s． As can be seen from the graph， a 30% reduction in modulus of elasticity occurs in going from room temperature to 1000oF． In this figure， we also can see that a part loaded below the proportional limit at room temperature can be permanently deformed under the same load at elevated temperatures． Figure 2.24 CREEP: A PLASTIC PHENOMENON Temperature effects bring us to a phenomenon called creep， which is the increasing plastic deformation o f a part under constant load as a function of time． Creep also occurs at room temperature， but the proce ss is so slow that it rarely becomes significant during the expected life of the temperature is raised to 3 00oC or more， the increasing plastic deformation can become significant within a relatively short period o f time． The creep strength of a material is its ability to resist creep， and creep strength data can be obt ained by conducting long-time creep tests simulating actual part operating conditions． During the test， the plastic strain is monitored for given material at specified temperatures． Since creep is a plastic deformation phenomenon， the dimensions of a part experiencing creep are perman ently altered． Thus， if a part operates with tight clearances， the design engineer must accurately predict t he amount of creep that will occur during the life of the machine． Otherwise， problems such binding or interference can occur． Creep also can be a problem in the case where bolts are used to clamp tow parts together at elevated te mperatures． The bolts， under tension， will creep as a function of time． Since the deformation is plastic， loss of clamping force will result in an undesirable loosening of the bolted joint． The extent of this parti cular phenomenon， called relaxation， can be determined by running appropriate creep strength tests． Figure 2.25 shows typical creep curves for three samples of a mild steel part under a constant tensile loa d． Notice that for the high-temperature case the creep tends to accelerate until the part fails． The time li ne in the graph (the x-axis) may represent a period of 10 years， the anticipated life of the product． Figure 2.25 SUMMARY The machine designer must understand the purpose of the static tensile strength test． This test determines a number of mechanical properties of metals that are used in design equations． Such terms as modulus o f elasticity， proportional limit， yield strength， ultimate strength， resilience， and ductility define properties that can be determined from the tensile test． Dynamic loads are those which vary in magnitude and direction and may require an investigation of the machine part’s resistance to failure． Stress reversals may require that the allowable design stress be based on the endurance limit of the material rather than on the yield strength or ultimate strength． Stress concentration occurs at locations where a machine part changes size， such as a hole in a flat plate or a sudden change in width of a flat plate or a groove or fillet on a circular shaft． Note that for the case of a hole in a flat or bar， the value of the maximum stress becomes much larger in relation to the average stress as the size of the hole decreases． Methods of reducing the effect of stress concentration us ually involve making the shape change more gradual． Machine parts are designed to operate at some allowable stress below the yield strength or ultimate stren gth． This approach is used to take care of such unknown factors as material property variations and resid ual stresses produced during manufacture and the fact that the equations used may be approximate rather that exact． The factor of safety is applied to the yield strength or the ultimate strength to determine the allowable stress． Temperature can affect the mechanical properties of metals． Increases in temperature may cause a metal t o expand and creep and may reduce its yield strength and its modulus of elasticity． If most metals are n ot allowed to expand or contract with a change in temperature， then stresses are set up that may be add ed to the stresses from the load． This phenomenon is useful in assembling parts by means of interference fits． A hub or ring has an inside diameter slightly smaller than the mating shaft or post． The hub is th en heated so that it expands enough to slip over the shaft． When it cools， it exerts a pressure on the sh aft resulting in a strong frictional force that prevents loosening． TYPES OF CAM CONFIGURATIONS Plate Cams． This type of cam is the most popular type because it is easy to design and manufacture． F igure 6． 1 shows a plate cam． Notice that the follower moves perpendicular to the axis of rotation of th e camshaft． All cams operate on the principle that no two objects can occupy the same space at the sam e time． Thus， as the cam rotates ( in this case， counterclockwise )， the follower must either move upwa rd or bind inside the guide． We will focus our attention on the prevention of binding and attainment of t he desired output follower motion． The spring is required to maintain contact between the roller of the f ollower and the cam contour when the follower is moving downward． The roller is used to reduce frictio n and hence wear at the contact surface． For each revolution of the cam， the follower moves through t wo strokes-bottom dead center to top dead center (BDC to TDC) and TDC to BDC． Figure 6.2 illustrates a plate cam with a pointed follower． Complex motions can be produced with this t ype of follower because the point can follow precisely any sudden changes in cam contour． However， th is design is limited to applications in which the loads are very light； otherwise the contact point of both members will wear prematurely， with subsequent failure． Two additional variations of the plate cam are the pivoted follower and the offset sliding follower， which are illustrated in Figure 6.3． A pivoted follower is used when rotary output motion is desired． Referring to the offset follower， note that the amount of offset used depends on such parameters as pressure angl e and cam profile flatness， which will be covered later． A follower that has no offset is called an in-lin e follower． Figure 6.3 Translation Cams． Figure 6.4 depicts a translation cam． The follower slides up and down as the cam tr anslates motion in the horizontal direction． Note that a pivoted follower can be