APCOM & ISCM -4 th December, 03, Sgapore Reearch o tructural optmzato deg for held beam of hydraulc upport Abtract baed o repoe urface method *Dogche Q, Huyu L, Zhul Lu, ad Jagy Che School of Mechacal Egeerg, Zhegzhou Uverty, Cha *Correpodg author: dcq@zzu.edu.c The held beam the ma load-bearg compoet of the hydraulc upport. The tructural optmzato deg of oe held beam fulflled by the repoe urface method. Ug the weght a the objectve fucto, the tructural optmzato mathematcal model of held beam et up. The expermetal deg performed the ANSYS oftware ad uform deg. The maxmum tree of held beam are gotte the dfferet ze. The repoe urface model of deg parameter ad maxmum tree are ftted by the leat quare method. The tructural optmzato deg of held beam completed by the radom drecto method. Th reearch mplemet the tructural optmzato deg of hydraulc upport held beam a moder deg method, ad provde a valuable gudace for the hydraulc upport reearch ad developmet. Keyword: hydraulc upport, held beam, tructural optmzato deg, repoe urface method. Itroducto The held beam oe of the ma compoet of the hydraulc upport to bear load. Optmzg the deg of the held beam tructure ca reduce t weght, whch play a mportat role for the utaable developmet of coal machery eterpre. Tradtoal tructural optmzato of the held beam tructure ca be roughly dvded to two type.oe that, accordg to the theory of materal mechac or mechacal formula, the repoe of the tructure ca be computed ad the deg varable ad objectve fucto ca be choe, the to optmze the deg ug effcet optmzato algorthm (Lu, 007). For umerou mplfcato to model, th method would yeld the optmzato reult morecoervatve outcome.whle the other that, the repoe of the tructure obtaed by ug fte elemet oftware ad choe a the cotrat codto, the to elect the utable optmzato trategy for more accurate tructure optmzato deg (Yao, 0a).Th approach, where each terato wll be made durg the optmzato proce wth fte elemet calculato, rug lowly. To overcome the uffcecy of above tradtoal optmal deg method, by ug the repoe urface methodology, th reearch ha realzed the tructure optmzato of held beam for a certa type hydraulc upport. Wth ecto dmeo of the held beam a varable, ANSYS ued to calculate the tre of the held beam uder partal load, ad the repoe urface method of uform deg expermet appled to obta the fuctoal relatohp betwee tre value ad ecto dmeo of the held beam. For the weght reducto purpoe, the tructure optmzato deg of held beam performed uder the cotrat of tructure tregth ad geometrcal dmeo. It proved that the optmzato method feable ad effectve by fte elemet aaly ad valdato reult. Optmzato Baed o Repoe Surface Method The optmzato baed o repoe urface method geerally clude uch certa tep a, expermet deg, repoe urface model, ad earchg for the optmal pot (Lag, etc.,00). Expermet deg for the ake of cetfc ad reaoable arragemet of tet cheme wth fewer expermet to get more properte of deg pace (Kleje, 005a). A cetfc expermet deg ca arrage varou expermetal factor reaoably ad aalye tet data effectvely, thu
realzg more rch ad relable data obtaed wth ug le reource. Commoly ued expermetal deg method are full factoral orthogoal deg of expermet ad uform deg expermetato, etc. The uform deg expermetato, whch wll dtrbute deg pot evely wth the deg pace, choe th reearch. Compared wth other method, the uform deg expermetato ca requre le expermet tme, ad mprove the preco of repoe urface to a certa extet (L, etc.,005b). Ug th approach, everal umercal mulato tet are carred out to obta a ere of deg pot, whoe umber ad locato are determed. O th ba, the fucto relatohp betwee cotrol varable ad target varable etablhed wth regreo method, amely, repoe urface model. The repoe urface model reflect the fucto relatohp betwee target varable (depedet varable) ad everal cotrol varable (depedet varable). A th fucto relatohp geerally curve or curved urface, whch called a repoe urface model. Becaue the repoe urface model baed o ere of regreo of tet data, the qualty of regreo aaly drectly determe the accuracy of repoe urface model (Todorok, A. ad Ihkawa, T., 004). I the feld of tructural mechac, the repoe urface fucto model ofte adopt the quadratc polyomal form, uch a 0 Y( X) = a + ax + ajxx j = = j= where, a 0, a ad aj are udetermed coeffcet, x (=,, ) are bac varable. I order to mplfy the calculato ad avod applcato rage retrcto for the repoe urface, the cotat term, frt-order term ad ecod-order quared are remaed, ad the ecod-order cro term eglected, amely, the mplfed form Y( X) = a + ax + ax 0 = = Searchg for the optmal pot the geerated repoe urface model typcally clude to elect the deg objectve, cotrat ad the optmal algorthm. For dfferet tuato, the mathematcal cotrat are appeded to the model, the deg objectve ad a ere of the earch algorthm for the optmal pot are provded, uch a gradet algorthm, radom drecto method, pealty fucto method, etc. The radom drecto method, whch poee the eay procedure ad fat coverget rate, adopted here. The Repoe Surface Model Etablhmet Sheld Beam Statc Aaly The held beam of a certa type hydraulc upport taked a the reearch object. Fte elemet model for the held beam etablhed uder ANSYS evromet, the the held beam mehed freely wth SOLID87 elemet. Accordg to the techcal pecfcato ad load-bearg tuato of hydraulc upport uder partal load (Q, etc.,0b), the correpodg boudary codto ad load are appled, ad ANSYS tructural tatc aaly performed to obta the tre dtrbuto ad deformato codto for the held beam, a how Fg. ad. The fgure how the held beam' tre tuato ad deformato uder partal load, where the maxmum tre value of the held beam 359.6 MPa, ad the maxmum deformato 8.96 mm. To verfy the relablty of the fte elemet aaly, the real phycal prototype tre tet for the held beam alo made. Accordg to the charactertc of tre dtrbuto of the held beam, pate poto of the fol tra gauge are determed for the phycal tre tet, ad the tre value of the tet pot are obtaed. The locato of the tetg pot are how Fg. 3. At the ame tme, the correpodg 6 poto at fte elemet model of held beam are elected too, where the average tre reult are recorded. A comparo of fte elemet calculato reult ad meaured value how Table. The fte elemet reult ad the expermetal reult are ot cotet to a certa degree, whch caued by the tet error ad calculato error. The log-tme expermet reult utable () ()
workg evromet of the tra gauge, poble dfferet charactertc of each tra gauge, ad agular devato ad poto devato for the gauge patch, all thee factor wll lead to tet error. Whe fte elemet model beg mulated, parameter ettg, grd dvo ad the dfferece amog the cotrat boudary codto wll caue calculato error. Therefore, t poble to caue larger relatve error of ome dvdual pot. Fgure. Sheld beam' tre dtrbuto Fgure. Sheld beam' deformato Number of meaurg pot Fgure 3. Locato of tet pot Table. Expermetal verfcato Fte elemet reult/mpa Meaured reult/mpa Relatve error/% 9.96 0.37 7.97 56.36 53.73 4.89 3 4.5 46.96-9.46 4 64.05 38.04 8.84 5 3.84 305.35 5.7 6 3.4 0.8-5.85 Uform Deg Expermetal Aaly A held beam tructure complex, there are more parameter affectg the compoet tregth. Sce the dtace betwee the held beam frot ad back hged pot already determed durg overall deg of hydraulc upport, the lghtet weght wll be treated a the optmzato objectve of held beam. I other word, the mmum ectoal area wll be regarded a optmzato objectve (Zhu, etc., 0). The held beam, made up of upper ad lower cover plate ad vertcal rb, a box welded tructure wth a cro ecto of 5 cavte, whch how Fg. 4. Fgure4. The held beam cro ecto 3
Where, x the dtace betwee the frt cavty ad mddle plae, x the wdth of the ecod ad thrd cavte, x 3 the heght of the cavty, x 4 ad x 5 are the thcke of upper ad lower cover plate ad the thcke of the vertcal rb, eparately. I th paper, the uform deg expermetato ued to carry out repoe urface expermet. Through the parameterzed modelg to realze the chage of ze of thcke, ad the fte elemet aaly of each group of dmeoal data, we ca obta the maxmum tre value of the held beam. The quadratc polyomal wthout cro term take a the repoe urface equato whch cota 5 parameter ad ukow coeffcet (that equal to +, the umber of parameter). So, 6 tme orthogoal tet, amely cludg 6 level 5 parameter, ca be determed ad performed. The tet reult are how Table. Table. Uform tet table Tme x /mm x /mm x 3 /mm x 4 /mm x 5 /mm σ max /MPa 90.00 8.00 60.00 4.33.0 340.5 93.33 38.00 7.00 7.00 0.3 334.67 3 96.67 48.00 50.00 4.00 9.07 356.4 4 00.00 4.00 6.00 6.67 8.00 364.59 5 03.33 34.00 74.00 3.67.47 37.0 6 06.67 44.00 5.00 6.33 0.40 350.47 7 0.00 0.00 64.00 3.33 9.33 346.4 8 3.36 30.00 76.00 6.00 8.7 35.3 9 6.67 40.00 54.00 3.00.73 340.67 0 0.00 50.00 66.00 5.67 0.67 346.9 3.33 6.00 78.00.67 9.60 35.40 6.67 36.00 56.00 5.33 8.53 35.94 3 30.00 46.00 68.00.33.00 350.93 4 33.33.00 80.00 5.00 0.93 336.66 5 36.67 3.00 58.00.00 9.87 335.8 6 40.00 4.00 70.00 4.67 8.80 347.5 Ug the leat-quare method to ft the repoe urface fucto, y e = 3849.4835.548x + x 6.754x.3887x3.69x4 8.4884x5 0. 006 + 0.065x + x where y e a repoe value of the maxmum tre. + 0.006x3 + 0.303x4 4. 4595 Accordg to the evaluato formula of multple correlato coeffcet (equato (4)), we ca evaluate the fttg degree ad get R for every repoe urface fucto. The relatve hgh evaluato dex (R =0.9664) for equato (3) prove that the ftted repoe urface fucto utable, whch mea that the repoe urface expermet well wth repect to practcal mulato, ad t wll provde a good foudato for the ext tep of tructure optmzato. R SSE = = SST = = ( y yˆ ) ( y y ) 5 (3) (4) The Optmzato Deg Optmal Deg Mathematc Model 4
The lghtet weght of the held beam, equvalet to the mmum cover of cro ecto area of the held beam. From the Fg., the objectve fucto ca be made a F( X) = x (x + 4x + 6 x ) + 6x x 4 5 3 5 (5) The cotrat codto of the tructural optmzato o held beam are dvded to the followg kd: Stregth codto: It eured that the the maxmum tre value of the held beam uder partal load mut ot exceed the allowable tre. There y e σ / (6) σ the materal' yeld lmt (MPa); allowable afety factor. The thcke retrcto of the held beam: Coderg the factor uch a the vetlato ecto, the ga emo, pedetra ad the overall effect of the upport, a thcke rage of held beam ofte pecfed the deg. There T x + x T m 3 4 max (7) T m the mmum thcke of the held beam; T max the maxmum thcke of the held beam (mm). The overall thcke retrcto of the abdome: Coderg that the held beam of hydraulc upport ha certa tffe, the abdome deg hould defe a mmum thcke. There c m + + (8) ( x x 3 x5) cm lower boud of the total thcke of the abdome (mm). Boudary codto: The value of the parameter retrcted by varou pecfcato of the plate, alo by the overall or partal tffe ad deformato. Therefore, the deg varable are wth a certa rage. There l x u =,,,5 l the lower boud of the varable (mm); u the upper boud of the varable (mm). So the mathematcal model ca be ummarzed a follow: M F( X) = x4(x+ 4x + 6 x5) + 6x3x 5 X=[x,x,x 3,x 4,x 5 ].t. ye σ / Tm x3 + x4 Tmax ( x + x + 3 x ) c l x u =,,, 5 5 m (9) Optmzato ad Valdato Reult I th paper, the radom drecto method programmed wth MATLAB to olve optmzato model. Combg wth actual producto requremet, the optmal reult of deg varable for egeerg proce ca be obtaed a how Table 3. 5
Before optmzato, the cro ectoal area of the held beam 0.0769 m, ad through optmzato, the cro ectoal area of the held beam decreae to 0.0678 m. That mea, the held beam themelve weght wll be reduced by.8%. Accordg to the above optmzato, the held beam ha to be modeled aga. Uder the ulateral loadg codto of top beam, the fte elemet aaly for the held beam performed aga. The cotour of tre ad dplacemet of the optmzed held beam are how Fg. 5 ad 6. Parameter Table3. Deg varable optmzato reult Upper Lower Orgal lmt lmt value/mm value/mm value/mm Optmal value/mm x 90 40 5 x 0 50 40 35 x 3 50 80 70 7 x 4 0 8 5 x 5 5 0 9 Fgure 5. Optmzed tre dtrbuto of the held beam Cocluo Fgure 6. Optmzed deformato of the held beam () Baed o the repoe urface method, the tructural optmzato o held beam propoed. Ad the repoe urface method ad the fte elemet aaly are appled for held beam tructure optmzato. The held beam ectoal dmeo of a certa type Hydraulc Support optmzed to verfy the practcalty of the method. () The depedet varable of repoe urface fucto are choe accordg to ectoal dmeo of held beam, ad the expermet deg carred out by ug uform expermetal method. The leat-quare ued to ft the repoe urface fucto, whch ca approxmately reflect the relato betwee the ectoal dmeo ad the maxmum tre. 6
(3) Sce the repoe urface fucto fttg depedet of the pecfc tructure hape, the method ha a certa uveralty ad ca be appled to other tructure optmzato for hydraulc upport. Referece Lu, W.W. (007), A mechacal aaly ad the deg of the ma tructural o the ma top coal hydraulc powered upport.the mater the of Laog Techcal Uverty. Yao, X.Y. (0a), A reeearch for tructural optmzato deg of hydraulc upport' held beam. The mater the of Zhegzhou Uverty. Lag, J.,Xu, J.S., Xe, J. etc. (00),Hull le automatc optmzato baed o deg pace explorato. Joural of Shp Mechac, 7, pp. 50-64. Kleje, P.C. (005a), A overvew of the deg ad aaly of mulato expermet for etvty aaly. Europea Joural of Operatoal Reearch, 64, pp. 87-300. L, X., L, W.J. ad Peg, C.Y. (005b), Repoe urface methodology baed o uform deg ad t applcato to complex egeerg ytem optmzato. Mechacal Scece ad Techology, 4, pp. 575-66. Akra Todorok ad Tetuya Ihkawa. (004), Deg of expermet for tackg equece optmzato wth geetc algorthm ug repoe urface approxmato. Compote Structure, 64, pp. 349-357. Q, D.C.,Yao, X.Y., Wu, H.X.,etc. (0b), Fte elemet aaly of hydraulc upport cavg held baed o Pro/E ad ANSYS.Coal Me Machery, 3, pp. 94-96. Zhu, Q.,Q, D.C. ad Yao, X.Y. (0), Study o tructural optmzato of hydraulc upport cavg held ug ANSYS.Coal Me Machery, 33, pp. -4. 7