; Vol. 8, No. 4; 014 ISSN 1913-1844 E-ISSN 1913-185 Published by Cndin Center of Science nd Eduction Anlysis for EPB Shield Brcket Bsed on Ansys Bojing Du 1, Yjun Yu 1, Pengpeng Ding 1,Weibin Lv 1 & Fei Zho 1 School of Mechnicl Engineering, University of Shnghi for Science nd Technology, Chin School of Engineering, Shnghi Ocen University, Chin Correspondence: Yjun Yu, School of Mechnicl Engineering, University of Shnghi for Science Technology, Chin. Tel: 86-188-186-081. E-mil: 31775038@ qq.com nd Received: April 1, 014 doi:10.5539/ms.v8n4p9 Accepted: My 6, 014 Online Published: June 5, 014 URL: http://dx.doi.org/10.5539/ms.v8n4p9 The reserch is supported by reserch project of Science nd Technology Commission of Shnghi Municiplity (project No: 11dz111300) Abstrct This pper studies the working condition of EPB, clcultes the bering thrust nd torque. It lso nlyzes the stress chrcteristics of EPB brcket in extreme working conditions by using the finite element method ndd gets the stress nd deformtion distribution of EPB brcket. Throughh grid refinement, the resultss of different mesh m size re nlyzed, the results show tht: the mximum strin is convergence, but the position of the mximum stress produces stress singulrity. The stress singulrity results re mended by theoreticl formul method inn this pper, menwhile presents n interpoltion method clled the criticl method of interpoltion, the vlue obtined by this method is more close to the true vlue. By using this method to interpoltion clculte the existing nlysis dt nd get the desired result. By compring the interpoltion results, clcultion results nd nlysis results, it proves the fesibility of this interpoltionn method, provides kind of effective method to solve the singulr stress results, provides n effectul reference for structurl improvements nd design mnufcturing of shield brcket. Keywords: finite element nlysis, EPB brcket, stress singulrity, criticl interpoltion 1. Introduction Shield tunneling mchine is specil tunneling construction mchinery, nd the EPB brcket is one of the principl constituent prts. The shield mchine will encounter different geologicl condition in underground mining, from silt, cly, snd nd hrd rock to soft rock nd other conditions. In the work process, the minly m prts of shield tunneling mchine tht is in contct with geologicll environment is cutter hed nd brcket. In the excvtion process, the EPB brcket suffers complex force, bd working environment, nd once the construction begins, the EPB will be plced in the ground nd ssembling only needs once forming, it is difficult to replce prts in the constructionn process. So if there is problem on the equipment, it will give bring huge loss to the whole tunnel. Brcket s structure nd qulity is directly relted to the tunneling engineering of shield tunneling mchine. Therefore, the structure design of the brcket is prticulrly importnt. Figure 1. Brcket model This pper uses the dvntges of computer nlysis, combines with the finite element theory nd mechnics 9
Vol. 8, No. 4; 014 knowledgee to nlyze the shield mchine s brcket structure, to contribute to the chievement of ided design nd improve reserch nd production cpcity. Menwhile, gives more effective pproch to solve the problem of stress singulrity. The results of this study on the structurl design of the brcket construction hve certin reference vlue.. Bulid Clcultion Model for Brcket The whole brcket usess the thicknesss of 50 mm-70 mm sheet, builds their models in SolidWorks. Since EPB brcket structure is complicted, so it s lso need to simplify the model to comply with the requirements of finite f element nlysis, it is lso convenient for designers to modify the model fter simplifiction. According to the model simplifiction method of EPB brcket, the simplified clcultion model of brcket is showed in Figure. Becuse the brcket is mirror symmetric structure, nd its force nd constrintss re symmetricl too. In the FEA (finite element nlysis) computtionl process, in order to improve the utiliztion of computer resources in the clcultion nd to reduce the impct on the ccurcy of the clcultion resultss due to the hrdwre limit. According to the theory of symmetry clcultion of finite element clcultion, youu cn choose its 1/4 to study fter cutting, it cn ensure the ccurcy of the finite element clcultion, nd improve the computtionl efficiency. To properly hndle the design model, you cn get the corbel finite element model, m pply the symmetry constrint on the symmetry plne fter cutting, then select 1/4 of the model to clculte, s shown in Figure 3. Figure. Brcket model s finite element clcultion model Figure 3. 1/4 model of brcket 3. Anlysis of the Forces The force bering by EPB brcket is minly from the cutter, so the study of the forces brcket should strt from the forces of the cutter. When shield cutter is working, it will hve intense friction with the surrounding soil to produce friction resistnce, effects of different soil environments re lso distinctive. Due to the difference of o the environment, the formul for clculting the friction resistnce tht you need to use is different. In cly-bsed geologicll environment conditions, the frictionl resistnce due to the soil nd the cutter is much smller thn the cohesive strength generted by the cly itself produce, thus the frictionl resistnce due to the soil nd the cutter c is often not considered when clculting the frictionl resistnce, nd only consider the frictionl resistnce generted by the soil cohesive strength. In snd-bsed geologicl environment condition, the friction resistnce is greter thn the cutter soil cohesive strength; therefore, you should regrd it s the frictionl resistnce to clculte. The clcultion on the friction between shield shell nd formtion cn ccording to different geologicl conditions nd the different sitution: Figure 4. Clcultion digrm of cutter s externl lod 30
Vol. 8, No. 4; 014 As shown in Figure 4, the shield cutter s frictionl resistnce formul: (1) in the cse of snd (soil cohesive strength: c = 0) : cn be clculted ccording to the following F 1 ( DLp 0 w p q p w) ( D L () in the cse of cly (soil friction ngle: 0 ): F1= D0Bc () Type in : B is the thickness of the shield mchine cutter (m) D0 is the shield mchine s outside dimeter (m) L is shield length (m) c is cutting section soil cohesive strength ( KP ) W is weight of the shield cutter ( KN ) is the friction coefficient between the strt nd the shield shell P e is the verticl erth pressure strength cting on the top of shield mchine ( KP ) The totl propulsion must be greter thn the sum of the resistnce of vrious dvnces, otherwise the shield cn t move forwrd. The resistnce includes peripherl nd soil shield friction resistnce, shield forwrd resistnce, the extrusion force of rock broken by the hob, rer trolley trction resistnce. In extreme working conditions shield cutter cn t rotte, thus the entire shield bering cpcity is the mximum crrying cpcity of the equipment mchine, the positive pressure nd torque is much lrger thn ny other forces, so you shouldd tke the positive pressure nd torque suffered by the cutter s the externl forces for the reserch. Brcket is thee prt to connect the cutter nd the shield mchine body, the positive pressure nd torque tht cutter suffers lso ct on the brcket. Though clcultion ccording to the corresponding formul: loding of thrust is 3580KN, resistnce torque in the geologicl environment is 5669 KN M. 4. Strength Anlysis of Brcket Cutter Hed 4.1 Anlysis of Results The mteril of brcket model is Q345B; mteril s density is 7850kg/m 3 ; poisson rtio is 0.8; elstic modulus is.06 100 5 MP; yield strength of the mteril is 75MP. According to the design size of brcket, you cn use 40mm, 0mm nd 10mm grid size to crry on the grid division of the brcket nd clculte. The mximumm equivlent stress, the mximum deformtion is shown in Figure 5, then nlyze the results. 0 e1 e1 e 4 q e w) (1). 40mm mesh b. 0mm mesh 31
Vol. 8, No. 4; 014 c. 10mm mesh Figure 5. Stress distribution, sfety fctor nd the mximum displcement distribution After comprison on the mximum deformtion nd mximum stress tht re clculted by ech mesh, youu cn get the result tht is shown in the Tble 1. The mximum deformtion is convergent, but with the mesh m refinement, the mximumm stress is more nd more big. The mximum stress is present t the ends of the support bem brcket, the position of mximum stress cross-section is shown in Figure 6. You cn find tht only few nodes stress is not norml, so the stress distortion hppens on this position. The stress obtined by the method of Finite element nlysis is not the exct stress vlue of the brcket. Tble 1. Comprison of results Mesh size Mximum deformtion (mm) 40mm 0. 969 0mm 0. 997 10mm 1. 003 conclusion Convergence Chnge rte Mximum stresss (MP) Chnge rte 0.9% 0.6% 351.8 476.3 67. 0 35.4% 41.1% Misconvergence Figure 6. The highest stress profile (10 mm mesh) In the course of the finite element clcultion, the stress singulrity mkes the convergence rte of the finite f element solution is very slow, especilly for the uniform grid division, the stress singulrity cn mke the result r tend to be infinite, thus ffect the ccurcy of the results, even lose the reference vlue for stress of structurl clcultion. In the finite element nlysis of the shield brcket, the geometric model structure should be simplified due to the clculte need. However, the stress singulrity phenomenon hppens in the clcultion, it is necessry to crry out further nlysis on it, which cn get more ccurte stress nlysis results. 4. Singulr Point Clibrtion Equtions By the nlysis of Figure 7 you cn see brcket is under the joint ction of the tngentil force Fb cused by xil thrust Fc of shield cutter hed nd the torque. You cn look ech brcket s single bem, the component perpendiculr to the bem xis of Fc nd Fb willl cuse brcket s torsion deformtion nd integrted view, the deformtion belongs to the bem s bending nd torsion deformtion. 3
Vol. 8, No. 4; 014 1) The brcket is simplified s bem nd the bending moment digrm is show in Figure 7. Figure 7. Shield brcket force simplified digrm In the XZ plne, decompose the force Fc, Fc cos is the component tht is perpendiculr to the xis direction, Fcsin is prllel to the xis direction, The corresponding bending moment perpendiculr to the xil direction is M1 Fccos l (3) In the XY plne, the bending moment generted s follows: M Fb l ) Norml stress nd sher stress produced by the bending moments Rectngulr cross-section of the bem is shown in Figure 8, synthesis the bending moment M nd M inn two directions to get the synthetic bending moment M. (4) M M M 1 ( F l) ( F cos l) b c (5) h w b w b h h Figure 8. Bem figure M W 6 ( Fbl) ( Fc cosl) (3hbh ) bw (3h w b w ) b h (6) F s A ( F l) As shield brcket belongs to the plstic mteril, nd it is in complex stress stte, therefore you should follow 33 b ( F cosl) hb h b h c w w (7)
Vol. 8, No. 4; 014 the fourth strength theory to clculte it: 1 1 r4 1 3 3 1 3 (8) Experimentl results show tht: for the plstic mteril, the fourth strength theory is in better greement with the experimentl results thn the third strength theory, it hs been widely used in engineering. Becuse the mteril of brcket is Q345B, so when performing the strength checking, you should use the fourth strength theory, so the results you cn will be more proximte to the ctul nlysis results. After the bove formul youu cn clculte: σ 93MP.Becuse the ctul model nd clcultion model is slightly different, so the results re not very ccurte, but the results cn be used s reference. 4.3 Singulr Point Interpoltion Computtion Sometimes, some detils of the model cn be simplified significntly, sometimes detils seems is not very importnt t the beginning, but the results show tht the detils re crucil. At this time, in the singulr region, you cn use stress liner interpoltionn nd stress fitting combined with Mtlb to clculte the stress vluee fst nd ccurtely. The previously mentioned formul checking method is kind of effective method for engineering whose w clcultion precision request is not high nd nlysis prt hs simple structure. But if the engineering requires high ccurcy nd hs complex structure, becuse it will suffer mny conditions limit such s computer hrdwre, model of externl conditions, then it is difficult to obtin ccurte results to follow the bove engineering checking method. This pper proposes n nlysis nd clibrtion method clled criticl interpoltion for the FEA results. In this method, you should conduct effective multiple FEA clcultion on engineering models, nd obtin the distribution of Equivlent (von-mises) vlues, generte the stress vlues s curve nd fits them, nd then study the vlues on the criticl point from the overlpping sections ndd the non-overlpping sections. You should get stress vlue towrd the coincidence of the direction subject to set s of numericl with high qulity meshes, tke the first djcent stress numericl difference of 10% stress points, nd the criticl point liner combintion gives liner trnsformtion equtions, then solve the results, get the singulr point stress vlue. The criticl vlues obtined by the FEA nd the fitting curve is ( x, y ), the numericl difference between the 10% stresss points is ( x 1, y 1 ), y1 y Slope: k (9) x1 x criticl interpoltion eqution yy k( x x ) (10) obtin the interpoltion equtions by ( 1), () x 3 lim y y x 1 ( 1 y x x x ) y (11) Figure 9. Stress picking route 34
Vol. 8, No. 4; 014 Mke the edge tht the mximum stress belongs to s the pth, s shown in Figure 9, you cn select the node stresss vlues bsed on three mesh size nd compre them., from Figure 10 you cn see tht the vlues in i the rnge of BD re consistent. Figure 10. Comprison of node stress vlue on the edge of three kinds of grid size When it s close to the stress singulrity A, the clcultion results divisive. Use the clculting dt of 10mm grid, you cn find the numericl difference between the 10% stress point ner point B. According to the method bove mentioned, you cn use liner interpoltion to estimte the stress vlue t the point A. Tke stress intensity fctor for 1, the point stress P A is 7(Mp). Compre the results of three different sizess of mesh ndd the interpoltion results, it s obvious tht the interpoltion results is closer to the mechnics nlysis results 35
Vol. 8, No. 4; 014 (93Mp). Therefore, the results obtined by criticl interpoltion method hve better ccurcy thn ny other results. 5. Conclusion This rticle proposes mesure to solve the stress singulrity phenomenon tht ppers in the structure stress nlysis, nd pplies the mesure in the finite element nlysis of shield brcket. Through the simultion clcultion of EPB brckets, we obtin the stress, deformtion nd other relted prmeters. Then, using interpoltion method combined with MATLAB to further nlyze the stress results, provide vlidtion bsis to shield brcket structure improvement. References Choi, S. K., Chtm, M. S., Vn Tyne, C. J., & Moon, Y. H. (006). Optimiztion of open die forging of round shpes using FEM nlysis. Journl of Mterils Processing Technology, 17(1), 88-95. http://dx.doi.org/10.1016/j.mtdes.009.06.046 Gun, H. S, & Go, B. (008). Composite erth pressure blnce shield mchine tool chip reserch of torque. tunnel technology, 45(), 73-78. Lurent, DucMne, & Anne Mrie Hbrken. (005). Anlysis of the sensitivity of FEM predictions to numericl prmeters in deep drwing simultions. Europen Journl of Mechnics A/Solids, 4(4), 6l4-69. Mondl, D. P., Amkrishnn, N. R., & Ds, S. (006). FEM modeling ofthe interfce nd its effect on the elstio-plstic behvior of metl mtrix composites. Mterils Science nd Engineering, 433(1-), 86-90. http://dx.doi.org/10.1016/j.mse.006.06.094 Sun, A. B. (013). Mechnicl Anlysis nd Improvement of Reserch in Shield cutter nd brcket. Shnghi: University of Shnghi for Science nd Technology, 45-47. Sun, A. B., Zhng, Y. L, Min, R, Ji, C. Q., & Zhuo, P. (01). Design nd Anlysis for EPB Shield Brcket Bse on Ansys., 6(8), 6-31. http://dx.doi.org/10.5539/ms.v6n8p6 Sun, G. Q., & Shng, D. G. (010). Prediction of ftigue lifetime under multixil cyclic loding using finite element nlysis. Mterils & Design, 31(1), 16-133. http://dx.doi.org/10.1016/j.mtdes.009.06.046 Copyrights Copyright for this rticle is retined by the uthor(s), with first publiction rights grnted to the journl. This is n open-ccess rticle distributed under the terms nd conditions of the Cretive Commons Attribution license (http://cretivecommons.org/licenses/by/3.0/). 36