Screws, Fasteners, and the Design of Nonpermanent Joints

Chapter Outline 8-1 Thread Standards and Definitions 8-2 The Mechanics of Power Screws 8-3 Strength Constraints 8-4 Joints-Fasteners Stiffness 8-5 Joints-Member Stiffness 8-6 Bolt Strength 8-7 Tension Joints-The External Load 8-8 Relating Bolt Torque to Bolt Tension 8-9 Statically Loaded Tension Joint with Preload 8-10 Gasketed Joints 8-11 Fatigue Loading of Tension Joints 8-12 Shear Joints 8-13 Setscrews 8-14 Keys and Pins 8-15 Stochastic Considerations

Announcements HW #5 Ch 18, on WebCT Due Date for HW #5 is Mon. DEC. 31, 2007 Quiz on Ch. 18, Mon. DEC. 31, 2007

LECTURE 33 8-1 Thread Standards and Definitions

Introduction The fundamental operation in manufacture is the creation of shape - this includes assembly, where a number of components are fastened or joined together either permanently by welding (Ch9) for example or detachably (nonpermanent) by screws, nuts and bolts and so on. Since there is such a variety of shapes in engineering to be assembled, it is hardly surprising that there is more variety in demountable fasteners than in any other machine element. Fasteners based upon screw threads are the most common, so it is important that their performance is understood, and the limitations of the fastened assemblies appreciated.

Introduction There are two distinct uses for screw threads and they usually demand different behavior from the threads : a   power screw such as a lathe leadscrew or the screw in a car lifting jack which transforms rotary motion into substantial linear motion (or vice versa in certain applications), and

Fasteners a   Threaded Fastener similar to a nut and bolt which joins a number of components together again by transforming rotary motion into linear motion, though in this case the translation is small.

Thread Profiles (c) Thread profiles. a) Square (b) ACME; (c) UN, ISO

Thread Profile Parameters Figure 8-1 Terminology of screw threads. Sharp Vee Threads shown for clarity; the crests and roots are actually flattened or rounded during the forming operation Lead=L=n p

Threads (a) Single (STANDARD)-, (b) double-, and (c) triple threaded screws. Text Reference: Figure 15.2, page 667

Thread Systems A thread 'system' is a set of basic thread proportions which is scaled to different screw sizes to define the thread geometry. Whitworth, Sellers, British Standard Pipe (BSP) are just three of the many systems which proliferated before the adoption of the ISO Metric thread system. The American National (Unified) Thread standards is used mainly in the US. Square and ACME

Thread geometry The basic profile of ISO Metric threads is built up from contiguous equiangular triangles of height  H disposed symmetrically about a pitch line which becomes the   pitch cylinder of diameter   d2 when the profile is rotated about the axis to form the thread. The distance between adjacent triangles - the pitch - is   p = 2 H /√3. The tips of the triangles are truncated by h/8 to form the major diameter ( size ) d of the thread, and the bases are truncated by h/4 to form the minor diameter  d1 . It follows that d1 =  d - 5 h/4 = d - 1.08 p. This leads to the rule of thumb for suitable tapping size

Thread Profile For Metric System (M, MJ) major H= 0.5(3)1/2 p pitch US N= # threads/in minor a ISO 68= a American National (Unified) thread standard= 60°

Tensile stress area At =p/4(dm+dr)/2 (see footnote T.8.1) Thread Standards ISO Metric thread system: Table 8-1 Major diameter (mm), 2a= 60° Standard thread is RH Specifications: e.g.: M12x1.75 or M = Basic Metric, J = round root; 12 = nominal major diameter (mm); 1.75 = pitch (mm) Tensile stress area At =p/4(dm+dr)/2 (see footnote T.8.1) MJ12x1.75

Thread Standards The American National (Unified) Thread standards is used mainly in the US: Table-8-2 (Size designation) use d UN=regular thread, UNR=round root (use root radius) Specifications: 5/8”-18 UN, UNC, UNF UNR, UNRC, UNRF 5/8”=d 18 = N (thread size) UN = Unified, F=fine, C=Coarse, R =Round Root

Thread Standards Square (a) and The ACME Threads (b)-used mainly in power screws Table 8.3 gives preferred pitches for ACME threads

Power screw thread forms. [Note: All threads shown are external (i. e Power screw thread forms. [Note: All threads shown are external (i.e., on the screw, not on the nut); dm is the mean diameter of the thread contact and is approximately equal to (d + dr)/2.]

ACME Thread Profile Figure 15.5 Details of ACME thread profile. (All dimensions are in inches.) Text Reference: Figure 15.5, page 670

ACME Thread Properties N Crest diameters, threads per inch, and stresses for Acme thread.

Mechanics of Power Screws A power screw is a device that is common to tools or machinery that are used to change angular motion into translation. It is also capable of developing a large amount of mechanical advantage. Familiar applications include clamps or vises, presses, lathes lead screws, and jacks. The joyce warm-gear screw jack

Mechanics of Power Screws Weight supported by three screw jacks. In each screw jack, only the shaded member rotates.

Mechanics of Power Screws Example of catalogue: http://www.roton.com/web/quick.power_screws.jsp

Vehicle Screw Jack

Power Screw with collar Different types of collars

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Chapter Outline 8-1 Thread Standards and Definitions 8-2 The Mechanics of Power Screws 8-3 Strength Constraints 8-4 Joints-Fasteners Stiffness 8-5 Joints-Member Stiffness 8-6 Bolt Strength 8-7 Tension Joints-The External Load 8-8 Relating Bolt Torque to Bolt Tension 8-9 Statically Loaded Tension Joint with Preload 8-10 Gasketed Joints 8-11 Fatigue Loading of Tension Joints 8-12 Shear Joints 8-13 Setscrews 8-14 Keys and Pins 8-15 Stochastic Considerations CH-8 LEC 35 Slide 32

LECTURE 35 8-3 Strength Constraints 8-4 Joints-Fasteners Stiffness 8-5 Joints-Member Stiffness 8-6 Bolt Strength CH-8 LEC 35 Slide 33

Example-3 A single-threaded 20 mm power screw is 20 mm in diameter with a pitch of 5 mm. A vertical load on the screw reaches a maximum of 3 kN. The coefficients of friction are 0.06 for the collar and 0.09 for the threads. The frictional diameter of the collar is 45 mm. Find the overall efficiency and the torque to "raise" and "lower" the load. CH-8 LEC 35 Slide 34

Example-3 Given CH-8 LEC 35 Slide 35

Example-3 (Cont.’d) Solution CH-8 LEC 35 Slide 36

Example-2 (Cont.’d) CH-8 LEC 35 Slide 37

Power Screws Stress Analysis The following stresses should be checked on both the nut and the screw: Shearing stress in screw body. Axial stress in screw body (8-7) (8-8) CH-8 LEC 35 Slide 38

Power Screws Stress Analysis Thread bearing stress (8-10) where nt is the number of engaged threads. Figure 8-8 Geometry of square thread useful in finding bending and transverse shear stresses at the thread root CH-8 LEC 35 Slide 39

Power Screws Stress Analysis Thread bending stress The bending stress at the root of the thread is given by (8-11) CH-8 LEC 35 Slide 40

Power Screws Stress Analysis Transverse shear stress at the center of the thread root (8-12) Notice that the transverse shear stress at the top of the root is zero CH-8 LEC 35 Slide 41

Power Screws Stress Analysis The state of stress at top of root “plane” is Von-Mises Stress at top of root plane is calculated using Eq. (6-14) of Sec. (6-5) and failure criteria applied (see example 8-1). CH-8 LEC 35 Slide 42

Power Screws Stress Analysis The engaged threads cannot share the load equally. Some experiments show that the first engaged thread carries 0.38 of the load the second engaged thread carries 0.25 of the load the third engaged thread carries 0.18 of the load the seventh engaged thread is free of load In estimating thread stresses by the equations above, substituting nt to 1 will give the largest level of stresses in the thread-nut combination CH-8 LEC 35 Slide 43

Power Screws Buckling Assuming that the column (screw) is a Johnson column where CH-8 LEC 35 Slide 44

Example-3 (Example 8-1 in Textbook) CH-8 LEC 35 Slide 45

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Example-3 (Example 8-1 in Textbook) CH-8 LEC 35 Slide 47

Example-3 (Example 8-1 in Textbook) CH-8 LEC 35 Slide 48

Example-3 (Example 8-1 in Textbook) CH-8 LEC 35 Slide 49

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Types of fasteners Three types of threaded fastener: (a) Screw (b)Bolt and nut; (c) Stud and nut, (d) Threaded rod and nuts CH-8 LEC 35 Slide 51

Threaded Fasteners Purpose: Parts: A- BOLTS: to clamp two or more members together. Parts: (1) Head (Square or Hexagonal) (2) Washer (dw=1.5d) (3) Threaded part (4) Unthreaded part Dimensions of square and hexagonal bolts are given in TABLE A-29 CH-8 LEC 35 Slide 52

Threaded Fasteners D is the nominal diameter The diameter of the washer face is the same as the width across the flats of the hexagon. The thread length (LT) is : D is the nominal diameter CH-8 LEC 35 Slide 53

Threaded Fasteners B- NUTS: Same material as that of a screw Table A-31 gives dimensions of Hexagonal nuts Good Practice: Never re-use nuts; Tightening should be done such that 1 or 2 threads come out of the nut; Washers should always be used under bolt head to prevent burr stress concentration. CH-8 LEC 35 Slide 54

Threaded Fasteners Common Cap screws Used for clamping members same as bolt except that 1 member should be threaded. The head of a hexagon-head cup screw H cap is slightly thinner than that of a hexagonal head bot H bolt . Figure 8-10 Typical cap-screw heads: (a) fillister head; (b) flat head; (c) hexagonal socket head CH-8 LEC 35 Slide 55

Figure 8.11: Types of heads used in machine screws Threaded Fasteners Figure 8.11: Types of heads used in machine screws CH-8 LEC 35 Slide 56

Joints: Fastener Stiffness In joint under tension the members are under compression and the bolt under tension: kb = equivalent spring constant of bolt composed of threaded (kt) and unthreaded (kd) parts acting as springs in series km From Ch 5 For short bolts kb= kt CH-8 LEC 35 Slide 57

Joints: Fastener Stiffness To find different parameters use table 8-7 CH-8 LEC 35 Slide 58

Joints: Member Stiffness Members act as springs under compression Frustum m Compression stress distribution from experimental data Equivalent spring constant km Integrating from 0 to l CH-8 LEC 35 Slide 59

Joints: Member Stiffness For Members made of Aluminum, hardened steel and cast iron 25 <a< 33° For a= 30° If Members have same E with symmetrical frusta (l= 2t) they act as 2 identical springs km = k/2 For a= 30° and D = dw = 1.5d CH-8 LEC 35 Slide 60

Joints: Member Stiffness Other equations From Finite element analysis results, A and B from table 8.8 for standard washer Faces and members Of same material CH-8 LEC 35 Slide 61

Bolt Strength Bolt strength is specified by minimum proof strength Sp or minimum proof load, Fp and minimum tensile strength, Sut The SAE specifications are given in Table 8-9 bolt grades are numbered according to minimum tensile strength The ASTM Specs for steel bolts (structural) are in Table 8-10. Metric Specs are in table 8-11. proof strength If Sp not available use Sp =0.85 Sy Fp = At Sp CH-8 LEC 35 Slide 62

Tension Joints Static Analysis a) External Load External Load P is shared by bolt and members Equilibrium Compatibility Relation P-d (4) C is the stiffness constant of the joint, For typical values of C see table 8-12 Most of external Load P is taken by members CH-8 LEC 35 Slide 63

Tension Joints Static Analysis b) Resultant Bolt & member loads: Fb& Fm Fm<0 Fi is preload; high preload is desirable in tension connections c) Torque required to give preload Fi Fi = 0.75 Fp For re-use Fi = 0.90 Fp For permanent joint K is torque coefficient K values are given in table 8-15 (Average Value = 0.2) CH-8 LEC 35 Slide 64

Tension Joints Static Analysis d) Joint Safety Failure of Joint occurs when: 1) Bolt yields or 2) Joint separates Let P0 be external load causing separation Fm=0 0 = (1-C) P0-Fi CH-8 LEC 35 Slide 65

Tension Joints 3 6 Static Analysis e) Gasketed Joints If a full gasket is present in joint The gasket pressure p is: To maintain uniformity of pressure adjacent bolts should not be placed more than 6 nominal diameters apart on bolt circle. To maintain wrench clearance bolts should be placed at least 3 d apart 0 = (1-C) P0-Fi 3 6 Db is the diameter of the bolt circle CH-8 LEC 35 Slide 66

Tension Joints Fatigue Analysis Pb Fi Fm Fa Fmax=Fb Fatigue Analysis In general, bolted joints are subject to 0-Pmax,e.g pressure vessels, flanges, pipes, … CH-8 LEC 35 Slide 67

Tension Joints Fatigue Analysis High Preload is especially important in fatigue. si is a constant the load line at Fi/At has a unit slope, r=1.0 To find sa use Goodman or Gerber Eq. 8.42 or ASME-elliptic. Eq. 8.43 Safety factor (using Goodman) for conservative assessment of n: Check for yielding also using proof strength: Eq. 8.48 CH-8 LEC 35 Slide 68

Tension Joints Fatigue Analysis In case of cut threads use the method described in chapter 7 with Kf values of table 8-16. The fully corrected endurance limit for rolled threads is given in table 8-17 CH-8 LEC 35 Slide 69

Fig. 8.19 CH-8 LEC 35 Slide 70

Fig. 8.21 CH-8 LEC 35 Slide 71

Failure Modes of Riveted Fasteners Under Shear Failure modes due to shear loading of riveted fasteners. (a) Bending of member; (b) shear of rivet; (c) tensile failure of member; (e) bearing of rivet on member or bearing of member on rivet. CH-8 LEC 35 Slide 72

Shear Joints Centroid of pins, rivets or bolts CH-8 LEC 35 Slide 73

Shear Joints Shear of pins, rivets bolts due to eccentric loading V & M statically indeterminate problem 4 steps (assuming same diameter bolts, load shared equally) Direct load F’ Primary Shear Centroid CH-8 LEC 35 Slide 74

Shear Joints Shear of pins, rivets bolts due to eccentric loading Moment load M Secondary Load The force taken by each bolt is proportional to its radial distance from the centroid Add Vectorially the direct and moment loads If bolts are not same size only bolts with max. R should be considered CH-8 LEC 35 Slide 75

See Examples 8.6 and 8.7 CH-8 LEC 35 Slide 76

Fig. 8.26 CH-8 LEC 35 Slide 77

Problem 8-50 ½ in-13 UNC SAE 5 CH-8 LEC 35 Slide 78

Problem 8-50 Direct load F’ Centroid is at O Secondary Load 4)Add Vectorially the direct and moment loads Is As=Ad? LT=2d+1/4=1.25” Hnut+2p+3/8=7/16+2(1/13)+3/8=0.97”<1.25” So As=At = 0.1419in2 and tB=12.7 Kpsi; n=4.2 CH-8 LEC 35 Slide 79

Problem 8-50 CH-8 LEC 35 Slide 80

Problem 8-50 CH-8 LEC 35 Slide 81