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GENERAL NOMENCLATURE* A b C d D E / g G / ID k Area, mm2 (in2) Width, mm (in) Spring index, D/d Wire diameter, mm (in) Mean diameter (OD minus wire diameter), mm (in) Modulus of elasticity in tension or Young's modulus, MPa (psi) Deflection, mm (in) Gravitational constant, 9.807 m/s2 (386.4 in/s2) Shear modulus or modulus of rigidity, MPa (psi) Moment of inertia, mm4 (in4) Inside diameter, mm | CHAPTER 24 SPRINGS Robert E. Joerres Applications Engineering Manager Associated Spring Barnes Group Inc. Bristol Connecticut 24.1 INTRODUCTION 24.2 24.2 GLOSSARY OF SPRING TERMINOLOGY 24.2 24.3 SELECTION OF SPRING MATERIALS I 24.4 24.4 HELICAL COMPRESSION SPRINGS 24.10 24.5 HELICAL EXTENSION SPRINGS 24.27 24.6 HELICAL TORSION SPRINGS 24.34 24.7 BELLEVILLE SPRING WASHER I 24.38 24.8 SPECIAL SPRING WASHERS 24.49 24.9 FLAT SPRINGS 24.53 24.10 CONSTANT-FORCE SPRINGS 24.56 24.11 TORSION BARS 124.60 24.12 POWER SPRINGS 124.61 24.13 HOT-WOUND SPRINGS I 24.64 REFERENCES 24.67 GENERAL NOMENCLATURE1 A b C d D E f g G I ID k Area mm2 in2 Width mm in Spring index D d Wire diameter mm in Mean diameter OD minus wire diameter mm in Modulus of elasticity in tension or Young s modulus MPa psi Deflection mm in Gravitational constant 9.807 m s2 386.4 in s2 Shear modulus or modulus of rigidity MPa psi Moment of inertia mm4 in4 Inside diameter mm in Spring rate N mm Ib in or N mm r lb in r The symbols presented here are used extensively in the spring industry. They may differ from those used elsewhere in this Handbook. 24.1 24.2 STANDARD HANDBOOK OF MACHINE DESIGN K Design constant Kn Stress correction factor for helical springs L Length mm in Lf Free length mm in Ls Length at solid mm in M Moment or torque N mm lb in n Frequency Hz N Number of active coils or waves N Total number of coils OD Outside diameter mm in P Load N lbf r Radius mm in S Stress MPa psi TS Tensile strength MPa psi t Thickness mm in YS Yield strength MPa psi p Density g cm3 lb in3 0 Angular deflection expressed in number of revolutions p Poisson s ratio 24.1 INTRODUCTION Spring designing is a complex process. It is an interactive process which may require several iterations before the best design is achieved. Many simplifying assumptions have been made in the design equations and yet they have proved reliable over the years. When more unusual or complex designs are required designers should rely on the experience