# Design and Calibration of a Tri-Directional Contact Force Measurement System
## 1 Introduction
Therefore, when multiple resonances are investigated, two types of tri-directional force measurement systems can be considered, i.e., (i) a multi-axis force sensor; (ii) a set of single axis force sensors mechanically connected to each other which is proposed in this study. Multi-axis force sensors are being broadly used in aerospace and automation industries these days. However, the commercially available  
Figure 1: Shrouded blades (**left**) and the shroud contact surfaces (**right**). multi-axis force sensors are very expensive and can be intricate considering their mounting requirements and calibration with respect to the shrouded blades. Alternatively, numerous studies have been carried out on the development of multi-axial force measurement technologies [20; 21; 22; 23; 24; 25; 26; 27; 28] that involved different arrangements of multiple strain gauges and various designs of the load transferring elements to achieve valued outcomes. Similarly, several three directional contact force measurement systems have been studied and implemented for different applications like surgical robots [29], tactile sensors [30; 31], clinical examination [32], and measurement of ground reaction force (GRF) [33; 34]. Nevertheless, the dimensions of most of these multi axial force sensors are not small enough to be placed in the constricted space where the blade shroud contact forces must be measured. Other multi-axis load cells lack the dynamic characteristics required to measure the periodic contact forces acting on the blade shroud. On the other hand, to achieve the required accuracy, reliability, and robustness, the set of single axis sensors and the elastic structure on which they are mounted on must be carefully designed [20]. Multiple axis force sensors can be constructed or arranged in a way that they can be mechanically decoupled or mechanically coupled. In mechanically decoupled force sensors, the applied loads are directly measured as the output of the sensor, i.e., minimum or no crosstalk. However, their complex geometry results in manufacturing complications. Mechanically coupled force sensors on the other hand also measure lateral force components upon load application requiring the computation of a decoupling matrix to obtain the actual loads. This also means that they can be designed with simple geometries [21]. Hence, an important design aspect to be considered is that the precision of a multi-axis force measurement system (both multi axis sensor and set of uniaxial force sensors mechanically connected) significantly depends on the configuration of force sensing components and minimization of errors arising due to coupling or noise. Therefore, accuracy must be ensured during the calibration process of a multi-axis force measurement system that involves logging the measured values corresponding to the known load set. In view of all the above-mentioned factors and limitations, it is necessary to design an accurate and robust measurement solution and test an alternate decoupled multi-axial force sensing method of combining three uniaxial force sensors capable of measuring the three orthogonal components of shroud contact forces simultaneously during the dynamic forced response tests of shrouded blade. The purpose of this study is to analyze the effectiveness of a cost effective and adaptable design configuration, calibration and decoupling process of a tri-directional force measurement system comprising of three uniaxial force sensors arranged orthogonally, that would be employed to measure static and dynamic shroud contact forces applied in three orthogonal directions simultaneously. The efficacy of orthogonal arrangement of the force sensors in a tripod configuration to reduce the mechanical coupling is investigated. The usefulness of the calibration procedure followed by the decoupling method to improve accuracy is also evaluated. Finally, the results are used to determine the feasibility of the proposed tri-directional force measurement system to measure shroud contact forces.