Blair, G., McCartan, C., and Cahoon, W., "Measurement and Computation of the Characteristics of Progressive Valve Springs," SAE Technical Paper 2010-01-1056, 2010, doi:10.4271/2010-01-1056.
Historically, when valve springs were wound with round wire and the coils were nominally equally spaced, it was relatively easy for the engineer to calculate the virtually-linear load carrying capacity, the almost non-varying stiffness and the relatively-constant natural frequency of the spring. This was the design data that was required then for some simplistic but effective calculations of the valvetrain dynamic stability. In recent times, valve springs have come to be commonly wound with other wire sections such as ovate and with coil-coil spacings that are unequal, giving the spring a variable load carrying capacity, variable stiffness and a variable natural frequency with deflection. Such springs are known as progressive wound springs. The computation of these spring characteristics is no longer a simple matter and neither is their incorporation within the calculation of the dynamic stability of the entire valvetrain. The technical literature is very sparse on these topics. This paper presents the detailed measured characteristics of stiffness and natural frequency of five differing progressive-wound valve springs and compares and contrasts the measurements with those computed by two methods, a commercially-available FEA software package and a more traditionally-based theoretical method.