Comparison between bond crushing energy and fracture energy of rocks in a jaw crusher using numerical simulation

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1 Sy Cm bw bd uhg gy d fu gy f k jw uh ug uml mul by A. Rfh*, J. Aghzdh Mhd, d B. Rz F dg h gy um dug h z-du, h Bd h f ud. I h wk, h FC3D d lm mhd (DEM) fw w mlyd mdl h uhg bhvu f m k wh dff mhl lby jw uh. FLAC3D fw w dd lyz h dbu h k. h k udd w mdlld gul mbl h h f h d/ ub ld bw w jw, d h wk d by h jw h uh w dmd. N dff y f k w udd d h g umd by h uh w md h f h Bd mmu gy md fm h Bd dx. h dbl dff bw Bd uhg gy d wk d by h jw uh f k. I h h Bd h ubl mhd f dg gl l fu gy d by h uh. vfy h ul bd fm DEM mdl, h fu bhvu f h uhd k w xmd d w md h FC3D ul. h l md f fug fvubly mdlld by h FC3D fw whl h dlm md b wll mdlld by FC3D fw. Kywd: jw uh; d lm mhd; uhg gy; Bd dx Idu h d lm mhd (DEM) w f d by Cudll d Sk mdl h bhvu f l l ubj dym ldg d1. Mh d Rjm d h l f DEM gdg mll d dmd h d h f h h DEM mul bd w dm (2D), h hqu bl d h w dw f mll wh bl uy v wd g f mll dm2,3. M h 10 y h, h DEM hqu h b ufully ld bll mll4 7, SAG mll8 10 d fugl mll11,12. DEM h l b ld udy m-dud l bkg. Ug DEM mul f m bkg f gglm13 15 d ggg h hdd by m16 18, dff m h flu h m fu hv b lyd. I m ud, h f lm mhd (FEM) uully dd dm, d DEM h b ud hw k dbu k ud ldg18. Al, ug DEM mdlg f h mv gh d d wgh, h lh bw, m gy d h dg f fgm h b dmd19. Svl m hv b md mdl h uh; Djdjv l. mdlld w y f m uh: h vl- d hzl-hf m uh. hy vgd h ff f h mh dg d l d vly d gy dbu f ll d h mllg hmb, d l h l bkg bhvu20. I h udy h-dml (3D) l flw d (FC3D), bd h DEM hqu, h b mlyd mdl h fu bhvu d uhg gy f dff k lby jw uh. Al, F Lgg Aly f Cu h dm (FLAC3D), bd h f dff mhd (FDM), w dd ly ly h dbu h k m h l bw h m d h jw. N k wh dff mhl w mdlld gul mbl h h f h d/ ub. Eh k gl l w mdlld whl w uhd lby jw uh, d fu bhvu h g z w udd ug FC3D fw. vfy h md ul, h fu mhm f h k h jw * Dm f Egg, Zj Uvy, Zj, I. Mg d Mllugl Egg Dm, Amkb Uvy f hlgy, h, I. h Suh Af Iu f Mg d Mllugy, SA ISSN X/ vd M. 2009; vd vd S h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER DECEMBER

2 Cm bw bd uhg gy d fu gy f k jw uh uh w udd, d h ul w dud wh h fu bhvu mdlld by FC3D fw. h, h dmd wk d by h jw f h uh w md wh h f h Bd uhg g (md fm h Bd uhbly dx) f h k. Al, h ff f h Bd uhbly dx h md uhg gy f h k w udd. Ml d mhd I h wk, dff k m w bd fm m m I. h mhl (ly mdulu d uxl mv gh) d h Bd uhbly dx f h k w xmlly vlud. F h u dd m w d u fv yldl m f 54 mm dm d 135 mm hgh ug I v hydul mh. mu h mdulu f ly, fv gug w ud. h Bd dx w md ug dd m uhbly h w ld 15 ub m f hgh 50 mm. h dy dy f h k udd w md by h u d l hqu, whh w dfd by h Il Sy f Rk Mh (ISRM). h Bd uhbly dx, uxl mv gh, ly mdulu d dy dy f h k udd hw bl I. Glly, h h Bd d: bll, d d uhbly. h Bd bll d d d dmd ug dd bll d d mll, vly, d ubl f gdg. h Bd uhbly dx, whh md ug dd m uhbly, ubl f uhg21. Bu h jw uh w mdlld h udy, h Bd uhbly dx f h k udd w dmd. udy fu mhm f h k h g z f uh, ub d hl m f lm w d, d h fu lby jw uh w udd ug hgh-d m. FC3D mdl f k d jw uh I d xm h fu bhvu f h k d dm h ld gy jw uh, FC3D mdl f jw uh w dvld. h mdl gl m-l mul uh, d mul-bdy gd. h uhg f gl ub d/ gl hl k h jw uh muld ug h FC3D mdl. I bl mdl h bhvu f l h my b ld wh f vlum by -dfmbl wll. h d k d f dvdul l d ud y wh h l wll. Eh lul lud h lu f qu f m l, ug f-dlm lw f h 1. h k mdlld mbly f ff l (bll) h bdd gh. h f h bd bw bll b dfd h FC3D fw22. F h u f mdllg, ub m 5 m hgh d hl m 6 m dm w d fm vu k h w udd. h k w mdlld ug dmly gd bll wh vu dm f mm (Fgu 1). FC3D fw mul m-l ml bhvu fm h f m-l m, h u m mmhl f u, whh ld bl II23. h mmhl b dvd dly fm mum f bl I Mhl f h k udd Fgu 1 Mdl f hl d ub k udd dlyd by FC3D fw Rk Bd Uxl Ely Dy dx mv mdulu kwh gh M G m 3 Amhbl B Blk-hl D G G d hyy g d Rhyl Lm bl II Mmhl f l d bd gh ud f mdllg lm (dmd fm muld uxl m by FC3D) Bll dy (ñb) 2090 kg/m 3 Bll-bll mdulu (E b ) 35 G Bll ff (K /K ) 2.5 lll-bd mdulu ( E ) 35 G lll-bd ff ( K / K ) 2.5 Bll f ff (Í) 0.70 lll-bd ml gh (σ ) 71 M lll-bd h gh (τ ) 71 M 710 DECEMBER 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

3 Cm bw bd uhg gy d fu gy f k jw uh lby m. m f u bll d h bdg gh f h u f mulg h k udd, h dg uxl m udd k w muld ug FC3D fw; h ud m-m w hgd ul h luld d ly mdulu d uxl mv gh fm h FC3D mdl mhd h md d fm h xml uxl m. h gh d h ly mdulu f lm, whh w dmd fm h muld uxl m, 52.4 M d 25.3 G, vly, mhg h xml vlu f lm bl I. bl II gv h mmhl d bd gh f Lm, whh dmd by mulg h uxl m. A lby jw uh w h mdlld ug h FC3D d. A jw uh h w l (jw), f whh fxd d h h, wgg d ld, g d uhg ml bw h w uf. h fdg 10 m wd, d mxmum dhg u 2.5 m ( u). h mmum bw h jw dug h uhg yl 17 mm (ld u). h l d f h mvg jw lm 300 m. h jw uf ugd; h hgh d wdh f ug 0.5 m (Fgu 2). Vu whh ub d hl m my b ld h jw uh hw Fgu 3. F h ub m, w y f bw k d h vl jw bl. h dbd l d l. I d mug h bkg gy h DEM mdl, h f wll gy h b ulzd. h wll gy qul h l umuld wk d by ll wll (h h jw f h uh) h gul mdl f k m h luld by h FC3D fw23. I umd h fu gy f k qul h wll gy m f k. I h dym d mull m bhvu f h uh h b gld. Mdlg fu bhvu f hl k Wh hl k ld bw h w jw, h uf bw h k d h jw dud mll h bly wll b xmd. A v bul u h. Fgu 5 hw h dbu f mj l, md fm f-dff ly, h lm m h f ; hgh m dvld h, d l fmd h h f h k. h fu g f gl hl m wh 6 m dm w hghd by hgh-d m dug h uhg. Fgu 6 gv h fu mhm f h hl lm h g z f h lby jw uh. Bu h m w dd h uh mully, d h uhg u vy dly, h du fg l h u. FLAC3D mdl f jw uh I d dm h dbu h k dug uhg, FLAC3D mdl ml lby jw uh w dvld; hl d ub k w ld bw vl d ld jw. I FLAC3D, h uu mdum ld by d, quvl whh ll f vlvd d h d f 3D mh ud h mdum. h, qu f m f h uum fmd d fm f Nw qu h d. h ulg ym f dy dffl qu h lvd umlly ug xl f-dff h m24. h FLAC3D mdl f ub d hl m bw w gd jw hw Fgu 4. h jw mdlld gd mdum, d h k mdlld l mdum. I umd h h uf bw m d h jw, lg d u. h vl jw fxd, d h ld jw mv wd h fxd jw ul h d bw h h lmg vlu f 17 mm h bm (Fgu 4). h dbu h b md f h f g f h. Fgu 2 FC3D mdl f lby jw uh () d (b) ld u Fgu 3 FC3D mdl, gvg f () hl m vwd fm h d d (b) ub m vwd fm bv jw uh h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER DECEMBER

4 Cm bw bd uhg gy d fu gy f k jw uh F du f dud h xm, h dly blw h ldg ly uhd. S h x f u gy h, f zd gy, hw Fgu 6, dud25. Hgh uhg u h whh m dvld (Fgu 5). I Fgu 5 h fm m l k l h budy f h m-lll g whh uhg wh f du u. h g w dfd h f f whh h my dub d k u ud ldg, hw Fgu 5. h md ul wh h f m l.17. h f f uully dud wh h uf bw h ldg l d h k l bg. Fgu 4 FLAC3D mdl f () ub d (b) hl m bw w gd jw Fgu 5 Mj l (σmx), dmd fm fdff ly, g hl lm h l h vl dm f h h Fgu 6 Il fu f hl lm lby jw uh, vwd fm bv 712 DECEMBER 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

5 Cm bw bd uhg gy d fu gy f k jw uh Fgu 7 hw h ul f h dg DEM mul f h fu g md by FC3D fw. Fgu 6 d 7 hw h f fm f h f f, h hl lm bk ud l fu md h vl l whh h dm mj l f l y (Fgu 5). Al, m h h l md f fu wll d by h DEM h hl m. Fm Fgu 6, l h w hmh-hd dud h f g f h uhg. Fgu 8 h fllwg g f h uhg ; h hmhl f lm d b bl whh h bw h k d h jw fd d, d l h h d. h f dbu h k h vy f h f ml h hw Fgu 5. Adgly, h fu mhm h hmhl lm g f h l md. Smlly, h fu mhm f h k h fllwg g f uhg l, hw by h FC3D mdl (Fgu 8). Cquly, DEM h ubl hqu mdl fu f gl hl k h jw uh. If h bw h k d h uhg l d b l d, h l fu mhm wll bm m dm h h hfu mhm. O h h hd, wh h uf bm l, h dm fu md my b h h mxd md f h d l fu26. Al, h ugd uf f h jw u hgh h h k. h dm fu md ud h um uully l. S h l gh f bl k muh l h h gh26, h umd gy jw uh g ugd jw d. I h wd, h hgh h bl f k, h hgh h ff f h, dug h fu gy. Wh FC3D fw bl lul h wll gy ld k by h jw. Fgu 9 hw h wll gy ld h hl lm vu h umb f m ; h mxmum wll gy qul 237 (jul). Cdg h m f hl lm, h umd gy h qul h mxmum wll gy h m f k f h z du f lm fm m lm 1002 (kj/). Al, f dg h gy um dug h z-du, h Bd lh, xd h fllwg, f ud27: Fgu 7 DEM mdllg f fu g f hl lm jw uh, vwd fm bv [1] wh W h Bd dx (kwh/), 80 h z whh 80% f h du ( m), F 80 h z whh 80% f h fd ( m) d W h gy um (kwh/). Cdg h Bd uhbly dx f lm, 12.8 kwh/, h Bd uhg gy f lm m f kj/ xd b 1030 ( 80 = d F 80 = m), whh m h h gy um md fm h FC3D mdl. Fgu 8 Squl uhg g f hl lm jw uh d DEM mdl f md g f uhg, vwd fm bv h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER DECEMBER

6 Cm bw bd uhg gy d fu gy f k jw uh dud l, h m ul bl bf h mmm f h fug (Fgu 10). Af h f h ub m, h ul fm DEM mdlg f h f l bw uhd k d h vl jw ml h f l. Wh h bw ub k d h vl jw l, dlm mhm uully u. Al, ml h hl m, ly uhd g fmd h l f h dug h uhg. Fgu 11 hw h mj l dbu h ub lm dmd by h FLAC3D mdl. h ly uhd g wh hgh m dvld m. h m f f fm h l bw ub k d h ldg l (Fgu 11). Fgu 9 Wll gy ld hl lm by jw Smlly, wll g h ld hl m f h f h k udd h w uhd by h jw hv b muld by FC3D fw. h ul, gh wh h dg Bd uhg g, hw bl III. h luld gy umd by FC3D, h qul h wll gy h m f k, dbly l h h Bd uhg g f hl m (bl III). Bu h mdl dvld gl ud- wll dfm d, d uly d h dym d mull m bhvu f h xml uh. Mv h k gy f h l fgm h b gld. h m jufy h hgh Bd gy h h h wll gy. A fm bl III, h hd h k h hgh h g f dff bw wll gy m f k d Bd gy. Bu h Bd m uhbly muh hgh h h jw uh whl by g h, m lwgh k, h fu gy f hd k dbly28. I dd h ff f md hd k h ugd jw uh muh m gf. Cquly h hg dff bw Bd uhg gy d wll gy bvd. h mkbl dff bw wll g bd fm FC3D mdl d Bd uhg g hw h h Bd qu ud gl l bkg. Cquly, h Bd uhbly ufully d h w dw f h lby jw uh f uhg gl hl k. Mdllg fu bhvu f ub k A hw Fgu 3, ub k my b vl jw uh. Rul hw h wh h bw h ub m d h vl jw bl III Bd uhg g (luld fm Equ [1]) d wll gy m f k (md fm FC3D fw) f hl m Rk Bd uhg Wll gy f dff gy m f bw wll d kj k bd uhg kj gy% Lm Blk-hl Rhyl hyy g-d G G-d D Amhbl B Fgu 10 R f ub m hvg l wh h vl jw, vwd fm bv 714 DECEMBER 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

7 Cm bw bd uhg gy d fu gy f k jw uh Fgu 11 Mj l (σmx) ub lm h dbu f h l ll h uf f x-x, whh hw Fgu 11 f lm, gv Fgu 12 (md fm FLAC3D mdl). Rfg Fgu 12, h dbu x-x f h ub lm uh h h ll l m dvld h m. Bu h jw f ugd, mkbly hgh my b dvld h uf d wg h mbd ff f ll d h umf f h m, h my h h fu gh f lm, hby mkg fvubl f k. Gwh f h l k u h vl l, ug dlm. h h d fm h umf f h lm, hw Fgu 13. Fgu 14 hw h DEM mdllg f h fu mhm f h ub lm m h jw uh. Rfg Fgu 14, m h h f dlm vgly mdlld by DEM. I m h h lm f DEM mdl f mulg h dlm my b hly du dbly f ly wh h uum quy d hf d x h l mbly, bu h mdum d. I h d FC3D mdl, f d l dlm mud. h qu uful wh udyg h ml bhvu m-l, bu hy b fd dly uum mdl23. Fgu 12 Dbu f ll l x-x f lm m (σm) Fgu 13 Fu f ub lm lby jw uh, vwd fm bv h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER DECEMBER

8 Cm bw bd uhg gy d fu gy f k jw uh bl IV Bd uhg g (luld fm Equ [1]0 d wll gy m f k (md fm FC3D d) f ub m Rk Bd uhg Wll gy f dff gy m f bw wll d kj k bd uhg kj gy% Lm Blk-hl Rhyl hyy g-d G G-d D Amhbl B Fgu 14 DEM mdlg f fu g f ub lm jw uh, vwd fm bv h mxmum wll gy ld h ub lm w dmd fm h FC3D mdl d qul J, hw Fgu 15. Cquly, h qud gy f dug h z f ub lm fm m 530 kj/, whh qul h mxmum wll gy h m f lm, wh h Bd uhg gy f lm 80 d F 80 f d m, vly, qul 852 kj/ (luld fm Equ [1]). h dbl dff bw h uhg gy dmd ug FC3D (530 kj/ ), d h uhg gy md ug h Bd dx Equ [1] (852 kj/) f lm. Smlly, h uhg bhvu f gh h k (gv bl I) w udd h fm f ub m d l muld ug FC3D fw. bl IV gv h Bd uhg gy f h k d h wll gy h m f h k. h mkbl dff bw h Bd uhg gy d h wll gy f h ub k. Cquly, lk h hl m, h Bd h ubl mhd f dg h fu gy f gl ub k. Clu Fgu 15 Wll gy ld ub lm m by jw h ul f mulg jw uh ug FC3D f dff k y h h d ub h fm h h mkbl dvy bw h wll g m f k d h Bd g f k. h dff bw h Bd d wll gy vyg fm 2.7% f h lw-gh k (hl lm k) 26.5% f h hd k (hl b k) d fm 37.8% f h lw-gh ub k 56.7% f h hd ub k. Cquly, m h Bd qu ubl mhd f mg fu gy f gl ub d/ gl hl k. hf, h Bd uhbly ufully d h w dw f h lby jw uh. 716 DECEMBER 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

9 Cm bw bd uhg gy d fu gy f k jw uh Bu h mdl dvld gl ud- wll dfm d, d uly d h dym d mull m bhvu f h xml uh. Mv h k gy f h l fgm h b gld. h dff bw wll d Bd g f hd k m h h f lw-gh k whh w du m vy f hd k d. h fu mhm f h hl k l md d wll dd by DEM mdl, ulk h ub k wh h gm wh h xml ul gd. h fu md f h ub m dlm h jw uh. S FC3D fw ly ll l- m h k, h f dlm mdlld by DEM. Akwldgm h uh wuld lk kwldg h Zj Uvy f fl u d Mh Cmy. Al, h uh wh kwldg h f Fzd Rfh f hgh-d hghy. Mg d Ml Egg, Uvy f Bh Clumb, Vuv, INOUE,. d OKAYA, K. Gdg mhm f fugl mll mul udy bd h d lm mhd. Il Jul f Ml g, vl , CLEARY,.W. d HOYER, D. Cfugl mll hg m d w dw: m f DEM d wh xm. Il Jul f Ml g, vl. 59, HORNON, C., CIOMOCOS, M.., d ADAMS, M.J. Numl mul f gglm m bkg. wd hlgy, vl KAFUI, K.D. d HORNON, C. Numl mul f m bkg f hl yll gglm. wd hlgy, vl. 109, MISHRA, B.K. d HORNON, C. Im bkg f l gglm. Il Jul f Ml g, vl. 61, OAOV, A.V. d CAMBELL, C.S. Cmu mul f m-dud l bkg. wd hlgy, vl. 81, OMAS, J., SCHREIER, M., GROGER,., d EHLERS, S. Im uhg f f lb d ylg. wd hlgy, vl. 105, Rf 1. CUNDALL,.A. AND SRACK, O.D.L. A d mdl f gul ml. Ghqu, vl. 1, MISHRA, B.K. d RAJAMANI, R.K. h d lm mhd f mul f bll mll. Ald Mhml Mdllg, vl. 16, MISHRA, B.K. d RAJAMANI, R.K. Smul f hg m bll mll: 1. Exml vf. Il Jul f Ml g, vl. 40, CLEARY,.W. dg hg m, w dw, gg, w d l bkg bll mll ug d lm mhd. Ml Egg, vl. 11 (11), CLEARY,.W. Chg bhvu d w um bll mll: vy mll g d, l gmy d hg m. Il Jul f Ml g, vl. 63, VAN NIERO, M.A., GLOVER, G., HINDE, A.L., d MOYS, M.H. A d lm mhd vg f h hg m d w dw f xml w-dml mll. Il Jul f Ml g, vl. 61, DJORDJEVIC, N. D lm mdlg f h flu f lf w dw f umblg mll. Ml Egg, vl. 16, RAJAMANI, R.K., MISHRA, B.K., VENUGOAL, R., AND DAA, A. D lm ly f umblg mll. wd hlgy, vl. 109, CLEARY,.W. R dv dm mdlg f umblg mll. Ml Egg, vl. 14, MORRISON, R.D., CLEARY,.W., d VALERY, W. Cmg w d fm d fm DEM d JK mdlg. SAG 2001, Dm f 18. SCHUBER, W., KHANAL, M., d OMAS, J. Im uhg f ll mud xm d mul. Il Jul f Ml g, vl. 75, WHILES, D.N., KINGMAN, S., LOWNDES, I., d JACKSON, K. Lby d uml vg h h f k fgm. Ml Egg, vl. 19, DJORDJEVIC, N., SHI, F.N., d MORRISON, R.D. Alyg d lm mdlg vl d hzl hf m uh. Ml Egg, vl. 16, BERGSROM, B.H. Cuhbly d gdbly. SME, M-. Hdbk, vl. II, OYONDY, D.O. d CUNDALL,.A. A bdd-l mdl f k. Il Jul f Rk Mh d Mg S, vl. 41, IASCA CONSULING GROU, INC. FC3D l Flw Cd 3 Dm, Ml, M, IASCA CONSULING GROU, INC. FLAC3D F Lgg Aly f Cu 3 Dm, Ml, M, DONOVAN, J.G. Fu ugh bd mdl f h d f w um, du z d y f jw uh. hd h, Vg lyh Iu, USA, REFAHI, A., REZAI, B., d AGHAZADEH, J. U f k mhl d h Bd uhg dx. Ml Egg, vl. 20, CSOKE, B., HAVANI, Z., ABANASASSIOU, D., d SOLYMAR, K. Ivg f gdbly f d bux dy, quu d lkl md wll f hgh u uhg. Il Jul f Ml g, vl. 74, LAJAI, E.Z., DUNCAN, E.J.S., d CARER, B.J. h ff f k gh. Rk Mh d Rk Egg, hl N, vl. 24,. 2, h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER DECEMBER