Analytical, Numerical and Experimental Calculation of Sound Transmission Loss Characteristics of Single Walled Muffler Shells
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1 Analytical, Numerical and Experimental calculation of sound transmission loss characteristics of single walled muffler shells A thesis submitted to the Division of Graduate Studies and Research of the University of Cincinnati in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE In the Department of Mechanical Engineering of the College of Engineering May 2007 by John George B. E., Regional Engineering College, Surat, India, 1995 M. E., Regional Engineering College, Trichy, India, 1997 Committee Chair: Dr. Jay Kim 2 Abstract Accurate prediction of sound radiation characteristics from muffler shells is of significant importance in automotive exhaust system design. The most commonly used parameter to evaluate the sound radiation characteristic of a structure is transmission loss (TL). Many tools are available to simulate the transmission loss characteristic of structures and they vary in terms of complexity and inherent assumptions. MATLAB based analytical models are very valuable in the early part of the design cycle to estimate design alternatives quickly, as they are very simple to use and could be used by the design engineers themselves. However the analytical models are generally limited to simple shapes and cannot handle more complex contours as the geometry evolves during the design process. Numerical models based on Finite Element Method (FEM) and Boundary Element Method (BEM) requires expert knowledge and is more suited to handle complex muffler configurations in the latter part of the design phase. The subject of this study is to simulate TL characteristics from muffler shells utilizing commercially available FEM/BEM tools (NASTRAN and SYSNOISE, in this study) and MATLAB based analytical model. The results obtained from analytical model and numerical model are correlated with experimental data. The predicted results agreed reasonably well with the experimental results. The effects of important design parameters are studied to provide design guidelines. 3 4 Acknowledgements First and foremost, I would like to express my sincere gratitude to my advisor Dr. Jay Kim for his valuable guidance and outstanding support during the course of this work. His constructive comments and thoughtful insights have greatly improved the quality of this work. I would like to thank Dr. David Thompson and Dr. Yijun Liu for accepting my request to serve on my masters’ thesis committee. I am truly grateful to Jim Egan and Dr. Chulho Yang, my colleagues at ArvinMeritor, Inc for their valuable help and suggestions. Their expert knowledge and assistance has helped me a great deal to complete this work successfully. My sincere thanks to Dave Leehaug, Chief Engineer at ArvinMeritor, Inc for appreciating this work and providing me with whatever I requested. Last but by no means least, I am forever indebted to my wife Vidhya for her unwavering support and encouragement throughout the course of my studies. 5 Table of contents 1. INTRODUCTION …………………………………………………………………………..9 2. THEOROTICAL BACKGROUND ……………………………………………………….12 2.1. INSERSTION LOSS ……………………………………………………………………….12 2.2. TRANSMISSION LOSS …………………………………………………………………...12 2.3. LEVEL DIFFRENCE ………………………………………………………………….......12 3. FORMULATION AND SOLUTION OF TL FOR SINGLE WALLED CYLINDRICAL SHELL BY ANALYTICAL METHOD …………………………………………………...13 3.1. FORMULATION AND SOLUTION OF TL FOR SINGLE WALLED CYLINDRICAL SHELL ……...14 3.2. TRANSMISSION LOSS (TL ) CACULATION FOR SINGLE WALLED CYLINDRICAL SHELL…...18 3.3. CORRECTIONS TO PAST WORK ON TL FOR SINGLE WALLED CYLINDRICAL SHELL …........20 3.3.1. Discussion of results ….........................................................................................20 4. DESCRIPTION OF THE PROTOTYPE MODEL USED FOR CORRELATION ……23 5. FINITE ELEMENT MODAL ANALYSIS ………………………………………………..24 5.1. OVERVIEW OF ANALYSIS USING NASTRAN ……………………………………………....24 5.2. OBTAINING NATURAL MODES USING NASTRAN …………………………………………25 5.3. RESULTS FROM FINITE ELEMENT MODAL ANALYSIS FOR PROTOTYPE MUFFLER ..............26 6. ACOUSTIC BOUNDARY ELEMENT ANALYSIS AND EXPERIMENTAL CORRELATION ....................................................................................................................28 6.1. OVERVIEW OF CALCULATING RADIATED NOISE USING SYSNOISE....................................28 6.1.1. Jump boundary condition .....................................................................................30 6.1.2. Modeling of acoustic source .................................................................................30 6.2. CALCULATION OF ACOUSTIC MODES OF THE CAVITY ......................................................32 6.3. TL CALCULATION FROM EXPERIMENT .............................................................................. 35 6.3.1. Frequency range for TL calculation .................................................................... 35 6.3.2. Acoustic pressure measurement inside the cavity .................................................35 6.3.3. Acoustic pressure measurement outside the cavity ...............................................37 6.3.4. Characterization of background noise ................................................................. 39 6.3.5. TL from test ……………………………………………………………………...41 6.4. TL CALCULATION USING BEA …………............................................................................43 6.5. COMPARISON OF RESULTS BETWEEN EXPERIMENT , BEA AND ANALYTICAL FORMULATION ..................................................................................................................46 6.5.1. Discussion of results .............................................................................................48 7. STUDY ON THE SENSITIVITY OF DESIGN PARAMETERS ON TL........................49 7.1. EFFECT OF THICKNESS .......................................................................................................49 7.2. EFFECT OF SHAPE ..............................................................................................................52 7.3. DISCUSSIONS ON DESIGN SENSITIVITY STUDY ..................................................................54 8. CONCLUIONS AND RECOMMENDATIONS FOR FUTURE WORK ........................56 6 List of figures 3.1 SCHEMATIC OF THE MODEL USED IN THE FORMULATION FOR SINGLE WALLED SHELL ............15 3.2 COMPARISON OF TL BETWEEN ORIGINAL FORMULATION AND CORRECTED FORMULATION OF SINGLE WALLED SHELL FOR INCIDENCE ANGLE =45 DEG . .......................................................21 4.1 GEOMETRIC DETAILS OF THE PROTOTYPE MUFFLER.................................................................23 5.1 FINITE ELEMENT MODEL OF THE CAVITY UNDER STUDY ..........................................................26 5.2 MODE SHAPES FOR 0.6 MM SHELL (PROTOTYPE MODEL ) .........................................................27 6.1 TEST /SYSNOISE MODEL OF THE SPEAKER..............................................................................31 6.2 MEASURED SPEAKER RESPONSE VS SYSNOISE SOURCE .........................................................31 6.3 MESH OF THE ACOUSTIC CAVITY AND APPLIED IMPEDANCE ....................................................33 6.4 ACOUSTIC MODES OF THE CAVITY ............................................................................................34 6.5 SCHEMATIC REPRESENTATION OF PRESSURE MEASUREMENT INSIDE THE CAVITY ..................36 6.6 MEASURED VALUE AND AVERAGE PRESSURE INSIDE THE MUFFLER ........................................37 6.7 TEST SET UP TO MEASURE ACOUSTIC PRESSURE OUTSIDE THE CAVITY ....................................38 6.8 MICROPHONE LOCATIONS TO MEASURE RADIATED NOISE .......................................................38 6.9 AVERAGE PRESSURE VALUES MEASURED INSIDE AND OUTSIDE THE MUFFLER .......................39 6.10 TEST SET UP TO MEASURE BACKGROUND NOISE ................................................................40 6.11 RESULTS FROM BACKGROUND NOISE MEASUREMENT .......................................................41 6.12 CORRECTED SOUND PRESSURE OUTSIDE THE CAVITY ........................................................42 6.13 TL FROM TEST ....................................................................................................................42 6.14 BE MODEL USED TO CALCULATE PRESSURE INSIDE THE CAVITY......................................43 6.15 CALCULATED VALUE AND AVERAGE PRESSURE INSIDE THE CAVITY FROM BEA ..............44 6.16 BE MODEL USED TO CALCULATE PRESSURE OUTSIDE THE CAVITY ...................................45 6.17 AVERAGE PRESSURE VALUE OUTSIDE THE CAVITY CALCULATED USING BEA ..........45 6.18 TL-CALCULATED USING BEA ............................................................................................46 6.19 COMPARISON OF AVERAGE ACOUSTIC PRESSURE INSIDE THE CAVITY ..............................47 6.20 COMPARISON OF TL’ S........................................................................................................47 7.1 MODEL WITH 1.2/1.8 MM SHELL ...............................................................................................49 7.2 COMPARISON OF RADIATED NOISE FOR DIFFERENT THICKNESS ...............................................50 7.3 COMPARISON OF TL FOR DIFFERENT THICKNESS FROM BEA ..................................................51 7.4 COMPARISON OF TL FOR DIFFERENT THICKNESS FROM ANALYTICAL CALCULATION .............51 7.5 MODELS WITH ELLIPTICAL /STAMPED CROSS -SECTION .............................................................52 7.6 COMPARISON