OPTIMISATION OF INDUCTOR PARAMETERS
FOR UNIFORM HEATING OF DISCS
ACROSS THE WIDTH OF THE HARDFACING ZONE,
ALLOWING FOR SCREENING
O .M . S H A B L Y 1, C h .V . P U L K A 1 a n d A .S . P IS M E N N Y Iv a n P u ly u j T e rn o p il S ta te T e c h n ic a l U n iv e rsity , T e rn o p il, U k ra in e 2T h e E .O . P a to n E le c tric W e ld in g In s titu te , N A S U , K y iv , U k ra in e
M e th o d o f c a lc u la tio n a n d o p tim iz in g o f p a ra m e te rs o f in d u c to r fo r h a rd fa c in g ed g es o f discs o f a n a r b itr a r y d ia m e te r a n d w id th o f th e h a rd fa c in g zone w ith a llo w a n c e fo r th e e ffe c t o f e le c tro m a g n e tic a n d h e a t scre e n in g o n th e d is trib u tio n o f e le c tro m a g n e tic fie ld p o w e r in th e h a rd fa c in g zone w id th is p re se n te d .
K e y w o r d s : induction hardfacing. steel discs, optimiza tion of parameters, two-turn ring-type inductors, protective shields, investigations, calculation
T h in steel d iscs o f d iff e r e n t th ic k n e s s w ith th e ed g e o f an ev en o r to o th e d sh a p e a re u sed in d iff e r e n t s e c to rs o f th e n a tio n a l e co n o m y , in c lu d in g a g ric u l tu r a l m a c h in e ry . T o p ro v id e s e lf-s h a rp e n in g o f th e e d g e s d u rin g th e disc o p e ra tio n , t h e i r w o rk in g su rfa c e is h a rd fa c e d w ith e ro s io n -re s is ta n t p o w d e r-lik e h a rd a llo y s P G -S 1 , P G -S 2 7 o r o f o th e r ty p e a t h e a tin g by H F c u rre n ts 11 1. In th is case th e size a n d sh a p e o f th e in d u c to r a re to be d e te rm in e d fo r th e re sp e c tiv e d ia m e te rs o f th e d iscs a n d d if f e r e n t w id th o f th e h a rd - fa c in g zon e, th is ta k in g tim e a n d c o s t.
S tu d y 12 1 d e sc rib e s a p ro c e d u re a n d g iv es th e r e s u lts o f th e o re tic a l a n d e x p e rim e n ta l in v e stig a tio n s on o p tim iz a tio n o f th e s tr u c tu r a l d im e n sio n s o f tw o - tu r n rin g -ty p e in d u c to rs , used fo r s im u lta n e o u s h a rd - fa c in g o f th in stee l to o th e d discs o v e r t h e e n tir e w o rk in g s u rfa c e . T h e re q u ire d w id th o f th e h a rd fa c in g zone is p ro v id e d , w h ich is g r e a te r th a n th e to o th h e ig h t ( F ig u r e 1). D e v e lo p e d a lg o rith m a llo w s d e te r m in a tio n o f o p tim a l p a ra m e te rs o f th e in d u c to r desig n for a r b itr a r y d ia m e te r o f th e disc a n d w id th o f th e d e p o sit, p ro c e e d in g from te c h n o lo g y re q u ire m e n ts . W o rk | 2 | p re s e n ts th e c a lc u la te d g e o m e tric a l p a ra m e te rs o f th e in d u c to r, d e p e n d in g on th e w id th o f th e h a rd fa c e d zo n e a n d d isc ra d iu s. It is fo u n d t h a t in a n u m b e r o f cases w ith su ch an a rra n g e m e n t o f th e p a rt re la tiv e to th e in d u c to r (se e F ig u re 1 ), th e p o w e r o f th e e le c tro m a g n e tic field is n o n -u n ifo rm ly d is tr ib u te d across th e w id th o f th e h a rd fa c e d zo n e: th e h ig h e s t p o w e r is c o n c e n tr a te d a t th e disc face. T h is le ad s to n o n - u n ifo rm m e ltin g o f th e h a rd a llo y on th e w o rk in g e d g e o f th e d isc to b e h a rd fa c e d , a n d t o o v e rh e a tin g o f th e b a se a n d d e p o s ite d la y e r o f th e m e ta l on its face.
A ll th e s e p ro cesses can be e x p la in e d as fo llo w s. S p e c ific p o w e r o f th e e le c tro m a g n e tic field o f h e a t
t O M Ml A M X O . V I'l/i.KA umi A.S I'lSMLNNY.
so u rc e s in th e a b se n c e o f th e s h ie ld is d e te r m in e d from th e fo rm u la |2 |: oco2|i5 W =---— X X 1 2Stc/i M l A z a i + A / f a V + 4 h d i l i C 2e ~ 2 [ r ' ' r ) A (1)
w h e re a , co, |io a re th e e le c tric c o n d u c tiv ity , c ir c u la r fre q u e n c y o f c u r r e n t a n d m a g n e tic p e rm e a b ility o f v a c u u m , re s p e c tiv e ly ; A = \ 2 (acojio) is th e d e p th o f c u r r e n t p e n e tr a tio n in to th e disc m e ta l; / u, I\ is th e c u r r e n t in th e u p p e r a n d lo w e r b ra n c h o f th e in d u c to r, re s p e c tiv e ly ; A ", B~, C~ a re th e c o e ffic ie n ts ( in te g r a ls o f e llip tic a l t y p e ) , d e p e n d e n t on th e in d u c tio n s y ste m d im e n sio n s, th e fo rm u las fo r th e ir c a lc u la tio n b e in g g iv e n in 1 2 1; th e o th e r g e o m e tric a l d im e n sio n s a re sh o w n in F ig u re 1.
T h is fo rm u la w as used to p e rfo rm c a lc u la tio n s , illu s tr a tin g th e d is trib u tio n o f sp ecific p o w e r o f th e e le c tro m a g n e tic field in th e zone o f d isc h a rd fa c in g , d e p e n d in g on its g e o m e tric a l d im e n sio n s. F ig u re 2 (c u rv e s / ) sh o w s c a lc u la tio n re s u lts fo r tw o cases o f h a rd fa c in g w ith zo n e w id th o f 10 a n d 50 m m , re sp e c tiv e ly , a t d isc ra d iu s r2 = 105 m m . A c c o rd in g t o th e
F igu re 1. Fragm ent o f th e stu d ied system (fo r d esign ation s see th e t e x t )
INDUSTRIAL
H tO \ W tn J
zo n e o f sid e s u rfa c e o f th e d isc . T h e in te n s ity o f e le c tr o m a g n e tic fie ld o f th e h e a t s o u rc e d e c re a se s n e a r t h e d isc face, a n d th e s u rfa c e to he h a rd fa c e d is e x p o se d t o a m o re in te n s iv e im p a c t o f th e e le c tr o m a g n e tic fie ld . A n o th e r p u rp o s e o f t h e s h ie ld is th e rm a l in s u la tio n o f th e disc fa c e fro m th e e n v ir o n m e n t a n d th u s r e d u c tio n o f h e a t lo sses in th e h a r d f a c in g zo n e.
L e t us ta k e th e d e g re e o f s c r e e n in g in to a c c o u n t, u s in g s c re e n in g c o e ffic ie n t K , w h ic h w e w ill in c o r p o r a te in to fo rm u la (1) in d e te r m in a tio n o f s p e c ific p o w e r o f e le c tro m a g n e tic fie ld o f h e a t so u rc e s in t h e d isc . In th is case, th e fo rm u la b eco m es
x [ aiIAWu acoV , 128^/1 X + A / f # X + K A hall'iC 'e-2(r2 - r) &
1
(
2)
F i g u r e 2 . D istrib u tio n o f pow er W o f electrom agn etic field o f heat sources across th e w id th o f th e hardfacing zone S: a — S = 10 mm;
b — 5 = 5 0 mm at d ifferen t screening o f d isc face; 1 — K = \
(w ith o u t screen in g ); 2 — K = 0.25; 3 — K = 0 (fu ll screening); 4 — assigned d istrib u tio n o f electrom agn etic field power
p re s e n te d g r a p h s , in th e d isc face th e v a lu e s o f sp ecific p o w e r o f th e e le c tro m a g n e tic field a re 3 tim e s g r e a te r th a n in th e m a in p a r t o f th e h a rd fa c in g zo n e. In p r a c tic e th is o fte n le a d s to su rfa c e m e ltin g o f th e d isc fa c e .
I t is k n o w n t h a t s h ie ld s o f e le c tro m a g n e tic a n d th e rm a l fie ld s a r e u sed fo r re d is tr ib u tio n a n d c o n c e n t r a tio n o f th e p o w e r o f e le c tro m a g n e tic fie ld o f h e a t so u rc e s in th e w o rk in g re g io n o f in d u c tio n h e a tin g of t h e p a r ts 13 1. T h e sam e te c h n iq u e w as u sed in t h is w o rk t o p r o v id e t h e re q u ire d p o w e r d is tr ib u tio n o f t h e e le c tr o m a g n e tic fie ld o f h e a t so u rc e s a cro ss th e h a r d fa c e d z o n e w id th . In th is c ase i t w as n e ce ssa ry t o o p tim iz e t h e d im e n s io n s o f tw o - tu r n rin g - ty p e in d u c to r , a llo w in g fo r th e p re s e n c e o f su ch s h ie ld s. T h is is p re c is e ly t h e s u b je c t o f th is s tu d y .
F ig u r e 3 g iv e s th e s c h e m a tic o f a p a r t a rra n g e m e n t in th e in d u c to r w ith a sh ie ld a n d w ith o u t it. In th e c a se s tu d ie d by u s th e s h ie ld e n c lo se d th e d is c b e in g h e a te d from th e s id e o f o u te r p e rim e te r a lo n g its sid e ( e n d ) s u rfa c e . S u c h a face s h ie ld d riv e s a v a ria b le m a g n e tic fie ld , g e n e r a te d by th e in d u c to r, o u t o f th e
In fo rm u la ( 2 ) s c re e n in g c o e f fic ie n t K v a rie s in th e ra n g e o f 10; 1 1. A t K = 0 fo rm u la ( 2 ) d e sc rib e s an id eal case o f c o m p le te s c re e n in g o f th e face, a n d a t K = 1 th e sc re e n in g e f f e c t is a b s e n t, a n d fo rm u la (2) w ill fu lly c o rre sp o n d t o f o r m u la (1) fro m |2 |. N ow in re a lity K * 0, a n d c a lc u la tio n o f th i s q u a n tity in v o lv e s c e rta in d iffic u ltie s o f c o m p u ta tio n a l n a tu re , as in th is case it c o m b in e s th e e le c tr o m a g n e tic a n d th e rm a l e ffe c ts. M e th o d o f c a lc u la tio n o f t h e sc re e n in g e ffe c t w ill be th e s u b je c t o f a s e p a r a te p u b lic a tio n . In th is p a p e r it is a ssu m e d to be e q u a l to 0, 0 .2 5 a n d
1.
D e te r m in a tio n o f in d u c to r p a r a m e te r s m ay b e p e r fo rm ed w ith th e re q u ire d a c c u ra c y a t th e a ssig n e d s c re e n in g c o e ffic ie n t, u s in g a p ro c e d u re , d e sc rib e d in
12 1. T h e d e p e n d e n c e from | 4 |
_ T ^ c a y m - ,
srl sh(tf7WT) (3 )
w as used in c a lc u la tio n s as th e a ssig n e d m o d e o f s u p p ly in g th e sp ec ific p o w e r Wse, to a p a r t , o p tim a l fo r in d u c tio n h a rd fa c in g . H e re , T M>, is th e s e t te m p e r a tu r e o f h e a tin g o f th e h a rd fa c in g zo n e, a t w h ic h so u n d h a r d f a c in g is e n su re d d u r in g tim e x; c, a , y a re th e s p e c ific h e a t c a p a c ity , te m p e r a tu r e c o n d u c tiv ity a n d d e n s ity o f d isc m a te ria l, re s p e c tiv e ly ; m = B i / 2 A2; Bi = 2 h a / \ \ 2 k is th e d isc th ic k n e s s ; a is th e h e a t re m o v a l c o e ffic ie n t; A. is h e a t c o n d u c tiv ity o f d isc m a te ria l; t is th e c u r r e n t v a lu e o f p ro c e ss tim e .
O p tim is a tio n o f d im e n s io n s a n d d e te r m in a tio n o f in d u c to r c u r r e n t w e re p e rfo rm e d b y m in im iz in g th e fo llo w in g fu n c tio n a l |2 |:
F Nrs*i) r d r d t, (4 )
0 r.
F ig u r e 3 . Disc w ith inductor w ith ou t a shield (a) and w ith a sh ield (0) 1 - part; 7 -- charge; 3 — ring-type in d u ctor w ith tw o turn», 4 - sh ield
w h e re r is th e c u r r e n t v a lu e o f t h e ra d ia l c o -o rd in a te . C a lc u la tio n s d e m o n s tr a te d t h a t th e h ig h e s t u n i fo rm ity o f d is tr ib u tio n o f e le c tro m a g n e tic fie ld p o w e r a c ro ss th e w id th o f th e h a r d f a c in g z o n e is a ch ie v e d in th e id eal c ase a t c o m p le te s c r e e n in g o f th e disc face. D e v ia tio n fro m th e s p e c ifie d p o w e r o f th e
IVjv'vtoiut* ot rual dimensions of Induction system on screening coefficient K and disc radius S, Him
K ** mm 10
<tu, MM MM //„, Mill h\, miii /. .1 au, him a\, iiiiii //„, llllll h\, mm I. A
0 105 115 89 1 18.5 23.50 115 10 0 0 14.5 20.82 0 125 135 107 1 14.5 21.90 135 1 2 0 0 14.5 2 0 . 1 0 0 145 155 123 1 16.5 21.80 155 140 0 14.5 19.53 0 165 175 144 1 19.5 21.71 175 159 2 14.5 19.00 0 185 195 161 1 20.5 21.50 195 179 1 14.5 18.70 0 205 215 182 1 20.5 2 1 .0 0 205 198 0 14.5 18.50 0 2 1 0 2 2 0 186 1 20.5 2 0 .1 0 2 2 0 2 0 2 2 14.5 18.50 0.25 105 115 88 7 18.5 23.52 116 10 0 20 *14.5 2 1 . 0 1 0.25 125 135 107 1 1 20.5 23.09 139 119 20 14.5 20.36 0.25 145 155 123 5 16.5 21.77 159 139 20 14.5 19.60 0.25 165 175 145 16 19.5 21.72 182 159 20 14.5 19.30 0.25 185 196 163 14 20.5 21.40 2 0 2 178 20 14.5 19.00 0.25 205 215 182 11 20.5 20.90 2 2 0 197 20 14.5 18.74 0.25 2 1 0 22 0 187 1 1 20.5 20.80 230 2 0 1 20 14.5 18.80 N o t e : c„ = 5 mm, c\ - 8 mm.
trom agnetic field is equal to 3 -5 %, depending on the
w idth of th e hardfacing zone and disc radius (see
Figure 2, curves
3
,
4 ) .
This procedure was the basis
to derive calculated dependencies of geom etrical pa
ram eters tfu,
ci\y
//u,
h\
(see Figure 1) and inductor
current / , depending on screening coefficient
K
and
disc radius ro. Sim ilar to Figure 2, th e width of hard-
facing zone 5 was taken to be 10 and 50 mm (T able).
Analysis of com putation results, given in the T a
ble, shows th a t introduction of a shield into th e tech
nological sequence of induction hardfacing only
slightly influences dimensions
a u, a\, h\
and integral
energy param eters of the induction system (which
influences the values of inductor current / ) . However,
presence of a shield with a certain screening coefficient
leads to a marked change of air gap /ju between the
inductor upper branch and disc surface. This is a t
trib u ta b le to strong electrom agnetic coupling of the
shield and th e inductor upper branch due to their
close location (F igure 3 ). Observed narrow ing of gap
h n
a t decrease of screening coefficient
Kis necessary
to ensure the required power in the disc being hard-
faced.
Thus, use of electrom agnetic and therm al shields
allow s co ntrolling pow er d istrib u tio n o f th e e le c tro
m agnetic field of heat sources across th e hard facin g
zone w idth. The required law of d istrib u tio n o f elec
trom agnetic field pow er may be derived for a rb itrary
dimensions of the discs and w idth of hardfacing zone.
Its most uniform d istrib u tio n across th e hardfacing
zone w idth is achieved in th e ideal case at com plete
screening of the disc face. Described calculation pro
cedure enables determ ination w ith th e assigned accu
racy of th e design param eters of th e in d u cto r for a r
bitrary diam eters of discs and w idth of hardfacing
zone, allow ing for screening effect.
1. T k a c h e v , V .N . ( 1 9 7 1 ) Wear and increase o f service life o f agricultural machinery. M o sc o w : M a s h in o s tr o e n ie .
2 . S h a b ly , O .M ., P u lk a , C h .V ., P is m e n n y , A .S . ( 1 9 9 7 ) O p t i m isa tio n o f d e sig n p a r a m eters o f in d u c to r fo r in d u c tio n har d fa c in g o f th in s te e l d is c s . Avtomatich. Svarka, 6 , 1 7 - 2 0 . 3 . L o zin sk y , M .G . ( 1 9 5 8 ) Industrial application o f induction
heating. M o sco w : A N S S S R .
4 . S h a b ly , O .M ., P u lk a , C h .V ., B u d za n . B .P . ( 1 9 8 7 ) O p t im i s a tio n o f p o w er in p u ts d u r in g in d u c tio n h a r d fa c in g o f th in - w a lle d sh a p ed d isc s. Avtomatich. Svarka, i , 3 6 - 3 9 .
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