Bourdon gage span linearization with non-circular gears

Abstract

It is reported the synthesis of a non-circular gear connection portion to be used in a Bourdon pressure gauge. The purpose of the gear connection is compensating the bellows’ deformation non-linearity. The connection Input-Output (I/O) gear ratio was deduced by identifying and analyzing a four-bar linkage. The bellows deformation was represented as a rigid element and its position angle was set as the mechanism input variable. The angle described by the pointer element (pressure indicator) is established as the connection output angle. The ideal output angles should allow a linear motion of the pointer while keeping same amplitude divisions along the scale. The I/O gear ratio, the input and output angles, in addition to the center distance allowed the primitive curve portion synthesis along which the teeth would be designed. The mathematical formulation was programmed in GNU Octave in order to visualize the output angles, I/O ratio, and the non-circular gear pitch curves. The nonlinearity of the Bourdon manometer was counteracted by the integration of non-circular (non-linear) profile mechanical elements. Measurement scale was linearized for uniform resolution across the entire measurement range. Findings were validated by comparing the pitch curves against the motion of a CAD model generated in SolidWorks. Thus, an uniform resolution along the measuring span was achieved.