DUB BEL Handbook of Mechanical Engineering DUBBEL Handbook of MECHANICAL ENGINEERING Edited by W Beitz and K.-H Kuttner English Edition edited by B.J Davies Translation by M.J Shields With 1258 Figures Springer-Verlag London Ltd Wolfgang Beitz, Professor Dr.-Ing Technische UniversWit Berlin, Institut fur Maschinenkonstruktion, 10623 Berlin, Germany Karl-Heinz Kiittner, Professor Dipl.-Ing Formerly at Technische Fachhochschule Berlin Address for correspondence: Miillerstrasse 120, 13449 Berlin, Germany Chairman, UK Advisory Board B.J Davies, Professor Queens Crescent, Putnoe, Bedford MK41 9BN, UK Translator M.J Shields, FIInfSc, MITI Literary and Technical Language Services, Unit 10, Centenary Business Centre, Attleborough Fields Industrial Estate, Nuneaton, Warwickshire CVII 6RY, UK ISBN 978-1-4471-3568-5 ISBN 978-1-4471-3566-1 (eBook) DOl 10.1007/978-1-4471-3566-1 British library Cataloguing in Publication Data Dubbel: Handbook of Mechanical Engineering I Beitz, Wolfgang II Kiittner, Karl·Heinz III Shields, Michael J 621 library of Congress Cataloging·in·Publication Data Dubbel, Heinrich, 1873·1947 [Taschenbuch fur den Maschinenbau English Handbook of mechanical engineering / Dubbe! ; [edited by W Beitz and K.·H Kiittner p cm Includes bibliographical references and index Mechanical engineering-Handbooks, manuals, etc I Beitz, Wolfgang II Kiittner, Karl·Heinz III Title TJ151.D8131994 621-dc20 94·16420 CIP Apart from any fair dealing for the purposes of research or private study, or criticism or review, as perntitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transntitted, in any form or by any means, with the prior perntission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright licensing Agency Enquiries concerning reproduction outside those terms should be sent to the publishers © Springer-Verlag London 1994 Originally published by Springer-Verlag London Limited in 1994 Softcover reprint of the hardcover 1st edition 1994 The publisher makes no representation, express or implied, with regard to the accuracy of the infor· mation contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made Typeset by Photo· graphics, Honiton, Devon 69/3830-543210 Printed on acid-free paper UK Advisory Board Chairman Professor B Technology J Davies, University of Manchester Institute of Science and Members Dr J N Ashton, University of Manchester Institute of Science and Technology Dr N C Baines, Imperial College of Science, Technology and Medicine, London Professor C B Besant, Imperial College of Science, Technology and Medicine, London Dr B Lengyel, Imperial College of Science, Technology and Medicine, London D A Robb, Imperial College of Science, Technology and Medicine, London Dr C Ruiz, University of Oxford Professor J E E Sharpe, Lancaster University Dr D A Yates, University of Manchester Institute of Science and Technology Contributors B Behr, Rheinisch-Westfalische Technische Hochschule Aachen Professor W Beitz, Technische Universitat Berlin Professor A Burr, Fachhochschule Heilbronn E Dannenmann, Universitat Stuttgart Professor L Dom, Technische Universitat Berlin Dr K.A Ebertt, Hattersheim Professor K Ehrlenspiel, Technische Universitat Munchen Professor D Fenler, Batelle-Institut e.Y., Frankfurt a.M Professor H Gelbe, Technische Universitat Berlin Professor K.-H Habig, Bundesanstalt fur Materialforschung und-prufung (BAt\1.) , Berlin Professor G Harsch, Fachhoschschu1e Heilbronn Dr K Herfurth, Verein Deutscher GieBereifachleute VDG, Dusseldorf Dr H Kerie, Technische Universitat Braunschweig Professor L Kiesewetter, Technische UniversWit Cottbus Professor K.H Kloos, Technische Hochschu1e Darmstadt Professor K.-H Kuttner, Technische Fachhochschule Berlin J Ladwig, Universitat Stuttgart G Mauer, Rheinisch-Westfalische Technische Hochschu1e Aachen Professor H Mertens, Technische Universitat Berlin Professor H.W Miiller, Technische Hochschu1e Darmstadt Professor R Nordmann, Universitat Kaiserslautern Professor G Pahi, Technische Hochschule Darmstadt Professor H Peeken, Rheinisch-Westfalische Technische Hochschu1e Aachen Professor G Pritschow, UniversWit Stuttgart W Reuter, Rheinisch-Westfalische Technische Hochschu1e Aachen Professor R Roper, Universitat Dortmund Professor J Ruge, Technische Universitat Braunchschweig Professor G Rumpel, Technische Fachhochschu1e Berlin Professor G Seliger, Technische Universitat Berlin Professor K Siegert, Universitat Stuttgart viii Contributors Professor H.D Sond.ershausen, Technische Fachhochschule Berlin Professor G Spur, Technische Universitat Berlin Professor K Stephan, Universitat Stuttgart Professor H.K Tonshoff, Universitat Hannover Professor H.-J.Warneeke, Universitat Stuttgart Professor M Week, Rheinisch-WestfaIische Technische Hochschule Aachen T Werle, Universitat Stuttgart Professor H Winter, Technische Universitat MOnchen H Wosle, Technische Universitat Braunchschweig Preface to the English Edition It has been an education and a pleasure to assist in the preparation of this first English version of the widely used "DUBBEL: Taschenbuch fUr den Maschinenbau", which has been a standard mechanical engineering reference book in German-speaking countries since 1914 All the chapters of primary interest to English-speaking mechanical engineers have been translated I trust that this "Pocket Book" will be a ready and authoritative source of the best current practice in mechanical engineering It is up to date, having been revised regularly, with the last revision appearing in 1990 It provides an easily accessible theoretical and practical treatment of a wide range of mechanical engineering topics with comprehensive explanatory diagrams, tables, formulae and worked examples Much care has been given to ensuring a correct and easily understood translarion of the German text For completeness, it was felt necessary to retain many German references and also DIN Standards Where possible, ISO equivalents have been given It is unlikely that this complex exercise is entirely error free but I believe that faith has been kept with the original text B John Davies Emeritus Professor, Department of Mechanical Engineering, UMIST May 1994 Introduction Since 1914 the Dubbel Handbook of Mechanical Engineering has been the standard reference text used by generations of students and practising engineers in the German-speaking countries The book covers all fundamental Mechanical Engineering subjects Contributions are written by leading experts in their fields This handbook is not primarily intended for specialists in particular areas, but for students and practitioners, who, within the framework of their responsibilities, also need to know about the basics outside their own special area The handbook deliberately focuses on fundamentals and on the solutions of problems, but it also covers a wide range of applications Charts and tables with general material values and specific parameters are included As a German handbook, it relies more on the German Industrial Standards (DIN) and focuses on the components of German manufacturers This should not be a problem in this English-international edition owing to the exemplary character of these applications and examples; and with the increasing referencing of EN- and ISO/IECstandards, the national DIN standard becomes less significant In parallel with the complete German edition, the selected subjects in this edition combine the fundamentals of theoretical sciences, materials and engineering design with important mechanical engineering applications I would like to thank all those involved in the production of this handbook for their enthusiastic co-operation, since this has made an important standard mechanical engineering text available to an international readership w Beitz Technische Universitat Berlin November 1993 Contents A Mechanics I Statics of Rigid Bodies Al 1 1.2 1.3 1.4 1.5 1.6 1.8 10 11 Introduction Combination and Resolution of Concurrent Forces Combination and Resolution of Non-Concurrent Forces Conditions of Equilibrium Types of Support; the 'Free Body' Support Reactions Systems of Rigid Bodies Pin-Jointed Frames Cables and Chains Centre of Gravity Friction Al A2 A4 A5 A7 A7 Kinematics 2.1 Motion of a Particle 2.2 Motion of a Rigid Body AlO AlO A12 A13 A15 AI9 A19 A22 ~ Dynamics 3.1 3.2 3.3 3.4 3.5 3.6 Basic Concepts of Energy, Work, Power, Efficiency Particle Dynamics, Straight-Line Motion of Rigid Bodies Dynamics of Systems of Particles Dynamics of a Rigid Body Dynamics of Relative Motion Impact Mechanical Vibrations 4.1 4.2 4.3 One-Degree-of-Freedom Systems Multi-Degree-of-Freedom Systems (Coupled Vibrations) Non-linear Vibrations A40 A44 S Hydrostatics A49 Hydrodynamics and Aerodynamics (Dynamics of Fluids) ASI 6.1 6.2 6.3 6.4 6.5 6.6 One-Dimensional Flow of Ideal Fluids One-Dimensional Flow of Viscous Newtonian Fluids One-Dimensional Flow of Non-Newtonian Fluids Forces Due to the Flow of Incompressible Fluids Multi-Dimensional Flow of Inviscid Fluids Multi-Dimensional Flow of Viscous Fluids A27 A27 A28 A30 A33 A39 A39 A40 A48 A51 A52 A59 A60 A60 A63 C Index Cauchy-Riemann differential equations A62 Cauchy's Similarity Law A70 Cavity sinking, ultrasonic K85 Cell control L36 Cell-type manufacturing systems L97 Cellulose derivatives (CA, CP, CAB) 056-57 Celsius Scale C2 Cementite 026 Cements 051,0112 Centre of gravity A13- 14 Centre of rotation, instantaneous A24-25 Centre-of-mass law A30, A36 Centrifugal casting K 11- 12 Centrifugal clutches F74 Centrifugal stresses, rotating components B43-44 Centroid gyro A38 Ceramic materials 049-50, 0111 inserts K50 moulding K7-8 Certnets, see Carbides, cemented Chain dtives FIOI, FI09-110, FI93 Chain transmission, machine tool LI3-14 Chains, see Cables Changes of state adiabatic C5, CI4 gases and vapours at rest C14-15 in motion C15-16 irteversible C4 isentropic CI4 for primary shaping K3 Channel bending, see U-bending Chatter, machine tool L4 Chemical analysis methods 023 Chemical industry, use of condensers H24, H25 Chemical milling/machining K57, K61 Chemical vapour deposition (CVD) 048, K49, K86, K91 Chill casting KlO low pressure KlO Chip formation grinding process K52 machining K35-36 non-defined tool edges KS I turning K38-39 Chipboard 053 Chipless machining laser beam K83 processes classification K85 Chromating 049 Chromising 032 Chromium (as alloying element) 033 Churchill & Chu equation (free convection) C32 Circuits, hydraulic G12, GI5-16, L61 Circular sawing K49 machines L88-89 Circular shears L52-53 Clack valves, see Valves, flap Clamp joints F27-28 Clamping/support mechanisms, lathe L67 Classification systems, item E30-31 Clausius-Clapeyron equation (entropy of evaporation) CI2 Clausius-Rankine process (reversible cyclic) C21 Clausius's inequality C7 Clevis joints F29 Clocked control L35 Closures domed H7-8 flat end H7 Cloud point, lubricating oils 073 Clutches F65, F69-73 automatic F74-5 dog F69 freewheel F75 friction F69-70 engagement slip F70-72 layout design F72 operating methods F73 size selection F72 type selection F72 overrun F75 press L58 slip clutches F74 Co-generation, see Combined power and heat generation Coating processes K86-87 laser beam K83 on metal 048-49 non-metallic 048-49 plastics on metals K86 surface K90-91 Cobalt (as alloying element) 033 Cocks (piping) H17 Cold forging K34, L61 Cold forming processes K20 effect on material properties 09 Colebrook-Nikuradse diagram A54 Colebrook's fortnula (pipe friction) A54 Collision forces, coupling L20 Collision time A39 Colour assessment, of plastics 062 Combined power and heat generation C23 Combined stresses axial load and torsion B32 bending and axial load B31 bending, axial load, shear and torsion B32 bending and shear B32 bending and torsion B32 shear and torsion B32 Combustion processes C 16-18 temperature in C 17-18 Commutators, d.c motor L8 Compacting, hot -cold (heat treatment process) 032 Compensation effects, overload E 14 Complex velocity potential A62 Compliance frequency response L4 Components, relative expansion El7 Composite design E19 Composite (integral) casting K12 Compressed air, pneumatic installations G 17 Compressible fluids, see Fluids, compressible Compression bars (spring) F52 Compression moulding K16 Compression refrigeration, see Refrigeration process, compression Compression strength test method 020 plastics 060 Compressors G16 Computer aided design (CAD) systems Ll05-106 Computer aided production planning K98 Computer aided quality control (CAQ) KlO4 Computer integrated manufacturing (CIM) system L37-38 Computer numerically controlled (CNC) systems L68 Conceptual design E 11-12 Concrete OSO blocks and slabs OS I lightweight 051 prestressed OS I reinforced 050-S Condensation process ClO, C32 principles H23-24 Condensers air-cooled H26 in chemical industry H24, H25, H26 direct-contact H25 injection H25 low-pressure saturated vapour H25 for power stations H26 in steam power plant H24 surface H24 Conduction, thermal C26-27 Configuration guidelines D66 Confrontation, problem-solving E4 Conical disc springs F55-56 Connecting rods F173, F174, F176 Connections adhesive F21 bolted F34 loading F40-45 strength F42-45 tightening F38-40 elastic, see Springs friction F23-28 positive F28-34 type selection F47-50 Consolidation index (material hardness) K21 Constant-power control G14 Constraiitts, task E4 Constructional interrelationships E4 Contact conformal 068 contraformal 068 stress B8 Index Contact controls L40-41 Contact corrosion E18 Contactor L40 Continuous casting processes K4 Continuous-path control L46, L58 robot LI03 Contraction coefficients D77 Control data processing L44-45 Control programs L35-36 Controls asynchronous L35 cam operated L38 clocked L35 electrical L40-4I electronic L40-41 hydraulic transmissions G 13-14 levels of L37 means of operating L3 - 38 organisation of L36-37 robot L102-104 safety standards L38 signal processing L35 system structure L34-35 Convection heat transfer C26, C3033 Coolants, refrigeration C22 Cooling lubricants, machining processes K52 Cooling ponds H27 Cooling towers H27 design calculations H27 - 28 Coordinate conversion L47 Coplanar forces A2 equilibrium conditions A6 Copper, weldability F8 Copper and copper alloys D33, D43, D93, D94 -aluminium ailoys (aluminium bronzes) D 102 -lead-tin alloys D103 -tin alloys (tin bronzes) D101102 -zinc alloys (brasses) D43-44, D95-98, D99-1oo bronzes D44 Core zone remelting D28 Coriolis acceleration A25 Correction values table (cutting processes) KI09 Corrosion design for avoidance E 17-18 types D5, El7-18 Corrosive media, effect on material properties D 10 Cost accounting KI07 Cost centre calculation E8 Cost location accounting K106 Cost type accounting KI05 Costing E9-1O operational K105-107 Costs, types of KI05 Cottered joints F30 Couette flow A63-64 Couette viscosimeter A64 Coulomb's law of friction A42, K23 Counterblow hammers L62, L63 Couples Al Couplings L20, F64-65 elastic F65-69 resilient metal F68 rigid F65 self-aligning F65 torsionally stiff F65 CR, see Polychioroprene rubbers Crack ductility, test methods D22 Crack formation/propagation D3-4 weld joints F6 Crank mechanisms A24 components F1n-l76 designs F 168 dynamics FI70-172 kinematics Fl68-l70 machine tool LI4 press L57 Crank-rocker mechanisms L14 Crankshafts FIn, F174, FI75 oscillatory system J11, J19 Creep 056 strength calculations DIS Cremona force diagram All Crevice corrosion E 17 Critical loads, approximation methods 046-47 Culmann's auxiliary force A3 Curing process, thermo-setting plastics K3 Curved shears L52-53 Cutouts, pressure vessel H8 Cutter location data (CLDATA) L44 Cutting off process K62 Cutting processes K35 speeds Ll steels for D38 Cutting tools, materials for K49, K50, K1l7 CycliC process C 19 Cyclo gear mechanisms L19-20 Cylinders bound hollow 042 elliptical 042 pneumatic LIS rotating 044 thick-wall 043 Cylindrical shells under external pressure H6-7 under internal pressure H6 Cylindrical ways L28 Cyril-Bath process (stretch forming) K28 D'Aiembert's Principle A29, A3637,043 constrained motion A3I hydrostatic paradox A62 Dalton's Law C23 Damping machine tool L4 modal J12 vibration A42-45, J12 Damping couplings F67 Databases, manufacturing system L37-38 Debye temperatures C 13 table of C49 Decimal-geometric series E20 Deep drawing plasticity theory K27 - 28 technology K28-29 Deep-hole drilling machine L 76 Deflection beams 020-26 oblique bending 025 slightly curved beams 026 Deformation E15, E16 material flow K20- 21 plastic H7 technology 056 test methods for determining D19 Deformation energy theory D5 Degrees of freedom A23 Delphi method (for problem solving) E5 Demand calculation, material K9899 Denavit - Hartenberg convention (robot structure) LI02 Density A49 DeSign process E 10-11 basic E13 conceptual, see Conceptual design detail, see Detail design embodiment, see Embodiment design redesign E 13 variants E 13 Detail design E 12 Deutsche Institut fUr Normung (DIN) Standards, see DIN Standards Development and design, problemsolving E4 Diathermal walls C2 Diathermic body C33 Die, wire drawing K25 Diesel engine C18 Differential design E 19 Diffusion coatings D48 Diffusion mechanisms, sintering K3 Diffusor flow C 16 drag coefficient A56 Digital absolute measuring systems L50-51, Ll02 Digital data logging L49-50 Digital incremental measuring systems L49-50, LI02 Digital locators LI02 Dilatant liquids A59 Dilatometer measurement D24 Dimensions, types of E25 DIN (Deutsche Institut fUr Normung) Standards E2324 Dip soldering L 100 Dipole current flow A62 Disc friction A65 Disc model, plasticity theory K25 Discs rotating 043-44 rotation of two A26 skewed angle rotation A34 under in-plane loads 041 E Index Discursive methods, problem-solving E5 Displacement control, motor LIO Displacement method, FEM B50 Displacement power, pump G5 Distortion B3 Distribution laws, sample evaluation D17-18 Dittus-Boelter-Kraussold equation (heat transfer) C31 DNC operation, robot control L103 Double-acting hammers L62, L63 Drag, solid bodies A65 Drag coefficient ASS-57 Drag force A67 -68 Drawing process L S9 Drilling machines L7 bench L74 column-type L74-75 deep-hole L 76 free-standing piller L7 multi-spindle L75 precision L 76 radial L7S-76 special purpose L 76-79 turret L76 Drilling process K41-43 laser beam K83 short-holes K43 Drives control of L7, L9-IO, L13 hydraulic G15-16, L61-62 control G13-14 machine tool LI, L4 pneumatic, see Pneumatic drives press L57-58 Drop forging K33 Drop hammers L62-6; Drop short circuits, welding L97 -98 Ductility D7 at fracture D3 crack D22 processes affecting D8-10 Dulong-Petit rule Dynamic loading, strength calculations D 13 Dynamic similarity A70-71 Dynamic stress, weld joints FI6 Dynamic viscosity AS3 cn Economic efficiency, manufacturing processes KI Effective motion L1 Effective principle E2, E4 Efficiency A28 heat exchangers H Eigenvectors J12, JI3 Elastic buckling, see Euler buckling Elastic couplings, see Couplings, elastic Elastic expansion, scale factor A69, A70 Elastic hardening material B56 Elastic limit D 19 Elastic modulus, test methods for determining D 19 Elasticity B 36 Elasto-plastic material B56 Elastomer couplings F68-69 Elastomers D54, D58-59 polyurethane (PUR) D59 thermoplastically processable (TPE) D59 for vibration reduction F66-67 Elastoviscous substances A59 Elbow pieces, drag coefficient A55 Electric slag remelting D28 Electrical discharge in gas cutting Fill Electrical machines, steels for D40, D41, D94 Electrical perturbation moments, excitation by J20 Electrochemical machining (ECM) K57, K60, K85 Electrodischarge machining (EDM) K57-59, K85 cavity sinking K58, K59 cutting by K 59 material pairs table K1l5-116 thread production K69 Electroforming KI9 Electrohydraulics L40 drives LlO-ll Electron beam processing applications K83-84 inscriber K88 lithography K1l4, K87 micro-analysiS method D23 principles K83 vapour deposition K84 Electroplating K91 Ellipsoid of inertia A34 Elongation B3, B4 permanent limit B5 Embodiment design E 12 basic rule E 13 guidelines E 16 principles E 14-16 Emission index C34 table of C53 Empirical temperatures C2 EN Standards (European Standards) E23 Enamelling D49 Encoders, digital absolute measuring systems L50 Energy C3 in closed systems c4 dissipated Cll forms of C3-4 internal (stored) C4, Cll, C12 in open systems C4-5 Energy conservation law A36, A38 Energy efficiency, overall C18 Energy equation A29, A30 Energy method, buckling load B4647 Energy transfer, fluid drives G I Engesser-von Karman's curve (buckling) B46 Engineering drawings conventions and scales E27 dimensioning E27 lines and lettering E27 sizes and formats E27 types E25-27 Engineering surfaces E24-25 Engines diesel C18 fan-type, force calculations J8-9 flat, force calculations J9 internal combustion CI8 machine vibrations JII pressure graph JI radial, force calculations J8-9 two-cylinder, force calculations J5 V-in-line, force calculations J8, J9 Engraving machines L82 Enthalpy C5, CI!, Cl2 humid air C24 Entropy C6, CI2 generation C6 Entropy flux C6 Environment, effect on material properties D 10 Epicyclic gears A26 Epoxy resins (EP) D58 EPS, see Polystyrene, expanded Equal embodiment strength principle EI6 Equations of motion machine vibrations JI!, J25-29 see also Motion Equilibrium conditions coplanar forces A6 forces in space A5 thermal C2 types of A7 ErgonOmics E18, K107-108 Ericson process C20 Error technology, manufacturing processes KI ETFE (plastic) D57 Ethylene propylene rubbers (EPM, EPDM) D59 Euler buckling B45 Euler datum system (fluid mechanics) CI Euler's equations of motion A23, A37, ASI, A60 for stream filament A51 Euler's rope friction formula Al718 Euler's similarity parameters A 71 Euler's velocity formula A23 Evaluation procedure, solution E6, E7, E8 Evaporation process C33 Excitation spectrum, noise J31, J34 Exergy C7 closed system C7-8 and heat C8 losses C8, H5 open system C8 Expanding process, plastics forming KI6 Expansion thermal CI2 design for El7 solids C12, C48 table of coefficients C48 Index G Expansion compensators H13 bellows drag coefficient A56 loops H13 Exponential equations, use of E2122 External forces Al Extruders (machines) L61 Extrusion processes K15 direct K34 hydraftlm K35 hydrostatic K35 indirect K34-35 plasticity theoty K26-27 plastics D63 F actors of safety, see Safety factors Fahrenheit Scale C2 Fail-safe principle E16 Failure causes of D2 stress failure criterion 86 under alternating stress D3-4 under complex stress conditions D4-5 under continuous stress D2-3 Fatigue crack corrosion E18 Fatigue endurance limit D6, D13 Fatigue life, rolling bearings F79-82, F83 Fatigue notch factor D12 Fatigue strength D6 Fatigue test, plastics D61 Feed drive components L 16 Feedgear mechanisms L18-20 Feedscrew mechanisms LI6 FEP (plastic) D57 Fibre-reinforced components, manufacture D63 Field-vector control L5 Filing machines L88-89 Fine machining K81 Finishing, plastic components D67 Finite element analysis, drive mechanisms FI75 Finite-element method (FEM) 85053 applications 852-53 displacements 851 elongations 851 machine tool design L25 oscillatoty systems J22 shears 8S1 stresses 8S2 Fit systems E2S Fits and tolerances E21, E25 Fixed points, temperature scale C3, C34, C3S Flame hardening D31 Flammability, of plastics D62 Flange joints F42 pressure vessel H8, H8-10 Flashpoint, oil D73 Flat-bed frames, machine tool L21 Flexibility matrix method, FEM 8S0 Flexible manufacturing systems L97, K102-103 Flexible turning centres L94 Floating bodies, stability ASO Flow criteria for material flow K21 incompressible fluids A60 laminar AS2-S3 multi-dimensional inviscid fluids A60-63 viscous fluids A63-68 non-Newtonian fluids AS9 non-stationaty ASI pipe losses HI0 plane potential A62-63 process theory I stationary ASI twisted bar analogy 831 Flow controllers 611 Flow curve, material K21 Flow distributors II Flow of force, see Force transmission Flow law, isotropic materials K21 Flow regulators 611 Flow straighteners, drag coefficient AS7 Flow stress K20 Fluid drives/transmissions 62-3, L40 Fluidics L39-40 Fluids compressible A53 incompressible A60 Fluorine rubber (FKM) DS9 Flywheel design JI-3 FMEA (Failure Mode and Effect Analysis) K104 Foam moulding, thermoplastic (TSG) DS8 Foaming process D64 Fog range C24 Folding (metal bending) K30 Force compensation principle E 15 Force of gravity, work A28 Force transmission E 14 by friction F23-28 diagram LI2, L13 Forces Al combinations of concurrent A2-3 non-concurrent A3-S coplanar systems A2, A4 excitation of out-of-balance J 19 method for statically indeterminate systems 833 resolution of concurrent A3 non-concurrent A4 spatial systems A2, AS Forging processes K32-34, L61, L63, L6S-66 aluminium alloys D4S steels for D38 Form drag, see Pressure resistance Form hardening, austenitic D32 Form milling K47 gear cutting K71 Form numbers D78 Formability K22 Formed parts, design and tolerances D66-67 FOrming cold, steels for D38 hot, steels for D38 powder metallurgy K18 theory K23- 2S FOrming limit curve K23 Forming machines LS4-S7 Fourier analysis non-periodic processes J17 periodic oscillations J17 Fourier index C28 Fourier's Law A7l, C26, C27 Fracture mechanics D2, D3-4, D7 test methods D22 Fracture strain, test methods for determining D 19 Frames machine tool L2, L21, LS7 embodiment design L23-2S materials L22 Framework, pin-jointed AlO-12 Freedom of motion, mechanism FlS8 Freeing principle A Freezing point C2 Frequencies natural JIl-13 response functions J13-14 Friction sliding AlS static AlS systems analysis D7l-72 tube AS3-SS types of D67, D68 Friction corrosion E18 Friction coupling L94 Friction drives calculations FI12-115 definitions F 11 types Fl11-112 use and operation FllS-1l6 Friction losses, heat exchanger HS Friction of motion, see Friction, sliding Friction pairings, table F182 Frictional force, work A28 Frictional gears L14 Frictional resistance A6S Froude's Model Law A70 Froude's Similarity Law A 70 Fuels calorific values table C49, C50 composition C50 liquid C50 Full mould casting K9 Function control L34 Functional interrelationships E2, E4 Gallery method (for problem solving) E5 Galvanic coatings D48 Gamma-ray test procedure D25 Gas constant, universal C9 Gas cutting processes F17-18 Gas fusion welding F2 Gas lubrication, bearings L30 Gas phase deposition coatings D48 Gas turbine system H • Index Gas turbine system (cont.) closed C20 open C18 Gas-shielded arc welding F2-3 Gases combustion characteristics C50 ideal C9 caloric properties C 10-11 flow CI5-I6 mixtures of C23, C24 physical properties C52 radiation of C34 real C9-JO caloric properties C II Gaskets H9 Gate valves H17 GE hypothesis (deformation) K21 Gear cone transmission units L 11- 12 Gear cutting by hobbing K73-7 by planing K72 by shaping K72-73 form-cutting processes K70 generating processes K70 worms K77-78 Gear manufacture fmishing K74-77 grinding K76, L92 materials and heat treatment F126-128 Gear pairs F 116 Gear ratio FI17 Gearbox, three-speed L II Geared transmissions bearings F 156-157 cases/housings F154-156 connections FI54 design FI54 types F153-154 Gears bevel A27 cutting by generating methods K79 by grinding K81 by milling K80-81 by shaping K78-79 straight F 13 - 138 bevelled spur F138-139 circarc FI22 compound planetary trains F150-152 cooling F126 crossed helical F139 crown FI38 cycloid FI22 cylindrical K70-77 efficiency F 117 epicyclic F143-152 frictional L14 grinding machine for L92 helical FI28-137 hydraulic L 14-15 involute F120-122 lubrication F125-126 machine tool Ll mangle F124 mechanical L II noise behaviour F116 planet, see Gears, epicyclic pneumatic LIS spiral bevel FI38 spur FI28-137 superposition F149-150 tooth geometry F117-124 Wildhaber-Novikov (W-N) F124 worm FI39-143, K77-78 Gearwheel an-mgement L 12 - 13 Geometrical data processing (GEO) L45 Geometrical features E2 Geometrically similar series E21 German Standards, see DIN Standards; VDE regulations; VDl guidelines Gibbs's fundamental equation C6 Glass 051-52 Gnielinski's equation C31 Gottingen-type profile (polar curve) A68 Graetz solution (infmite series) C31 GRAFCET (programming standard guideline) L42 Grain characteristics, for machining K50-51, K114 Graphite-bearing metals, bearings F98 Grashof number C30, C32 Grashofs criterion (linkages) F158 Grdtings incremental measuring systems L49 incremental scanner L49 Gravitational forces, scale factor A69, A70 Gray code, digital absolute measuring systems L51 Greases, see Lubricants, greases Green's function (influence coefficient) B54 Grey cast iron, weldability F8 Grey radiators C33-34 Grids and screens, drag coefficient A57 Grinding machines L89 centreless cylindrical L90-91 cylindrical L89-90 developments L92 gear L92 internal cylindrical L91 screw thread L92 surface L89 Grinding processes belt K54-55 gear finishing K76 inside-diameter cutoff K57 rotating tool K52-54 thread production K69 Grinding wheels K52 dressing K53-54 Griibler's equation (degrees of freedom) FI58 Guided gyro A38 Guides linear L2S-31 machine tool L rotary, see Bearings Gyroscopic motion