Lecture 8 Design of Springs Revised (4)-madany rev3 - KSU

65337_3design_of_springs.pdf

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

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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.

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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
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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 )