{"product_id":"performancebased-gear-metrology-9781119961697","title":"PerformanceBased Gear Metrology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA mathematically rigorous explanation of how manufacturing deviations and damage on the working surfaces of gear teeth cause transmission-error contributions to vibration excitations\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSome gear-tooth working-surface manufacturing deviations of significant amplitude cause negligible vibration excitation and noise, yet others of minuscule amplitude are a source of significant vibration excitation and noise. Presently available computer-numerically-controlled dedicated gear metrology equipment can measure such error patterns on a gear in a few hours in sufficient detail to enable accurate computation and diagnosis of the resultant transmission-error vibration excitation. How to efficiently measure such working-surface deviations, compute from these measurements the resultant transmission-error vibration excitation, and diagnose the manufacturing source of the deviations, is the subject of this book.\u003c\/p\u003e \u003cp\u003eUse of the technology in this book will allow quality spot checks t\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003ePreface xi\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAcknowledgments xvii\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Transmission Error 2\u003c\/p\u003e \u003cp\u003e1.2 Mathematical Model 4\u003c\/p\u003e \u003cp\u003e1.3 Measurable Mathematical Representation of Working-Surface-Deviations 6\u003c\/p\u003e \u003cp\u003e1.4 Final Form of Kinematic-Transmission-Error Predictions 10\u003c\/p\u003e \u003cp\u003e1.5 Diagnosing Transmission-Error Contributions 12\u003c\/p\u003e \u003cp\u003e1.6 Application to Gear-Health Monitoring 13\u003c\/p\u003e \u003cp\u003e1.7 Verification of Kinematic Transmission Error as a Source of Vibration Excitation and Noise 14\u003c\/p\u003e \u003cp\u003e1.8 Gear Measurement Capabilities 15\u003c\/p\u003e \u003cp\u003eReferences 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Parallel-Axis Involute Gears 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Involute Tooth Profile 21\u003c\/p\u003e \u003cp\u003e2.2 Parametric Description of Involute Helical Gear Teeth 24\u003c\/p\u003e \u003cp\u003e2.3 Multiple Tooth Contact of Involute Helical Gears 27\u003c\/p\u003e \u003cp\u003e2.4 Contact Ratios 27\u003c\/p\u003e \u003cp\u003eReferences 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Mathematical Representation and Measurement of Working-Surface-Deviations 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Transmission Error of Meshing-Gear-Pairs 32\u003c\/p\u003e \u003cp\u003e3.2 Tooth-Working-Surface Coordinate System 34\u003c\/p\u003e \u003cp\u003e3.3 Gear-Measurement Capabilities 36\u003c\/p\u003e \u003cp\u003e3.4 Common Types of Working-Surface Errors 37\u003c\/p\u003e \u003cp\u003e3.5 Mathematical Representation of Working-Surface-Deviations 38\u003c\/p\u003e \u003cp\u003e3.6 Working-Surface Representation Obtained from Line-Scanning Tooth Measurements 45\u003c\/p\u003e \u003cp\u003e3.7 Example of Working-Surface Generations Obtained from Line-Scanning Measurements 54\u003c\/p\u003e \u003cp\u003eReferences 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Rotational-Harmonic Analysis of Working-Surface Deviations 69\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Periodic Sequence of Working-Surface Deviations at a Generic Tooth Location 69\u003c\/p\u003e \u003cp\u003e4.2 Heuristic Derivation of Rotational-Harmonic Contributions 70\u003c\/p\u003e \u003cp\u003e4.3 Rotational-Harmonic Contributions from Working-Surface Deviations 71\u003c\/p\u003e \u003cp\u003e4.4 Rotational-Harmonic Spectrum of Mean-Square Working-Surface Deviations 75\u003c\/p\u003e \u003cp\u003e4.5 Tooth-Working-Surface Deviations Causing Specific Rotational-Harmonic Contributions 79\u003c\/p\u003e \u003cp\u003e4.6 Discussion of Working-Surface Deviation Rotational-Harmonic Contributions 83\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Transmission-Error Spectrum from Working-Surface-Deviations 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Transmission-Error Contributions from Working-Surface-Deviations 96\u003c\/p\u003e \u003cp\u003e5.2 Fourier-Series Representation of Transmission-Error Contributions from Working-Surface-Deviations 99\u003c\/p\u003e \u003cp\u003e5.3 Rotational-Harmonic Spectrum of Mean-Square Mesh-Attenuated Working-Surface-Deviations 101\u003c\/p\u003e \u003cp\u003e5.4 Example of Rotational-Harmonic Spectrum of Mean-Square Mesh-Attenuated Working-Surface-Deviations 103\u003c\/p\u003e \u003cp\u003eReferences 108\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Diagnosing Manufacturing-Deviation Contributions to Transmission-Error Spectra 109\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Main Features of Transmission-Error Spectra 109\u003c\/p\u003e \u003cp\u003e6.2 Approximate Formulation for Generic Manufacturing Deviations 113\u003c\/p\u003e \u003cp\u003e6.3 Reduction of Results for Spur Gears 119\u003c\/p\u003e \u003cp\u003e6.4 Rotational-Harmonic Contributions from Accumulated Tooth-Spacing Errors 121\u003c\/p\u003e \u003cp\u003e6.5 Rotational-Harmonic Contributions from Tooth-to-Tooth Variations Other Than Tooth-Spacing Errors 126\u003c\/p\u003e \u003cp\u003e6.6 Rotational-Harmonic Contributions from Undulation Errors 131\u003c\/p\u003e \u003cp\u003e6.7 Explanation of Factors Enabling Successful Predictions 158\u003c\/p\u003e \u003cp\u003eReferences 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Transmission-Error Decomposition and Fourier Series Representation 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Decomposition of the Transmission Error into its Constituent Components 166\u003c\/p\u003e \u003cp\u003e7.2 Transformation of Locations on Tooth Contact Lines to Working-Surface Coordinate System 171\u003c\/p\u003e \u003cp\u003e7.3 Fourier-Series Representation of Working-Surface-Deviation Transmission-Error Contribution 175\u003c\/p\u003e \u003cp\u003e7.4 Fourier-Series Using Legendre Representation of Working-Surface-Deviations 186\u003c\/p\u003e \u003cp\u003e7.5 Fourier-Series Representation of Normalized Mesh Stiffness \u003ci\u003eK\u003c\/i\u003e\u003ci\u003eM\u003c\/i\u003e(\u003ci\u003es\u003c\/i\u003e)\u003ci\u003e\/\u003c\/i\u003e\u003ci\u003eK\u003c\/i\u003e\u003ci\u003eM \u003c\/i\u003e191\u003c\/p\u003e \u003cp\u003e7.6 Approximate Evaluation of Mesh-Attenuation Functions 195\u003c\/p\u003e \u003cp\u003e7.7 Accurate Evaluation of Fourier-Series Coefficients of Normalized Reciprocal Mesh Stiffness \u003ci\u003eK\u003c\/i\u003e\u003ci\u003eM\u003c\/i\u003e\u003ci\u003e\/\u003c\/i\u003e\u003ci\u003eK\u003c\/i\u003e\u003ci\u003eM\u003c\/i\u003e(\u003ci\u003es\u003c\/i\u003e) 200\u003c\/p\u003e \u003cp\u003e7.8 Fourier-Series Representation of Working-Surface-Deviation Transmission-Error Contributions Utilizing only Real (Not-Complex) Quantities 210\u003c\/p\u003e \u003cp\u003eReferences 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Discussion and Summary of Computational Algorithms 241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Tooth-Working-Surface Measurements 242\u003c\/p\u003e \u003cp\u003e8.2 Computation of Two-Dimensional Legendre Expansion Coefficients 246\u003c\/p\u003e \u003cp\u003e8.3 Regeneration of Working-Surface-Deviations 248\u003c\/p\u003e \u003cp\u003e8.4 Rotational-Harmonic Decomposition of Working-Surface-Deviations 251\u003c\/p\u003e \u003cp\u003e8.5 Explanation of Attenuation Caused by Gear Meshing Action 251\u003c\/p\u003e \u003cp\u003e8.6 Diagnosing and Understanding Manufacturing-Deviation Contributions to Transmission-Error Spectra 252\u003c\/p\u003e \u003cp\u003e8.7 Computation of Mesh-Attenuated Kinematic-Transmission-Error\u003c\/p\u003e \u003cp\u003eContributions 253\u003c\/p\u003e \u003cp\u003eReferences 257\u003c\/p\u003e \u003cp\u003eSubject Index 259\u003c\/p\u003e \u003cp\u003eFigure Index 267\u003c\/p\u003e \u003cp\u003eTable Index 269\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528868340055,"sku":"9781119961697","price":89.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119961697.jpg?v=1731873339","url":"https:\/\/bookcurl.com\/products\/performancebased-gear-metrology-9781119961697","provider":"Book Curl","version":"1.0","type":"link"}