Torsion Springs and Double Torsion Springs Design Considerations
After determining the force of torque required a designer usually estimates a suitable space or size limitations. During torsion spring design, space should be considered approximate until the wire size and number of coils have been determined. The wire size depends solely on the torque.
Torsion Springs and Double Torsion Springs Specifications
If spring works on a rod, give size of same, as spring must not bind when wound up to its limit of travel.
Free length and number of coils. If spring cannot increase in length as wound up, allow sufficient space between coils.
Right or Left Hand Wound.
Wire Size. Decimal size if possible. Material, Kind and Grade.
Style of Ends, (see illustrations). Number of turns deflection to hold given load and radius of loaded arm. This length may be the length of the arm, or the arm may be attached to a movable machine member, in which case the length to point of application of load is given.
Proportions: Spring index, inside diameter divided by wire diameter between 4 and 14 is best. The larger the ratio the more the average tolerance. Ratios of 3 or less often cannot be coiled on spring coiling machines because of arbor breakage.
Spring Index: Spring index must be used with caution.
Total coils:Torsion springs with less than 3 coils buckle and difficult to test. Best to specify to the nearest fraction in eights or quarters whenever possible.
Rods: Torsion springs should be supported by a rod running through center.
Diameter Reduction: Should compute the reduction of inside diameter during deflection. Allowances should be considered for normal spring diameter tolerances.
Winding: Coils of a torsion spring may be closely or loosely wound. Should not be wound with coils pressed tightly together. Tight-wound springs with initial tension in coils do not deflect uniformly and are difficult to test accurately. A space between 20 to 25 percent of wire thickness is desirable.
Hand: Hand or direction of coil should be specified. Deflecting the spring in an unwinding direction causes high stress and early failure. When spring is sighted down the longitudinal axis it is right hand when direction of wire into spring takes clockwise direction or angle of coils follow angle similar to threads of bolt or screw, otherwise it is left hand. A spring must be coiled right hand to engage threads of a standard machine screw.
Arm Length: All wire in a torsion spring is active between the points where the forces are applied. Deflection of long extended arms can be calculated by allowing one third of the arm length from the point of force contact to the spring body converted in coils. If the length of arm is equal or less than one half the length of one coil it can be safely neglected in most applications.
Bends: Arms should be straight as possible. Sharp bends are stress raisers that cause early failure. Bend radii should be as large as practicable. Hooks tend to open during deflection. Hook stresses can be calculated in the same way as for extension springs.
Double Torsion: Consistence of a left-hand-wound series of coils and a series of right-hand-coils connected at center. Torque and stress calculations, each series is calculated separately as individual springs, then torques are added together but deflection are not added together.
Torsion Springs Design Formulas and Specifications
The basic torsion spring design formulas used for torque or Moment (M) and bending stress (S) are shown below.
In the formulas the constants 10.8 and 6.6, while strictly theoretical, give results closer to the actual values obtained.
Mean Coil diameter, in. (mm)
Diameter of round wire, in. (mm)
Number of coils
Modulus of elasticity, psi (MPa)
Deflection, number of turns or revolutions of spring
Bending Stress, psi (MPa)
Momment of torque, lb*in (N*mm)
Width, in. (mm)
Thickness, in. (mm)
Graphic layout of Specificiations for Torsion Springs