CALCULATION OF SIZE OF STRUCTURAL CONSTITUENTS OF METAL DEPOSITED BY INDUCTION METHOD WITH APPLICATION OF MECHANICAL VIBRATION

CALCULATION OF SIZE

OF STRUCTURAL CONSTITUENTS OF METAL

DEPOSITED BY INDUCTION METHOD

WITH APPLICATION OF MECHANICAL VIBRATION

V .S . S E N C H IS H IN and C h .V . P U L K A

T ern o p o l Ivan P u lu j N ational T echnical U n iv ersity , M S E U

56 R usskaya S tr ., 46001, T ern o p o l, U kraine. E-m ail: V ik to r_ S y n ch y sh y n @ i.u a

P o ssib ility of re g u la tio n of s tru c tu re of d ep o sited m etal allow s im p ro v in g service p ro p e rtie s o f th e p a rts. P resent w o rk stu d ie s th e processes of refin in g o f stru c tu re ol d eposited m etal a t a p p lic a tio n of h o rizo n tal m echanical v ib ra tio n . C a lc u la tio n m odel lo r d e term in atio n of p aram eters o f m etal s tru c tu re of PG-S1 ty p e allo y , d ep o sited by in d u c tio n m ethod a p p ly in g m echanical v ib ra tio n , w as developed. G rap h ic dependencies of c a rb id e c o n s titu e n ts in th e d eposited m etal on v ib r

received re la tio n sh ip s. 9 R ef., 5 Figures.

K e y w o r d s : d e p o site d m e ta l, in d u c tio n surfacing, stru ctu re, vib ra tio n , s im u la tio n

W o rk s [1 -3 ] trie d to d ev elo p a q u a n tita tiv e th e ­ ory of effect of p a ra m ete rs of m echanical v ib ra ­ tio n on solid ificatio n of m etal m elts. The c alc u ­ lations w ere based on ideas of au th o rs of w ork [4] on e v alu a tio n o f b reak in g of co ag u latio n stru c tu re s in e le c tro ly te s by v ib ra tio n field. P re­ sen t w ork also uses d a ta of th ese in v estig atio n s [4] in developm ent of m ath em atical model for refin in g of s tru c tu re of d ep o sited m etal of high- carbon chrom ium PG-S1 ty p e allo y (so rm ite 1) by v ib ratio n field.

C a lc u la tio n m o d el fo r e v a lu a tio n o f c ffe c t o f v ib ra tio n p a ra m e te rs on s tru c tu r e o f d e p o ­ s ite d m e ta l. W o rk [5] based on resu lts of e x p eri­ m ental in v estig atio n s show ed th a t a p p licatio n of m echanical v ib ra tio n s d u rin g su rfacin g can have am biguous effect on c h arac te ristic s of deposited m etal. Aim of th e p resen t w ork is developm ent of m ath em atical m odel, w hich allo w s d e term in ­ ing optim um values of v ib ra tio n a m p litu d e and frequency using c a lc u la tio n m ethod. They will provide th e b est service c h arac te ristic s of depos­ ited m etal. Size of carb id e inclusions in deposited m etal is tak en as o p tim a lity c riterio n .

Let us consider (F ig u re 1) s u b stra te -m e ta l m elt on su b stra te system , w hich v ib ra te s along th e deposit surface w ith frequency w and am p li­ tu d e a. The th ick n ess of m etal m elt is regarded as relativ ely sm all (5].

G roups o f m etal p a rtic le s jo in e d in c lu sters as a re su lt of c o ag u latio n , i.e. adhesion of these particles (see F igure 1), are form ed in m olten

C V.s. M'N( JifsiliN 4(1(1 Cli.V. PULKA, 2015

at ion a m p litu d e and frequency w ere p lo tte d based on

m etal in su rfacin g . P a rticle s, rep resen tin g th e m ­ selves sm all clu sters (>0.1 |im ), are jo in ed in larg er on size (<100 }im). T his process ta k es p lace in th e follo w in g w ay [6]. M o lten m etal is con­ sidered as e lec tro ly te. Forces of d ifferen t n a tu re (F ig u re 2) a ct betw een th e p a rtic le s of m olten m etal. A pp ro ach in g of disperse phase p articles prom otes for d isjo in in g pressure of m etal liquid w hich is betw een them . T his pressure is d e te r­ m ined by m olecular a ttra c tin g forces and elec­ tro s ta tic rep u lsiv e forces. A ttra c tin g forces are V an d er W aals forces, w hich co n sist of forces of o rie n ta tio n , in d u ctio n and dispersion in teractio n . R epulsive forces a p p ear in o v e rla p p in g of p article diffusion layers.

C o n d itio n of th e system is d e term in ed by b a l­ ance of a ttra c tio n an d rep u lsiv e energies, w hich is d eterm in ed by eq u atio n

v = fic ~ kh - A h ' 2 , (1 )

w here U is th e sum energy of p a rtic le in te ra ctio n ;

B is th e m u ltip lie r d e p en d in g on valu e of e lectric

--- O --- 1 1

--- ► Attracting 4 - ■ - ■ Repulsive

Figure 2. Force action betw een th e particles in m etal melt

potentials, properties of environm ent, and tem ­ perature; k is th e value inverse to diffusion layer thickness; h is th e distance betw een particles; A is the constant of m olecular a ttractin g forces (H am aker co n stan t). Sum energy U will be nega­ tive (secondary potential m inim um ) a t large dis­ tances betw een th e particles. Energy U at average distances (around 100 j,im) will be positive, th at means form ation of energy barrier, i.e. electro­ static repulsive forces prevail at th is distance. At close distances w ith prevailing attractiv e forces, sum energy U of interaction of particles will be positive (prim ary potential m inim um ). If energy, which corresponds to potential barrier, is lower th an kinetic energy of particles, then they can overcome electrostatic repulsive forces and ap­ proach to very small distance (overlapping of double electric layers take place), at which mo­ lecular attractive forces prevailing.

Particles are stuck together as a result (i.e. fall in th e closest potential w ell) (Figure 3 ). This deep potential well explains mechanical strength of coagulate. The particles at close distances are bonded due to Van der W aals forces, and formed aggregates acquire some properties of solid body. If energy barrier is high, the particles can not overcome it and develop aggregates.

Figure 3. O verlapping of double electric layers and adhesion

o f particles in m elt

Reduction of energy barrier decreases aggre­ g ate resistance of th e system. For exam ple, add­ ing of electrolyte can reduce thickness of diffu­ sion layer and, thus, decreasing repulsive forces so th a t energy barrier will escape and particles stick to each o ther a t approaching.

Thus, there are prim ary and secondary poten­ tial wells, depth of which is marked by potential constituents Ej, E 2 and w idth by h\ and h2, re­

spectively. M ovement of particles of diam eter D in the vicinity of each potential maximum is rep­ resented as oscillations of harm onic oscillator re­ spectively to own frequencies /^, /*2, which are found based on solution of Schroedinger equation [4, 7] approxim ated in th e following way:

f\ ~ ^ E xir?mTx. /2 * ^E 2h22m~l . <2>

where E v E 0 values are determ ined based on [4] in such a way:

Ex = nBD[0Mh~xl - 0.5y40( l - In (12/40^1yi“1) ) l1 E2 = nBDh22(0.5 - r t f j 1)* (3)

* = ^&nq2Mz'lT~l •

In this case A Qt A , B are the constants which depend on system properties [4]; n is th e number of particles in structure which are close to the considered; N is the electrolyte concentration (m olten m etal); T is th e tem perature in energy units; q is th e charge of electrolyte ions; z is the dielectric constant; m is th e particle mass.

Under static conditions criterion of structure stability will be determined [4] by such inequality:

£ , > 0.5(p0 - p)D*ghx,

3 1 (4)

E2 > O.D(p0 - p)D gh2,

Ex > pr, E2 > pT. (5) Here p0, p are th e density of dendrite and m olten m etal, respectively; g is th e gravitation accelera­ tion; (i 55 1.

Let us consider effect of vibration on structure of m olten m etal, when dendrites of larger size H are formed in it from average size clusters, th a t in given case corresponds to inequality

H2 » r v » - ' p- \ (6> where r) is the average dynam ic toughness of mol­ ten metal.

Such big aggregates are not going to oscillate in molten m etal. F u rth er, oscillations of m elt w ith am plitude a and frequency co are recoded. At th a t, rate i :(£) of oscillation of m elt along the deposit surface on coordinate x can be w ritten in the following way:

X ( t ) = Obi s in to t. (7)

T h e n p o w e r P , a c tin g o n su ch m o v in g p a rtic le o f d ia m e te r D , w ill b e d e te r m in e d a c c o rd in g to 14, 81 in su ch a w ay :

(8₎

T a k in g in to a c c o u n t m e n tio n e d above, eq u atio n of forced v ib ra tio n s of s tu d ie d d e n d rite p a rtic le is w ritte n resp ectiv ely in th e p rim ary p o te n tia l well (p rim a ry c o a g u la tio n ) u n d e r effect of v ib ra tio n and e x te rn a l force in such a form [4, 7]:

x + 2 \x + f \ x = Pm~x sin cot.

In th is case £ » n r\D 2m ~xh~x{.

L in e a r d iffe re n tia l e q u a tio n o f th e second o r­ d e r w ith c o n s ta n t c o e ffic ie n ts ( 9 ) is so lv ed via re p re s e n ta tio n o f th e re q u ire d fu n c tio n x ( t ) in trig o n o m e tric form . As a r e s u lt th e n e x t law of p a rtic le o s c illa tio n in d e n d r ite v o lu m e is re ­ ceived:

(9)

x ( t ) = V Q sin ((Of + a 0),

(

10

)

w h ere it is fo rm a lly ta k e n t h a t in itia l phase a 0 e q u a ls zero a n d a m p litu d e V 0 of forced o scilla ­ tio n s o f th e p a rtic le e q u a ls

d o

a) is a lw a y s c o n s ta n t, p ro m o te s re c eiv in g o f th e fo llo w in g re la tio n s h ip s for e v a lu a tio n o f v ib ra ­ tio n p a ra m e te rs fo r e a rlie r s e le c te d v a lu es o f d i­ a m e te r D o f th e p a rtic le s fo r w h ich d e n d r ite is deco m p o sed : 2 ^ 0.5(2/? - 442 jr~ 2 n § L |J

(»

lr2 + 4 p~2ET2r\*a*h + ‘^0.25(2/’j ~ 442 + 4p 2D V * V > 2 “ /? *

f xp2D2hU<o4 - (2f] - 4 & V + /11

(16) If p a rtic le o f d ia m e te r D ju m p s o u t from th e p o te n tia l w ell in v ib ra tio n , th a n p h y sica lly it m eans t h a t d e n d rite c o n sistin g of such p a rtic le s w ill s ta r t to c o lla p se . I t is p o ssib le o n ly if am ­ p litu d e V 0 of its o sc illa tio n s is la rg e r th a n w id th o f th e p rim ary p o te n tia l w ell Aj, i.e. it com es o u t o f th e lim its o f e ffe ct o f su rfa c e force, o r receive such en erg y , w hich ex ceeds d e p th of p o te n tia l w ell E j, a n d m oves as in ab sen ce of su rface forces. B ased on re la tio n s h ip s ( 3 ) , ( 8 ) a n d (1 1 ) th ese co n d itio n s can be w r itte n m a th e m a tic a lly in such a form:

Vo

(12)

T h u s, if c h a ra c te ris tic s o f m o lte n m etal f u g ,

p, rj, //j a re s e t, th a n c o rre sp o n d in g p a ra m e te rs o f v ib ra tio n co a n d a based on re la tio n s h ip s (1 6 ) can be found for set g ra in size D o f s tru c tu r e o f d e p o sited m etal.

C a lc u la tio n o f p a r a m e te r s o f s tr u c tu r e o f d e ­ p o s ite d m e ta l. In v e s tig a tio n s o f s tru c tu re o f m e t­ al d e p o sited by in d u c tio n m e th o d w ith o u t a n d w ith a p p lic a tio n o f v ib ra tio n s [5] w ere c arrie d o u t for v e rific a tio n o f c o rre ctn ess o f s ta te d m o d e l.

F la t specim ens from steel S t3 w ere d ep o sited ( F ig u re 4 ) w ith h o riz o n ta l v ib ra tio n a n d w ith o u t it for p e rfo rm an ce of in v e stig a tio n s by in d u c tio n m eth o d u sin g c h arg e c o n ta in in g p o w d e r of PG-S1 a llo y . T h e su rfa c in g w as c a rrie d o u t u sin g high- freq u en cy g e n e ra to r of V C h G - 6 0 /0 .4 4 ty p e a t c o n s ta n t specific p o w er W a n d tim e o f su rfa cin g

I:. T he m odes w ere s im ila r for tw o su rfa c in g v a ri­

a n ts, i.e. an o d e v o lta g e 10 kV ; c irc u it v o lta g e 5.4 kV; c u rre n t o f lam p g rid 2.2 A; lam p ano d e c u rre n t 2 A; su rfa c in g tim e 35 s; o s c illa tin g am ­ p litu d e 0 .2 mm a t 50 Hz freq u en cy .

E le c tro ly tic m eth o d (e tc h in g in 20 % so lu tio n o f ch ro m iu m acid , v o lta g e 20 V a n d h o ld in g tim e 10 s) w as used for d e te rm in a tio n o f s tru c tu r e of d e p o sited m etal. S tr u c tu re o f th e base m etal w as disco v ered by chem ical e tc h in g in 4 % so lu tio n o f n itro g en acid . It is d e te rm in e d t h a t c arb id es in m etal d e p o sited w ith o u t v ib ra tio n h ave 1 0

-2 2

-m\

q(o £

E

j . (13) P a n d Vq are re p re se n te d acc o rd in g to (8 ) , (1 1 ) in ( 1 2 ) , ( 1 3 ) , as a r e s u lt o f w h a t th e fo l­ lo w in g is received: (A4 - <d2(2/? - 4^2 + n2D W / * 7 4) + /? * 0, (14) ( E \l r\*m~x D* h~2 a 2 - l)co4 +

+ (2

f]

- 4i; V - /t 2 0.

(15) ' ' / / / / / / / / / / j /7 ' / / -Z-Z-<-Z-Z-Z-Z-Z '//. 7 7 7 /7 7 /7 7 7 ///,

_zl

TZZZZZ

_l

I B

W 7 7 / / / / / / / / / / / / / / t f / / / / / ^ S o lu tio n acc o u n t

ion o f in e q u a lity ( 1 4 ) , ( 1 5 ) , ta k in g in to Fl#urc Schem e o f in d u c tl ~ j « a. r r\ 3 ____ i p a rt; 2 — p o w d ered ch arg e;

( 2 ) a n d assu m in g t h a t rn * 0 .5 p D an d directk)n of horizontal vll*nt

'lio n su rfacin g : / - d e p o site d 2 — in d u c to r (a rro w s show

ration)

8/2015

*

SCIENTIFIC AND TECHNICAL

D , iini _{D, |ini}

a , mm 20

a b

F igure 5 . D ependencies o f c a rb id e size D on am p litu d e a ( a ) and frequency co (6) o f v ib ratio n

12 jim size, a n d if h o rizo n tal v ib ra tio n s are ap­ p lied th e y are refin ed to 3 .5 -7 .0 fim size.

T he re su lts w ere co m pared w ith calculation ones by model given above. The follow ing approxi­ m ated averaged values of characteristics in rela­ tionships (1 6 ) are given for th is purpose for high- chrom ium alloy based on reference d ata [4, 9]:

p = 7 .8 1 0-6 mm. 3 ’ q =s 7 1 0 -6 kg mm s ’ (1 7 ) £D I 60 H z; A * 2 1 0 3D 1 Hz; -6 mm.

D ependencies D - a and D-co are p lo tted for m ore obvious rep resen tatio n of dependence of size D of carbide inclusions on vibration param eters a and co. Only second relationship (16) was used for that. Considering th a t f \ > co4 - (2f \ - 4£,2)co2, th e second relatio n sh ip can be represented approxi­ m ately as

3 8-lOt5p2/*4 ₍₁₈₎

2 2 4

a~ rj (i)

E quation of dependencies D - a (co = 50 Hz) and D-co ( a = 0.2 m m ) based on relationship (1 8 ) is w ritten in such a form:

D * 1.45<z~2 /3 l-im, D = 785o)"4/3 M l (19)

G raphical dependencies D - a and D-co are p lo tte d based on relationships (1 9 ) (F ig u re 5). The circle on diagram s m ark coordinates, where m atching of calcu latio n and received in w ork [5] values of size of carbides on set v ib ratio n param e­

ters is observed. This indicates correctness and sufficient accuracy of proposed calculation m odel. F igure 5 show s th a t increase of vibration param eters a and co prom otes for significant re­ d u ctio n of carbide size D .

T hus, app ly in g relationships (1 6 ) and (1 7 ) th e previously set values of v ib ratio n s param eters

a and co can be chosen, using which desired stru c­

tu re of deposited m etal layer can be produced.

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W eld in g J ., 1, 23 -2 5 .

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