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Vol. 37, No. 5 (2000) pp. 377-383

  VF
                   (UTJ~ªê¢æêÖj*‚Þ¦*‚Î

                                              ´¼A Ádæ





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     Abstract : The present study represents the algorithm using Fortran language in order to simplify the
     previous method for the calculation of the Bond's grinding work index. The primary data used in this
     algorithm, such as particle size of ground product and circulation load, make possible the simultaneous
     calculation of the stable revolution number of mill, the grindability, and the grinding work index. The
     procedure for the data inputs and calculations is minimized by 93 percent and is stable, hence to yield
     better grinding work index than that of the previous method with problems of increasing cycle number
     originated from its complex calculation nature.

     Key words : Bond's grinding work index, grindability, stable revolution number, mill, Fortran algorithm

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                                                                      1)


 NB
. ªê“ ªêËf êò~ ªê8 ’Ú                              »f Hardgrove » Bond~ ªê¢æ(grinding
                                                               2)


;ê¢ ¾æÚº ~š
. ªê“f êò¢ ªê~ î                             work index)~ G;»š ®
. Hardgrove »f ß®          3)



   j ú ¢ %                 j ú ¢ j                        Cê~ ªê;ö wϺ* B‚B šö, Bond~ ª
1999 10 29
*Û³]ç ~] 
                      , 2000 7 14
                                                            ê¢æº 7b 5 ©ö ~º ëöò Îv¢  
(Department of Chemistry, Sangji University)                çb‚ ~V r^ö Bond~ ªê¢æ 
 ¢'š
Á E-mail; chsim@mail.sangji.ac.kr
                                                            ¢ †  ®Æ
.
Á Address; 660, Woosan-dong, Wonju, Kangwondo 220-
                                                             ªêö.æ¢ G;Žö ®ÚB ¢'b‚ ¢ï «êæ
  702, Korea


                                                      377
378                                            ´¼eÁdæ
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ž . Kick, Rittinger, Bond~ 3 ªê»š
.          2,4)


Bond~ ªêš†f ªê¢ çb‚ ‚ Rittinger~                          (UTJ     ~ (GRR SORR ªêË /;ö ®ÚB~ n;²*~
š† –ªê¢ çb‚ ‚ Kick~ š†j –‚ ©š                       ºÖ
–, V¢B  çê 7*ªê‚ šš ®
.  ’                         ~ n;²*¦ Bond Bn‚ B~j(cl) 2.5                                                          5)


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. Bond
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. P control sieveº Bond~ ªê
                                                                 1




j ’†  ®b–, ²ºÿKf ~ Jê j'ž V                        »ö 8¢ ªêWb~ 80% Ûªš £ 100 µm
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  Bond~ ªê¢æ¢ ’~º O»b‚Bº Nematollahi,            6)
                                                       (¯, ~ n;²*)¢ .G† jº ®
. ~ n;²*
KS E 3600, Miwa, JIS M 4002 ~ O»š ®
.
           7)             8)        9)
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Nematollahi~ O»f Bond B~ ®º ~ 
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.               10)


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Ú ®æ p
.                                                     t           F                   1      (1)

  ¢'b‚, Bond~ ªê¢æ~ êÖf ^ æ~                       VB, R º ªê* töB~ ªêWb~ ïö ‚
                                                       P control sieve~ º~ï~ j, R º ªê~V *öB
                                                                             t


;j –~² B
. ¯, Ñ ® ;öBº 
r Òšš~                       ~ feed~ ïö ‚ P control sieve~ º~ï~ j,
                                                        1                                                                     F


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      9)

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r ?f j áj  ®
.
                                                                 (n+1)


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                                                             (n+1)            / R' } / log{R / R' }]
                                                                                  (n)                N(n+1)         F(n+1)                N(n)      F(n)
                                                                                                                                                           1/m



êÖ;j Bz~, †ž * Úö ;{‚ Bond~                                                                                                                            (4)
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š
.                                                    ššö 8¢B 
r ?š Ö;B
.
‚“¶ö²æ
Bond   ~ ªê¢æ êÖj *‚
Þ¦*RÎ                                                           379




Fig. 1. Material balance in grinding operation.


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.
                   Á
  R'F(n) = {QF(n) RF + Qcl(n−1)} / Qo                        (6)     VB, Bond  B‚ (n+1)® Òšš V~ B
                                                                                          5)


                                                                   ~j cl = Q / Q = 2.5 êƒ ªêË G;–š
                                                                   j 'Ï~š, Fig. 1öB Q = Q + Q šæ‚, 
                                                                                cl(n+1)    p(n+1)
  RN(n+1) = Qcl(n+1) / Qo                                    (7)
           Á
  R'F(n+1) = {QF(n+1) RF + Qcl(n)} / Qo
                                   (8)                             (7)f 
r ?š B
.
                                                                                                    o      p(n+1)     cl(n+1)




VB, Q º ö Ë«º feed~ Cï, R º feed~
·ö ‚ P control sieve~ º~ï~ j, Q 
           o                                       F
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Q f '' ªê–·~ n ®f (n+1) ® Òššö B
               1                                       cl(n-1)
                                                                            = 2.5/(1+2.5) = 0.713                                  (9)

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 cl(n)

                        F(n)   F(n+1)                                         p(n+1)                                                    1



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                                                                                                                   i




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r š WãB
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                                                               N(n+1)
                                                                                                                                                                                                             (13)

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                                                                                                            ê¢ 'Ï~š 
r ?f š B
.
                                                                                                   (10)                         80        80



Ö'b‚  (10)f n ® Òšš~ ªê–·~ Ö‚
¦V (n+1)® Òšš~  n;²* N ~ êÖö                                                                              W = 10 Wi (1/ P80 − 1/ F80 )                                                                    (14)
ÒÏB
.
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r ?f ãþ j ÒÏ~
.
                                                                                                                                                              i
                                                                                                                                               2,4)

  ªêË~ /;
  Ñ ®~ Òšš~ ªêöBº ¢;ï~ š Ï*B                                                                                                                           44.5
                                                                                                             W i = --------------------------------------------------------------------------------------- × 1.10 (15)
ªêË G;Ï ö š j‚ ò 700 ml(Q )¢ Ë«                                                                                ( P1 ) ⋅ Gbp ⋅ ( 10 ⁄ P80 – 10 ⁄ F 80 )
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                                                                                        o


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                                                                                       1
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6‚ 8, (Q − Q )~ Z²ò¢ î‚Ú ò¢ º‚ ê,                                                                         v ® ;öBº B~j 2.5Û0.125 º*öB ªê
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Ñ ®~ Òšš ÿ¢‚ ªê–·j ¯‚
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                  o          cl


                                                                                                            Wïš n;š, îæï 3B~ Òšš~ ªêÖ‚¦V
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                                                bp


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  öBº Lewis~ ¢, ¯  (11)j ÒÏ~                                                                         ‚ Ö ªê¢æ¢ ~V *šBº £ 350²ö
ªê¢æ W ¢ êÖ~
.        i
                                                                                                            žöB –šV¢ «K~, êÖ~º ;j ~º 
f
 dW/dD = −kÁD                     (11)−n
                                                                                                            ¢  î
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r~ êÖêö 'Ëj ~² B
(J~
              p                       p


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š
. = öB ç n~ 8f Bond Bn‚ 1.5¢ 
                                                                p
                                                                                                            ® : error propagation). š©f z® ®j  ®º
‚ ê, D ö šB 'ª~š Wº  (12) − ¯, Bond                                                                       ¢š–,  Ö‚Bº JN Ã~² F ©š–, 8¢B
~ ªê»b‚ R*B
.
              p
                                                                                                            B~j Z† H ræ~ Òšš ²¢ Ãʲ 
                                                                                                            æ‚B G;*ê Ã~² , JN 66 z Ã~
  W = kB (1/ Dp2 − 1/ Dp1 )                                                                        (12)
                                                                                                            º ©f ~
.
8B k º Bond~ ç, D º ªêWb~ «¶ã,                                                                             
B‚ JIS M 4002~ êÖO»j ‚ 'Ï‚ Ö
D f ªêò~ «¶ãš
. Bondº  (12)öB, Z                                                                          , –šV¢ V«~º ;öB~ 
ž ‚ ‚ ¦ª
              B                                       p2
                                                                         5)


‚~ «¶ãj 100 µm ræ ªê~º– jº‚ ¢j                                                                             (Table 1~ 9¯ 14~ -0.019º +0.019 š
)j Bž
 p1




grinding work index(ªê¢æ)‚ ;~~, ªê¢æ                                                                      ~z¢ê ¾^æ 
U ¦ªöB êÖ~ 
ªj r  ®
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রামপাল নিয়ে চিন্তা করার আছে সৈয়দ মনজুরুল ইসলাম
 
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37509

  • 1. ‚“¶ö²æ Vol. 37, No. 5 (2000) pp. 377-383 VF (UTJ~ªê¢æêÖj*‚Þ¦*‚Î ´¼A Ádæ ,58:8'4 6XUMXGS LUX ZNK )GRI[RGZOUT UL (UTJ Y -XOTJOTM =UXQ /TJK^ )NUR.U 9OS GTJ 9K[TM1_U 5N Abstract : The present study represents the algorithm using Fortran language in order to simplify the previous method for the calculation of the Bond's grinding work index. The primary data used in this algorithm, such as particle size of ground product and circulation load, make possible the simultaneous calculation of the stable revolution number of mill, the grindability, and the grinding work index. The procedure for the data inputs and calculations is minimized by 93 percent and is stable, hence to yield better grinding work index than that of the previous method with problems of increasing cycle number originated from its complex calculation nature. Key words : Bond's grinding work index, grindability, stable revolution number, mill, Fortran algorithm º £ º ªê¢æ êÖO»j Bzʺ
  • 2. Þ¦ rÒ¾j B~ . ªêW~ «ê 5 B~ ï ?f 8. ;òb‚ r Òšš~ ~ n;²*, ªêË 5 ªê¢æ¢ ÿö êÖ~, 8š~ O»ö jš ªê¢æ~ êÖ ;j £ 93% 6²8 . 8š~ O»f –š8 «K; 5 êÖ;š Ç~ Òš š ² Ã~º ãÖ ®æò, êÖ;~ n;Wj æò rÒ¾f ~ Jê ö j'ž ªê¢æ – š8¢ 8š~ O» z× ;{~² êÖ† ® . ºÚ Bond~ ªê¢æ, ªêË, n;²*, ,
  • 3. Þ¦ rÒ¾ * V ‚Ú *~ Rš'j Ãʺ– jº‚ ¢ïb‚ ¾æ Ú, Rittinger š . ªêËf ªê~ š ªê8~ Jê # ªê–š~ Ö; ö ®ÚB ÖF š ¢ ¾æÚº ë'ž ¿êš . Öš¢ † ^Bº, ö~º «ê~ ªêWbj á8 *~ ÚÊ ß;‚ ªêV # ªêO»j Ïz~, š©j âîò¢~ ¢ïš jº~, ªê8ö Ú¶ ;ê~ ÿ šÏ~ ªê þj ¯~, ç~‚B~ ªêË(_f ª Kš ²ºF ©žæ, ¯ ªêö jº‚ ö.æ~ ·j ê“)j ’~º ©š ¢'š . šf ?f O»ö ‚ k~º ¢š . ªêö.æ~ G;f ªê“ _f ªêË Bnš ®b¾, 7 Ë ôš ÒÏ ®º O 1) NB . ªê“ ªêËf êò~ ªê8 ’Ú »f Hardgrove » Bond~ ªê¢æ(grinding 2) ;ê¢ ¾æÚº ~š . ªê“f êò¢ ªê~ î work index)~ G;»š ® . Hardgrove »f ß® 3) j ú ¢ % j ú ¢ j Cê~ ªê;ö wϺ* B‚B šö, Bond~ ª 1999 10 29 *Û³]ç ~]  , 2000 7 14 ê¢æº 7b 5 ©ö ~º ëöò Îv¢ (Department of Chemistry, Sangji University) çb‚ ~V r^ö Bond~ ªê¢æ ¢'š Á E-mail; chsim@mail.sangji.ac.kr ¢ † ®Æ . Á Address; 660, Woosan-dong, Wonju, Kangwondo 220- ªêö.æ¢ G;Žö ®ÚB ¢'b‚ ¢ï «êæ 702, Korea 377
  • 4. 378 ´¼eÁdæ z~ ê¢ z ~º ¢š ¯šæ ®b–, R' š V ž . Kick, Rittinger, Bond~ 3 ªê»š . 2,4) Bond~ ªêš†f ªê¢ çb‚ ‚ Rittinger~ (UTJ ~ (GRR SORR ªêË /;ö ®ÚB~ n;²*~ š† –ªê¢ çb‚ ‚ Kick~ š†j –‚ ©š ºÖ –, V¢B çê 7*ªê‚ šš ® . ’ ~ n;²*¦ Bond Bn‚ B~j(cl) 2.5 5) öB ÒϺ Bond~ ªê¢æº ªê~ B 3š†š¢ º ~ ²*¢ ö‚ . 8B, B~j¦ ªêWb ®Òº Bond~ ªêš† ö V.¢ v ® . Bond 5) j P control sieve‚ ÚªÒ ~j H º~ï Û ~ ªê»ö ~~ Bond~ ªê¢æ‚¦8 ²ºÿK ª~ jNj ö‚ . P control sieveº Bond~ ªê 1 j ’† ®b–, ²ºÿKf ~ Jê j'ž V »ö 8¢ ªêWb~ 80% Ûªš £ 100 µm 1 .–š8‚ ÒÏB . šf ?š ªêV~ ²ºÿKj G; º sieve~ ..(VBº 149 µm¢ P control sieve † ®º Bond~ ªê¢æº Ú* Òç 5 Jê ‚B jŽ)j ö‚ . B~j 2.5ö 7†ƒ ªêË 1 ç š†'b‚ ‚~ ÎNj áV *‚ æŽb‚B Ö š ¢;‚ 8j Fæ~² B . 8¢B ªêËš ¢;‚ 8 FÏ~–, ªê~ Âšê¢ ¾æÚº 7º‚ ¿ê B . j Fæ~V *šBº B~j 2.5 êƒ ~ ²* Bond~ ªê¢æ¢ ’~º O»b‚Bº Nematollahi, 6) (¯, ~ n;²*)¢ .G† jº ® . ~ n;²* KS E 3600, Miwa, JIS M 4002 ~ O»š ® . 7) 8) 9) ~ .Gf B® jfêÖö ~š~º ©š ¢'š¾, Nematollahi~ O»f Bond B~ ®º ~ 6) öBº Miwa Bn‚ ªê³êj ÒÏ~ . 10) Ïj »²*B ªê¢æ¢ ’~ ®b¾ jç ž R = R Áexp(−b Át ) m Ú ®æ p . t F 1 (1) ¢'b‚, Bond~ ªê¢æ~ êÖf ^ æ~ VB, R º ªê* töB~ ªêWb~ ïö ‚ P control sieve~ º~ï~ j, R º ªê~V *öB t ;j –~² B . ¯, Ñ ® ;öBº r Òšš~ ~ feed~ ïö ‚ P control sieve~ º~ï~ j, 1 F n;²*¢ êÖ~, v ® ;öBº ªêËj êÖ b f ³êç, tº ªê*, mf ªêËö êº ç 1 ~, ‚« ;öB j‚² ªê¢æ¢ êÖ~² B . š . ~ n;²* .GêÖö šÏº Ξj Fig. 1 –, KS E 3600 öBº Ñ ® ;ž ¯, 7) 1ö ¾æÚî . ªê* t f ~ C ²* Nf jf r Òšš~ n;²*~ êÖ~º– 4*òb‚ *Û~² ê Wã~æ‚, t¢ Nb‚ ¾æÚ, ªê–·~ n® J«j ~ ®ÚB, Vö J«Ú ®º ©òb‚º ª Òšš 5 (n+1)® Òšš~ C ²*‚ ~~š ê¢æ êÖš ®Ë~ (š©ö j~ JISöBº ÿ r š Wã‚ . ¢‚ êÖö ~ 3-4Ë~ ªïb‚ ç^® BF~ ® ). R = R' Áexp{ −bÁN } N(n) F(n) (2) m (n) $‚ Miwa Bn‚ JIS M 4002ö ~~š, ªê 8) 9) R = R' Áexp{ −bÁN } (3) m ¢æ¢ ’~V *šBº £ 350²ö žöB ''~ N(n+1) F(n+1) (n+1) –š8¢ «K~, êÖ~º ê¢ ~² B . V¢ VB, R R f '' ªê–·~ n ® Òšš 5 (n+1)® ÒššöB WB ªêWb~ ·ö ‚ N(n) N(n+1) B ¢N~ êÖ ;7 ‚ ®~ º r~ êÖ P control sieve~ º~ï~ j, R' R' f '' êö 'Ëj ~² Ú JN Ã~² F ©š–, V ªê–·~ n® Òšš 5 (n+1)® ÒššöB feed~ 1 F(n) F(n+1) ¢B Òšš~ ² Ãæ‚B G;* 5 JN ·ö ‚ P control sieve~ º~ï~ j, bº ²* z× z Ã~² Nf ~ . B‚ JIS M 4002 ö êº ;, Ò N N f ªê–·~ n® 1 öBê 6–– ¢ º~ ® . V¢B, š O»f 9) Òšš 5 (n+1)® ÒššöB ~ C ²*š . (n) (n+1) Bond~ ªê¢æ¢ *, ³ 5 ;{~² G;† ®êƒ BFF jº ® . (2)f (3)j ;b‚ æ;‚ ê, ·æ~ j¢ á ’~ Ï'f JIS M 4002öB áf ;‚¦ 9) Ú N ö š ;Ò~š r ?f j áj ® . (n+1) 8, Vš~ O»š æ ®º Ç‚ –š8 «K 5 N = N Á[log{R (n+1) / R' } / log{R / R' }] (n) N(n+1) F(n+1) N(n) F(n) 1/m êÖ;j Bz~, †ž * Úö ;{‚ Bond~ (4) ªê¢æj êÖ† ®º rÒ¾j B~º © (4)~ ' R 8f, Fig. 1öB ®š ªêÒ š . ššö 8¢B r ?š Ö;B . ‚“¶ö²æ
  • 5. Bond ~ ªê¢æ êÖj *‚
  • 6. Þ¦*RÎ 379 Fig. 1. Material balance in grinding operation. RN(n) = Qcl(n) / Qo (5) f (n+1)® Òššö º‚ Ë«º feed~ ·š . Á R'F(n) = {QF(n) RF + Qcl(n−1)} / Qo (6) VB, Bond B‚ (n+1)® Òšš V~ B 5) ~j cl = Q / Q = 2.5 êƒ ªêË G;–š j 'Ï~š, Fig. 1öB Q = Q + Q šæ‚, cl(n+1) p(n+1) RN(n+1) = Qcl(n+1) / Qo (7) Á R'F(n+1) = {QF(n+1) RF + Qcl(n)} / Qo (8) (7)f r ?š B . o p(n+1) cl(n+1) VB, Q º ö Ë«º feed~ Cï, R º feed~ ·ö ‚ P control sieve~ º~ï~ j, Q o F RN(n+1) = Qcl(n+1) / Qo = Qcl(n+1) / { Qp(n+1) + Qcl(n+1) } Q f '' ªê–·~ n ®f (n+1) ® Òššö B 1 cl(n-1) = 2.5/(1+2.5) = 0.713 (9) ~º ò~ ·, Q Q f '' ªê–·~ n® VB, Q f (n+1)® Òšš~ ªêWb7 P cl(n) F(n) F(n+1) p(n+1) 1 *37² *5^
  • 7. 380 ´¼AÁdæ ~ Ûïš . Miwa þj Ûš á control sieve 10) W ¢ r ?š R*~ . f m = 1.2 5 (9)öB áf R = 0.713j (4) i ö 'Ï~š r š WãB . Wi = kB(1/ 100 − 1/ ∞ ) = kB / 10 N(n+1) (13) N = N Á log{0.713 / R' 1/1.2 (12)öB, ªêò 5 ªêWb~ 80% ÚÛ«¶ ãj '' F , P b‚ R~, (12)ö (13)~ (n+1)[ (n) } / log{R / R' }] F(n+1) N(n) F(n) ê¢ 'Ï~š r ?f š B . (10) 80 80 Ö'b‚ (10)f n ® Òšš~ ªê–·~ Ö‚ ¦V (n+1)® Òšš~ n;²* N ~ êÖö W = 10 Wi (1/ P80 − 1/ F80 ) (14) ÒÏB . (n+1) (14)öB ªê¢æ W ~ êÖöº Bond Bn‚ r ?f ãþ j ÒÏ~ . i 2,4) ªêË~ /; Ñ ®~ Òšš~ ªêöBº ¢;ï~ š Ï*B 44.5 W i = --------------------------------------------------------------------------------------- × 1.10 (15) ªêË G;Ï ö š j‚ ò 700 ml(Q )¢ Ë« ( P1 ) ⋅ Gbp ⋅ ( 10 ⁄ P80 – 10 ⁄ F 80 ) 0.23 0.82 ‚ ê j 100 ²*Î . ²*š ƒ¾š, P control o * öB P f control sieve~ ..š . sieve¢ ÒÏ~ ªêWbj ÚªÒ~, control 1 1 sieveö º~~º · − ¯, B~ï Q 5 control sieve ö Û~º · Q ¢ Ö;‚ . cl Ö # 8 r Òšš~ ªê–·~ ²* .Gf (10)ö p ªê¢æ~ êÖ;f r ? . Ñ ® ;öB ~~ Ñ ® Òšš~ ªê–· Ö‚¦V Ö;B . º n ® Òšš~ ªê–·~ Ö‚¦V r Òšš~ ¯, 2²~ ªêº, çF‚ jò~ 7ïöB B~ïj ¯, (n+1)® Òšš~ n;²* N j êÖ‚ . 6‚ 8, (Q − Q )~ Z²ò¢ î‚Ú ò¢ º‚ ê, v ® ;öBº B~j 2.5Û0.125 º*öB ªê (n+1) Ñ ®~ Òšš ÿ¢‚ ªê–·j ¯‚ . *f ?f o cl Wïš n;š, îæï 3B~ Òšš~ ªêÖ‚¦V –·š š, B~j Q /Q 8š 2.5Û0.125¢ Fæ G ~ ‚8 ‚²8~ Nš 3% ò¢ H ï8j ~šB n;B ªêË G ( 1²* ªêWï)j cl p ~, ©j ªêË G ‚ Ö;‚ . ^ ® ;ö bp . š H îæï 3²ª~ n;B G ~ ï8j bp Bº n;B ªê–·b‚¦V áf ªêËj ÒÏ~ ª bp ~ 8j ªêË G ‚ Ö;‚ . , îæï 3B bp ê¢æ¢ Ö;‚ . ~ Òšš~ G ‚8f ‚²8~ Nš ï~~ 3% bp JIS M 4002ö ~~š, r Òšš~ n;²* 9) òšÚ¢ ‚ . bp ¢ ~º– 17ê~ êÖ, ªêËj ~º– 9ê~ 9) êÖ 5 ªê¢æ¢ ~º– 1ê~ êÖj º‚ . ªê¢æ ~ /; -XOTJOTM =UXQ /TJK^ zך SiCö ~ š ?f –·j 13²ö žöB öBº Lewis~ ¢, ¯ (11)j ÒÏ~ ‚ Ö ªê¢æ¢ ~V *šBº £ 350²ö ªê¢æ W ¢ êÖ~ . i žöB –šV¢ «K~, êÖ~º ;j ~º f dW/dD = −kÁD (11)−n ¢ î . Ö'b‚, ¢N~ êÖ; 7öB ‚®~ º r~ êÖêö 'Ëj ~² B (J~ p p 8B Wº ªêö 4«º ¢, D º «¶ã, kº ç š . = öB ç n~ 8f Bond Bn‚ 1.5¢ p ® : error propagation). š©f z® ®j ®º ‚ ê, D ö šB 'ª~š Wº (12) − ¯, Bond ¢š–, Ö‚Bº JN Ã~² F ©š–, 8¢B ~ ªê»b‚ R*B . p B~j Z† H ræ~ Òšš ²¢ Ãʲ æ‚B G;*ê Ã~² , JN 66 z Ã~ W = kB (1/ Dp2 − 1/ Dp1 ) (12) º ©f ~ . 8B k º Bond~ ç, D º ªêWb~ «¶ã, B‚ JIS M 4002~ êÖO»j ‚ 'Ï‚ Ö D f ªêò~ «¶ãš . Bondº (12)öB, Z , –šV¢ V«~º ;öB~ ž ‚ ‚ ¦ª B p2 5) ‚~ «¶ãj 100 µm ræ ªê~º– jº‚ ¢j (Table 1~ 9¯ 14~ -0.019º +0.019 š )j Bž p1 grinding work index(ªê¢æ)‚ ;~~, ªê¢æ ~z¢ê ¾^æ U ¦ªöB êÖ~ ªj r ® ‚“¶ö²æ
  • 8. Bond ~ ªê¢æ êÖj *‚
  • 9. Þ¦*RÎ 381 Table 1. Calculation for prediction number of mill revolution9) (Qo = 1418 g , Rf = 0.937) (1) (2) (3) (4) (5) (6) (7) (8) cycle of grinding revolution N oversize of P1 additive feed(g) sieve(g), Qcl(n) QF(n) ( 2) ------- Qo Ü (3) Rf ( 5) ------- Qo Ü (3)n+1 Rf ( 7) + (2) -------------------- Qo 1 100 1245 1418 0.879 1328 0.938 162 0.993 2 392 1105 173 0.779 − 0.993 293 0.985 3 497 992 313 0.700 − 0.985 399 0.981 4 468 987 426 0.696 − 0.981 404 0.982 5 442 1006 431 0.710 − 0.982 385 0.982 6 437 1003 412 0.708 − 0.982 389 0.982 7 429 1005 415 0.709 − 0.982 387 0.982 8 421 1013 413 0.715 − 0.982 379 0.982 9 408 1021 405 0.721 − 0.982 372 0.983 10 423 1006 397 0.710 − 0.983 386 0.982 11 415 1013 412 0.715 − 0.982 379 0.982 12 402 1026 405 0.724 − 0.982 367 0.983 13 392 − (9) (10) (11) (12) (13) (14) (15) (16) (17) cycle of revolution for 0.713 ( 4) ( 10) ( 14 ) Ü grinding next cycle -------------- - log(9) ------- log(11) ---------- - log(13) ---------- - 10(15) (8 ) ( 6) ( 12) 1.2 (1) (16) N(n+1) 1 0.718 -0.144 0.937 -0.028 5.15 0.712 0.593 3.92 392 2 0.724 -0.141 0.784 -0.106 1.33 0.123 0.103 1.27 497 3 0.727 -0.138 0.711 -0.148 0.932 -0.031 -0.026 0.942 468 4 0.726 -0.139 0.710 -0.149 0.934 -0.030 -0.025 0.944 442 5 0.726 -0.139 0.728 -0.141 0.986 -0.006 -0.005 0.989 437 6 0.726 -0.139 0.721 -0.142 0.979 -0.009 -0.008 0.982 429 7 0.726 -0.139 0.722 -0.142 0.979 -0.009 -0.008 0.982 421 8 0.726 -0.139 0.728 -0.144 0.965 -0.016 -0.013 0.970 408 9 0.725 -0.139 0.736 -0.133 1.045 -0.019 0.016 1.038 423 10 0.726 -0.139 0.722 -0.142 0.979 -0.009 -0.008 0.982 415 11 0.726 -0.139 0.728 -0.144 0.965 -0.016 -0.013 0.970 402 12 0.725 -0.139 0.737 -0.133 1.045 0.019 0.016 1.038 417 13 î . ¯, Table 1öBº 8¯ 12~ -0.144º -0.138 9) . šº ' Òššî ªêWbj ïï† H ¶ ‚ ‚, 11¯ 12~ -0.144º -0.138‚, 9¯ 14~ -0.019 ž‚ JNö Vž~º ©b‚ º;B . $‚ Miwa~ – º +0.019‚ ;Ú¢ ‚ . $‚ Table 2öBº 13 9) šVöBº B13² ÒššöB ªê–·j «ò~ B 9) ¯ 3~ 312º 392‚, 1¯ 4~ 8.9º 89‚, 3¯ 6 11~13² Òšš~ ªêË~ ï8 G = 0.923j ~ ~ 485º 385‚ ;Ú¢ ‚ . ¾ öB , š‚¦V ªê¢æ¢ êÖ‚ Ö 27.3 kWh/t ªj bp B‚ O»j ÒÏ~š *f ?f êÖ;öB~ ¢ C® ® . šö jš, öB º;‚ –šV¢ Ú VB† ®î . Ú š B6~8² Òšš~ G ‚8 ‚²8~ Nš Miwa B‚ SiC~ ªêËö ‚ G; –šVf 3% òšÚB B 8² ÒššöB š ªêWïš n; bp 9) öB º;‚ –šV¢ jL‚ ©j Fig. 2ö ¾æ ®bæ‚, ªêË~ ï8j ~š G = 0.897š Úî . Miwa~ –šV öB êÖ‚ –šV , š‚¦V ªê¢æ¢ êÖ~š 28.0 kWh/t ªj r bp ' Òššî ¦ª 3% º*ÚöB +JN¢ æ ® ® . 8¢B Miwa~ ªêËf êÖ~ £ 3% š *37² *5^
  • 10. 382 ´¼AÁdæ Table 2. Calculation for measurement of grindability9) (Qo = 1418 g, Rf = 0.937, P1 = 149 µm, P = 134 µm, F = 1500 µm) (1) (2) (3) (4) (5) (6) (7) (8) (9) increased net predicted revolution undersize of weight of net weight for next cycle cycle of revolution oversize of additive P1 sieve undersize of P1 to be Grindability grinding P1 sieve(g) feed(g) before sieve after ground(g) N(n+1) grinding(g) N grinding(g) Gbp Ü Qcl(n) QF(n) Qo / 3.5-(4) approximation eq.(10) (3) (1-RF) Qp - (4) 1 100 1245 1418 8.9 86 396 458 392 0.86 2 392 1105 173 11 305 394 623 497 0.778 3 497 992 313 20 408 485 459 468 0.821 4 468 987 426 27 406 378 436 442 0.867 5 442 1006 431 27 386 378 434 437 0.873 6 437 1003 412 26 392 379 423 429 0.897 7 429 1005 415 26 389 379 418 421 0.907 8 421 1013 413 26 383 379 416 408 0.910 9 408 1021 405 26 374 379 415 423 0.917 10 423 1006 397 25 385 380 417 415 0.910 11 415 1013 412 26 384 379 410 402 0.925 12 402 1026 405 26 366 379 417 417 0.912 13 417 1007 312 25 388 380 0.932 öê JN * Ú Òšš Å Ãîbæ‚, JN¢ *šV *~ ’öB B~º O»j ÒÏ ‚ š ~ n;²*¢ ¦ z ;{® ./† ®bæ ‚ Òšš Åê z× z »Ò ®bÒ¢ . ’~ êÖO»f Òššî B~ï(Q )j «K ~š r Òšš~ n;²*f ªêËj ÿö ’ cl † ®b–, îæï ÒššöB ªêWb~ «ê(P ) ¢ º‚ «K~š ªê¢æræê ÿö ’† ® 80 êƒ ’WÚ ® . Òšš ªê¢æ êÖö 27 ê¢ º’~º Vš O»ö jš, ’º v êò º’Ú ªê¢æ~ êÖj *‚ –š8 «K 5 êÖ ê¢ £ 93% 6²8 . $‚, *öB BF‚ Vš~ O»öBº –š8 «K; 5 êÖ;öB z® ®j ®º ‚ ž~ Òšš~ ² ÃÚ JN ú ©ö jš, ’öBº ‚ ¯OJ' O Fig. 2. Change of grindability of SiC in grinding cycle. »j VBÚb‚B /;*j »Ê, ;{‚ ªê¢æ¢ ’† ®º Ë6š ® . Ú‚ ’ º ©j r ®b–, š©f ‚ ªêWï š n;º ªêÒšš~ »b‚ ž‚ Nš‚ šCB . Ö V $‚ ªêË~ JN‚ žš ªê¢æöB êÖ8 £ 3% ;ê ½Ú¾ ® . šf ?š ’öB B~º Bond~ ªê¢æ¢ ;{~ ³~² êÖ~V *‚ O»j šÏ~ ªê¢æ¢ ’~² š ªêÒšš~
  • 11. Þ¦ *‚Îj BB‚ Ö¢ º£~š r ? . ²ê »Ò ®rf b†š . $‚ „B æ'‚ ’öB B‚ rÒ¾j ÒÏ~š ÒššöB « Miwa~ ‚ žš r Òšš~ n; ²*~ ./ Kš¢ † –š8º v B öš . ¯, Òššî B ‚“¶ö²æ
  • 12. Bond ~ ªê¢æ êÖj *‚
  • 13. Þ¦*RÎ 383 ~ï(Q )j «K~, îæï ÒššöB ªêWb~ « RP(n) : the ratio of oversize of P1 sieve of Qp(n) ê(P )¢ º‚ «K~š, ~ n;²*, ªêË 5 cl to Qp(n) at n-th cycle [−] ªê¢æ¢ ÿö êÖÚ, Vš~ O»ö jš ªê¢ 80 Rt : the cumulative oversize percentage at æ~ êÖj *‚ –š8 «K 5 êÖê¢ £ 93% time t [%] 6²8 . $‚, ’º /;*j »Ê, t : the grinding time [s] ÖW ®º ªê¢æ¢ ’† ®º Ë6š ®ÚB, W : the work input per ton of the feed Jê ö ;{‚ V.–š8¢ B† ® . ž 7b [KWh/t] ö šBê, ’öB B‚ *‚Îf JIS M 4002 Wi : Bond's Work Index [KWh/t] O»b‚¦8 ; FÎ~ š £² wφ ® . ^^ò 453+4)2':;8+ 1. ßÁ- Pèm'cï ~““ , 1971, “ ,” , Vol. 35, No. 3, pp. 268-276. 2. PꐓÈ% Pꐓ S ðQg›Ã , 1986, “ ,” , b : a constant related to the revolution number of the mill [−] , pp. 487-496. 3. ASTM D 409, 1997. 4. øäì^ Ÿäñ¦ ×õ¦ uèL ?¬n ^% b1 : a rate constant appearing in Eq.(1) [−] , , , , , cl : the circulation ratio, Qcl / Qp [−] Pê ¸Ô!­ ¬ ’W 1979, “ − ,” 2 , , , pp. Dp : the particle size [µm] 543-555. Dp1 : the particle size of feed [µm] 5. Bond, F.C., 1952, “The third theory of comminution,” Dp2 : the particle size of ground product [µm] Trans. AIME, Vol. 193, pp. 484-494. Dp50 : the median size of particle [µm] 6. Nematollahi, H., 1994, “New size laboratory ball mill for Bond Work Index determination,” Mining F80 : the size of a sieve aperture permitting Engineering, Vol. 46, No. 4, pp. 352-353. the passage of 80% of the feed [µm] 7. KS E 3600, 1991. Gbp : the grindability [g/rev.] 8. ïûð , 1967, “Bond 'Pè¡ŸÝý PꐓÈó ,” , k : a constant related to the particle size Vol. 4, No. 2, pp. 776-785. appearing in Eq. (11) [−] 9. JIS M 4002, 1976. 10. ïûð 8ÁÇPè¥
  • 14. '®÷›© ~“ , 1965, “ ,” kB : a constant related to Bond's law [−] “ , Vol. 29, No. 2, pp. 113-118. 11. ïûð PꐓäÔ ðQg›Ã m : a constant related to grindability [−] , 1980, , , , N(n) : the total revolution number of the mill pp. 159-163. at n-th cycle [rpm] 12. é¨|¡ì ïûð% , ~““äÔ Co, 1969, “ II,” n : a constant appearing in Eq.(11) [−] 3Þ , , pp. 45-53. P1 : the opening of control sieve [µm] P80 : the size of a sieve aperture permitting ´ ¼ A *Ò çæv š z v the passage of 80% of P1 pass product (]Èó *36. *6a BI) [µm] Qcl : the weight of the circulating load [g] QF : the weight of the additive feed [g] Qo Qp : the weight of a mill charge [g] : the weight of undersize of P1 sieve [g] d æ 1984j 7v z Ò Qp(n) : the value of Qp in ground product at 1989j University of s. Florida, n-th cycle [g] z +Ò 1993j University of s. Florida, RF : the ratio of oversize of P1 sieve to feed [−] z ;Ò R'F(n) : the ratio of oversize of P1 sieve to feed at n-th cycle [−] RN(n) : the ratio of oversize of P1 sieve to *Ò š·v ~ãz ¦v (E-mail; sunkist@kytis.konyang.ac.kr) ground product at n-th cycle [−] *37² *5^