The Study of EDM with Forced Vibration of Tool-Electrode*

The Study of EDM with Forced Vibration of Tool-Electrode" St. Enache (1). C. Opran, G. Stoica, E. StrBjescu; Polytechnical Institute of Bucharest/Romania Received on January 16,1990 The preaent Paper d e a l s with t h e phenomena t h a t appear i n E.D.M. using t h e i n t r o d u c t i o n o f t h e t o o l - e l e c t r o d e having forced v i b r a t i o n coupled w i t h t h e v i b r a t i o n of t h e t e c h n o l o g i c a l machining system. A mathematical model c o n f i r med by experimental research. is proposed f o r t h e t o o l - e l e c t r o d e motion and f o r t h e machining i t s e l f . There a r e a l e o prelrented t h e r e s u l t 8 o f t h e experimental r e a s a r c h e s performed f o r t h e small dimension machining.

m.:. ';16di%

:

e l e c t r i c a l discharge machining, t o o l e l e c t r o d e , forced v i b r a t i o n , v i b r a t i o n o f t h e t e c h n o l o g i c a l machining aystem, technological force, a a t h e n e t i c a l model

1. INTROUUCTIOR The a p p l i c a t i o n of e l e c t r i c a l discharge machining (EDM) under optimum c o n d i t i o n s r e q u i r e s thorough knowledge of t h e occurring technological phenomena, a s well a s a c t i v a t i o n of machining for i n c r e a s i n g production r a t e s , accuracy and q u a l i t y . For t h e s e purposes s e v e r a l new t e c h n o l o g i c a l elements are emoloyed i n machining, L e . , a d d i t i o n a l movements of t h e t o o l e l e c t r c d e , use of forced u l t r a s o n i c energy l o t h e working gap, uae of imposed magnetic f i e l d i n t h e working gep and forced v i b r a t i o n of t h e t o o l e l e c trode.

-

This paper describes a study o f FDM w i t h forced v i b r a t i o n of t h e t o o l e l e c t r o d e , coupled w i t h t h e techn o l o g i c a l v i b r a t i o n of t h e t e c h n o l o g i c a l machining system. I n v e s t i g a t f o n a have s t a r t e d from t h e assumption that, i n t h e machining p r o c e s s , t h e t e c h n o l o g i c a l v i b r a t i o n of t h e t o o l e l e c t r o d e is given by e t e c h n o l o g i c a l force. The t e c h n o l o g i c e l f o r c e is obtained by quantif y i n g t h e e f f e c t given by t h e p r e s a u r e waves occurring end developing i n t h e working gap, d u e t o t h e gee end vepour bubbles produced by mlcrodiechargee

:21* 133 The concept of t e c h n o l o g i c a l f o r c e has been i n t r o d u ced out of the n e c e s s i t y of modelling a s a c c u r a t e l y as p o s s i b l e t h e phenomena o c c u r r i n g during machining. I n EDY t h e t e c h n o l o g i c a l force is of a p u l s a t i n g nat u r e and can t h e r e f o r e be ooneidered a s a g e n e r a t o r of maintained t e c h n o l o g i c a l v i b r a t i o n s of t h e mschiD i n g head. The e f f e c t s of t h e t e c h n o l o g l c e l v i b r a t i o n coupled w i t h t h e f o r c e d l y introduced one c o n e i e t i n i n c r e a s i n g t h e machining e f f i c i e n c y , improving t h e removal of erosion products, decre8sing t h e roughness of t h e machined s u r f a c e , enhancing t h e e t e b i l i t y of t h e machining process.

Due t o t h e s e p o s i t i v e e f f e c t s , t h e EDM w i t h forced v i b r a t i o n of t h e t o o l e l e c t r o d e (EXM-FV) l a worth a thorough t h e o r e t i c a l and experimental study.

2. DXNAMIC STABILITY ANALYSIS OF THE BDY The e l e c t r i c e l diacharge p r o c e s s is b o r n t o involve two d i s t i n c t machining etages. I n t h e first, treneit o r y s t a g e , a p a r t from a c t i v e pulses r e s u l t i n g i n met e r i a l removal, t h e r e ale0 oocur i d l e p u l s e s or s h o r t c i r c u i t pulses. The second s t a g e , a s t a b l e one, is c h a r a c t e r i z e d by a l a r g e r amount o f metal removal, t h e machining c e n t r e of t h e machine b e i n g s t a t i o n a r y . The automatic a d j u s t i n g movement of t h e machining

Annals of the ClRP Vol. 3S?/l/liW

head w i t h t h e t o o l e l e c t r o d e is t h e b a s i c harmonic on whlch t h e random r i b r e t i o n e due t o t h e technologic a l f o r c e a r e superimposed.

I n t h e machining process, t h e ,,technologicel force: p t ( t ) is obtained by edding up, et a given moment and on a c e r t a i n s u r f a c e , t h e elementary f o r c e s of t h e p r e s s u r e waves d u e t o t h e occurence and expansion of g a s bubbles. The mathematicel expression i s d e r i v e d according t o equation ( 1 )

f /t) = / / P C ( t , r )-J'A t

(fl

(N

A

2 where A i e t h e t o o l e l e o t r o d e eurfaoe (m ), Pt(t,r) t h e technological specific pressure a s a function of t h e time t ( s ) and t h e r a d i u e r (m) o f t h e t o o l e l e c t r o d e (Pa).

-

Since, by c o n s t r u c t i o n , t h e machining heed of the machine has a high degree of r i g i d i t y , I n t h e first machining s t a g e t h e amplitude of t h e v i b r a t i o n s gener e t e d by t h e teohnological f o r c e is p r a c t i c a l l y neg l i g i b l e as a p i n e t t h a t due t o t h e t o o l r e s e t t i n g movement. Considering that t h e succession of p u l s e s f e a t u r e s e normal curve of u n i t s u r f a c e d i s t r i b u t i o n , t h e i r add i t i o n results i n t h e p l o t t i n g of a Gauas-Laplace type curve a s i n pig. 1.

fisl.

Variation

law of tchnologiral

forre

The v a r i a t i o n curve r e p r e e e n t e an o v e r a l l dependence of t h e technological p r e s s u r e on time over t h e d i s charge pulse duration. Hence t h e technological s p e c i f i c p r e s s u r e i s c a l c u l a t e d by meens of equation (2)

pt ( t , r ) =pot

.{(t)

(Pm

1

t2)

where pot(r) i s t h e a m p l i t u d e o f t h e t e c h n o l o g i c e l s p e c i f i c p r e s s u r e , end f ( t ) t h e v e r i a t i o n l a w of t h e technological f o r c e

-

(3)

The v a r i a t i o n of t h e teohnological e p e o i f i c p r e s s u r e depends on t h e e l e o t r i o e l parameters of t h e e l e o t r o -

167

discharge procsae troduced i n t o t h e epecific preasure r a d i u s end of t h e p o l g t r o p i c l a w 1s form (4)

where: C 'e 'e

(1) l

determining t h e energy amount l n working gap. A e t h e t e c h n o l o g i c a l is a f u n c t i o n of t h e t o o l electrode e l e c t r i c a l energy of t h e p u l s e , a proposed f o r e x p l l c i t n e a e i n t h e

a a c o e f f i c i e n t depending on t h e t o o l e l e c t rode charac t erlet i c e

-

The experimental study of t h e t e c h n o l o g i c a l f o r c e var i a t i o n depending on t h e p u l s e duration i s given i n Fig. 3. The v a r i a t i o n law i s of e l i n e a r type, acuording t o equation ( 8 ) t t h e c o e f f i c i e n t s have been determined by t h e method of l e e a t equares f o r a given i n t e n s i t y , being expreeeed i n equation (9).

a parameter depending on t h e p u l e s e l e o t r i c a l energg i n EDY.

m e n uelng a t u b u l a r e l e c t r o d e of e x t e r n a l r a d i u s r2 end i n t e r n a l r a d i u s r,a. i n t h e m c h i n i n g w i t h d i e l e c t r i o I n j e c t i o n , d u r i n g t h e s t a b l e machining e t a g e t h e t e c h n o l o g i c a l f o r c e eeeumee t h e followlng form (5)

(N1

I ! I

(5)

Equation (5) enablee t h e modelling of t h e dynamlc prooeee t o which t h e e l m t r o d e t o o l is subjected dur i n g machining becauee i t c o n t a i n s t h e t e c h n o l o g i c a l f a c t o r e c o n t r i b u t i n g t o t h e occurrence of t h e ineteb l l i t y phenomenon w i t h EDM. O f p a r t i c u l a r weight among t h e m a r e t h e o e c i l l a t i o n e introduced by t h e eystem of automatic adjuetment a n d f e e d , t h e v i b r e t i o n a eet up by t h e mlcrodischargea i n t h e working gap and t h e v i b r a t i o n a Introduced by t h e preeeure v a r i a t i o n e of t h e d i e l e c t r i c b e i n g c i r c u l a t e d i n t h e working gap. The v a r i a t i o n of t h e t e c h n o l o g i c a l f o r c e , t h e dynamice I n t h e gap r e p r e e e n t e one of t h e d i e t u r b i n g f a c t o r e of t h e t e c h n o l o g i c e l machining process.

600

ZOO

Fig. 3.

12A;

I adoI I I I I

6dO

WO lZ00 1400 1600

I

I f; u s ) .. Y

Tehnological fwce puls duration

Ft(f;J = ( 2 7 9

t

I

voriotion depending on

5,265.jO-lt;

(9)

The experimental study o f t h e t e c h n o l o g i c a l f o r c e var i a t i o n depending on t h e a c t u a l working s u r f e c e of t h e t o o l e l e c t r o d e I s given i n Fig. 4. Analyeis of t h e experimental r e s u l t s presented above emphasizes t h e double dependence of t h e t e c h n o l o g i c a l f o r c e on t h e worMng s u r f a c e and working i n t e n s i t y , i n accordance w l t h Fig. 5.

The experimental determioatlone of t h e t e c h n o l o g i c a l f o r c e have r e s o r t e d t o an annular dynamometer w l t h i n d i r e c t convereion having r e s i e t i v e tensometric t r a n a ducera. T h i s dynamometer h e been l n e e r t e d between t h e machining heed and t h e t o o l electrode. The meaeured parametere have been rendered evident by means of a BrIiel & Kjam meaeurlng l i n e . Tool e l e c t r o d e mat e r i a l , e l e c t r o l y t i c copper. Workpiece e l e c t r o d e material C 120 a l l o y e t e e l - X 2 1 0 C r 1 2 (WI-2080). Mac h i n e t o o l employed , ELBR-Ol-GEP 50-F-Ehctrotimig.

I

,

Fig. 4

The experimentel etudy of t h e t e c h n o l o g i c a l f o r c e var i a t i o n v e r e u s t h e c u r r e n t i n t e n e i t y l e g i v e n i n Fig. 2 , w l t h a r e s u l t i n g mlnimum about t h e v a l u e of 10 A. A s t a b i l i z a t i o n of e l e c t r i c a l diechargee occurs i n t h i e zone s i n c e t h e proceee t a k e s p l a c e under condit i o n a of mximum e t a b i l i t y .

0;

'

2

3

5

A(Cn)'

Variation of tehoioacal force o function of working surfore

5 IN 1 20

10

Fig 2 Technological force variation depending on average worklng current A s t h e variation law i e a p a r a b o l i c t y p e law, accord i n g t o equation (6), t h e c o e f f i c i e n t e have been determined by t h e m e t h o d of l e a s t equaree f o r a given p u l s e d u r a t i o n according t o equation (7).

168

V

0

*

9 12 IfA) Fig. 5. Variation o f tehnological force a s a function O f overage tforking current ond working surface

3

6

Making use, when i n t e r p r e t i n g t h e experimentel r e a u l t e , of t h e method of ,,responee eurfacee" and of t h e Taglor s e r i e s expansion about a c e n t r a l p o i n t i n

t h e i n t e r p o l a t i o n of t h e first degree polynomial 2 with two independent v a r i a b l e a , Xi=Ai (cm ) and %=I i(A) one o b t a i n s t h e v a r i a t i o n law of t h e ,,techn o l o g i c a l force" f u n c t i o n according t o equation (10).

F~ = 6 , + b,x, + h2x2

shown i n Fig. 7, i.e. a ayetem w i t h two degrees of freedom i n which t h e two masses a r e e l a s t i c a l l y coupled and i n v i b r a t i o n .

(f0)

The parameters bo, bl8 b2, determined following t h e experiments performed, r e s u l t i n t h e e x p l i c i t exp r e s s i o n f o r t h e technologioal f o r c e according t o equation (11).

5 ( A , I ) = -2,f4/66tf,79/66.A

iff)

+0,2889*1

The response s u r f a c e o f t h e f u n c t i o n Ft(A,I), o b t a i ned from t h e s p a t i a l diagram i n Fig. 5, r e p r e s e n t s a p l a n e i n space modelling t h e proceea atudied and o f fers a c l e a r image of t h e e l e c t r o e r o s i v e process. The r e s u l t s of t h e experimental i n v e s t i g a t i o n e p r e eented i n equations (7), (9), ( l l ) , confirm t h e theor e t i c a l assumptions. This f a c t enables t h e concept of t e c h n o l o g i c a l f o r c e t o be f u l l y cleared up, by d e t e r mining its magnitude and t h e way i t e f f e c t s t h e f o r o e equilibrium e x i s t i n g i n t h e working gap.

3. PHYSICAL AND MATHEMATICAL MODEL OF THX TOOL BLECTRODE BEHAVIOUR UNDER VIBRATORY CONDITIONS I N EDM I n t h e following, t h e determination of t h e equation of motion of t h e t o o l e l e c t r o d e w i l l be presented upon i n t r o d u c i n g forced v i b r a t i o n s . The v i b r a t o r y mot i o n of t h e t o o l e l e c t r o d e r e s u l t s from t h e v i b r a t i o n due t o t h e t e c h n o l o g i c a l f o r c e coupled w i t h t h e e l e c t r o m a g n e t i c a l l y introduced forced v i b r a t i o n . The electromagnetic v i b r a t o r y system is interposed between t h e machining head and t h e t o o l electrode. The 808l y s i a is made only f o r v i b r a t i o n s i n t h e v e r t i c a l mac h i n i n g d i r e c t i o n , on t h e machining head a x l e , t h e h o r i z o n t a l v i b r a t i o n 8 comparatively having n e g l i g i b l e v a l u e and influence.

-

It has been noticed experimentally t h a t , f o r t h e s t a b i l i t y s t a g e , a maximum v a l u e of t h e EDM meed i s obt a i n e d for a forced amplitude of t h e t o o l e l e c t r o d e v i b r a t i o n s between 2 and 4 / u m , a t a frequency of 100 m, Fig. 6 [3]. Or

R

300V 900fl

P

'T' Fat- 5

Fig. 7.

Fhisical model of E P N . w t h forced vibration of fool.&r-

bode ( C R M - F . V )

sin (w,

t)

Fig.8.

A

Physical model of forces with f m e d nbrofion of fml-

elerfmde ( t : D r i - F V )

I n f i g u r e s 7, 8 t h e following n o t a t i o n s have been used : M = mass of t h e machining head of t h e machine t o o l , (kg) I e l e s t i c constant of t h e machining head,(N/m)l m = mass of v i b r a t o r y e l e c t r o d e holder t o g e t h e r w i t h t h e t o o l electrode, (kg)r I$, e= l a s t i c constant of t h e forced v i b r a t o r y system,

(N/m) ' is much The r i g i d i t y and i n e r t i a o f t h e , ~ element g r e a t e r t h a t tho6e of ,,m"by v i r t u e of t h e machine t o o l d e s i g n . Consequently one may introduce t h e aimp l i f y i n g assumption t h a t t h e system w i t h two degrees of freedom can b e changed i n t o two systems w i t h one degree of freedom. The system made up of ,,W and t h e e l a s t i c element of c o n s t r n t KM n o t influenced by t h e v i b r a t i o n s of ,,m*l and t h e system formed by ,,m" a n d t h e e l a s t i c element of constant $, influenced by t h e v i b r a t i o n s o f ,,W*. As t h e first aystem has been p r e v i o u s l y examined u n d e r item 2 of t h e p r e s e n t paper, requires t o only t h e second system of t h e mass b e analyaed. During t h e s t a b l e condition s t a g e , t h e t o o l e l e c t r o d e is acted upon by t h e system of f o r c e s given i n Fig.8, made up of t h e p u l a a t i n g t e c h n o l o g i c a l f o r c e Fot and t h e p u l s a t i n g electromagnetic f o r c e generated by t h e v i b r a t i o n s o f t h e e l e c t r o m a g n e t i c a l l y introduced f o r c e s Foe,.

The d i f f e r e n t i a l equation of t h e e l e c t r o d e motion is given by equation (14).

-0-0-0-0-

2

Fig. 6

3

naferiaf removal rate

4

5

C3 -68 nF -iOOnF

' AemW

variation as a funchon of

joorccd vibrafion amplitude

i n t h e first t r a n s i t o r y s t a g e , t h e forced v i b r a t i o n amplitude is much less than t h e amplitude of t h e machining head o s c i l l a t i o n s , t h e forced v i b r a t i o n s can b e considered t o i n f l u e n c e t h e machining p r o c e s s only i n t h e s t e a d y - s t a t e stage.

AS

The p h y s i c a l model of t h e behaviour of t h e EDM techn o l o g i c a l system w i t h forced v i b r a t i o n of t h e t o o l is

The s o l v i n g of t h e d i f f e r e n t i a l equation r e s u l t s i n s o l u t i o n of type ( l 5 ) , considering t h e f a c t t h a t t h e system belongs t o t h e category of l i g h t damping, hence c e r t a i n terms may be neglected. r

where L d d is t h e own p u l s a t i o n of t h e s y s t e m u n d e r consideration

169

d d =m J 5

where: 117)

j-j/5)

Ce

U Hence t h e v i b r a t o r y motion o f t h e mass ,,m*' C o n s i s t s of X em, t h e v i b r a t i o n due t o t h e e l e c t r o m g n e t i c a l l y introduced forced v i b r a t i o n and X t , t h e 01b r a t i o n d u e t o t h e t e c h n o l o g i c a l force. The frequency of t h e v i b r a t i o n s due t o t h e technological f o r c e 4 is o f t h e o r d e r Id t 10 Hz, a s a g a i n s t t h e frequency of t h e electromagnetic v i b r a t i o n s of maximum 800 Hz. Therefore a g r a p h i c a l Overlap i n t h e l e a s t favour a b l e c a s e of t h e superposition of v i b r a t i o n s is shown in Fig. 9.

L

d yr

N

- constant of t h e v i b r a t o r used - supply v o l t a g e of t h e electromagnetic ( V) - c o i l length. (am)

vibrator,

- a i r gap l e n g t h , (nun) - &.lo+', (Wm) e l s t i v e magnetic p e r m e a b i l i t y of c o i l c o r e -- rnumber of c o i l windings - s u r f a c e of magnetic i n t e r e c t i s n ,

(ma2) s1 The amplitude of t h e t e c h n o l o g i c a l v i b r a t i o n of t h e e l e c t r o d e holder, t o g e t h e r with t h e t o o l e l e c t r o d e (,,m*') is determined by means of equation (24)

(25)

Fig 9.

Graphicul model o f vibration

vrbmhon

0'

i n E.DN tool-electrode(EDfl-FV)

with

'The mathematical expressions (ll), (18), (21), (24). e s t a b l i s h e d i n this paper enable a judicious d e t e r mination of t h e parameters $, $em, i n terms of I, ti, t o , A, such a s t o obtain maximum machining e f f i c i e n c y , improved exhaust of erosion products, enhanced q u a l i t y of machined s u r f a c e , increased s t a b i l i t y of t h e machlning process.

at

forced

-

It can b e noticed from t h i s f i g u r e t h a t t h e v i b r a t i o n amplitude 10 EDM has t h e following mathematical expression

4. CONCIUSIONS 1. The experimental i n v e s t i g a t i o n s have confirmed

where : $ = amplitude of r e s u l t i n g v i b r a t i o n hem = amplitude of forced electromagnetic v i b r a t i o n

(rm)

OJ m)

A,t

= amplitude of t h e v i b r s t i o n due t o technologic a l force ( p a ) ;

KAv = amplifying constant.

The operetion of t h e t e c h n o l o g i c a l system under cons i d e r a t i o n r e q u i r e s t h e ob j e c t i v e condition of avcid i n g t h e resonance between t h e v i b r a t o r y element of t h e e l e c t r o d e and t h e machining head, such that t h e e l e o t r o d e v i b r a t i o n s may not a f f e c t t h e work of t h e machining head r e s u l t i n g i n machining i n s t a b i l i t y . T h i s condition r e s u l t s from equation (20)

where : e l a s t i c i t y m o d u l u s of t h e working fluid,(H/m 2 ) S s e c t i o n of t h e hydraulic engine c y l i n d e r , ( m 2 ) Zu maximum s t r o k e of t h e machining hend p i s t o t i ,

B

--

(m>. The amplitude of t h e electromagnetic v i b r a t i o n o f t h e e l e c t r o d e holder, t o g e t h e r w i t h t h e t o o l e l e c t r o d e (,,mtt), is determined by means of equation (21).

170

t h e t h e o r e t i c a l assumptions, according t o which dur i n g EDM t h e r e oocur v i b r a t i o n s of t h e t o o l e l e o t r o d e due t o a technological f o r c e , c h a r a c t e r i s t i c of t h e machining. 2. The t e c h n o l o g i c a l f o r c e is a d i s t u r b i n g f o r c e of t h e t e c h n o l o g i c a l machining system, depending on t h e p u l s e d u r a t i o n , working i n t e n s i t y and working s u r f a c e of t h e t o o l electrode. The mathematical modell i n g haa enabled t h e EDM phenomena t o be cleared up. 3. I n EDH, t h e c o n t r o l l e d forced v i b r a t i o n of t h e t o o l e l e c t r o d e , p a r t i c u l a r l g f o r small machining d i mensions, r e s u l t s 1 0 increased p r o d u c t i v i t J I imprwed exhaust of r e s u l t i n g p a r t i c l e s , enhanced q u a l i t y of t h e machined surface, increased s t a b i l i t y of t h e mac h i n i n g process. 4. The v i b r a t o r y motion of t h e t o o l e l e c t r o d e is yielded by adding t h e v i b r a t i o n s of t h e t e c h n o l o g i c a l machining system t o t h e v i b r a t i o n s of t h e f o r c e d l y i n trod uc ed v i b r a t ory s g s t em. 5. Electrodischarge machining w i t h forced v i b r a t i o n of t h e t o o l e l e c t r o d e (EDM-FV) p r o v i d e s s i g n i f i c a n t t e c h n i c a l and economic advantages. REFERENCES R.Motoki, T.Ono, Bridge phenomenon in t h e gap l n s t a b i l i t y of low c u r r e n t discharge and high f r e quency o s c i l l a t i o n , 1977, 1.S.E.M.-5, WolfsburgSwiteerland, p. 49-52 H.Tsuchiya, T.IOOUe, Y.Mori, 1982, Generation and propagation of p r e s s u r e wave by spark discharge in l i q u i d , Annals CIKP, vol.31/1, p.107-110 G.StOiCa, 1 9 5 , T h e o r e t i c a l and Experimental Res e a r c h on t h e Influence of t h e Dynamic s t a b i l i t y o f t h e Tool Electrode-Linkpiece System i n BDM. Doctoral Thesis, Bucherest Polytechnic I n s t i t u t e V i l f r i e d Kllnig, 1979, Fertigungsverfahren, Band 3, Abtragen, MI Verlag GmbH, Dtisseldorf, F.R.G.