Calculation formula for spring design

Most of the spring designs used in LCA are compression coil springs or extension coil springs. These two spring designs involve the following items. Here will explain about a), b), c).

a) In the range of use, spring load and deformation: spring constant
b) Space to install the spring: length x shape
c) How to fix the spring: the shape and fixing method of both ends of the spring···(Refer to Lecture 230)
d) Others: spring stiffness (permanent deformation), fatigue

(1) The relationship between spring constant and spring shape and size

The relationship between spring deformation and load (force) was introduced in Lecture 224. Hooke’s law.

  P = k x δ

P: spring load

k: spring constant

δ: spring deflection (deformation amount)

“K: Spring constant” can be expressed by the following formulas in terms of spring material properties and spring shape. This formula applies to both compression coil springs and extension coil springs.

  k = P/δ = G x d4/8 xnx D3 ・・・ (A)

G: transverse elastic modulus (Young’s modulus)

d: wire diameter

n: effective number of turns

D: Average coil diameter

By deforming the formula (A), temporarily setting D (average coil diameter), d (wire diameter), k (spring constant) to calculate the effective number of turns: n, or according to the known P, D, d, n, To calculate the deformation variable: δ.

(2) Design of the length and shape of the spring

The length of the spring is selected and designed according to the relationship between the “allowable deformation amount” and the spring load.
“Allowable deformation amount” is the maximum amount of deformation that will deform or damage the spring (refer to [Figure 1]).

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