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6.1 INTRODUCTION / 6.4 6.2 GLOSSARY OF SPRING TERMINOLOGY / 6.4 6.3 SELECTION OF SPRING MATERIALS / 6.6 6.4 HELICAL COMPRESSION SPRINGS / 6.12 6.5 HELICAL EXTENSION SPRINGS / 6.29 6.6 HELICAL TORSION SPRINGS / 6.36 6.7 BELLEVILLE SPRING WASHER / 6.40 6.8 SPECIAL SPRING WASHERS / 6.51 6.9 FLAT SPRINGS / 6.55 6.10 CONSTANT-FORCE SPRINGS / 6.58 6.11 TORSION BARS / 6.62 6.12 POWER SPRINGS / 6.63 6.13 HOT-WOUND SPRINGS / 6.66 REFERENCES / 6.69
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GENERAL NOMENCLATURE
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 (lb/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.
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SPRINGS 6.4
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K Kw L Lf Ls M n Na Nt OD P r S TS t YS
Design constant Stress correction factor for helical springs Length, mm (in) Free length, mm (in) Length at solid, mm (in) Moment or torque, N mm (lb in) Frequency, Hz Number of active coils or waves Total number of coils Outside diameter, mm (in) Load, N (lbf) Radius, mm (in) Stress, MPa (psi) Tensile strength, MPa (psi) Thickness, mm (in) Yield strength, MPa (psi) Density, g/cm3 (lb/in3) Angular deflection, expressed in number of revolutions Poisson s ratio
6.1 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 of a spring manufacturer. The information in this chapter is offered for its theoretical value and should be used accordingly.
6.2 GLOSSARY OF SPRING TERMINOLOGY
active coils: those coils which are free to deflect under load. baking: heating of electroplated springs to relieve hydrogen embrittlement. buckling: bowing or lateral displacement of a compression spring; this effect is related to slenderness ratio L/D. closed and ground ends: same as closed ends, except that the first and last coils are ground to provide a flat bearing surface. closed ends: compression spring ends with coil pitch angle reduced so that they are square with the spring axis and touch the adjacent coils.
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SPRINGS 6.5
SPRINGS
close-wound: wound so that adjacent coils are touching. deflection: motion imparted to a spring by application or removal of an external load. elastic limit: maximum stress to which a material may be subjected without permanent set. endurance limit: maximum stress, at a given stress ratio, at which material will operate in a given environment for a stated number of cycles without failure. free angle: angular relationship between arms of a helical torsion spring which is not under load. free length: overall length of a spring which is not under load. gradient: see rate. heat setting: a process to prerelax a spring in order to improve stress-relaxation resistance in service. helical springs: springs made of bar stock or wire coiled into a helical form; this category includes compression, extension, and torsion springs. hooks: open loops or ends of extension springs. hysteresis: mechanical energy loss occurring during loading and unloading of a spring within the elastic range. It is illustrated by the area between load-deflection curves. initial tension: a force that tends to keep coils of a close-wound extension spring closed and which must be overcome before the coils start to open. loops: formed ends with minimal gaps at the ends of extension springs. mean diameter: in a helical spring, the outside diameter minus one wire diameter. modulus in shear or torsion (modulus of rigidity G): coefficient of stiffness used for compression and extension springs. modulus in tension or bending (Young s modulus E): coefficient of stiffness used for torsion or flat springs. moment: a product of the distance from the spring axis to the point of load application and the force component normal to the distance line. natural frequency: lowest inherent rate of free vibration of a spring vibrating between its own ends. pitch: distance from center to center of wire in adjacent coils in an open-wound spring. plain ends: end coils of a helical spring having a constant pitch and with the ends not squared. plain ends, ground: same as plain ends, except that wire ends are ground square with the axis. rate: spring gradient, or change in load per unit of deflection. residual stress: stress mechanically induced by such means as set removal, shot peening, cold working, or forming; it may be beneficial or not, depending on the spring application.
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