Force transducer design: a new approach combining nonlinear finite element analysis and robust design

Designing a strain gage based force transducer is considered more of an art than an engineering process. Only general guidelines are available, and many trial and error iterations are needed to optimize the geometry and minimize the errors caused by nonlinear behavior of the structure. A new method, based on nonlinear finite element analysis and robust design principles, is proposed. A matrix of experiments considers relevant geometric and loading parameters. The behavior of the structure under different combinations of these parameters is determined by calculating the strain at different locations (suitable for strain gage installation) using finite element models. The nonlinear behavior of the transducer is identified by comparing the results of the nonlinear finite element analysis with those obtained using a linear finite element analysis. A signal-to-noise ratio is defined to quantify the nonlinearities and how the considered parameters affect them. An analysis of variance is employed to determine their relative influence. Based on the results of the statistical analysis, it is possible to identify the best value for each geometric parameter that would reduce, if not eliminate the nonlinearities. Once these optimal geometric parameters are chosen, a prototype can be built, instrumented with strain gages, and tested, to validate the obtained design. To illustrate this new proposed methodology, and appreciate its advantages over current practice of designing a force transducer, an example of the step-by-step procedure is illustrated considering a thin-wall cylindrical transducer.