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U l t r a s o n i c W e l d i n g

T h e o r y

- P r i n c i p l e s

H P o t e n t e

Technologie der Kunstoff Universitfit-Gesamthochschule, Pohlweg 47/49

4790 Paderborn, Federal Republic of Germany

This paper looks into the fundamental phenomena of ultrasonic welding. It starts with a simple model rod, covering the

sound field, energy conversion and energy transmission. The geometrical dependence of ultrasonic energy transmission

and the energy conversion in the energy director are then examined on simple joined parts with real contact surface

geometries. Finally, criteria are set out fo r assessing the welding capacity of thermoplastics. The paper concludes by

showing the signO canee of oining pressurg for welded seam quality.

I n t r o d u c t i o n

Ultrasound welding has come to gain a

significant share of the market over the

past twenty years. A survey of the

developments and research of these

years may be found in references 1-2 2.

Welding machines are available both

as compact units and as ultrasonic kits.

The latter are purpose-designed for

incorporation in special machines pro-

duction lines and multiple-head plants.

Automatic welding machines with up to

62 sound generators are now built for

large parts - such as motor car instru-

ment panels and bumpers.

The key to the success of this process

lies chiefly in the very short welding

times. These are generally in the order

of magnitude of 0.1 to 1 sec. I t must

however be added that the moulded

part and the process must be precisely

tailored to each other since the shape

of the part influences the welding

process to a much greater degree than in

any other method. Failures with this

process are generally due to a lack of

coordination between the machine manu-

facturer and the user.

This paper will look into the basic

principles and the theory behind ultra-

sonic welding.

S o u n d f ie ld a n d e n e r g y c o n v e r s i o n

When plastics are joined by ultrasonic

welding longitudinal vibrations are

transmitted from the sonotrode to the

parts being joined. The frequency of the

vibrations lies between 20 and 50 kFIz.

A stationary wave field forms in the

joined parts. This has a decisive in-

fluence on the energy transmission and

the energy conversion. Theoretical

predictions about the wave field are

only possible in the simplest of geo-

metrical cases.

This is to be explained in greater

F i g . 1

F r i n g e p a t t e r n o f th e s o u n d f i e ld a n d e n e r g y

c o n v e r s i o n i n a r o d 1 0 1 3

2 2 8 M A T E R I A L S D E S IG N V oL 5 O C T O B E R / N O V E M B E R 1 9 8 4

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d e t ai l t a k i n g th e e x a m p l e o f a r o d

i r r a d ia t e d b y u l t r a - s o u n d 1 0 , 1 3 . F ig u re 1

l e f t ) s h o w s t h e f r i n g e p a t t e r n o f a

s t a t i o n a r y l o n g i t u d i n a l w a v e . T h e r o d i s

p l a c e d o n a r e v e r b e r a n t s u p p o r t s t e e l

a n vi l) . W e l l - f o c u s e d z o n e s a n d o u t - o f -

fo c u s , i . e . b lu r re d r e g io n s a re v i s ib l e in

t h e F i g u r e .

P r o c e e d i n g f r o m t h e s u p p o r t u n d e r

th e ro d , i . e. t h e s t e e l a n v i l , t h e f i r s t w e l l -

f o c u s e d z o n e o c c u r s a t a r o d l e n g th o f

l

---- X / 4 t h e s e c o n d a t 3 X / 4 a n d t h e n t h

a t 1 = n X / 2 + ) , / 4 , w h e r e ) k i s t h e

w a v e l e n g t h . T h e s e r e g i o n s a r e t h e

z o n e s o f m a x i m u m v i b r a t i o n a l a m p li -

t u d e . T h e p o i n t s o f m a x i m u m a l t e r n at i n g

s t r a i n o r a l t e r n a t i n g s t r e s s a r e p h a s e -

s h i ft e d b y a q u a r t e r w a v e l e n g t h i n e a c h

c a s e . T h e s e a r e t h e b l u r r e d a r e a s i n

F i g , 1 . T h e y l ie m i d w a y b e t w e e n t w o

w e l l - f o c u s e d z o n e s . T h e p l a s t i c o n l y

s o f t e n s a n d f u s e s i n t h e r e g i o n o f

m a x i m u m s t r a i n o r s t r e s s F i g . 1 , r i g ht ) .

A f u r t h e r z o n e o f f u s e d p l a s t i c o u g h t

t h e o r e t i c a l l y t o h a v e o c c u r r e d i n t h e

r e g i o n o f t h e r o d s u p p o r t . T h e r e a s o n

f o r i t s a b s e n c e i s t o b e f o u n d

a ) i n t h e h i g h s o u n d a b s o r p t i o n o f th e

f u s e d z o n e s a b o v e i t

b ) i n t h e h i g h h e a t t r a n s f e r h e a t

c o n d u c t i o n ) i n t h e s t e e l a n v i l .

W i t h a so u n d - a b s o rb e n t s u p p o r t - i n

t h e e x t re m e c a se , a i r - t h e m a x i m u m

v i b r a t io n a l a m p l i t u d es o c c u r a t r o d

l e n g t h s o f l = n ) k / 2 w h e r e n = 0 , 1 , 2 .. ..

a n d t h e m a x i m u m s t r a i n o r st r e s s a t I =

n ) k / 2 + ) k / 4 .

T h e c o n c l u s i o n t o b e d r a w n i n it i al l y

f r o m t h e s e m o d e l i n v e s t i g a t i o n s i s t h a t

w e l d e d s e a m s m u s t b e p l a c e d i n t h e

a r e a o f m a x i m u m s t r ai n o r s tr e ss .

T h e e n e r g y t r a n s m i s s i o n f r o m t h e

s o n o t r o d e t o t h e r o d i s li k e w i s e d e p e n d -

e n t o n g e o m e t r y . W i t h a r e v e r b e r a n t

t e r m i n a t io n , m a x i m u m e n e r g y t r a n s -

m i s s i o n i s o b t a i n e d w i t h r o d l e n g t h s o f

1 - - n ) k / 2 + ) k / 4 w h e r e n = 0 , 1 , 2 . . .)

a n d w i t h a s o u n d - a b s o r b e n t t e r m i n a -

t i o n a t 1 = n ) k / 2 . M i n i m u m e n e r g y

t r a n s m i s s i o n o c c u r s a t r o d l e n g t h s

p h a s e - s h i f t e d b y a q u a r t e r w a v e l e n g t h

i n e a c h c a s e .

T h e s e s i m p l e m o d e l i n v e s t i g a t i o n s

a l r e a d y s h o w t h e d e c i s i v e i n f lu e n c e o f

m o u l d e d p a r t g e o m e t r y o n t h e t r a n s -

m i s s i o n o f u l t r a -s o u n d a n d o n t h e

c o n v e r s i o n o f th e s o u n d i n t o h e a t.

E n e r g y t r a n s m i s s io n

F l a t c o n t a c t s u r f a c e s a r e u n s u i t ab l e f o r

u l t r a s o n i c w e l d i n g . T h e r e a s o n f o r t h is

w i l l b e g i v e n l at e r. T h e c o n t a c t s u r f a c e

g e o m e t r i e s d e p i c t e d i n F i g s . 2 a n d 3

h a v e p r o v e d s u c c e s s f u l , w i t h t h e g e o -

m e t r i e s s h o w n i n F i g . 2 g e n e r a l l y b e i n g

u s e d f o r a m o r p h o u s t h e r m o p l a s t i c s a n d

t h o s e i n F i g . 3 f o r s e m i - c r y s t a l l i n e

- : - 0 1

F i g 2

C O

Q U

C o n t a c t s u r f a ce g e o m e t r i e s r e f 2 0

MATERIALS DESIGN VoL 5 OCTOBER/NOVEMBER 1984 229

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t hermop l as t i cs .

Al m os t a l l con t ac t su rf ace geomet r i es

h a v e a V - s h a p e d t o n g u e . T h i s i s c a l le d

t he ene rgy d ir ec t o r. Th i s energy d i r ec t o r

c a n b e v i e w e d i n g o o d a p p r o x i m a t i o n

a s a f e a t h e r k e y w h i c h c o n n e c t s t h e

u p p e r a n d l o w e r j o i n c o m p o n e n t s t o

e a c h o t h e r .

H e r e a g a i n th e r e a r e j o i n e d p a r t

geomet r i es and c r i t i ca l l eng t hs where

n o e n e r g y t r a n s m i s s i o n t a k e s p l a c e

f r o m t h e s o n o t r o d e t o t h e p a r t b e i n g

j o i ne d . W i t h s i m p l e jo i n e d p a r t g e o -

m e t r i e s s u c h a s r o d , p a n e l o r p i p e

sys t ems , t hese c r i t i ca l l eng t hs can be

c a l c u l a t e d b y t h e f o l l o w i n g e q u a t i o n

ref. 11, 13:

s - 7 m I . +

T h e p a r a m e t e r s c o n t a i n e d i n t h i s

equat i on a re p resen t ed i n F i g , 4 . Para-

me t er s lb and Sb can be i n f l uenced w i t h in

cer t a i n l i mi t s by t he j o i n i ng p ressu re

s t a t i c con t ac t p ressu re) .

I f the v i b ra t i ona l am pl i t ude a t t he

s o n o t r o d e o u t p u t is e n t e r e d a s a m e a s u r e

o f t h e e n e r g y t r a n s m i s s io n , t h e n t h e

cr i t i ca l l eng t hs can be es t ab l i shed expe r i -

m e n t a l l y . F i g u r e 5 s h o w s a n e x a m p l e o f

t h i s r e f. 12 , 13 . The c r i t i ca l va l ue here i s

24 .4 hUrL Th e va l ue o b t a i ned t heo re t i -

ca l l y i s 24 .6 mm.

I - - -

1

' / / / A

t . ~

Fig . 3 Contact surface geom etr ies re f 20

+ 1 . = ?

T h i s p r o n o u n c e d d e p e n d e n c e o f t h e

t r a n s m i tt a b l e e n e r g y o n t h e g e o m e t r y o f

t h e j o i n e d p a r t o c c u r s p r i m a r i ly a t h i g h

j o i n i n g p r e s s u r e s . I t c a n b e r e d u c e d

a l m o s t c o m p l e t e l y i f th e j o i n in g p r e s s u r e

s t a t i c con t ac t p ressu re) i s l owered

a c c o r d i n g l y F i g 6 ) . T h e r e is t h e n,

h o w e v e r , a d a n g e r o f t h e s o n o t r o d e

l e a v in g m a r k s o n t h e s u r f a c e o f t h e j o i n e d

p a r t . T h e s e m a r k s c a n b e a v o i d e d i f

po l ye t hy l ene f i l m o r s i mi l a r i s p l aced

b e t w e e n t h e s o n o t r o d e a n d t h e p a r t b e i n g

j o i ned .

A p a r t f r o m t h e j o i n in g p r e s s u r e , t h e

sono t rode mass a l so has an i n f l uence .

T h e g e o m e t r y - d e pe n d e n c e o f th e e n e r g y

t r ansmi ss i on f a l l s wi t h an i ncreas i ng

sono t rod e mass r e f . 12 , 13 .

En e r g y c o n v e r s i o n

A s h a s a l r e a d y b e e n s h o w n w i t h t h e

exam pl e o f t he rod i r r ad i a t ed wi t h u l t r a -

sound , t he m at er i a l fu ses a t po i n t s o f h igh

a l t e rna t i ng s t r a i n o r s t r ess . Fo r t he

e n e r g y d i r e c t o r t h i s m e a n s t h a t a h i g h

v i b ra ti ona l ampl i tude , A , mus t be p resen t

at i t s input . A t i t s output , i .e . at the poin t

o f c o n t a c t w i t h t h e l o w e r j o i n e d p a r t , b y

con t r as t , t he ampl i t ude shou l d be as

smal l as poss i b l e , o r i n t he i dea l case ,

zero . The m ax i m um s t r a i n ~ i s t hen , by

wa y o f a fi r s t app rox i mat i on , t he qu o t i en t

o f t he d i f f e r ence i n v i b ra t i ona l ampl i -

t u d e s A A a n d t h e h e i g h t o f th e e n e r g y

d i r e c t o r Ib E ~ A A f l b ) .

F i g u r e 7 s h o w s m e a s u r e d v i b r a t io n a l

osci l lat ion dis tr ibut ions in d i f feren t p lane s

SO ~

L

~ S C D

/ / / / / / / / / / / / / / /

/ / / / / / ~ /

Fig . 4 Diagram matic sketch of a

rod shaped jo ine d part geometry

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1 2

p m

9