Mechanical Fasteners Tensile and Shear Stress Areas

Transcription

1 Mechanical Faseners Tensile and Shear Sress reas Lecure 28 Engineering 473 Machine Design

2 Threaded Faseners Bol Threaded fasener designed o pass hrough holes in maing members and o be secured by ighening a nu from he end opposie he head of he bol. Screw Threaded fasener designed o be insered hrough a hole in one member and ino a hreaded hole in a maing member. Mo, Fig. 18-1

3 Bols Mo, Fig. 18-2

4 Machine Screws Mo, Fig. 18-3

5 Shee Meal and Lag Screws Shee meal screws are ofen self-apping. Mo, Fig. 18-4

6 Se Screws Se screws are used o develop a normal force beween wo objecs (e.g. collar and shaf). Mo, Fig. 18-5

7 Thread Sandards (Inch Series) merican Sandard B Firs merican sandard o cover he Unified Thread Series agreed upon by he Unied Kingdom, Canada, and he Unied Saes. Represens he basic merican sandard for fasener hreads. Threads made o his sandard are called unified hreads. NSI B /SME 1989/SME B Revised sandard ha sill incorporaes much of he original sandard.

8 Thread Sandards (Meric Series) NSI B1.13M (R1989) Conains sysem of meric hreads for general fasening purposes in mechanisms and srucures. Faseners made o his sandard are ofen referred o as M-series.

9 Thread Profiles The pich line or diameer is locaed a ½ he heigh of he heoreical sharp v-hread profile.

10 Thread Series Thread Series groups of diameer-pich combinaions disinguished from each oher by he number of hreads per inch applied o a specific diameer. Unified Coarse-Thread Series (UNC or UNRC) Mos commonly used in he bulk producion of bols, screws, nus for general engineering applicaions. Unified Fine-Thread Series (UNF or UNRF) Use when more hreads per inch are required (i.e. where are shor lengh of engagemen is available). M-Series Series Meric sysem of diameers, piches, and olerance/allowances.

11 Thread Classes Thread Classes Define he amoun of olerance and allowance associaed wih a paricular hread. Classes 1, 2, 3 apply o exernal hreads. Class 2 is he mos commonly used. Classes 1B, 2B, 3B Classes 1B, 2B, 3B apply o inernal hreads. Class 2B is he mos commonly used.

12 Thread Designaions (Inch Series) The following is an example of he sandard mehod used o designae bol and screw hread requiremens on a drawing or in a specificaion. Threads per inch Thread Class UNC 2 Exernal Thread Nominal Size Thread Series

13 Thread Designaions (Meric Series) The following is an example of he sandard mehod used o designae bol and screw hread requiremens on a drawing or in a specificaion. Pich (mm) Nominal Diameer Lowercase> exernal hread M6x1 4g6g(22) Meric Series Tolerance Classificaion

14 Maerial and Srengh Designaions Mo, Table 18-1

15 Maerial and Srengh Designaions (Coninued) Mo, Table 18-2

16 Maerial and Srengh Designaions Mo, Table 18-3

17 Tensile Sress rea The average axial sress in a fasener is compued using a ensile sress area. σ ave π 4 F Dr + 2 D p 2 F xial Force D D σ r p ave Roo Diameer Pich Diameer Tensile Sress rea verage axial sress Tess of hreaded rods have shown ha an unhreaded rod having a diameer equal o he mean of he pich diameer and he minor diameer will have he same ensile srengh as he hreaded rod.

18 Tensile Sress rea (Coninued) D H d b 1 2n 2 an 3 8 H + ( 60 ) 3 16 H D d b diameer a criical plane diameer of bol H heoreical heigh of hread n 1 p hreads/in Ma Scolforo, Sverdrup Technology

19 Tensile Sress rea (Coninued) D d b H H π 4 D 2 H 1 2n an ( 60 ) π 4 d b n 2 D D d d b b an n n ( 60 ) This is he formula used by manufacurers of inch series faseners o publish he ensile area in heir caalogs.

20 Tensile Sress rea (Coninued) The following formula may be obained in a similar manner for meric series hreads. π 4 d b n 2

21 Shear rea of Exernal Thread Consideraion of he ineracion beween maing hreads mus be considered o esablish he shear area of an exernal hread. Ma Scolforo, Sverdrup Technology

22 Shear rea of Exernal Threads (Coninued) s,e an π K ( 30 ) n,max e n 0.5 e 0.75H gap K e s,e n,max shear area of exernal hread maximum minor diameer of inernal hread hickness of exernal hread a criical shear plane n hreads per inch

23 an H s,e ( 30 ) π K 1 2n an n,max ( 60 ) Shear rea of Exernal e 0.5e 0.75H gap n 3 2n Threads (Coninued) gap e e n K n,max n 1 2 ( E K ) s,min 3 2n 1 2 K E n,max n,max s,min E s,min minimum pich diameer of he exernal hread n E s,min e 2 an ( 30 ) 0.75 gap 2n 3 The gap equaion is based on olerance daa.

24 Shear rea of Exernal Threads (Coninued) 1 1 π n K n,max + s,min n, max 2n 3 ( ) E s, e K This equaion appears in he NSI sandards and gives he shear area per uni lengh of engagemen. I mus be muliplied by he lengh of engagemen, L e, o obain he acual shear area. This area is ofen repored in manufacurers daa shees for bols and screws. 1 2n ( E ) s,min K n,max e s, e π n K n,max + L 1 3

25 Shear rea of Inernal Threads s, i π Ds,min i n D i s,min Minimum major diameer (exernal hread) hickness of inernal hread (criical plane) Ma Scolforo, Sverdrup Technology

26 Shear rea of Inernal Threads (Coninued) Similar o he previous derivaion, an equaion ha akes ino accoun he olerances of he hread sysem can be derived o compue he shear area of he inernal hread. s,i π D s,min n 1 2n ( D E ) s,min n,max E n,max maximum pich diameer of he inernal hreads

27 Lengh of Engagemen (Equal Srengh Maerials) If he inernal hread and exernal hread maerial have he same srengh, hen Tensile Srengh (Exernal Thread) S F max Shear Srengh (Inernal Thread) 0.5S F s,i max L e F max S 0.5S s,i L e L e 2 s,i

28 Lengh of Engagemen (Unequal Srengh Maerials) If he inernal hread and exernal hread do no have he same maerial, hen Tensile Srengh (Exernal Thread) S,e F F max max S,e Shear Srengh (Inernal Thread) 0.5S 0.5S,i,i s,i F L e s,i max L e L e 2 s,i S S,e,i

29 Bol/Nu Design Philosophy NSI sandard bols and nus of equal grades are designed o have he bol fail before he hreads in he nu are sripped. The engineer designing a machine elemen is responsible for deermining how somehing should fail aking ino accoun he safey of he operaors and public. Lengh of engagemen is an imporan consideraion in designing machine elemens wih machine screws.

30 ssignmen 5/16-18UNC-2 fasener is made from a maerial having a yield srengh of 120 ksi. The fasener will be engaged wih a nu made from he same maerial. Compue he ensile sress area, shear sress area per lengh of engagemen, and minimum lengh of engagemen. Dimensional informaion on he hreads is given below. The minimum pich diameer of he exernal hread is in., and he maximum minor diameer of he inernal hread is inch, minimum major diameer of he exernal hread is in, and he maximum pich diameer of he inernal hreads is (reference Table 4, page1544, Machinery s Handbook).