In order to achieve more accurate friction damping of turbine blades equipped with shroud covers and under-platform dampers, it is necessary to clarify such friction behaviors as tangential contact stiffness, micro-slips, and dissipated energy, under periodically varied normal force instead of constant normal force. Although some analytical studies were reported on the contact mechanics under alternating normal force, only minimal research has been conducted on the experimental verification of such behaviors, as friction tests were commonly done under constant normal force. In this study, we developed an original two-directional friction test system that can apply any combination of alternating normal and tangential forces by changing the displacement-controlled loading direction. In this system, relative displacement and contact force were measured simultaneously by using a laser Doppler displacement sensor and force transducers of the strain gage type.
By using our original test system, we examined the dissipated energy under constant normal force and periodically-varied normal force whose amplitude is the same as that of tangential force with no phase difference. We then obtained a new finding that dissipated energy depends on alternating normal force under the same mean normal force and alternating tangential force. More specifically, when the tangential force coefficient, defined as the ratio of the amplitude of alternating tangential force to mean normal force, is large enough to cause a macro-slip, dissipated energy under variable normal force is smaller than that under constant normal force. Conversely, when tangential force coefficient is small in the micro-slip region, dissipated energy under variable normal force is larger than that under constant normal force. This behavior was successfully reproduced by FE analysis based on a macro-slip model, where an array of macro-slip elements was used to describe micro-slip behavior. It was found that alternating normal force makes it easier to cause a micro-slip in a certain area of the contact surface under variable normal force, resulting in higher dissipated energy than at constant normal force when tangential force coefficient is small.
In this study, basic friction data were also obtained regarding the tangential contact stiffness with variations in contact pressure, as well as the relation between a micro-slip and the tangential force coefficient. Tangential contact stiffness increases as contact pressure increases. In addition, tangential contact stiffness increases with the nominal contact area, but is not proportional to the area. The non-dimensional slip range (corresponding to the ratio of slip range to stick displacement) was confirmed as being described in a unified form against different contact area (6 and 18 mm2) and contact pressure ranging from 3 to 40 MPa.
Closed-Form Equations for Contact Force and Moment in Elastic Contact of Rough Surfaces