# Design and Calibration of a Tri-Directional Contact Force Measurement System
## 1 Introduction  
In low pressure turbine (LPT) stages, high static loads caused by centrifugal forces and oscillating forces of working fluid result in highly pre-stressed forced vibrations [1]. In order to avoid high cycle fatigue (HCF), there is a need to estimate and reduce these vibration amplitudes. Friction damping is commonly utilized in turbomachinery [2] in the form of under platform dampers, snubbers, and shrouds to reduce the blade vibration amplitude at resonance due to its efficacy, simplicity, and reliability. In case of shrouded blades, friction forces act at the blade tip, where adjacent blade covers, called shrouds, are in contact with each other (Figure 1). Each blade shroud has therefore two contact surfaces, where tangential relative displacements determine stick/slip phenomena [3]. The frictional contact surfaces are characterized by hysteresis loops that indicate the variation of tangential contact forces with respect to relative displacements. The area bounded by the hysteresis loop depicts the energy dissipation at the contact surface and the slope of hysteresis loop defines the contact stiffness. These two parameters, i.e., the dissipated energy and contact stiffness influence the dynamic characteristics of the shrouded blade assembly. For the numerical prediction of LPT blade response levels, contact models [4; 5; 6] are implemented in nonlinear solvers for forced response analysis whose experimental validation is mandatory to describe the contact parameters accurately. For shrouded blades, the experimental validation is usually performed in test rigs where one blade is put in contact with supports that simulate the adjacent blades. Numerous experimental test rigs were developed where the dynamic response of the shrouded blades in contact was measured [7; 8; 9; 10; 11; 12; 13]. These studies emphasized on the measurement of displacements or accelerations along with the excitation forces to compute and analyze the effects of shroud contacts on vibration amplitudes and resonant frequencies. Although these methods are useful to assess the advantages offered by the shrouded blades with respect to friction damping, they do not provide a complete in-depth understanding of the dynamic behavior at the shroud contacts, as they do not measure the contact forces. On the other hand, several experimental test rigs were developed to facilitate the measurement of unidirectional [14; 15; 16; 17] and two directional contact forces [18; 19] for flat contact surfaces and under platform dampers under laboratory conditions. Apart from the dynamic response, these techniques were useful in measuring the contact parameters, i.e., the coefficient of friction and the contact stiffness of two surfaces in contact. While the two directional contact force measurement methods are limited to one normal component and one tangential component, this is not enough for shrouded blades due to the three-dimensional characteristics of shroud contacts. For this reason, the second orthogonal tangential component should also be measured. Therefore, the measurement of three directional contact forces is mandatory for a detailed representation of the shroud contact parameters and is essential for a more reliable experimental validation of the simulation tools and its effect on the system dynamics. Such an experimental setup that allows simultaneous measurement of the response of the blade and three directional contact forces between the blade shroud and adjacent supports has not yet been studied and implemented to the authors' knowledge. Hence, this study will present a design of a force measurement system capable of measuring contact forces in three directions that will be integrated in an experimental test rig to accommodate a shrouded blade with two shroud contacts. Design considerations for the tri-directional contact force measurement relies on the nature of the contact forces and the orientation of contact forces in vibrating blades depends on the vibration mode being investigated.