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Analytical Investigation of the Pericyclic Variable

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Analytical Investigation of the Pericyclic Variable The Pennsylvania State University The Graduate School Department of Aerospace Engineering ANALYTICAL INVESTIGATION OF THE PERICYCLIC VARIABLE-SPEED TRANSMISSION SYSTEM FOR HELICOPTER MAIN-GEARBOX A Dissertation in Aerospace Engineering by Zihni Burçay Sarıbay © 2009 Zihni Burçay Sarıbay Submitted in Partial Fulfillments of the Requirements for the Degree of Doctor of Philosophy December 2009 The dissertation of Zihni Burçay Sarıbay was reviewed and approved * by the following: Edward C. Smith Professor of Aerospace Engineering Dissertation Co-Advisor Co-Chair of Committee Suren Rao Senior Scientist, Applied Research Laboratory Dissertation Co-Advisor Co-Chair of Committee Robert C. Bill Research Associate Dissertation Co-Advisor Special member Kon-Well Wang William E. Diefenderfer Chaired Professor in Mechanical Engineering Dissertation Co-Advisor Joseph Horn Professor of Aerospace Engineering Liming Chang Professor of Mechanical Engineering George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering *Signatures are on file at the Graduate School ii ABSTRACT In the recent years, there has been significant interest in the new developments and improvements of the rotorcraft transmission systems. The main goal of the rotorcraft transmission research is the reduction of overall gear train weight while maintaining the efficiency and reliability. The Pericyclic Variable-Speed Transmission (PVT) System is one of the potential candidates of the future rotorcraft drive trains to achieve these goals. Hence, this thesis explores the feasibility of the Pericyclic Variable Speed Transmission (PVT) for rotorcraft transmissions. The contributions of this research are grouped in two main categories. These two categories are in the component level and in the system level. These contributions are originated from the analysis of the Pericyclic Variable Speed (PVT) System. In the component level, a new concept of face-gear meshing is presented first time in the gear research field. The meshing of a face-gear with another face-gear is presented at high shaft angles as an alternative to bevel gears. The conjugacy of this new face-gear meshing concept is formulated and demonstrated. The geometry, unloaded mesh kinematics and loaded mesh kinematics of the conjugate meshing face-gear pair is analyzed. The physics behind the meshing face-gear teeth contact is revealed using theory of gearing, differentiable geometry and elastohydrodynamic lubrication theory. The existence of the lubricant film formation between the meshing teeth is demonstrated. The behavior of the sliding friction coefficient is analytically simulated through the meshing cycle. In the system level contributions, the Pericyclic Variable Speed (PVT) Transmission is presented as a new unique innovative gear train mechanism. The speed change capability is analyzed for rotorcraft demands. The power flow behavior is explored for its use in variable speed transmission systems. The established component iii level contributions are evaluated with the PVT at the system level. The efficiency and load carrying capacity of the PVT face-gears are analyzed at the helicopter torque levels. The dynamic motion of the nutating gear mechanisms is studied to capture the load carrying capacity of the PVT support bearings. A design analysis of the PVT system with 24:1 reduction ratio at 764HP power level is conducted to replace 3 reduction stages of the existing K-MAX intermeshing rotor transmission system. The design and analysis tools established in this research are applied in the design study. The achieved design is compared to the existing K-MAX transmission. Approximately 50% weight reduction and 70% volume reduction are accomplished with the PVT system with less than 1% lower efficiency than existing K-MAX drive train gears. iv Table of Contents List of Figures ................................................................................................................ix List of Tables...............................................................................................................xxii List of Symbols ......................................................................................................... xxiii ACKNOWLEDGEMENTS........................................................................................xxxi CHAPTER 1....................................................................................................................1 1 INTRODUCTION ...................................................................................................1 1.1 Literature Review on the Current State of the Art Rotorcraft Transmission Systems .......................................................................................................................2 1.1.1 Fixed Axis Ordinary Gear Trains..................................................................4 1.1.2 Theory of Gearing and Power Transmission by Gears ..................................8 1.1.3 Dynamics of the Gear Trains......................................................................13 1.1.4 Efficiency of the Ordinary Gear Trains.......................................................15 1.1.4.1 Sliding and Rolling Losses..............................................................15 1.1.4.2 Windage losses and other losses......................................................21 1.1.5 Planetary Gear Trains (PGT)......................................................................23 1.1.5.1 Kinematics, Power Transmission and Efficiency of the PGT Systems 24 1.1.5.2 Effect of the Number of Planets on the PGT Design........................27 1.1.6 Face-Gear Drives .......................................................................................30 1.1.6.1 Design of the Face-Gear Drives ......................................................32 1.1.6.2 Face-Gear Drives in the Rotorcraft Transmissions ..........................36 1.1.7 Variable Speed Transmission Systems for the Rotorcraft Platform .............38 1.1.7.1 Traction Drives...............................................................................40 1.1.7.2 Clutch Actuated Two Speed Planetary Gear Trains .........................45 1.1.8 Innovative Concepts for Future Rotorcraft Transmissions...........................50 1.1.8.1 Pericyclic Variable Speed Transmission System .............................52 1.2 Summary and Conclusions of the Literature Review ......................................55 1.3 Problem statement and research objectives .....................................................57 1.4 Organization of the Thesis..............................................................................58 CHAPTER 2..................................................................................................................61 2 Kinematical Analysis of the Pericyclic Variable-Speed Transmission ....................61 2.1 The PVT Architecture....................................................................................62 v 2.2 Kinematics of the PVT Gears.........................................................................65 2.3 Speed Reduction Ratio Relationships .............................................................70 2.4 Power Flow Analysis of the PVT ...................................................................75 2.5 Kinematical Design Analysis Case Study.......................................................83 2.6 Summary........................................................................................................86 CHAPTER 3..................................................................................................................88 3 Concept of Meshing Face-gears .............................................................................88 3.1 Principal Relations of the Face-Gears.............................................................89 3.1.1 Face-gear to Face-gear Relations ................................................................91 3.1.2 Shaper and Face-gear Pair Relations...........................................................94 3.2 Mathematical Modeling of the Face-Gear Tooth...........................................102 3.2.1 Determination of Shaper Tooth Surface....................................................103 3.2.2 Development of Coordinate Transformation Matrix .................................108 3.2.3 Mathematical Model of a Face-Gear Tooth Surface..................................112 3.2.4 Proof of Conjugacy between Shaper and Face-gear and Derivation Equation of Meshing...........................................................................................................115 3.2.5 Critical Dimensions of the Face-Gears......................................................122 3.2.5.1 Detection of face-gear undercut ....................................................124 3.2.5.2 Detection of face-gear tooth pointing ............................................125 3.2.5.3 Procedure to calculate critical dimensions and parameters.............128 3.3 Summary......................................................................................................135 CHAPTER 4................................................................................................................136 4 Face-gear to Face-gear Meshing and Proof of Conjugacy.....................................136 4.1 Generating Meshing Face-gear Pairs by Using Equation of Meshing............137 4.2 The Unloaded Meshing Kinematics..............................................................146
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