University of Central Florida STARS Electronic Theses and Dissertations, 2004-2019 2006 Design Optimization Of Solid Rocket Motor Grains For Internal Ballistic Performance Roger Hainline University of Central Florida Part of the Mechanical Engineering Commons Find similar works at: https://stars.library.ucf.edu/etd University of Central Florida Libraries http://library.ucf.edu This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2004-2019 by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation Hainline, Roger, "Design Optimization Of Solid Rocket Motor Grains For Internal Ballistic Performance" (2006). Electronic Theses and Dissertations, 2004-2019. 934. https://stars.library.ucf.edu/etd/934 DESIGN OPTIMIZATION OF SOLID ROCKET MOTOR GRAINS FOR INTERNAL BALLISTIC PERFORMANCE by R. CLAY HAINLINE B.S. Southwest Missouri State University, 1998 A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical, Materials, and Aerospace Engineering in the College of Engineering and Computer Science at the University of Central Florida Orlando, Florida Summer Term 2006 © 2006 R. Clay Hainline ii ABSTRACT The work presented in this thesis deals with the application of optimization tools to the design of solid rocket motor grains per internal ballistic requirements. Research concentrated on the development of an optimization strategy capable of efficiently and consistently optimizing virtually an unlimited range of radial burning solid rocket motor grain geometries. Optimization tools were applied to the design process of solid rocket motor grains through an optimization framework developed to interface optimization tools with the solid rocket motor design system. This was done within a programming architecture common to the grain design system, AML. This commonality in conjunction with the object-oriented dependency-tracking features of this programming architecture were used to reduce the computational time of the design optimization process. The optimization strategy developed for optimizing solid rocket motor grain geometries was called the internal ballistic optimization strategy. This strategy consists of a three stage optimization process; approximation, global optimization, and high- fidelity optimization, and optimization methodologies employed include DOE, genetic algorithms, and the BFGS first-order gradient-based algorithm. This strategy was successfully applied to the design of three solid rocket motor grains of varying complexity. The contributions of this work are the application of an optimization strategy to the design process of solid rocket motor grains per internal ballistic requirements. iii This work is dedicated to my wife, Sachie, my parents, Roger and Nancy, and parents-in- law, Katsuhide and Chieno. Thank you for your support during the time it took to complete this thesis. iv ACKNOWLEDGMENTS I would like to express sincere appreciation to my advisors, Jamal F. Nayfeh, Ph.D.; Alain Kassab, Ph.D.; and P. Richard Zarda, Ph.D. for their support and advise during my time as a graduate student. Special thanks are extended to Carlos G. Ruiz and Dean T. Kowal for technical advise and support shared while working on this research. Gratitude is extended to Lockheed Martin, Missiles and Fire Control; Vanderplaats Research and Development Inc.; and TechnoSoft Inc. for supplying me the necessary software and licensing to successfully complete this research. The support received by the staff of the aforementioned companies was greatly appreciated. v TABLE OF CONTENTS LIST OF FIGURES ...................................................................................... IX LIST OF TABLES........................................................................................ XI LIST OF TABLES........................................................................................ XI CHAPTER 1: INTRODUCTION.................................................................1 1-1 Introduction ................................................................................................................ 1 1-2 Scope of Work ............................................................................................................ 3 1-3 Software Application and Integration......................................................................... 4 1-4 Research Contributions............................................................................................... 6 CHAPTER 2: TECHNICAL SUMMARY...................................................8 2-1 Principles of Optimization.......................................................................................... 8 2-1-1 Objective Function ................................................................................................ 9 2-1-2 Design Variables ................................................................................................. 10 2-1-3 Constraints........................................................................................................... 11 2-2 Objective Function: Damped Least Squared Method............................................... 12 2-3 Solid Rocket Motor Grains....................................................................................... 13 2-3-1 Principle Components of a Solid Rocket Motor Grain ....................................... 14 2-3-2 Solid Propellant Grain Geometry........................................................................ 16 2-3-3 Burn Process of a Solid Rocket Motor Grains .................................................... 17 2-3-4 Nozzle Geometry................................................................................................. 19 2-3-5 Thrust Calculations.............................................................................................. 20 2-4 Approximation Techniques ...................................................................................... 22 2-4-1 Design of Experiments (DOE) ............................................................................ 22 2-4-2 Response Surface Methodology.......................................................................... 24 2-5 Optimization Algorithms.......................................................................................... 25 2-5-1 First-order Gradient Based Methods ................................................................... 25 2-5-2 Second-order Gradient Based Methods............................................................... 26 2-5-3 Genetic Optimization Methods ........................................................................... 28 CHAPTER 3: THRUST OPTIMIZATION FRAMEWORK AND IMD ..31 3-1 Adaptive Modeling Language .................................................................................. 31 3-1-1 Object-Oriented Programming Language ........................................................... 32 3-1-2 Demand-Driven Dependency Tracking Language.............................................. 34 vi 3-1-3 Solid Rocket Motor Design Module ................................................................... 36 3-2 Optimization Interface.............................................................................................. 37 CHAPTER 4: OPTIMIZATION PROBLEM STATEMENT ...................41 4-1 Optimization Problem Statement.............................................................................. 41 4-2 Design Variables....................................................................................................... 43 4-3 Design Constraints.................................................................................................... 44 4-4 Design Objective ...................................................................................................... 45 CHAPTER 5: OPTIMIZATION FORMULATION AND STRATEGY ..46 5-1 The Internal Ballistic Optimization Strategy............................................................ 46 5-1-1 Internal Ballistic Optimization Strategy Overview............................................. 46 5-1-2 Internal Ballistic Optimization Strategy Stage 1: Design Approximation .......... 48 5-1-3 Internal Ballistic Optimization Strategy Stage 2: Design Optimization ............. 49 5-1-4 Internal Ballistic Optimization Strategy Stage 3: High-Fidelity Optimization... 52 5-2 Optimization Formulation ........................................................................................ 54 5-2-1 Thrust Optimization Formulation........................................................................ 55 5-2-2 Burn-Area Optimization...................................................................................... 56 5-3 Resolved Issues with the Optimization Strategy ...................................................... 57 5-3-1 Issue 1: Error in Surface Recession Model ......................................................... 57 5-3-2 Issue 2: Unexpected Halting of High Fidelity Optimization............................... 58 CHAPTER 6: OPTIMIZATION ANALYSIS ...........................................59 6-1 Internal Ballistic Optimization Strategy Trial #1 ..................................................... 59 6-1-1 Optimization Model Definition........................................................................... 61 6-1-2 Internal Ballistic Optimization Strategy Stage 1: Design Approximation .........