In common software and standards, the initial angle α0 is not considered. They usually only consider the angular deflection αh1, αh2 and αh. We propose to increase the range of applications by suggesting to consider the external operating angles α1 and α2.

You can find hereafter how to evaluate the initial free external angle α0 of a torsion spring.

DIN standards considers that the spring and the shaft remain coaxial.

α0 according to DIN standards

Considering this hypothesis, a formula can be defined:

With Sγa and Sγb that depend on the end type:

As an example, the initial free angle of a torsion spring with tangential ends become:

The following figure shows the position of a spring having an angle of 180 degres between legs (Na is an integer and a half).

Click here to download a small video (1.4 Mo) that shows a torsion spring in operating conditions.

Next picture shows the geometrical hypothesis exploited to a spring in contact with a shaft.

α0 for a spring with tangential legs

This enable to build the next formula for a spring with tangential legs:

The designer can choose the most appropriate formula realted to the considered application. In both formulae, α0 depends on both the end type and the radius where the external loads are applied. For that reason, α0 is not an intrinsic property of a torsion spring but depends on the considered application. You can clearly see that α0 is modified when Ra and/or Rb is modified.