New Approaches To Gear Design And Production

Description

This is the third book in a series devoted to gear design and production. Comprising papers by scientists and gear experts from around the globe, it covers recent developments in practically all spheres of mechanical engineering related to gears and transmissions. It describes advanced approaches to research, design, testing and production of various kinds of gears for a vast range of applications, with a particular focuses on advanced computer-aided approaches for gear analysis, simulation and design, the application of new materials and tribological issues. Foreword......Page 6 Introduction......Page 7 Contents......Page 9 About the Editors......Page 12 1 Russian School of the Theory and Geometry of Gearing. Part 2. Development of the Classical Theory of Gearing and Establishment of the Theory of Real Gearing in 1976–2000......Page 13 1.1 Introduction......Page 14 1.2 Review of Works Published in Russian in 1976–2000......Page 15 1.2.1 New Geometric and Geometry and Kinematic Concepts......Page 18 1.2.2 Development of Methods for Synthesis and Optimization of Gearing......Page 28 1.2.4 Software: Development and Application......Page 34 1.3.3 The Important Practical Results—A Great Number of Very Adverse Types of Gearing Was Investigated (and Often Implemented: In Gears, in Hydraulic and Pneumatic Machines, in Machine-Tool Gearing)......Page 36 Appendix 1: Review of Publications of Russian Authors in Foreign Editions in 1976–2000 (Published in English)......Page 37 Appendix 2: Theory of Gearing in Persons......Page 40 References......Page 49 2 Bulgarian Experience in Applying and Improving Knowledge in the Field of Theory and Application of Modern Gears......Page 59 2.1.1 Introduction......Page 60 2.1.2 Place of Gear Drives in the Bulgarian Industry......Page 62 2.1.3 Higher Education Aspects of Gears Education in Technical Universities in the Republic of Bulgaria......Page 63 2.1.4 The Usage of Software Products in Education of Gear Mechanisms......Page 66 2.2.1 Introduction......Page 68 2.2.2 History of Gear Manufacture in Japan......Page 69 2.2.3 Educational Agenda of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT)—Japan......Page 72 2.2.4 Theoretical and Practical Gearing Education at Akita University for Students from the Bachelor Program......Page 73 2.3.1 Postgraduate and Ph.D. Education......Page 76 2.3.2 Predictions for Improving the Education on the Gear Transmissions......Page 78 References......Page 80 3 Advanced Computer-Aided Gear Design, Analysis and Manufacturing......Page 83 3.1 Introduction......Page 84 3.2 Tooth Modelling: The Tooth Flank Generator......Page 85 3.2.1 Spiral-Bevel Gears......Page 88 3.2.2 Straight-Bevel Gears—2-Tool Generator......Page 89 3.2.3 Coniflex™ Straight-Bevel Gears......Page 90 3.2.4 Cylindrical Gears......Page 92 3.3.2 Comparison with Klingelnberg’s KIMoS......Page 94 3.4.2 Ease-off Surface and Transmission Error......Page 95 3.5 Loaded Tooth Contact Analysis—LTCA......Page 97 3.6 Closed Loop......Page 99 3.7 TCA Optimization and Numerical Contact Pattern Development......Page 102 3.7.2 Change in Cutter Radial Distance......Page 103 3.7.4 Change in Work Offset......Page 105 3.7.5 Change in Work Mounting Distance......Page 106 3.7.6 Change in Cutter Tilt......Page 107 3.7.7 Change in Helical Motion......Page 108 3.7.9 Change in Modified Roll 6D......Page 109 3.7.11 Sample Contact Pattern Development......Page 110 3.8 Reverse Engineering—RE......Page 114 3.8.1 Replicate an Unknown Existing Part......Page 118 3.8.2 Pinion Re-Design Based on Existing Gear......Page 120 3.8.3 In Situ Behavior—Coniflex™ Straight-Bevel Gear Set......Page 121 References......Page 124 4.1 Introduction......Page 126 4.2 Meshing Stiffness, Load Sharing, and Tooth Deflection......Page 128 4.3 Extended Contact Interval......Page 130 4.4 Actual Contact Conditions......Page 133 4.5 Profile Modifications......Page 135 4.6 Specific Applications......Page 137 4.6.1 Smooth Fluctuation of the QSTE......Page 138 4.6.2 Balancing Tooth-Root and Pitting Load Carrying Capacities......Page 139 4.7 Conclusions......Page 140 References......Page 141 5.1 Introduction......Page 143 5.2.1 Conical Involute Surface......Page 145 5.2.2 Synthesis Parameters......Page 146 5.2.3 Modified Conical Involute Surface......Page 147 5.3 The Mathematical Model of Tooth Meshing......Page 148 5.3.1 Calculation of the Contact Point of the Teeth......Page 149 5.3.2 The Calculation of the Transmission Error Curve and the Contact Path......Page 150 5.3.3 The Plotting of the Instantaneous Contact Areas and the Bearing Contact......Page 151 5.4 Methods of Selection of Synthesis Parameters......Page 152 5.6 Calculation of Tooth Contact Characteristics in an Arbitrary Meshing Phase......Page 154 5.7.1 Example 1......Page 157 5.7.2 Example 2......Page 162 5.8 Conclusion......Page 163 References......Page 164 6 Computer-Aided Design of Gears and Machine-Tool Meshing with Application of New Concepts, Images and Indices......Page 166 6.1.1 Overview of the Development of Computer-Aided Design of Gears......Page 168 6.1.2 Problems Arising at Solving the Main Issues of TG......Page 169 6.1.4 Problems Studied in This Manuscript......Page 170 6.2.1 Main Problems of Classic TG and TKG......Page 171 6.2.2 Development of Methods of Solving the Main Problems of TG and TKG......Page 172 6.2.3 Basic Concepts Used in Mechanics, Geometry, TG, TKG......Page 173 6.2.4 Update of Basic Concepts—The Next Stage of Development of TG and TKG......Page 179 6.3.2 Types of Jogs on Teeth and Images Generated by Jogs......Page 180 6.3.4 Curvilinear Coordinates on Lines, Surfaces and in Jogs......Page 184 6.3.5 Local and Global Quality Parameters of Meshing......Page 185 6.3.6 Multi-parametric Meshing—An Important Part of TG and TKG......Page 186 6.3.7 Theoretical Investigations and Computer-Aided Developments Made by the Alternative TG......Page 188 6.4.1 Specification of “Accepted” Terms for New Concepts and Images......Page 189 6.4.2 Choosing of Russian and English Terms for New Primary Geometrical Images......Page 191 6.5 Conclusions......Page 192 References......Page 193 7 Aspects of the Kinematic Theory of Spatial Transformations of Rotations: Analytic and Software Synthesis of Kinematic Pitch Configurations......Page 195 7.1 Introduction......Page 196 7.2 Kinematic Model of the Process of Spatial Rotations Transformation......Page 198 7.3.1 Scalar Field of the Relative Velocity Vector barV12......Page 202 7.3.2 Vector Field of the Relative Velocity Vector barV12......Page 204 7.4.1 Normalized (Normed) Relative Helices......Page 207 7.4.2 Orientation of the Normalized Relative Helices Towards the Axes of Rotation 1 - 1 and  2 - 2......Page 208 7.5.1 Synthesis of Isokinematic Quasi-hyperboloids......Page 210 7.5.2 Kinematic Pitch Circles......Page 217 7.6 Computer Programs for Software Synthesis and Visualization of Kinematic Pitch Configurations......Page 220 7.7 Conclusion......Page 223 References......Page 224 8.1 Introduction......Page 226 8.2 Regeneration of Gear Tooth Surfaces......Page 228 8.3 Tooth Contact Analysis......Page 229 8.4 Stress Analysis......Page 232 8.5 Numerical Examples......Page 234 8.5.1 Design of a Master Gear......Page 235 8.5.2 Generation of Point-Clouds for the Theoretical Pinion......Page 237 8.5.4 Application of the Proposed Finite Element Model to the Stress Analysis Between Regenerated Theoretical Pinion from Its Point-Clouds and the Master Gear......Page 238 8.5.5 Application of the Proposed TCA Algorithm and Finite Element Model to the Meshing and Stress Analyses Between the Being-Inspected Gears and the Master Gear......Page 239 References......Page 243 9 Tooth Surface Stress and Flash Temperature Analysis with Trochoid Interference of Gears......Page 245 9.2 Overview of Edge Contact Stress Analysis......Page 246 9.3 Gear Specifications and Tooth Surface Measurement Data......Page 248 9.4 Tooth Surface Stress Analysis (Edge Contact Analysis Disabled)......Page 249 9.5 Edge Contact Stress Analysis......Page 254 9.6 Comparison of Analysis Results and Experimental Results......Page 255 9.7 3D-FEM Stress Analysis......Page 259 9.8 Optimal Tooth Surface Modification......Page 261 9.9 Conclusion......Page 265 References......Page 266 10 Estimation of Bearing Capacity and Wear Resistance of Spur Gear Meshing Taking into Account Tooth Profile Correction and Sliding Friction Coefficient......Page 267 10.1 Introduction......Page 268 10.2 Problem Solution Method......Page 269 10.3 Numerical Solution......Page 272 References......Page 277 11 On Possibility of Cutting Bevel Gearwheels by Hobs......Page 279 11.2 Several Preconditions......Page 280 11.3 General Scheme of Calculation. Setting Parameters......Page 282 11.4 Scheme of Machine-Tool Gearing, Pitch Surfaces of Elements......Page 284 11.5 Tooth Flanks—Enveloping Surfaces of One-Parametric Family of Generating Helicoids......Page 285 11.6 Conjugated Surfaces of Gearwheel Teeth......Page 286 11.7 Calculation of Root Fillet and Undercut Areas......Page 288 11.8 Choice of Setting Parameters for Generation of Gearwheel Teeth......Page 290 11.9 Choice of the First Approximation......Page 293 11.10 Several Results and Features of Calcualtions......Page 296 11.11 Conclusion......Page 298 References......Page 299 12 New Possibilities of Tooth Cutting by Running Cutter Heads......Page 301 12.1 Introduction......Page 302 12.2 Tooth Machining Technique by Means of a Flying (Running) Cutter and Its Possible Development......Page 303 12.3 Method of Calculation of the Setting Parameters and the Idea of Its New Application......Page 304 12.4 Examples of Gear Calculation for Multi-thread Running Cutter Heads......Page 311 12.5 Prospects of Implementation of the Method......Page 314 References......Page 315 13.1 Introduction......Page 316 13.3 Aim of the Paper......Page 317 13.4 Essence and Capabilities of the Torque Method......Page 318 13.5 Sequence of Biplanetary Gear Train Analysis......Page 320 13.6 Examples......Page 321 13.7 Conclusions......Page 326 References......Page 327 14 Optimization of Planocentric Gear Train Characteristics with CA-Tools......Page 328 14.2 Kinematic Circumstances of a Planocentrcic Gear Train......Page 329 14.4 Gear Tooth Flank Geometry......Page 332 14.5 Planocentric Gear Box Prototypes......Page 336 14.6 Influences of Tolerances......Page 339 14.6.1 Gearing Tolerances (Analysis of Tolerance Influences)......Page 340 14.6.2 Contact Analysis......Page 343 14.6.3 Influence of Bearing Tolerances and Carriers on the Position of the Gear Train......Page 348 14.8 Conclusions......Page 350 References......Page 351 15.1 Introduction......Page 353 15.2 Related Work......Page 354 15.3.1 Linear Modified Hsu Graphs......Page 355 15.3.2 Contour Graph of Planetary Gear......Page 356 15.4 Gears’ Layouts and Assigned Graphs......Page 357 15.4.1 Compound Gear......Page 360 15.4.2 Linear Graph Representing the Considered Compound Planetary Gear......Page 361 15.4.3 Contour Graph Representing the Considered Compound Planetary Gear......Page 362 15.4.5 Linear Graph for Pseudo-Compound Planetary Gear......Page 364 15.4.6 Contour Graph for Pseudo-Compound Planetary Gear......Page 365 15.5 Classical Approach to Gear Analysis for Compound Gear......Page 366 References......Page 367 16 Simulation of the Teeth Profile Shaping During the Finishing of Gears......Page 369 16.2 Methodology of Shaping Model Developing......Page 370 16.3 Analysis of Objective Functions of the Model......Page 377 16.4 Analysis of Linear Contact Objective Functions......Page 379 16.5 Synthesis of Processing Methods and Tools that Provide Line Contact......Page 382 References......Page 388 17 Design Automation of Cylindrical Gear Manufacturing Processes......Page 389 17.1 Introduction......Page 390 17.1.1 The Method of Selection of the Processing Route of the Teeth of Cylindrical Gears......Page 391 17.1.2 Method of Selection of Requirements to Accuracy of Cylindrical Gear Teeth on Intermediate Operations of Their Processing......Page 396 17.1.3 Method of Selection of Requirements to Accuracy of Base Surfaces of Cylindrical Gears Before Gear Cutting and on Intermediate Operations of Their Processing......Page 403 17.1.4 The Choice of Best Cutting Conditions by Hobbing of Cylindrical Gears......Page 407 17.2 Conclusions......Page 414 References......Page 415 18.1 Introduction......Page 416 18.2 Mathematical Model of Gearwheels......Page 417 18.3 Solid Modeling of Gearwheels......Page 422 18.4 Production of Experiments Models of Gears with Application of Additive Technologies......Page 426 References......Page 428 19 New Approach to Computer-Aided Design of Gearbox Systems: Models and Algorithms......Page 430 19.2 Classification Factors of the Design Process......Page 431 19.3 Shortly About Features and Forbidden Figures......Page 434 19.4 Model of the Class of Designed Objects and the Process of Synthesis......Page 436 References......Page 440 20.1 Introduction......Page 442 20.2 Development of Generalized Model of Class of Objects......Page 443 20.3 Extension of Generalized Model......Page 445 20.4 Set of Forbidden Figures: Structure and Classification......Page 448 20.5 Actualization of Informational Support......Page 450 20.6 Methods of Computer-Aided Search and Filtration of Information......Page 451 20.7 Settings of Search and Analysis of Results......Page 459 20.8 Process of Search for New Knowledge Within the Development of Informational Support......Page 460 References......Page 463 21 Improvement of Methods of Design and Analysis of Load-Carrying Capacity of Case-Hardened Cageless Bearing Units for Power Drives of Mobile Machines......Page 464 References......Page 473 22.1 Introduction......Page 475 22.2 Problems and Requirements in the Design of Gearboxes......Page 478 22.2.1 Gear Design Issues......Page 479 22.2.2 Test Bed Design......Page 480 22.3.1 Wavelet Transform......Page 482 22.4.1 Two-DOF Planetary Gearbox......Page 483 22.4.2 Experiments......Page 485 22.5.1 Test at Constant Speed and Varying Load......Page 486 22.5.2 Test at Varying Speed and Varying Load......Page 487 22.6 Conclusions......Page 491 References......Page 494 23 Selection of Vibration Norms and Systems Structures When Designing Means of Monitoring Units with Gear Transmissions......Page 497 23.1 Introduction......Page 498 23.2 Gear Vibration Monitoring......Page 499 23.3 Limits of Vibration of Gears......Page 502 23.5 Features of Vibration Gear Mechanisms. Frequency and Dynamic Ranges......Page 505 23.6 Repeatability Interval and Ergodicity of Processes......Page 507 23.7 Structural Methods for Improving the Metrological Characteristics of Monitoring Systems. Methods for Expanding the Frequency and Dynamic Ranges......Page 508 23.8 Diagnosis Gears......Page 509 23.9 3-Axials Vibration Gear Mechanisms......Page 511 Referenes......Page 512 24 Curvature Interference Characteristic of ZC1 Worm Gear......Page 514 24.2.1 Geometry of Toroidal Grinding Wheel......Page 515 24.2.2 Cutting Meshing of ZC1 Worm......Page 517 24.2.3 Meshing of ZC1 Worm Pair......Page 520 24.3 Calculating Method of Curvature Interference Limit Line......Page 522 24.4.1 Main Parameters of ZC1 Worm Pair......Page 525 24.4.2 Computational Results of Curvature Interference Limit Line......Page 526 References......Page 529