design of threaded fasteners

8/10/2019 Design of threaded fasteners

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I/C: KALLURI VINAYAK


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Thread Standards and Definitions


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Lead and multi-threaded screws

Lead is the distance moved by nut parallel tothe screw axis when the nut is given one turn.

l = p * multiplicity of threading

ng e t rea e , =p Double threaded, l=2p

Triple-threaded, l=3p

Single & Double thread screws


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The Metric Thread:

M12 1.75 mmnominal major diameter of 12 mm

pitch of 1.75 mmmetric designation

d = major diameter

d r = minor diameter = d - 1.226 869 p

d p = pitch diameter = d - 0.649 519 p

p = pitch

p H 23

=basic ISO 68 profile with 60 symmetric threads


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(a)Square

(b) Acme threads


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Power screw or Screw jack mechanism

A device used in machinery to change angular motion intolinear motion, and, usually, to transmit power

Find use in machines such as universal tensile testing

machines, lead screws of lathes and other machine tools,automotive jacks, vises, linear actuators, adjustable floor posts and micrometers etc


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The Mechanics of Power Screws

square-threaded power screwsingle threadMean diameter d m

pitch plead angle helix angle loaded by the axial compressive force F

Helix angle: Angle that thread makes with plane perpendicular to thread axis

Lead angle : Angle between the helix and a plane of rotation


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( )

sincoscossin

f f F P R

+=

+

=

m

m R

d l f

f d l

F P

.1

+=

fl d fd l Fd T

m

mm R

2

Raising:

Lowerin :

( )

sincossincos

f f F

P L +=

+

=

m

m L

d l f

d l f F P

.1

+= fl d l fd Fd

T m

mm L

2


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Self locking of power screws

T L gives the torque required to overcome thefriction in order to lower the load

In certain instances, the load may itself lower bycausing the screw to spin In such cases, T is either zero or negative.

Whenever, the load does NOT lower by itself unless a positive T L is applied, the screw is saidto be self-locking


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Self-locking of power screws

The condition for self-locking is

l fd T m L

> 0

Divide both sides by d m. Since l / d m =tan

The screw is self locking whenever thecoefficient of friction is greater than thetangent of the lead angle.

tan> f


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Accounting for collar friction

Normally a collar is employed to enable the power screw system to have sufficient bearing area hold thecomponent being raised

Since the collar slides against the component beingraised, additional torque needs to be applied to raise theload, this is called as collar friction torque T c

c, ,is enough to use a mean diameter, d c, at which the collar friction force is concentrated

2cc

c

d Ff T =

Total torque required to rise the load; T R = T R + Tc

Total torque required to rise the load; T L= T L + Tc


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Power screw s raising efficiency

It is the ratio of raising torque without friction tothe raising torque with friction

Can be defined both with and without collar friction

2 Fl

T o =QoT

Fl T T

e 2

==

Use Tables 8-5 and 8-6 for values of coefficient of f and f c .

Table 85Coefficients of Friction f for Threaded Pairs

Table 86Thrust-Collar Friction Coefficients


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Raising torque for ACME screws

A simple approximate equation is

The effect of the thread angle in ACME thread is to increase

+=

sec

sec

2 fl d

fd l Fd T

m

mm

R

the friction force between the screw and the nut due to thewedging action of the thread

For power screw application, though the ACME thread is not

suitable due to higher frictional force resulting from wedgingaction, is invariably used because it is easier to manufacturethan the square threads.


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Bearingpressure

Body stresses in power screws

Critical element at which thevon-Mises stress is evaluated

T

F


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Body stresses in power screws

Bending stress, x Torsional shear stress, xz Axial compressive stress, y Transverse shear (no contribution to von-Mises

stress because it is maximum where bending stress

resultant is von-misesstress at top of theroot plane

maximum; hence needs to be only independentlychecked for)

Bearing pressure (no contribution to von-Misesstress because it is distributed over the thread andis maximum at the middle of thread and is zero atthe root of the thread)


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Body stresses in the screw: those that need only to beindependently checked (no need to take into account in von-Mises

stress)

pnd F

pnd F

t mt m B

2

2==

Must be less than the safe bearingpressure given in Table 8-4. Causestoo much wear and sometimescrushing.

The engaged threads cannot share theload equally. Some experiments showthat the first engaged thread carries amaximum of 0.38 of the load. Inestimatin thread stresses b the

Table 84Screw Bearing Pressure

pd

F

pnd

F

pnd

F

A

V

r t r t r

14.13

22

3

2

3 ====It is at the centre of theroot area. Must be lessthan the shear yieldstrength of material.

equations above, substituting 0.38 F for F and setting n t to 1 will give the largestlevel of stresses in the thread-nutcombination.

pd F

pnd F

mt m B

76.02==


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Body stresses in the screw threads: those to be taken into accountfor estimation of the von-Mises stress at the critical element

316r

R xz d

T

= 316r

L xz d T =or 24

r y d F A F

==

Power screws are operated normally at low speeds andhence static design is enough.

pd F

pnd F

c I r t r b x

28.26 ====

( ) ( ) ( ) ([ ]

21

222222 62

1'

zx yz xy x z z y y x

+++++=

42)(121;4

3

pcand pnd I p F M t r = == Q

Resultant von-Mises stress


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Problem

A power screw has triple thread of major diameter 25 mm,minor diameter 21.5 mm, pitch diameter 23 mm and

pitch of 3 mm. A vertical load on the screw reaches a

maximum of 6 kN. The coefficient of friction is 0.06 for threads and 0.03 for collar. The friction diameter of thecollar is 30 mm. Find the following: (a) total torque

requ re o ra se e oa , o a orque requ re olower the load, (c) efficiency, (d) bending stress, axialnormal stress, torsional shear stress and the resultantvon-Mises at the root for one thread (by assuming thefirst engaged thread carries a maximum of 0.38 of theload). (e) bearing and transverse shear stress


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Force, F = 6 kNd = major diameter = 25 mm;d r = minor diameter = 21.5 mm;d p = pitch diameter= 23 mm

p = pitch = 3 mm; For triple threads, l= 3p = 9 mmf= 0.06; f c = 0.03; d c =30 mmmean diameter d = d+d /2 = 23.25 mm

+

(a) Total torque required to raise the load,

+

fl d

fd l Fd

m

mm

2 2

cc d Ff TR = T R + Tc = +

+

+)9)(06.0()25.23(

)25.23()06.0(92

25.23106 3

x x

230)03.0(106 3 x

=

= 12.874 + 2.7 = 15.574 N-m


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22cc

m

mm d Ff fl d l fd Fd +

+

m- N3.371-=2.7+6.071-2

30)03.0(106

)9)(06.0()25.23(

9)25.23()06.0(

2

25.23106 33

=

+

+

= x x x

3

(b) Total torque required to lower the load

TL= T L + Tc =

frictioncollar with

x

x x

T

Fl

T

T e

R R

o %18.55

)10574.15(2

9106

2

,Efficiency 33

====

frictioncollar without xT T e R Ro

%75.66)10874.12(22 ,Efficiency(c) 3 ====


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MPa x x

x x xd

b x5.67

)103)(1)(105.21(

10638.06 stress,Bending)

33

3

===

( ) MPa

x

x x

d

F

r z

52.16105.21

10644 stress,normalAxial

23

3

2 ===

xT )574.15(1616

xd r xz .

)105.21(,

333

===

( ) ( ) ( ) ( )[ ]

( ) ( ) ( ) ( )[ ]

material theof strength yeild MPa

zx yz xy x z z y y x


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pressure bearingsafe81.203125.23

10638.02

22

3


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Bolts/Screws

The ideal bolt length is one in which only one or twothreads project from the nut after it is tightened

Locations of stress concentration in a bolt At the fillet

1 3

e run-ou At the thread-root fillet in the plane of the nut

The washer face and washers are used to distribute theload under the bolt head and nut face. It also preventfatigue failure of bolt that may result when the burs on theimperfectly drilled bolt holes cut into the bolt head

2


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Nomenclature of bolt

or 0.4 mm

(See Table A-29; page-1053)

d, Nominaldiameter ormajor diameter

48

200

200125125

__ __

252

12262

,

>


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Table A-29; page-1053


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CAP screws

Fillister Flat Socket; may be hexagonal or square

may have hexagonal head also similar to a bolt but with a thinner head (not shown here)

See Table A-30, page-1054 for dimensions.


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Machine screws:

notice that there is no shank

driven all the way up to thehead into the art

sometimes having a hole forscrew head to seat in the part


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Note : that the dimension H includes the washer face thickness which isnormally 0.4 mm.

Table A31; Dimensions of Hexagonal Nuts


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A bolt may be used in two different cases

(1) with nut, and (2) without nutIMPORTANT: The grip length needs to be differently estimated in the twocases.

Case 1

Case 2

D i h d l i f h d ib d i h l lid


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Design methodologies for the two cases described in the last slide.Given: fastener diameter d and pitch p or number of threads.

-Roundup Table A-17

t d l l l +=,lengthGrip H l L +Length,Fastener

T d L Ll =grip,in portionunthreadedof Length

d t l l l =grip,in portionthreadedof Length

+=

2,2min'length,Grip2 d t hl

d h L 5.1Length,Fastener +

T d L Ll = portion,unthreadedusefulof Length

d t l l l = ' portion,threadedusefultheof Length

48

200

200125

125

__ __

252

122

62

,

>

design of threaded fasteners

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