Design information for engineers, such as spring calculation formulas,
which are the basis of spring design, can be found here.
The symbols used for spring design are shown in Table 1 below. The values of the longitudinal elastic modulus (E) are based on Table 2.
Table 1. Symbols and units used in calculations
|Di||Coil inner diameter||mm|
|D0||Coil outer diameter||mm|
|D||Coil average diameter D=( Di + D0)/2||mm|
|ΔD||Reduction in coil average diameter with load applied||mm|
|N||Number of coils||—|
|v||Poisson’s ratio of materials（0.3)||—|
|c||Spring index c=D/d||—|
|E||Longitudinal elastic modulus||GpaまたはN/mm2|
|l||Second moment of area|
|P(P1, P2)||Load (Force) applied to the spring||N|
|M||Torsion moment (Torque) acting on the spring||N・mm|
|a1, a2||Arm length||mm|
|L||Active extension length of the spring||mm|
|kr (krd)||Spring constant||N・mm/rad(N・mm/deg)|
|φ(φd)||Spring torsion angle||rad(deg,°)|
|R(R1, R2)||Load radius||mm|
|Ds||Guide stud diameter||mm|
|kb||Bending stress correction factor||—|
|σ||Bending stress||Gpa or N/mm2|
Table 2.Longitudinal elastic modulus：E（N/m㎡）
|Spring steel material
Hard steel wire
|Phosphor bronze wire||98×103|
|Beryllium copper wire||127×103|
The torsion coil spring must be designed in consideration of the bending deflection that occurs in the arm which extends from the coil part.
The necessity to consider the arm part can be judged with the following formula.
If a1 + a2 is 0.09π DN or more, it is recommended to consider the arm length.
Figure 2. Arm Length of Torsion Springs
The spring constant (KT) of the torsion springs can be calculated with the following formula.
When the Length of the Arm Is Negligible
When the Length of the Arm Is Not Negligible
In addition, any stress (σ) can be calculated by the following formula.
Figure 3. Relationship between Spring Index “c” and Bending Stress Correction Factor “κb”