D-optimal strain sensor placement for mechanical load estimation in the presence of nuisance loads and thermal strain

The measurement of loads in circular cross-section geometries using strain gauges or other types of strain sensors is well-known in the field of mechanical engineering. Typical stress measurement configurations use 4 strain sensors strategically placed on the surface of the shaft and connected in the form of a complete Wheatstone bridge. Thus, 4 strain sensors are used to estimate each of the six load components to which a shaft may be subjected. Some typical configurations are designed to compensate for temperature effects, making them robust to temperature changes. Despite being used for decades, there is no record of any algorithm that serves to calculate these configurations, demonstrate that they are optimal or determine new configurations with other requirements. In this article, an algorithm is developed that allows calculating the optimal configurations of strain sensors to estimate one or several load components, compensating for the effect of other loads and temperature variations. This algorithm is based on the measurement of the strain of each gauge using Wheatstone quarter bridges and uses the same set of sensors for the estimation of various load components. The results are two-fold: on the one hand the traditional configurations are shown to be optimal and on the other hand a series of additional optimal configurations are obtained to estimate various sets of load components compensating for the influence of the rest. Additionally, a means of calculating the estimation variance of the loads of interest is provided.