Presentation on theme: "ME Mechanical Engineering Design"— Presentation transcript:
1 ME 3180 - Mechanical Engineering Design Stresses in ThreadsLecture Notes
2 Stresses in ThreadsWhen nut engages thread, theoretically all threads in engagement should share loadIn actuality, due to inaccuracies in thread spacing, first pair of threads takes virtually all loadConservative approach for calculating bolt stresses is to assume worst case of one thread-pair taking entire loadOther extreme approach for calculating bolt stresses is to assume that all of engaged threads share load equallyBetter compromise is to assume that true stress lies between these two extremes, but most likely is closer to one thread-pair assumption.
3 Stresses in Threads Cont’d Power screws and fasteners for high-load applications are usually made of hardened high-strength steels.Power screw nuts may also be of hardened material for strength and wear resistance.Fastener nuts, on the other hand, are often made of soft materials, and thus, are typically weaker than screws (i.e. – regular fastener and nut).This promotes local yielding in nut threads when fastener is tightened, which can improve thread fit and promote load sharing between threads.Hardened nuts are used on hardened high-strength bolts.
4 Axial StressWhile power screw can see either tensile or compressive axial load, threaded fastener sees only axial tensile loadThis equation can be used to compute axial tensile stress in screw.Eq. 14-2For power screws loaded in compression, possibility of column buckling must be investigated. Use screw’s minor diameter to compute slenderness ratio.Slenderness ratio is factor that determines if column is short or long.For short column,where is radius of gyration.If it is short column, use its compressive yield strength as limitingstress (Page 200, Norton), if it is long column, then use buckling to perform failure analysis.
5 Shear StressPossible shear-failure mode involves stripping of threads:Out of nutOff of screwPossibility of either of these scenarios occurring depends on relative strengths of nut and screw materialsIf nut material is weaker, it may strip its threads at its major diameterIf screw is weaker, it may strip its threads at its minor diameterIf both materials are of equal strength, assembly may strip along pitch diameterIn order to calculate stresses, we must assume some degree of load sharing among the threads
6 Shear Stress Cont’dSince complete failure requires all threads to strip, all of threads can be considered to share load equallyThis is good approach as long as nut or screw (or both) is ductile, allowing each thread to yield as assembly begins to failIf both nut and screw are brittle (e.g., high-hardness steels or cast iron) and thread fit is poorOne can envision each thread taking entire load in turn until it fractures and passes job to the next thread.The reality is again somewhere between these extremes.
7 Shear Stress Cont’dStripping-shear area for each screw thread is area of cylinder of its minor diameter dr:wherep = thread pitchwi = factor that defines percentage of pitch occupied by metal at minordiameter (see Table 14-5)This area can be multiplied by number of threads in engagement based ondesigner’s judgment.
8 Shear Stress Cont’dFor nut stripping at its major diameter, shear area for one screw thread is:wo is the factor found in Table 14-5Shear stress for thread stripping is:Minimum Nut Length – If the nut is long enough, the load required to strip the threads will exceed the load needed to fail the screw in tension. The equations for both modes of failure can be combined and a minimum nut length computed for any particular screw size. For any UNS/ISO threads or Acme threads of d ≤ 1in, a nut length of at least 0.5d will have a strip strength in excess of the screw’s tensile strength. For larger diameter ACME threads, strip-strength of nut with length ≥ 0.6d will exceed the screw’s tensile strength. These figures are valid only if the screw and nut are of the same material, which is usually the case.Minimum Tapped-Hole Engagement – When a screw is threaded into a tapped hole rather than a nut, a longer thread engagement is needed. For same material combinations, a thread-engagement length at least equal to the nominal thread diameter d is recommended. For a steel screw in cast iron, brass or bronze, use 1.5d. For steel screws in aluminum, use 2d of minimum thread-engagement length.
9 Torsional Stress Torsional stress will develop when: Nut is tightened on screwTorque is transmitted through power screwTorque that twists screw is dependent on friction at screw-nut interfaceIf screw and nut are well lubricated, less of applied torque is transmitted to screw, and more is absorbed between nut and clamped surfaceIf nut is rusted to screw, all applied torque will twist screw, which is why rusty bolts usually shear even when you attempt to loosen nutFor power screw, if thrust collar has low friction, all applied torque at nut will create torsional stress in screw (since little torque is taken to ground through low-friction collar).In order to accommodate worst case of high thread friction, use total applied torque in equation for torsional stress in round section (page 183, Norton)for this calculation: dr = minor diameter
10 Types of Screws/Fasteners Fasteners can be classified in different ways: by their intended use, by thread type, by head style, and by their strength.These fasteners are available in variety of materials including steel, stainless steel, aluminum, brass, bronze, and plastics.Classification by Intended UseBolts and Machine screws:Same fastener may take on different name for particular application.Bolt is fastener with head and straight threaded shank intended to be used with nut to clamp assembly together. See Fig 14-10aHowever, same fastener is called machine screw or cap screw when it is threaded into tapped hole rather than used with nut. See Fig bStuds:Headless fastener, threaded on both ends and intended to be semi-permanently threaded into one-half of assembly. See Fig c
11 FIGURE 14-10Bolt and Nut, Machine Screw and Stud
12 Types of Screws/Fasteners Classification by Thread TypeAll fasteners intended to make their own hole or make their own threads are called tapping screws, as in self-tapping, thread-forming, thread cutting, and self-drilling screws. See FigThese are used in sheet metal or plasticClassification by Head StyleSlotted Screw:Many different types of head styles are made, including: straight-slot, cross-slot (Phillips), hexagonal, hexagonal socket and others. Head shape can be round, flat (recessed), filister, pan,etc. See FigSocket-Head Cap Screw:Typically made of high-strength, hardened steel, stainless steel or other metals, and are used extensively in machinery. See Fig
15 FIGURE 14-13Various Styles of Socket-Head Cap ScrewsCourtesy of Cordova Bolt Inc., Buena Park, Calif.
16 Nuts and WashersNuts: Please read up on nuts on pp 897 Norton. See Fig , & Fig on next slideWashers:Plain washer is doughnut -shaped part that serves to increase area of contact between bolt head or nut and clamped part. See Fig. 10.Hardened -steel washers are used where bolt compression load on clamped part needs to be distributed over larger area than bolt head or nut providesAny plain washer also prevents marring of part surface by nut when it is tightenedSofter washer will yield in bending rather than effectively distribute load
17 Various Styles of Standard Nuts FIGURE 14-14Various Styles of Standard NutsCourtesy of Cordova Bolt Inc.,Buena Park, Calif., 90621
18 Nuts and Fasteners Cont’d Lock Washers:Help prevent spontaneous loosening of standard nuts (as opposed to lock nuts)Can be used under nut of bolt or under head of machine screw. See FigSEMS:Are combinations of nuts and captive lock washers that remain with nutTheir main advantage is to ensure that lock washer will not be left out at assembly or reassembly. See Fig
19 FIGURE 14-16 Types of Lock Washers Courtesy of Cordova Bolt Inc., Buena Park, Calif., 90621
20 Bolts and Fasteners Strengths of Standard Bolts and Machine Screws Bolts and screws are selected based on their proof strength Sp.Proof strength is quotient of proof load and tensile-stress areaProof Load Fp is maximum load (force) that bolt can withstand without acquiring permanent set.Preloaded Fastener in TensionPrimary application of bolts and nuts is to clamp parts together, such that applied loads put bolt(s) in tension. See FigJoints are preloaded by tightening bolts with sufficient torques to create tensile loads that approach their proof strengths.
21 Fasteners Cont’dFor statically loaded assemblies, preload that generates bolt stress as high as 90% of proof strength is sometimes used.For dynamically loaded assemblies (fatigue loading) preload that generates bolt stress as high as 75% or more of proof strengths is commonly used.If bolts are suitably sized for applied loads, these high preloads increase reliability of the bolts.Reasons for this are subtle and require an understanding of how elasticities of bolts and clamped members interact when bolt is tightened and when external load is later applied.Clamped members have spring constant .Bolt, being elastic, will stretch when tightened.
22 Spring Constants of Bolt Fig shows bolt clamping cylinder of known cross section and length.We want to examine loads, deflections, and stresses in both bolt and cylinder under preload and after an external load is applied.To examine above parameters, we must determine spring constants of bolt and members.
23 Spring Constants of Bolt For bolt of diameter d and axially loaded thread length lt within its clamped zone of length l as shown in Fig , spring constant is14.11awhere:Ab is total cross-sectional area and At is tensile stressed area of bolt, andls is length of unthreaded shank.
24 Spring Constants of Bolt Cont’d Table 8.7 (Shigley)Bolts shorter than standard thread lengths are threaded as close to head as possible
26 Determining Joint Stiffness Factor Cont’d Fig shows results of finite element analysis (FEA) study of stress distribution in two-part joint-sandwich clamped together with single, preloaded bolt.Stress distribution around bolt resembles truncated-cone (or cone-frusta) barrel shape, as shown in Fig a.
27 FIGURE 17.19Lines of equal compressive stress in joint. Bolt loadedto 100 kip. (Reprinted from , courtesy Marcel DekkerInc.)
28 Spring Constants of Members (Cylindrical Model) For cylindrical material geometry shown in Fig (ignoring flanges), material spring constant becomes:14.11bwhere:Am are effective areas of clamped materials and Deff are effective diameterof those areas14.11cIf both clamped materials are same14.11dIf Am can be defined as solid cylinder with effective diameter Deff equation 14.11d becomes
29 External Load on Bolted Connection Let us consider what happens when external tensile load P is applied to boltedconnection in FigAssume clamping force which we call preload Fi, has been correctly appliedby tightening nut before P is applied.Fi = preloadP = external tensile loadPb = portion of P taken by boltPm = portion of P taken by membersFb = Pb + Fi = resultant bolt loadFm = Fi - Pm = resultant load on members Fm < 0
30 External Load on Bolted Connection Cont’d These results are valid as long as some clamping load remains in the members.P = Pb + Pm aThe load P causes connection to stretch, or elongate.14.13b14.13cPb = CP, whereC is called joint’s stiffness constant or joint constant.C is typically less than 1, and if Kb is small compared to Km, C will be small fraction. This confirms that bolt will see only portion of the applied load P.
31 External Load on Bolted Connection Cont’d Pm 0.8P. Also members can take even greater percentage of P, if grip islonger. See Table 8.12 (Shigley)14.13d14.14a14.14bLoad Po required to separate the joint can be found from equation 14.14a bysetting Fm = 0.14.14cSafety factor (or load factor) guarding against joint separation is14.14d
33 External Load on Bolted Connection Cont’d Tensile stress in bolt can be found by dividing Fb = CP + Fi by At.section 8.9 in ShigleyLimiting value of b is the proof strength Sp. Thus with introduction of loadfactor, above equation becomes:Any value of load factor (factor of safety), n 1, ensures thatb SpThis implies that bolt will not fail.
34 External Load on Bolted Connection Cont’d From ShigleyFp = AtSpFor other materials not in Tables 14.6 and 14.7, use Sp = 0.85SyWhere Sy is yield strength of that material.
42 Joints-Member Stiffness (Cone Frusta Model) Both stiffness of members and fasteners must be known in order to learn what happens when assembled connection is subjected to external tensile loading.More than two members could be included in grip of fastener. All together these act like compressive springs in series, and hence total spring rate of members is(Equ.8-18 Shigley)If one of members is soft gasket, its stiffness relative to other members is usually so small that for all practical purposes others can be neglected and only gasket stiffness is used.
43 Joints-Member Stiffness (cont.) Figure 8-15 illustrates general cone geometry using half-apex angle α. Angle α = 45° has been used, but Little reports that this overestimates clamping stiffness. In this book we shall use α = 30° except in cases in which material is insufficient to allow frusta to exit.3Thus spring rate or stiffness of this frustum is(8-19)
44 Joints-Member Stiffness (cont.) With α = 30°, this becomes(8-20)Equations (8-20), or (8-19), must be solved separately for each frustum in the joint. Then individual stiffnesses are assembled to obtainusing Eq.(8-18).If members of joint have same Young’s modulus E with symmetrical frusta back to back, then they act as two identical springs in series. From Eq.(8-18) we learn that Using grip as l=2t and as diameter of washer face, we find spring rate of members to be(8-21)
45 Joints-Member Stiffness (cont.) Diameter of washer face is about 50 percent greater than fastener diameter for standard hexagon-head bolts and cap screws. Thus we can simplify Eq.(8-21) by letting If we also use α = 30°, the Eq.(8-21) can be written as(8-22)