Criteria of design for progressive torsion-bar springs

The paper discusses the necessary conditions for attaining a design yielding a spring-rate function which is variable. The dynamic response is expressed in terms of velocity and displacement by means of a phase plot (integral curve). A method is presented which allows the generation of a ramp function of multiple shaft splines fitting into a serrated hub to yield the required spring-rate function of the torsion bar. It is shown that the engagement length of splines results in a change of the effective length of the elastic torsion spring. The ramp function can be generated directly from a known spring-rate function. In particular, the constant-frequency variable-mass system is considered.