Torsional stress: S, total corrected stress transpose for D, P,or t Wahl curvature-stress correction factor: K a1 = 1 ++ +where C = Rectangular Wire Rate (see Fig 7 2 for factors K 1 and K 2): R = K 2 transpose for b, t, N, or D Torsional stress, corrected: S =? transpose for P or D ? is obtained from Fig 7 2 7 2 1 Solid Height of
The coil of a torsion spring experiences bending stress (despite the name of the spring) Including a stress-correction factor, the stress in the coil can be represented by The stress-correction factor at inner and outer fibers has been found analytically for round wire to be K i is always larger, giving the highest stress at the inner fiber
Every spring configuration has a spring rate, k,defined as slope of its force-deflection curve If slope is constant, it is a linear spring, and y F k = Where: F is applied force, and y is deflection When spring rate varies with deflection, it is called a nonlinear springnonlinear spring We often want a linear springto control loading
1 1 The stress correction factor relative to the spring index (C) can be determined by using the following formula or based on Fig 1 Symbols Used 1 2in Spring Design Formulae Symbols used in spring design formulae are shown in Table 1 Basic Formulae Used in Designing of Springs 1 2 1Compression Springs, and TensionSprings without Initial D1 L D
The spring legs were loaded using Ø9mm pins at a radius of 40mm from the jig centre When deflecting to a fixed angle, the torque, and hence stress, was lower when using a smaller mandrel, but the spring visibly sheared producing stresses that were not the same at each of the strain gauge location The average stress measured with each mandrel was
The stress equation at a given load (P) is a function of the coil diameter and wire diameter Our goal is for the stress at solid to be 40 of the minimum tensile strength (MTS) The MTS is a function of the wire size, which we don’t know The Advanced Spring Design program uses an iterative process to solve this snarled mess of equations
Stresses in Helical Springs Th C boards Spring rate and stress distribution can be controlled with The curvature correction factor can now be obtained by
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Mechanical SpringsMechanical Springs
ME 305 Mechanical Engineering Design 2
1
Topics to be Covered
Stresses in Helical SpringsTh C t Eff t
Th e C urva t ure Eff ec t
Deflection of Helical Springs
Compression Springs
Stability
Spring Materials
Helical Compression Spring Design for static Service
Helical
Compression
Spring
Design
for static
Service
Critical Frequency of Helical Springs
Fatigue Loading of Helical Compression SpringHli lC i S i D i f Fti L di H e li ca l C ompress i on S pr i ng D es i gn f or F a ti gue L oa di ng
Extension Springs
Helical Coil Torsion Springs
2
Mechanical Springs
Produce a pull, a push, or a twist (torque) force when displaced. St b b St ore or a b sor b energy.
May be made of
round or rectangular wire May be made of round or rectangular wire bent into a suitable form such as a coil, or made of flat stockloaded as a beam. 3
Mechanical Springs
Types of Spring
4
Push Function
Push functionis provided by helical compression
springs, spring washers, volute springs, and beam i
Th h i th i
spr i ngs. Th ese are s h own i n th e prev i ous page.
Helical Compression Springs
: Used in applications involving large deflections ,suchas shock absorbers involving large deflections , such as shock absorbers in automobiles or to hold batteries in consumer products. Used in valve-return springsin engine, die springs etcsprings , etc .
Conical Springs
: Spring rate is nonlinear. By varying coil p itch, a nearl y constant s p rin g rate can be obtained. pypgAdvantage is the ability to close to a height as small as one wire diameter if the coils nest. 5
Push Function - Cont'd
Barrel/Hourglass/Variable Pitch Springs
: Can be thought of a two conical springs back to back, also having a nonlinear spring rate.
Barrel hourglass and variable pitch springs are
used to minimize
Barrel
, hourglass , and variable pitch springs are used to minimize resonant surging and vibration.
Spring Washers
: Used for small deflectionsassociated with motion along a bolt or other guide
Used to
load something axially such along a bolt or other guide . Used to load something axially , such as to take up endplay on a bearing.
Volute Springs
: Can be used for damping and also to resist buckling.
Very expensive
Shear cutter for trimming
and has significant Very expensive . Shear cutter for trimming , and has significant friction and hysteresis (significant energy loss)
Beam Springs
: Can be used to push or pull. Examples are diving boards Spring rate and stress distribution can be controlled with boards .
Spring
rate and stress distribution can be controlled with changes in beam width or depth along its length. Loads can be high but deflections are limited. 6
Pull Function
Pull function
is provided by helical extension springs Pull function is provided by helical extension springs and constant forcesprings.
Helical Extension Springs
: Capable of large deflection.
Used in
door closers and counterbalances automobile Used in door closers and counterbalances , automobile wiper blades, children's car seats and car hoods. Hooks more highly stressed than coils and usually fail first more highly stressed than coils and usually fail first .
When hook fails this spring becomes unsafe.
7
Twisting Function
Twisting functionis provided by helical torsionsprings and spiralsprings (coils in the same plane).
Helical Torsion Springs
: Used for garage-door counter- balancersand counterbalancing of such things as doors hich rotate abo t a hori ontal edge
Clothespins
w hich rotate abo u t a hori z ontal edge .
Clothespins
, mousetraps and finger exercisers are examples.
Spiral Springs
:
Spiral
Springs
: Hairsprings are used in instruments and mechanical clocks and watches. One of their characteristics is low hysteresis(small energy loss).
Brush Springs: Hold motor and generator brushes
against their commutators. 8
Twisting Function - Cont'd
Motor, Clock or Power Springs
: Used to supply il ddi id l k d rotat i ona l energyan d use d i n w i n d up c l oc k s an d mechanical toys.
Prestressed Power Springs
: Has large energy storage capacity. Used in seatbelt retractors.
Constant-Torque Spring Motor
: Used to provide level torque.
Drawbar Springs
: Unlike helical extensionspring, it will support the load safely when it fails. 9
Spring Rate
Every springconfiguration has a spring rate, k,defined as slope of its force-deflection curve.
If slope is constant, it is a linear spring, and
y F k
Where: F is applied force, and y is deflection.
When spring rate varies with deflection, it is called a nonlinear springnonlinear spring .
We often want a linear springto control loading.
Many spring configurations
have constant spring rates and Many spring configurations have constant spring rates and few have zero rates(constant force). 10
Spring Rate - Cont'd
When multiple springsare combined, resulting spring rate de p endson whether the y are combined in series or p y parallel. Springs in series have same force passing through them, as each contrib tes to total deflection as each contrib u tes to total deflection . ntotal kkkkk1...1111 321
11
Spring Rate - Cont'd
Springs in parallel have same deflection, and total force is s p lit amon g them. For s p rin g s in p arallel , individual pg pg p , spring rates add directly. k total = k 1 + k 2 + k 3 + .... + k n total 1 2 3 n 12
10.1 Stresses in Helical Springs
Rl T FD /2 d /2 AF JTr max
A round-wire helical compression
spring is loaded by the axial force F. R ep l ace T = FD /2 , r = d /2 ,
J = d
4 /32, A= d 2 /4, max = : (10 1) 4 8 F FD (10 - 1) 23
4 8 d F d FD D C .
Define the spring index as:
d D C
For most springs the range for
C is: 6 C 12
The mean coil diameter D
The wire diameter d.
3 8 d FDK S For most springs the range for C is: 6 C 12 . 13 d CCK S 212
Where K
S is a shear-stress correction factor
10.2 The Curvature Effect
is based on the wire being straight. 3 8 dFDK S In fatigue load: It is important to include the curvature stress.
To include the curvature effect, the factor K
S needs to be modifiedmodified . The curvature of the wire increases the stress on the inside of the spring but decreases it only slightly on the outside.Iildh llbldb I n stat i c l oa d : t h ese stresses can norma ll y b e neg l ecte d b ecause it will be relieved by local yielding with first application of a load. C K
615.014
Wahl factor:
Bergstrasser
factor: CC K W 44
24
C K 14
Bergstrasser
factor: 34
C K B The curvature correction factor can now be obtained b y y canceling out the effect of the direct shear form K B , thus 2 4 2 C C K (10-7)
T di t th l t h t ill th ti
1234
2 4 2 CC C C KK K SB C T o pre di c t th e l arges t s h ear s t ress we w ill use th e equa ti on: 8 FD 3 8 d FD K B 1515
10.3 Deflection of Helical Springs
Using the strain energy method to include both the torsional and shear com p onents , thus p, AG lF GJ lTU 2 2 22
Substituting T= FD/2, l =DN, J=d
4 /32, A d 2 / 4 ih i i h AG GJ 2 2 A = d 2 / 4 , i n t h e prev i ous equat i on we h ave:
DNFNDF
U 2 2 4 32
24
W h e r e N = N a =n u m be r o f act i ve co il s G d G d U 2 4 16 Wee N N a u be o act ve co s
The total deflection ycan now be calculated by:
FDN N FD U 3 4 8
Since, C = D/d, the deflection
y becomes: G d FDN G d N FD F U y 24
4 8 w y (10-8) G d NFDy 43
8
The spring rate can be calculated by
G d (10-9) N DGd y Fk 34
8 17 y
10.4 Compression Springs
There are four standard types of ends in helical compression s p rin g s. The y are p lain end , s q uare d end , p lain- g roun d end , pg y p , q , p g , and squared-ground end. 18
A spring with plain ends has a noninterrupted helicoids; theends are the same as if a long spring had been cut intosections
. sections . A spring with plain ends that are squared or closed is obtainedby deforming the ends to a zero - degree helix angle by deforming the ends to a zero - degree helix angle . Springs should always be both squared and ground forimportant applications because a better transfer of the load is important applications , because a better transfer of the load is obtained.A i ith d d d d d bt A spr i ng w ith square d an d groun d en d s compresse d b e t weenrigid plates can be considered to have fixed ends. 19 The type of end used affects the number of active coils N a and the solid hei g ht of the s p rin g . gpg Square ends effectively decrease the number of total coils N t by approximately two: N t = N a +2 •For y s g ives an ex p ression for calculatin g the solid len g th of y gp g g squared and ground ends L s =(N t -a)d Where avaries, with an average of 0.75 which means in this case that the entry dN t in table 10-1 may be overstated. The way to check these variations is to take a spring and count the wire diameters in the solid stack 2020
Table 10-1 shows how the type of end used affects the number of coils and the spring length.
Types of Springs Ends
Term PlainPlain and
groundSquared or
ClosedSquared and
Ground
End coils,
N e 0122
e
Total coils,
N t N a N a +1 N a +2 N a +2
Free length,
L 0 pN a + dp ( N a +1) pN a +3 dpN a +2 d
Solid length,
L s d ( N t +1) dN t d ( N t +1) dN t
Pitch,
p ( L 0 - d )/ N a L 0 /( N a +1) ( L 0 -3 d )/ N a ( L 0 -2 d )/ N a21
Set removal or presetting:
22
Set removal or presetting:
A process used to
induce useful residualstresses.
It is done by makingthe
spring longer than the spring longer than needed and then compressing it to its lid hih L so lid h e i g h t L s . 23
This o
p eration sets the s p rin g to the re q uire d final free len g th p pg q g L 0 and, since the torsional yield strength has been exceeded, it induces residual stresses opposite in the direction to those induced in service induced in service . Set removal increases the strength of the spring and so is
especially useful when the spring is used for energy-storagepurposes.But, set removal should not be used when springs
are subjects to fatigue. 24
10.5 Stability
Compression coil springs may buckle when the deflection becomes too large.
The critical deflection is given by the equation:
( 10 10 )
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