Calculate the spring rate (k) of a helical compression spring based on its geometry and material.
Spring rate (k) is a measure of the stiffness of a spring. It is defined as the amount of force required to compress or extend a spring by a unit distance (e.g., Newtons per meter).
For a helical spring, the rate is determined by the material's shear modulus and the geometry of the coil. Increasing the wire diameter significantly increases stiffness, while increasing the coil diameter or the number of turns decreases it.
Where:
• k is the spring rate (N/m)
• G is the shear modulus of the material (Pa)
• d is the wire diameter (m)
• D is the mean coil diameter (m)
• n is the number of active turns
Active turns are the coils that actually contribute to the spring's deflection. For squared and ground ends, the total turns is usually n + 2.
The spring rate is proportional to the 4th power of the wire diameter (d⁴). Doubling the wire diameter increases the stiffness by 16 times!
The spring index (C) is the ratio of mean coil diameter to wire diameter (D/d). It should ideally be between 4 and 12 for good manufacturability.
The shear modulus (G) represents the material's resistance to twisting. Steel is much stiffer than aluminum or copper, leading to a higher spring rate for the same geometry.
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