Notes: springs.pdf |
There are 3 things that control the properties of a spring. Wire diameter d, coil diameter D and number of active coils n. Increase d, spring is stiffer. Increase D, spring is softer. Increase n, spring is softer.
The most basic factor for a spring is k - the stiffness in N/mm. This can be increased several ways - Use thicker wire, less number of coils, or a smaller diameter.
Stress increases with an increase in force F, a larger coil diameter D or reduced wire diameter d.
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Spring Constant
The spring constant k is a function of the spring geometry and the spring material's shear modulus G,
where G is found from the material's elastic modulus E and Poisson ratio n,The rise angle of the spring coils (the angle between the coils and the base of the spring) is found from the arctangent of the coil-pitch divided by the spring circumference,
The solid height of the spring is found by summing the widths of all the spring coils. The total number of spring coils is equal to the active coils in the spring interior plus the 2 coils at the spring ends,
The length of wire needed to make the spring is found from,
The maximum shear stress in the spring associated with the maximum force is given by,
where W is the Wahl correction factor (accounting for spring curvature stress) and C is the spring index (essentially an aspect ratio of the spring cross-section),
This depends on how the ends of the spring are formed. See the following illustration for different n* values: