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Springs

Active Coils: Those coils which are free to deflect under load.

Angular relationship of ends: The relative position of the plane of the hooks or loops of extension spring to each other.

Beam fixed at each end, load in centre

where
E = Youngs modulus [Nm^-2]
I = area moment of inertia [m⁴]
l = length [m]

Buckling: Bowing or lateral deflection of compression springs when compressed, related to the slenderness ration (L/D).

Cantilever beam with load at end

where
E = Youngs modulus [Nm^-2]
I = area moment of inertia [m⁴]
l = length [m]

Closed ends: Ends of compression springs where the pitch of the end coils is reduced so that the end coils touch.

Closed and ground ends: As with closed ends, except that the end is ground to provide a flat plane.

Close-wound: Coiled with adjacent coils touching.

Coils per inch: Same as "Pitch"

Deflection: Motion of the spring ends or arms under the 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 which any given material may operate indefinitely without failure for a given minimum stress.

Free angle: Angle between the arms of a torsion spring when the spring is not loaded.

Free length: The overall length of a spring in the unloaded position.

Helical spring

where
k = stiffness [Nm^-1]
G = shear modulus [Nm^-2]
d = wire diameter [m]
D = mean coil diameter [m]
n = number of turns

Hysteresis: The mechanical energy loss that always occurs under cyclical loading and unloading of a spring, proportional to the are between the loading and unloading load-deflection curves within the elastic range of a spring.

Initial tension: The force that tends to keep the coils of an extension spring closed and which must be overcome before the coil starts to open.

Loops: Coil-like wire shapes at the ends of extension springs that provide for attachment and force application.

Mean coil diameter: Outside wire diameter minus one wire diameter.

Modulus in shear or torsion: Coefficient of stiffness for extension and compression springs.

Modulus in tension or bending: Coefficient of stiffness used for torsion and flat springs. (Young's modulus).

Natural Frequency: The lowest inherent rate of free vibration of a spring itself (usually in cycles per second) with ends restrained.

Open ends, not ground: End of a compression spring with a constant pitch for each coil.

Open ends ground: "Opens ends, not ground" followed by an end grinding operation.

Permanent set: A material that is deflected so far that its elastic properties have been exceeded and it does not return to its original condition upon release of load is said to have taken a "permanent set".

Pitch: The distance from centre to centre of the wire in adjacent active coils.

Quarter-elliptic laminated leaf spring

where
E = Youngs modulus [Nm^-2]
n = number of leaves
b = width of leaves [m]
t = thickness of leaves [m]
l = span [m]

Rate: Changes in load per unit of deflection, generally given in pounds per inch (lbs/in).

Remove set: The process of closing to a solid height a compression spring which has been coiled longer than the desired finished length, so as to increase the elastic limit.

Rod under axial load

where
E = Youngs modulus [Nm^-2]
A = cross sectional area [m²]
l = length [m]

Semi-elliptic laminated leaf spring

where
E = Youngs modulus [Nm^-2]
n = number of leaves
b = width of leaves [m]
t = thickness of leaves [m]
l = span [m]

Set: Permanent distortion which occurs when a spring is stressed beyond the elastic limit of the material.

Simply supported beam

Load applied at the centre.

where
E = Youngs modulus [Nm^-2]
I = area moment of inertia [m⁴]
l = length [m]

Slenderness ratio: Ratio of spring length to mean coil diameter.

Solid height: Length of a compression spring when under sufficient load to bring all coils into contact with adjacent coils.

Spring index: Ratio of mean coil diameter to wire diameter.

Stress range: The difference in operating stresses at minimum and maximum loads.

Squareness of ends: Angular deviation between the axis of a compression spring and a normal to the plane of the other ends.

Squareness under load: As in squareness of ends, except with the spring under load.

Tapered rod under axial load

where
E = Youngs modulus [Nm^-2]
D,d = end diameters [m]
l = length [m]

Torque: A twisting action in torsion springs which tends to produce rotation, equal to the load multiplied by the distance (or moment arm) from the load to the axis of the spring body.

Total number of coils: Number of active coils plus the coils forming the ends.