Building on the first edition published in 1995 this new edition of KinematicGeometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure’, cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the ‘3 laws of gearing’, the firstlaw re-written to better parallel the existing ‘Law of Gearing” as pioneered by Leonard Euler, expanded from Euler’s original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing aunique relation between gear sizes, and the 3rd law completely reworked from its original form to uniquely describe a limiting condition on curvature between gear teeth, with new relations for gear efficiency are presented based on the kinematics of general toothed wheels in mesh. There is also a completely new chapter on gear vibration load factor and impact.Progressing from the fundamentals of geometry to construction of gear geometry and application, KinematicGeometry of Gearing presents a generalized approach for the integrated designand manufacture of gear pairs, cams and all other types of toothed/motion/force transmission mechanisms using computer implementation based on algebraic geometry. INDICE: CHAPTER 1: INTRODUCTION TO THE KINEMATICS OF GEARING1.1 Introduction1.2 An Overview1.3 Nomenclature and Terminology1.4 Reference Systems1.5 The Input/Output Relationship1.6 Rigid Body Assumption1.7 Mobility1.8 Arhnold-Kennedy Instant Center Theorem1.9 Euler-Savary Equation for Envelopes (correct!; use arc-lengths)1.10 Conjugate Motion Transmission1.10.1 Spur gears1.10.2 Helical and crossed axis gears1.11 Contact Ratio1.11.1 Transverse contact ratio1.11.2 Axial contact ratio1.12 Backlash1.13 Special Toothed Bodies1.13.1 Micro gears1.13.2 Nano gears1.14 Non €” Cylindrical Gearing1.14.1 Hypoid gear pairs1.14.2 Worm gears1.14.3 Bevel gears1.15 Non-Circular Gears1.15.1 Gear and cam nomenclature1.15.2 Non-working profile1.15.3 Rotary/translatory motion transmission1.16 Schematic Illustration of Gear Types1.17 Mechanism Trains1.17.1 Simple drive trains1.17.2 Epicyclic gear trains1.17.3 Circulating power1.17.4 Harmonicgear drives1.17.5 Non-circular planetary gear trains1.18 SummaryPart IICHAPTER 2: KINEMATIC GEOMETRY OF PLANAR GEAR TOOTH PROFILES2.1 Introduction2.2 A Unified Approach to Tooth Profile Synthesis2.3 Tooth Forms used for Conjugate Motion Transmission2.3.1 Cycloidal tooth profiles2.3.2 Involute tooth profiles2.3.3 Circular-arc tooth profiles2.3.4 Comparative evaluation of tooth profiles2.4 Contact Ratio2.5 Dimensionless Backlash2.6 Rack Coordinates2.6.1 The basic rack2.6.2 The specific rack2.6.3 The modified rack2.6.4 The final rack2.7 Planar Gear Tooth Profile2.8 SummaryCHAPTER 3: GENERALIZED REFERENCE COORDINATES FOR SPATIALGEARING-THE CYLINDROIDAL COORDINATES3.1 Introduction3.2 Cylindroidal Coordinates3.2.1 The special features of cylindroidal coordinates3.2.2 The benefits of cylindroidal coordinates3.3 Homogeneous Coordinates3.3.1 Homogeneous point coordinates3.3.2 Homogeneous plane coordinates3.3.3 Homogeneous line coordinates3.3.4 Homogeneous screw coordinates3.4 Screw Operators3.4.1 Screw dot product3.4.2 Screw reciprocity3.4.3 Screw cross product3.4.4 Screw intersection3.5 The Generalized Equivalence of the Pitch Point - The Screw Axis3.5.1 The theorem of three axes3.5.2 The cylindroid3.5.3 Cylindroid intersection3.6 The Generalized Pitch Surfaces - The Axodes3.6.1 The theorem of conjugate pitch surfaces3.6.2 The striction curve3.6.3 The hyperboloid of osculation3.7 The Generalized Transverse Surface3.8 The Generalized Axial Surface3.9 SummaryCHAPTER 4: DIFFERENTIAL GEOMETRY AND THE TOOTH SPIRAL4.1 Introduction4.2 The Curvatureof a Spatial Curve4.3 The Torsion of a Spatial Curve4.4 The First FundamentalForm4.5 The Second Fundamental Form4.6 Principle Directions and Principle Curvatures4.7 Torsure of a Spatial Curve4.8 The Cylindroid of Torsure4.9 Ruled Surface Trihedrons4.10 Formulas of Fernet-Serret4.11 Coordinate Transformations4.12 Characteristic Lines and Points4.13 SummaryCHAPTER 5: ANALYSIS OF TOOTHED BODIES FOR MOTION GENERATION5.1 Introduction5.2 Spatial Mobility Criterion5.3 Reciprocity-The First Law of Gearing5.4 The Line Complex5.5 The Tooth Spiral5.5.1 The tooth spiral curvature5.5.2 The tooth spiral torsion5.6 Tooth Spiral Angle-The Second Law of Gearing5.6.1 The I/O relationship5.6.2 The phantom I/O relationship5.7 Reduced Tooth Curvature-The Third Law of Gearing5.7.1 Absolutetooth curvature5.7.2 Tooth profile modification5.8 Classification of Gear Types5.9 Contact Ratio5.9.1 Transverse contact ratio5.9.2 Axial contact ratio5.10Spatial Backlash5.11 Relative Displacements5.11.1 The sliding velocity5.11.2 The rolling velocity5.11.3 The pitch line velocity5.12 Efficiency5.13 SummaryCHAPTER 6: THE MANUFACTURE OF TOOTHED BODIES6.1 Introduction6.2 Manufacturing Background6.2.1 Form type fabrication6.2.2 Generation type fabrication6.2.3 Spiral-bevel/hypoid gear fabrication6.2.4 Non-circular gear fabrication6.3 Crossed Hyperboloidal Gears6.4 Fabrication of Cutters6.4.1 The hyperboloidal cutter6.4.2 The cutter spiral angle6.4.3 The face spiral angle6.4.4 Cutter constraints6.4.5 Speed ratio6.4.6 Hyperboloidal cutter coordinates6.5 Gear Cutting Machine Layout6.6 Envelope of the Cutter6.7 Material Removal Rate6.8 Surface Cutting Speed6.9 Manufacturing Errors6.9.1 Scalloping6.9.2 Tessellation6.10 Inspection6.11 Hyperboloidal Blank Dimensions6.12 SummaryCHAPTER 7: VIBRATIONS AND DYNAMIC LOADS IN GEAR PAIRS7.1 Introduction7.2 Excitations7.3 Transmission Error7.3.1 Static transmission error7.3.2 Loaded transmission error7.3.3 Dynamic transmission error7.4 Fourier Transforms7.5 Impact Loading7.6 Mesh Stiffness7.7 Inertial Properties7.7.1 Center of mass7.7.2 Mass moments of inertia7.8 Manufacturing Dynamics7.9 SummaryPart IIICHAPTER 8: GEAR DESIGN RATING8.1 Introduction8.2 Modes of Gear Failure8.3 Reaction Loads8.4 Gear Parameters for Specified Deflections8.5 The Fillet Stress8.5.1 Discretization of gear tooth8.5.2 Element stiffness matrix8.5.3 Global stiffness matrix8.5.4 Nodal strain8.5.5 Nodal stress8.6 Inertial Stress8.7 Contact Stress8.8 Minimum Film Thickness8.9 Wear8.10 Friction Coefficient8.10.1 Sliding friction8.10.2 Rolling friction8.11 Flash Temperature8.12 Thermal Stress8.13 Failure Analysis8.13.1 Reliability analysis8.13.2 Fatigue analysis8.13.3 Cumulative loading8.14 Windage Losses8.15 Optimization8.16 SummaryCHAPTER 9: THE INTEGRATED CAD/CAM PROCESS9.1 Introduction9.2 Modular Components for Geometric Synthesis9.2.1 The Motion specification module9.2.3 The Tooth parameters module9.2.2 The Gear parameters module9.2.4 TheCutter parameters module9.2.5 The Loading specifications module9.2.6 The Material specification module9.2.7 The Lubricant specification module9.2.8 The Dynamic factors module9.2.9 The Shaft deflections module9.2.10 The Manufacturing specifications module9.3 The Integrated CAD-CAM Process9.4 Illustrative Example9.5 SummaryCHAPTER 10: CASE ILLUSTRATIONS OF THE INTEGRATEDCAD-CAM PROCESS10.1 Introduction10.2 Case 110.3 Case 210.4 Case 310.5 Case 410.6 Case 510.7 Case610.8 Case 710.9 Case 810.10 Case 910.11 Case 1010.12 Case 1110.13 Case 1210.14 Case 1310.15 Case 1410.16 Case 1510.17 Case 1610.18 Case 1710.19 Case 1810.20 Case 1910.21 Case 2010.22 Case 2110.23 Case 2210.24 SummaryAPPENDIX A: Differential ExpressionsAPPENDIX B: Notation & OperationsAPPENDIX C: Motion GenerationAPPENDIX D: The Delgear Software ProgramAPPENDIX E: SplinesAPPENDIX F:Contact StressAPPENDIX G: Glossary of TermsAPPENDIX H: Equilibrium and Diffusion EquationsAPPENDIX I: On The Base Curve of Planar Non-Circular GearsAPPENDIX J: On The Spatial Euler-Savary EquationsREFERENCESINDEX
- ISBN: 978-1-119-95094-3
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 504
- Fecha Publicación: 11/05/2012
- Nº Volúmenes: 1
- Idioma: Inglés