Visualization for Runner System Design in Die Casting Thesis Presented in Partial Fulfillment for the Requirements for the Degree Master of Science in the Graduate School of the Ohio State University By Zhaohui Ning, M.A Graduate Program in Industrial & System Engineering The Ohio State University 2009 Thesis Committee: Dr. R.Allen Miller, Adviser Dr. Jerald R. Brevick Copyright by Zhaohui Ning 2009 Abstract The research focuses on the development of a die casting runner system design process, and the visualization of this process. It provides a simple and flexible data representation for the runner system data and a user interface in CastView to create this data. The design process includes two steps. The first step is to create profiles. The second step is to create runner system data. Profile creation utilizes b-spline curve fitting algorithms to generate profiles with a uniform number of profile points from user defined sketches with a none-uniform number of sketch points. Runner system surfaces are created by sweeping interpolated profiles along user defined curve paths. To fully define runner system surfaces and promise their smoothness, curve paths’ shapes and interpolation methods need to be defined. Different shapes and different interpolation methods can be applied to a sweep path. In the implementation presented here, circle is used for path shape and s-function interpolation is applied to normal and planar points. With these configurations, smooth sweep runner system surfaces have been illustrated. ii Dedication Dedicated to my parents, wife and friends iii Acknowledgments I would like to express my sincere gratitude to my advisor, Dr. R. Allen Miller, for his guidance, support and encouragement over these years. He has been so enthusiasm and dedicated as a great researcher. I would like to state my sincere appreciation to Dr. Jerald R. Brevick for enhancing me with the background knowledge and encouraging me at time I need. I would like to say thanks to my parents, who brought me up, bestowed me capacities and skills and taught me never to give up. I would also like to say thanks to my friends in China, whose sincerity gave me so much strength to face difficulties. At last, I would like to express my deepest gratitude to my beloved wife, Hongyan He, who gave me so much support, attention and consideration for more than ten years. iv Vita January 1st, 1974 …………………………… Born – Qingdao, Shandong, P. R. China September, 1992 – July, 1996 ……………… B.S. Mechanical Engineering Qingdao University Qingdao, P. R. China September, 1996 – March, 1999 …………… M.S. Mechanical Engineering Shanghai University Shanghai, P. R. China September, 2003 – Present ………………… Graduate Research Associate Industrial and Systems Engineering The Ohio State University Ohio, USA Fields of Study Major Field: Industrial & System Engineering Minor Field: Computer Science and Engineering Areas of Interest: CAD/CAM, Computer Graphics and Animation, Software Engineering, Game Development v Table of Contents 1.TU INTRODUCTIONUT......................................................................................................... 1 1.1.TU Die Casting...............................................................................................................UT 1 1.2.TU Die Casting ProcessUT ................................................................................................. 2 1.3.TU Thesis OutlineUT .......................................................................................................... 3 2.TU DIE CASTING DIE DESIGNUT ...................................................................................... 4 2.1.TU Die Casting DieUT ........................................................................................................ 4 2.2.TU Die Casting ShotUT ...................................................................................................... 5 2.2.1.TU CavityUT ................................................................................................................ 5 2.2.2.TU BiscuitUT ............................................................................................................... 5 2.2.3.TU RunnerUT ............................................................................................................... 5 2.2.4.TU GateUT ................................................................................................................... 6 2.2.5.TU OverflowUT ........................................................................................................... 7 2.3.TU Die Casting Design PrinciplesUT ................................................................................. 8 2.3.1.TU Runner design guidelinesUT .................................................................................. 8 2.3.2.TU Fan gate design guidelinesUT ................................................................................ 8 2.4.TU CastViewUT .................................................................................................................. 9 3.TU PROBLEM STATEMENT AND RESEARCH OBJECTIVESUT ............................. 12 3.1.TU Problem StatementUT ................................................................................................. 12 3.2.TU Research ObjectivesUT ............................................................................................... 15 4.TU DIE CASTING DESIGN LITERATURE REVIEWUT ............................................... 17 4.1.TU Parametric DesignUT .................................................................................................. 17 4.2.TU Die Design SystemsUT ............................................................................................... 17 4.3.TU Die Casting Process Studies...................................................................................UT 22 4.4.TU ConclusionsUT ............................................................................................................ 26 5.TU CAGD LITERATURE REVIEWUT .............................................................................. 28 5.1.TU IntroductionUT ............................................................................................................ 28 5.2.TU Bezier CurveUT .......................................................................................................... 28 5.3.TU B-spline CurveUT ....................................................................................................... 29 5.4.TU Open Uniform B-spline CurveUT ............................................................................... 30 5.5.TU B-spline Knot InsertionUT .......................................................................................... 30 5.6.TU B-spline Curve Fitting............................................................................................UT 32 5.7.TU SurfacesUT .................................................................................................................. 35 5.7.1.TU Ruled SurfaceUT .................................................................................................. 35 5.7.2.TU Coons SurfaceUT ................................................................................................. 36 5.7.3.TU B-spline SurfaceUT .............................................................................................. 38 5.8.TU Ray-Curve IntersectionUT .......................................................................................... 38 5.8.1.TU Bisection MethodUT ............................................................................................ 39 vi 5.8.2.TU Regula-Falsi MethodUT ....................................................................................... 40 5.8.3.TU Newton Raphson MethodUT ............................................................................... 42 5.9.TU Curve-Curve IntersectionUT ....................................................................................... 43 5.9.1.TU Newton Raphson MethodUT ............................................................................... 43 5.9.2.TU Bezier Clipping MethodUT .................................................................................. 44 5.9.3.TU Recursive Subdivision MethodUT ....................................................................... 46 5.10.TU Curve-Surface IntersectionUT .................................................................................. 48 5.11.TU Surface-Surface IntersectionUT ................................................................................ 48 6.TU ALGORITHM DEVELOPMENTUT ............................................................................ 50 6.1.TU Surface LoftingUT ...................................................................................................... 50 6.1.1.TU Problem StatementUT .......................................................................................... 50 6.1.2.TU SolutionUT ........................................................................................................... 51 6.2.TU Surface Sweeping...................................................................................................UT 52 6.2.1.TU Problem StatementUT .......................................................................................... 52 6.2.2.TU SolutionUT ........................................................................................................... 53 6.3.TU Ray-Curve IntersectionUT .........................................................................................