Chapter 8 Screw, Fasteners and the Design of Nonperanent Joint Lecture Notes Dr. Rakhad Arief Siregar Kolej Universiti Kejuruteraan Utara Malaysia Mechanical Engineering Design Sixth Metric Edition J.E. Shigley and C. R. Mischke 1
Introduction In earlier ties, casting was iportant to realization of desirable fors in etal However, casting has liitations on the shapes and sized restrict geoetries The idea of JOINTS places where separate bodies could be assebled to create geoetric fors not possible with casting The helical-thread screw is an iportant invention and the basis of threaded fasteners
Thread Standards and Definitions 3
d Major diaeter is the largest diaeter of a screw thread d r d p Minor diaeter is the sallest diaeter of a screw thread Mean diaeter of a screw thread Pitch is the distance between adjacent thread fors easure parallel to the thread axis. 4
Thread (a) lp (b) lp l: lead p: pitch (c) l3p (a) Single, (b) Double, and (c) Triple threaded screws 5
Basic thread profile M and MJ threads H 0.5 p tan 30 o 6
Notes M profile is the basic ISO 68 profile with 60 o syetric threads MJ profile has a rounded fillet at the root of the external thread and a larger inor diaeter of both the internal and external threads (useful if high fatigue is required) 7
Experiental data An unthreaded rod having a diaeter equal to the ean of the pitch diaeter and inor diaeter will have the sae tensile strength as the threaded rod The area of unthreaded rod is called the tensile-stress area A t of the threaded rod 8
Noinal Major Diaeter d Pitch p Coarse-Pitch Series Tensile-Stress Area A t Minor-Diaeter Area A r Pitch p Fine-Pitch Series Tensile-Stress Area A t Minor- Diaeter Area A r 1.6 0.35 1.7 1.07 0.4.07 1.79.5 0.45 3.39.98 3 0.5 5.03 4.47 3.5 0.6 6.78 6.00 4 0.7 8.78 7.75 5 0.8 14. 1.7 Metric Threads (All diensions in illieters) ANSI B1.1-1974 B18.3.1-1978 6 1 0.1 17.9 8 1.5 36.6 3.8 1 39. 36.0 10 1.5 58.0 5.3 1.5 61. 56.3 1 1.75 84.3 76.3 1.5 9.1 86.0 14 115 104 1.5 15 116 16 157 144 1.5 167 157 0.5 45 5 1.5 7 59 4 3 353 34 384 365 30 3.5 561 519 61 596 36 4 817 759 915 884 4 4.5 110 1050 160 130 48 5 1470 1380 1670 1630 56 5.5 030 1910 300 50 64 6 680 50 3030 980 7 6 3460 380 3860 3800 80 6 4340 4140 1.5 4850 4800 90 6 5590 5360 6100 600 100 6 6990 6740 7560 7470 110 9180 9080 9
Metric thread M14x1.5 The clue to the etric designation pitch of 1.5 Noinal ajor diaeter of 14 10
Square and Ace thread p p p p p 9 0 p d d d r Square thread d r Ace thread Usually used when power is to be transitted 11
ACME Thread Properties Crest diaeters, threads per inch, and stresses for Ace thread Crest diaeter, d c, in. 1/4 5/16 3/8 7/16 1/ 5/8 3/4 7/8 1 1 1/8 1 1/4 1 3/8 1 1/ 1 3/4 1/4 1/ 3/4 3 3 1/ 4 4 1/ 5 Nuber of threads per inch, a n 16 14 1 1 10 8 6 6 5 5 5 4 4 4 4 3 3 3 Tensile stress area, A t, in 0.0663 0.04438 0.06589 0.0970 0.15 0.1955 0.73 0.4003 0.5175 0.6881 0.8831 1.030 1.66 1.811.454.98 3.80 4.711 5.181 7.338 9.985 1.97 16.351 Shear stress area, A s, in 0.3355 0.4344 0.576 0.6396 0.778 0.9180 1.084 1.313 1.493 1.7 1.95.110.341.803 3.6 3.610 4.075 4.538 4.757 5.700 6.640 7.577 8.511 1
Metric Conversion of Preferred for Ace Threads d p 6.35 7.93 9.5 11.7 11.7 15.87 19.05. 5.4 31.75 38.1 44.45 50.8 63.5 76. 1.58 1.81.11.54 3.17 4.3 4.34 5.08 5.08 6.35 6.35 6.35 6.35 8.46 1.7 Modification on thread angle of 10 o to 15 o Modified to a stub for by aking the teeth shorter 13
The Mechanics of Power Screws To change angular otion into linear otion Failiar applications; lead screws of lathes, the screws for vises, presses and jacks The Joyce wor-gear screw jack 14
A Square-thread power screw Mean diaeter Force Helix angle Pitch Lead angle 15
16 Force diagras Raising the load Lowering the load + 0 cos sin 0 cos sin λ λ λ λ N N f F F N f N P F V H + 0 cos sin 0 cos sin λ λ λ λ N N f F F N f N P F V H
Torque P for the raising load P for the lowering load P P F 1 ( sin λ + f cosλ) F cosλ f sin λ [( l π d ) + f ] ( f l π d ) P P F 1 ( f cosλ sin λ) F cosλ + f cosλ Eliinate the noral force N since it was not our interest [ f ( l π d )] + ( f l π d ) The Torque (T ): The Torque (T ): T Fd 1+ π f π d d f l T Fd π f π d d + l f l Eq. (8-1) Eq. (8-) 17
For self-locking This condition ay occur if the lead is large or the friction is low The load will lower itself by causing the screw to spin without external effort Torque T fro Eq. (8-) will be negative or zero T Fd π f π d d + f l l π π d f f d > > tan λ l l π d 18
Efficiency In the case of raising the load (Eq. 8-1), if we let f 0 (no frictions), then: The efficiency is: T 0 Fl π e T T 0 Fl π T Eq. (8-4) 19
Power Screw Application T T R c Fd Ffcd ( l + fπd secα ) ( πd fl secα ) c 0
Stress Analysis Torque collar : T c Ff c d c Noinal Shear Stress: τ 16T π 3 d r F 4F Axial Stress: σ A π d r 1
Noinal thread stresses in power screw Bearing Stress F σ B π d n t p / F σ B π d n t p
Exaple 8-1 A square-thread power screw has a ajor diaeter of 3 and a pitch of 4 with double threads, and it is to used in an application of screw jack. The given data include f f c 0.08, d c 40 and F 6.4 kn per screw 3
Exaple 8-1 Find the thread depth, thread width, pitch diaeter, inor diaeter, and lead Find the torque required to raise and lower the load Find the efficiency during lifting the load Find the body stresses, tensional and copressive Find the bearing stress 4
Threaded Fasteners The propose of a bolt is to clap two or ore parts together The claping load stretches or elongates the bolt The load is obtained by twisting the nut until the bolt has elongated alost to the elastic liit 5
A standard hexagonal-head bolt Point of stress concentration are at the fillet See Table E-4 for diensions 6
Thread length of etric bolts L t D D + 6 + 1 15 < L L 15 00 D 48 D + 5 L > 00 where all diensions are in illieters 7
The Thread Length vs Noinal Diaeter 50 00 Thread Length (L t ) 150 100 50 0 0 0 40 60 80 100 10 Noinal Diaeter (D ) 8
Table of thread length vs. noinal diaeter 9
A variety of achine-screw head style As bolt holes ay have burrs or sharp edge after drilling that can increase stress concentration, so use washer under the bolt head, and also under the nuts Fillister head Flat Head Hexagonal socket head 30
Round head Flat head Types of heads used on achine screw Fillister head Truss head Oval head Binding head Hex head (tried) Hex head (upset) 31
Hexagonal Nuts End view general Washer-faced regular nut Regular nut chafered on both sides Ja nut with washer face Ja nut chafered on both sides See Table E-9 for diensions 3
Three types of threaded fastener Bolt and Nut Cap screw Stud 33
Joints Fastener Stiffness In this section we will deterine the stiffness of the fastener in the claped zone A siple bolted joint using hardened-steel washers can be used for a joint which: can be disassebled without destructions ethods is strong enough to resist external tensile loads, oent loads and shear loads, or a cobination of those loads Such a joint can also be dangerous unless it is properly designed and assebled 34
A bolted joint Twisting the nut stretches the bolt to produce the claping force This claping force is called the pre-tension or bolt preload Washers Clearance spaces 35
Another tension-loaded joint Not using a nut Washer Cap screws threaded Any idea on using different type of bolt? 36
Joint that siulated as Bolt and Springs k j k b 37
1 k k b b 1 k A T d A l Stiffness Bolt and Nut + t d 1 k t d A E + A l t d k d k T A l d t d E At E l A t : tensile-stress area (Table 8-1) A d : Major diaeter area of fastener E : Elastic odulus of fastener 38
L t d l d L G L l d L L t length of unthreaded portion in the grip l t L G l d length of threaded portion of grip 39
Proble 8-11 A bolted joint is to have a grip consisting of two 1 steel plates and one 1 etric plain washer to fit under the head of the M1 coarse hex-head bolt. a) What is the length of the thread L T for this diaeter inch-series bolt? b) What is the length of the grip L G? c) What is the height H of the nut d) Is the bolt long enough? If not, round to the next larger preferred length (Table E-15 not true) e) What is the length of the shank and threaded portions of the bolt within the grip? These lengths are needed in order to estiate the bolt spring rate k b 40
Solution 8-11 a) L T D + 6 (1) + 6 30 b) L G 1 + 1 +.8 6.8 (see Table E-30 for washer diension) c) H 10.8 for regular hexagonal (see Table E-9, page 110) d) L in L G + H 6.8 + 10.8 37.6 (the bolt should have length > 37.6 ) e) l d L L t and l t L G l d 41
Joints Meber Stiffness In this section we wish to study the stiffness of the ebers in the claped zone There ay be ore than two ebers included in the grip of the fasteners It can be assued that all ebers are perfor like copressive springs in series 1 1 1 1 1 + + + + k k k k k 1 3 i 4
43 General cone geoetry for stiffness calculation A half-apex angle α 30 5 α 33 Osgood ( ) + + + + tan tan tan 1 0 d D x d D x A d D x r r A α α π α π π EA Pdx d δ See Eq. 4.3 Area of the eleent is:
Stiffness of ebers Substituting area of eleent to elongation equation and integrating the t left side: dx P δ πe Using a table of integration, we find: P δ ln πe tanα Thus the spring rate or stiffness is: With α 30, this becoes: k k P δ ln ln [ x tanα + ( D + d )/ ] [ x tanα + ( D d )/ ] 0 ( t tanα + D d )( D + d ) ( t tanα + D + d )( D d ) π E d tanα ( t tanα + D d )( D + d ) ( t tanα + D + d )( D d ) 0.577π E d ( 1.5t + D d )( D + d ) ( 1.5t + D + d )( D d ) k k / l t D d w d w : diaeter of washer face 44
Stiffness of ebers The spring rate of the ebers to be: k ln π E d tanα ( l tanα + d w d )( d w + d ) ( l tanα + d + d )( d d ) w w The diaeter washer face is about 50% greater than the fastener diaeter d w 1.5d and α 30 then: k In the for of k /E d : ln 0.577π E d 0.577l + 0.5d ( 5) 0.577l +.5d k E d ln π tanα ( l tanα + d w d )( d w + d ) ( l tanα + d + d )( d d ) w w 45
Stiffness vs. aspect ratio of the ebers of a bolted joint Table 8-7 For stiffness paraeters of various eber aterials k A exp / Ed ( Bd l) d / l 0.4 α 30 46
Table 8-7 Stiffness Paraeters of Various Meber Materials Material Used Poisson s ratio, ν Modulus of Elasticity, E, GPa Nuerical Constants A B Steel Aluinu Copper Gray cast iron General expression 0.91 0.334 0.36 0.11 06.8 71.0 118.6 100.0 0.78715 0.79670 0.79568 0.77871 0.7895 0.6873 0.63816 0.63553 0.61616 0.6914 47
Exaple 8- Two 1 -thick steel plates with a odulus of elasticity of 07 GPa are claped by washer-faced 1 -diaeter UNC SAE grade 5 bolts with a.5 thick washer under the nut. Find the eber spring rate k using the ethod of conical frusta, and copare the results with finite eleent analysis (FEA) curve-fit ethod of Wileen et. al. 48
Solution 8- The grip, l 1+1+.5 6.5 By knowing l 6.5, d 1, E 07Gpa then the stiffness of ebers k : k ln () 5 ( 07000) 1 ( 6.5) + 0.5( 1) ( 6.5) +.5( 1) 0.577π 6.615 10 0.577 0.577 Fro Table 8-7, A0.78715, B0.6873 gives k (07000)(1)(0.78715) exp[0.6873(1)/6.5] k.599 x 10 6 N/ N A good agreeent / 49
Bolt Strength The strength is specified by stating ASTM iniu quantities: Miniu proof load Miniu proof strength Miniu tensile strength The proof load is the axiu load that a bolt can withstand The proof strength is corresponds to the proportional liit in the fastener 50
Bolt Strength The value of the ean proof strength, the ean tensile strength and the corresponding standard deviations are NOT part of the specification codes The designer s responsibility to obtain these value before designing to a reliability specification 51
The distribution of ultiate tensile strength 1000 MPa 71 MPa Designer does not see this histogra Instead, in Table 8-8, designer sees the entry S ut 85 MPa under in A449 bolts 80 890 960 1030 1100 1170 140 MPa 5
53 Tension Joint The External Load b b k P δ k P δ b b k k P P b b b k k P k P + P P δ P P 0 < + + + + i i b b i b b F F P C F k k P k F P F 0 ) 1 ( < + + i i b i F F P C F k k P k F P F The load P is tension and it causes the connection to elongate through soe distance δ Since P P b + P thus: The resultant bolt load is: The resultant load on connected ebers is:
Hoework- Solve The Probles No. 8-6, 8-7, 8-8, 8-10 8-1, and 8-13 You ay just do 5 instead of 6 probles Do the best you can By doing it you ay archive soething new! 54
End of this class Week-3 (/1/06) Iportant info Next week there is a 30 inutes QUIZ The question consist of 5 questions You ay open your text book and lecture notes Do the best you can! Any Questions? 55