Design of a Variable Radius Piston Profile Generating Algorithm

One of the main sources of efficiency loss in heat engines is the inability of a sinusoidally displaced piston engines to approximate the ideal heat volumetric cycles the engines require. While attempts have been made to address this issue in the past, recent developments in Stirling engine technology utilizing rolling diaphragm seals on the cylinders has offered an opportunity to greatly increase the correlation between an engines volume-time profile to the ideal profile. By changing the radius of the piston used to drive the rolling diaphragm connection over its length, the piston can effectively be used as a ”transfer function” translating the sinusoidal displacement of the crankshaft into a near ideal heat cycle volumetric displacement. This work presents a methodology for determining the ideal shape of such a piston, and a model used to most effectively match a desired input linear displacement profile with output volumetric displacement profile, without compromising the operating conditions required to maintain the diaphragm itself. NOMENCLATURE Cp Contact point. The point where the diaphragm first contacts the piston after leaving contact with the cylinder wall Cv Convolution radius, the radius of the fold in the rolling diaphragm. R(l) The profile of the radius of the piston with respect to its length ∗Address all correspondence to this author. S(t) The axial displacement function of the input piston with respect to time Vo(t) The desired volumetric output displacement function with respect to time Vl(l) The volume length relationship of the piston being developed TP Total perimeter of half the rolling diaphragm length Al(t) Axial length displacement of input piston with respect to time