springs 304

Outline Spring Functions & Types Helical Springs

CompressionExtensionTorsional

The Function(s) of Springs

Most fundamentally: to STORE ENERGY

Many springs can also: pushpulltwist

Some Review

F

y

k

linear springs: k=F/y

nonlinear springs:dy

dFk

Parallel

ktotal=k1+k2+k3

Series

321

1111

kkkktotal

Types of SpringsHelical:

Compression

Extension Torsion

More Springs

Washer Springs:

Beams:Power springs:

Helical Compression Springs

d diameter of wireD mean coil diameterLf free lengthp pitchNt Total coils

may also need:Do and Di

Length Terminology

Free Length AssembledLength

Max WorkingLoad

Bottomed Out

minimum of 10-15%clash allowance

Lf La Lm Ls

End ConditionsPlain

Square

Plain Ground

Square Ground

Na=Active Coils

F

F

F

F

Stresses in Helical SpringsSpring Index C=D/d

C

CKwhere

d

FDK ss 2

12,

83max

FF

T

T

Curvature Stress

under static loading, local yielding eliminates stress concentration, so use Ks

under dynamic loading, failure happens below Sy: use Ks for mean, Kw for alternating

Inner part of spring is a stress concentration(see Chapter 4)

Kw includes both the direct shear factor and the stress concentration factor

CC

CKwhere

d

FDK ww

615.0

44

14,

83max

Spring Deflection

Gd

NFDy a

4

38

Spring Rate

Gd

NFDy a

4

38

aND

Gdk

3

4

8

k=F/y

Helical Springs Compression

NomenclatureStressDeflection and Spring ConstantStatic DesignFatigue Design

Extension Torsion

Static Spring Design Inherently iterative

Some values must be set to calculate stresses, deflections, etc.

Truly Designthere is not one “correct” answermust synthesize (a little bit) in addition to

analyze

Material Properties

Sut ultimate tensile strengthFigure 13-3Table 13-4 with Sut=Adb

Sys torsional yield strengthTable 13-6 – a function of Sut and set

Spring/Material Treatments Setting

overstress material in same direction as applied load» increase static load capacity 45-65%» increase energy storage by 100%

use Ks, not Kw (stress concentration relieved) Load Reversal with Springs Shot Peening

What type of failure would this be most effective against?

What are You Designing?

Given

F, yk, y

Find

kF

Such that:Safety factor is > 1Spring will not buckleSpring will fit in hole, over pin, within vertical space

d, C, D*, Lf*, Na

*, clash allowance ()**, material**

design variables

+

* - often can calculate from given** - often given/defined

Static Spring Flow Chart

STRESSES

Ns=Sys/

for shut spring if possibleif not, for max working load

if GIVEN F,y, then find k; If GIVEN k, y, then find F

D, Ks, Kw

material strengths

DEFLECTION

Lf, yshut, Fshut

Three things to know:• effect of d• shortcut to finding d• how to check buckling

ITERATE?

d, C

material

Na,

CHECK

buckling, Nshut, Di, Do

Nshut=Sys/shut

Static Design: Wire Diameter


3max8

d

FDKs

Gd

NFDy a

4

38

**see Example 13-3A on MathCad CD*maintain units (in. or mm) for A, b

use Table 13-2 to select standard d near calculated d

)2(115.08

b

m

initialworksAK

FFCNd

Based on Ns=Ssy/ and above equation for :

Km=Sys/Sut

Buckling

f

workinginit

f

L

yyy

D

LRS

..




Extension Torsion

Material Properties Sus ultimate shear strength

Sus0.67 Sut

Sfw´ torsional fatigue strengthTable 13-7 -- function of Sut, # of cycles repeated, room temp, 50% reliability, no corrosion

Sew´ torsional endurance limit for steel, d < 10mmsee page 816 (=45 ksi if unpeened, =67.5 ksi if

peened) repeated, room temp., 50% reliability, no corrosion

Modified Goodman for Springs Sfw, Sew are for torsional strengths, so von

Mises not used

0.5 Sfw

0.5 Sfw

a

m

Repea

ted

SfsC

B

Sus

A

fwus

usfwfs SS

SSS

5.05.0

Fatigue Safety Factor

0.5 Sfw

0.5 Sfw

a

m

Sfs

Suslo

ad li

ne

Sa

a

i m

mload

mgooda

afs

SN

a,load = a,good at intersection

ausimfs

iusfsfs SS

SSN

…on page 828

Fi=Fmin

Fa=(Fmax-Fmin)/2

Fm=(Fmax+Fmin)/2

What are you Designing?

Given

Fmax,Fmin, yk, y

Find

kF

Such that:Fatigue Safety Factor is > 1Shut Static Safety Factor is > 1Spring will not buckleSpring is well below natural frequencySpring will fit in hole, over pin, within vertical space

d, C, D*, Lf*, Na

*, clash allowance ()**, material**

design variables

+

* - often can calculate from Given** - often given/defined

Fatigue Spring Design Strategy

d, C

if GIVEN F,y, then find k; If GIVEN k, y, then find F

Nshut=Sys/shut

CHECKbuckling, frequency,Nshut, Di, Do

D, Ks, Kw

material strengths

DEFLECTION

Lf, yshut, Fshut

Two things to know:• shortcut to finding d• how to check frequency

ITERATE?

material

Na,

STRESSES

ausimfs

iusfsfs SS

SSN

Fatigue Design:Wire Diameteras before, you can iterate to find d, or you can use an equation

derived from relationships that we already know:

)2(1

min 134.11

67.0

8b

awfw

b

sfs

fsms

fsFK

S

AdFK

N

NFK

A

CNd

use Table 13-2 to select standard d near calculated d


**see Example 13-4A on MathCad CD*maintain units (in. or mm) for A, b

Natural Frequency: Surge


Surge == longitudinal resonance

for fixed/fixed end conditions:

an W

kgf

2

1 (Hz)

…see pages 814-815 for more

ideally, fn will be at least 13x more than fforcing… it should definitely be multiple times bigger

Review of Design Strategy

Find LoadingSelect C, d

Find stressesDetermine material propertiesFind safety factor

Solve for d, pick standard dFind stressesDetermine material propertiesCheck safety factor

Find LoadingSelect C, safety factor

ITERATIVE USING d EQUATION

Strategy Review Continued

Find spring constant, Na, Nt

Find FSHUT (must find lengths and y’s to do this)Find static shut shear stress and safety factor

Check Buckling

Check Surge

Check Di, Do if pin to fit over, hole to fit in

Consider the Following:



Extension Torsion

Extension Springs

As before, 4 < C < 12

However, no peening, no setting,no concern about buckling

aws forKused

FDK

,

83max

surge check is same as before

Lb=d(Na+1)

Difference 1: Initial Force

deflection y

force F

Fi

“preloading”

F=Fi+kya

i

ND

Gd

y

FFk

3

4

8

Difference 1a: Deflection

Gd

NDFFy ai

4

3)(8

Difference 2: Initial Stress

take initial stress as the average stress between these lines, then find Fi

Difference 3: Ends!: Bending

23416

d

F

d

DFKba

Cd

D

d

RC

CC

CCKb

2

22

)1(4

14

11

11

121

67.0

)(

)(

min

min

ese

altutmeane

utefb

SS

SS

SSN

standardend

Difference 3a: Ends: Torsion

44

14,

8

2

23max 22

C

CK

d

FDK ww

C2=2R2/d

pick a value >4

Materials

Sut – Same

Sys, Sfw, Sew – same for body

Sys, Sfw, Sew – see Tables 13-10 and 13-11 for ends

Strategysimilar to compression + end stresses - buckling



Extension Torsion

Torsion Springs

• close-wound, always load to close

Deflection & Spring Rate

Ed

MDN

DNwireoflengthLEI

ML

aroundwirerev

aww

rev

4, 8.10

,2

1

rev

Mk

Stresses

Compressive is Max – Use for Static – Inside of Coil

3maxmax 32

max d

MK

I

cMK

ii bbi

)1(4

14 2

CC

CCK

ib

For Fatigue – Slightly lower Outside Tensile Stress – Outside of Coil

)1(4

14 2

CC

CCK

ob

3max32

max d

MK

obo

3min32

min d

MK

obo

Materials

see Tables 13-13 and 13-14, page 850

follow book on Sewb=Sew/0.577… for now

Strategy

M K

• fit over pin (if there is one)• don’t exceed stresses

Select C, d



Extension Torsion

springs 304

Documents

active coils f f f fstresses

springswasher springs

power springs

fynonlinear springs

c material na

sysshut static design

store energymany springs

effect of dshortcut