On the use of variable bending stiffness clothoidal strips for the analysis and synthesis of low variability torque-angle turned curves in spiral torsion springs

Due to their size and weight advantage over spiral springs with no turns of the coil in contact with each other, variable free strip length spiral springs are used for low torque variability around a nominal torque. However, the analytical design of the torque–arbor angle turned curve is not straightforward when turns of the coil contact each other and lump together. Highly nonlinear expressions arise for obtaining the torque–angle turned curve, so the inverse problem is to be numerically solved by trial and error, leading to a lack of insight on the system behaviour. This work presents a variable free strip length spiral spring design permitting an analytical approach with torque variability as design parameter, so that the inverse problem can be analytically solved, which in turn permits the development of a systematic design procedure: a clothoidal strip and certain variation law in bending stiffness throughout its length lead to equations that permit a closed-form solution. A design example is included and tested to demonstrate the validity of the developed model and the design procedure.