커넥팅로드단조공정시뮬레이션및타결과와비교 이민철 전만수 * A Connecting-Rod Forging Simulation and its Comparison with Other Results Min Cheol Lee and ManSoo Joun Key Words : Connecting Rod( 커넥팅로드 ), Forging Simulation( 단조시뮬레이션 ), Mesh Quality( 요소품질 ) Abstract In this paper, we apply a forging simulator to automatic simulation of a connecting-rod forging process and compare its results with others found in the literature. The process information comes from the distributed examples of DEFORM3D. The process is fully automatically simulated using the tetrahedral element capability of AFDEX3D, developed by the authors. Our results are compared with the results found from the related literature, already simulated using DEFORM3D by other researchers. The comparison shows that our results are relatively excellent especially in terms of mesh quality on which the solution accuracy depends mainly. 1. 서론 단조공정시뮬레이션기술은유한요소법 (1) 과유한체적법 (2) 에의하여발전되어왔다. 유한요소법은유한체적법에비하여결과의정확도와신뢰성이높다는장점이있다. 반면, 유한체적법은복잡한문제와계산시간측면에서유리한것이현재로써는장점이되고있다. 계산시간문제는컴퓨터의발전으로머지않아해결될것으로전망된다. 그러나매우복잡한문제에대해서는장담할수없는상황이다. 복잡한단조공정에대한유한요소해석가능여부는요소망자동생성기술에좌우될수밖에없다. 유한요소법의장점인결과의정확성도요소망의품질에좌우된다. 유한요소해석의생산성도요소망의생성기술과직결되어있다. 따라서유한요소법에바탕을둔단조시뮬레이션기술은요소망의자동생성기술에종속되어있다고해도과언은아니다. 회원, 경상대기계항공공학부박사후과정 E-mail : mclee@gnu.ac.kr TEL : (055)751-6585 FAX : (055)751-5316 * 경상대기계항공공학부정교수 이러한까닭으로많은연구자들이적응적요소망자동생성기술에관한연구를실시하였다. (3-6) 저자들에의하여특성경계를살리는표면요소망생성기법 (7,8) 과금형과소재사이의간섭을고려한적응적요소망재생성또는자동생성기술 (9,10) 이개발되었다. 그리고저자들 (11) 은최근단조시뮬레이션중변화하는경계조건을요소망생성시에고려함으로써지능적요소망자동생성기법을개발하였다. 본연구에서는전술한지능적요소망자동생성기법을근간으로개발된단조공정해석용시뮬레이터인 AFDEX3D 를커넥팅로드단조공정에적용하고, 그결과를 DEFORM3D 의결과와비교함으로써개발된기법의장단점을분석하고자한다. 2. AFDEX 3D 를이용한커넥팅로드 단조공정의해석 유한요소법을이용한단조시뮬레이션기술의연구자들에게커넥팅로도와크랭크샤프트의단조공정해석 (12-18) 은연구자들이지향하는궁극적인목표중의하나이다. 많은연구자들이유한요소법
을이용한단조시뮬레이션기술과그응용에관하여연구하였으나, 아직커넥팅로드단조공정에관한해석사례는많지않다. 국내에서도일부의연구자들 (16-18) 이이에관한연구를실시하였으나, 실공정과는다소거리가있다. 최근들어유한요소법에근거한단조시뮬레이터인 SFTC 사의 DEFORM 3D, MSC 사의 MSC.SuperFORM, TRANSVALOR 사의 FORGR 3D 등을이용한커넥팅로드단조공정의해석이이루어지고있으며, 이제단조시뮬레이션기술이발전하여커넥팅로드의단조공정을대상으로결과를비교검토하는시대에접어들었다. 물론, 유한체적법에바탕을두고있는 MSC.SuperForge 는국내의열간단조회사에서도복잡한단조공정의시뮬레이션목적으로비교적널리사용되고있다. 본연구에서는 Wan 등 (6,19) 이 2004 년도에연구한 DEFORM 3D 의해석결과와저자들이개발한 AFDEX 3D 의결과를비교하기위하여동일한문제에관하여해석을실시하였다. Fig. 1 은해석에사용된금형과소재정보를나타내고있으며, 이정보는 DEFORM 3D 의예제목록에서발췌하였다. Punch Workpiece Die Fig. 1 Process geometries including dies and material 해석에사용된공정조건은다음과같다. 0.18 Flow stress: σ = 60.76 ε (MPa) Frictional constant: m = 0.2 Workpiece temperature: 1000 ( ) Total relative stroke: 41.7 (mm) (a) Initial (nodes: 9421, elements: 47990) (b) Stroke 34% (nodes: 28747, elements: 152657) (c) Stroke 48% (nodes: 24290, elements: 124401) (d) Stroke 62% (nodes: 29067, elements: 147137)
(e) Stroke 73% (nodes: 37821, elements: 189339) (f) Stroke 85% (nodes: 37961, elements: 187892) (g) Stroke 94% (nodes: 39858, elements: 196413) (h) Stroke 99% (nodes: 33230, elements: 160804) (i) Stroke 100% (nodes: 32251, elements: 155703) Fig. 2 Global view of simulation results (bottom view)
본연구에서는요소망재구성이후에사면체요소의수가 150000 개내외가되도록자동생성하였다. 소재의아래쪽방향과위쪽방향에서바라본형상을각각 Fig. 2 와 Fig. 3 에나타내었다. 이두그림으로부터 AFDEX 3D 의요소망품질이매우우수함을확인할수있다. 특히, 주목할점은요소망의패턴이단조공정중재료의형상과유사하다 는점이다. 이러한특징으로작은요소의수로도복잡한형상의물체의표현이가능하다. 이러한특징을정교한해석을위해서필수적으로갖추어져야한다. 그림에서보는바와같이변형중의재료와유사한패턴의요소망이생성된것은 AFDEX 3D 가채택하고있는지능형요소망자동생성기능의효과이다. (a) Initial (nodes: 9421, elements: 47990) (b) Stroke 34% (nodes: 28747, elements: 152657) (c) Stroke 48% (nodes: 24290, elements: 124401) (d) Stroke 62% (nodes: 29067, elements: 147137) (e) Stroke 73% (nodes: 37821, elements: 189339) (f) Stroke 85% (nodes: 37961, elements: 187892) 4
(g) Stroke 94% (nodes: 39858, elements: 196413) (h) Stroke 99% (nodes: 33230, elements: 160804) (i) Stroke 100% (nodes: 32251, elements: 155703) Fig. 3 Global view of simulation results (top view) Fig. 4 Simulation results with DEFORM 3D (top view, nodes: 13893, elements: 61787)
3. AFDEX 3D 와 DEFORM 3D 의비교 2004 년도문헌 (19) 에수록된 DEFORM 3D 의해석결과를 Fig. 4 에나타내었다. 최종해석결과에서보는바와같이전반적으로유사한결과를나타나고있다. 그러나요소망의분포및품질에있어서는매우큰차이를보이고있다. 따라서유한요소법의특성상전반적으로는유사한결과가얻어졌지만, 세부적으로는다소의결과차이가발생할것으로판단된다. 4. 결론 본논문에서는지능적단조시뮬레이션기법에근거한단조시뮬레이터 AFDEX 3D 의적용성을평가하기위하여커넥팅로드단조공정을해석하였으며, 그결과를관련문헌에발표된 DEFORM 3D 의예측결과와비교하였다. 전체적인변형해석결과는두소프트웨어모두유사하게나타났다. 그러나 AFDEX 3D 는우수한품질의요소망, 즉소재의형상과변형구간을매우잘표현하고있다. 이는지능형요소망재구성기법의결과이다. 후기 본논문은 2 단계 BK21 사업및산업자원부지역혁신인력양성사업에의해지원되었음. 참고문헌 (1) Lee, C.H. and Kobayashi, S., 1973, "New Solution to Rigid Plastic Deformation Using a Matrix Method," Trans. ASME, J. of Eng. for Ind., Vol. 95, pp. 865-873. (2) Che, J., 1999, "3-D Forging Process by Finite Volume Method," Proc. of KSME '99 Fall Annual Meeting, Pusan national university, Pusan, November 5, Vol. A, pp. 413~417. (3) Borouchaki, H., Laug, P., Cherouat, A. and Saanouni, K., 2005, "Adaptive Remeshing in Large Plastic Strain with Damage," Int. J. Numer. Methods Eng., Vol. 63, No. 1, pp. 1-36. (4) Zhu, J. and Gotoh, M., 1999, "Automatic Remeshing of 2D Quadrilateral Elements and its Application to Continuous Deformation Simulation: Part I. Remeshing Algorithm," J. Mater. Process. Technol., Vol. 87, No. 1-3, pp. 165-178. (5) Kwak, D.-Y., Cheon, J.-S. and Im, Y.-T., 2002, "Remeshing for metal forming simulating- Part I: Two-dimensional quadrilateral remeshing," Int. J. Numer. Methods Eng., Vol. 53, No. 11, pp. 2463-2500. (6) Wan, J., Kocak, S. and Shephard, Mark S., 2005, "Automated Adaptive 3D Forming Simulation Processes," Eng. Comput., Vol. 21, pp. 47-75. (7) Lee, M.C. and Joun, M.S., 2007, "Adaptive Triangular Element Generation and Optimization- Based Smoothing, Part 1- On the Plane," Adv. Eng. Softw., doi:10.1016/j.advengsoft.2006.11.004. (8) Lee, M.C. and Joun, M.S., 2007, "Adaptive Triangular Element Generation and Optimization- Based Smoothing, Part 2- On the Surface," Adv. Eng. Softw., doi:10.1016/j.advengsoft.2006.11.005. (9) Lee, M.C., Joun, M.S. and Lee, J.K., 2007, "Adaptive Tetrahedral Element Generation and Refinement to Improve the Quality of Bulk Metal Forming Simulation," Finite Elem. Anal. Des., March 2007, in Press. (10) Joun, M.S. and Lee, M.C., 1997, "Quadrilateral Finite-Element Generation and Mesh Quality Control for Metal Forming Simulation," Int. J. Numer. Methods Eng., Vol. 40, No. 21, pp. 4059-4075. (11) Lee, M.C. and Joun, M.S., 2007, "Intelligent Three-dimensional Metal Forming Simulation," Proc. of International Symposium on Mechanics, Aerospace and Informatics Engineering 2007 ISMAI 2007-Meiji University, Japan, February 25-28, 2007 (12) Grass, H., Krempaszky, C. and Werner, E., 2006, "3-D FEM-simulation of Hot Forming Processes for the Production of a Connecting Rod," Comput. Mater. Sci., Vol. 36, pp. 480-489. (13) Vazquez, V. and Altan, T., 2000, "Die Design for Fashless Forging of Complex Parts," J. Mater. Process. Technol., Vol. 98, pp. 81-89. (14) Takemasu, T., Vazquez, V., Painter, B. and Altan, T., 1996, "Investigation of Metal Flow and Preform Optimization in Flashless Forging of a Connecting Rod," J. Mater. Process. Technol., Vol. 59, pp. 95-105. (15) Behrens, B.-A., Doege, E., Reinsch, S., Telkamp, K., Daehndel, H. and Specker, A., 2007, "Precision forging processes for high-duty automotive components," J. Mater. Process. Technol., Vol. 185, No. 1-3, pp. 139-146. (16) Kwak, D.-Y. and Im, Y.-T., 2002, "Remeshing for Metal Forming Simulations-Part II: Threedimensional Hexahedral Mesh Generation," Int. J. Numer. Methods Eng., Vol. 53, No. 11, pp. 2501-2528. (17) Cho, J.R. and Yang, D.Y., 1998, "Threedimensional Finite Element Simulation of Connecting Rod Forging Using a New Remeshing Scheme," Eng. Comput., Vol. 15, No. (6-7), pp. 777-803. (18) Choi, W.-Y., Son, I.-H. and Im, Y.-T., 2004, "Locally Refined Tetrahedral Mesh Generation Based on Advancing Front Technique with Optimization and Smoothing Scheme," Commun. Numer. Methods Eng., Vol. 20, pp. 681-688. (19) Wan, J. and. Shephard, Mark S., Comparison on Remeshing and Mesh Enrichment Based Forming Simulations, Scientific Computation Research Center, Rensselaer Polytechnic Institute, April 07, 2004