This paper describes a measurement system designed to determine the hysteresis that develops between two surfaces as a result of small-amplitude tangential relative motion. Hysteresis is determined by measuring the tangential force and relative displacement of the contacting surfaces as they oscillate. These measurements also produce values of contact parameters such as friction coefficient and tangential contact stiffness. Although these parameters depend on the tribological properties, most of them also exhibit strong sensitivity to measurement errors. The measurement system described here avoids or at least reduces many of the measurement artifacts. This paper validates the measurement system by analyzing and estimating potential errors and describes corrections to systematic errors where possible.
This paper discusses approach for characterizing the dynamic behavior of a friction damper. To accomplish this, the deflection of the damper is measured as a function of an applied force for a range of amplitudes, normal loads, and excitation frequencies. The resulting hysteresis curves are used to generate curves of nonlinear stiffness and damping as a function of the amplitude of motion. A method of presenting this information in a dimensionless format is demonstrated. This format allows direct comparisons of the nonlinear stiffness and damping of actual dampers with that often used in analytical models to compute the dynamic response of frictionally damped turbine blades. It is shown that for the case of a damper with a spherical head significant differences exist between the actual behavior of the damper and that often assumed in simple analytical models. In addition, Mindlin’s analysis of a sphere on a half space is used to estimate the damper’s stiffness as well as its theoretical hysteresis curves. The hysteresis curves are then used to determine dimensionless stiffness and damping curves. The results compare favorably with those found experimentally.
Ceramic coatings applied by air plasma spray or electron beam techniques as thermal barrier coatings or to improve the erosion or corrosion resistance of blades in gas turbine engines are found to add damping to the system. However, such coatings display nonlinear mechanical properties in that the Young’s modulus and the measure of damping are dependent on the amplitude of cyclic strain. To account for the coating nonlinearity, a new methodology for predicting blade response was developed and applied to an actual component coated with a titania-alumina blend ceramic infiltrated with a viscoelastic material. Resonant frequencies, mode shapes, and the forced response of a one blade segment of an integrated disk from a fan stage rotor were computed and compared with results from bench tests. Predicted frequencies agreed satisfactorily with measured values; predicted and observed values of system damping agreed to within 10%. The results of these comparisons are taken to indicate that it is possible to use laboratory-determined material properties together with an iterative finite element analysis to obtain satisfactory predictions of the response of an actual blade with a nonlinear coating.
In this work, an integrated testing and calibration procedure is presented for performing mistuning identification (ID) and traveling wave excitation (TWE) of one-piece bladed disks (blisks). The procedure yields accurate results while also being highly efficient and is comprised of three basic phases. First, selected modes from a tuned blisk finite element model are used to determine a minimal set of measurement degrees of freedom (and locations) that will work well for mistuning ID. Second, a testing procedure is presented that allows the mistuning to be identified from relatively few vibration response measurements. A numerical validation is used to investigate the convergence of the mistuning ID results to a prescribed mistuning pattern using the proposed approach and alternative testing strategies. Third, a method is derived to iteratively calibrate the excitation applied to each blade so that differences among the blade excitation magnitudes can be minimized for single blade excitation, and also the excitation phases can be accurately set to achieve the desired traveling wave excitation. The calibration algorithm uses the principle of reciprocity and involves solving a least squares problem to reduce the effects of measurement noise and uncertainty. Because the TWE calibration procedure re-uses data collected during the mistuning ID, the overall procedure is integrated and efficient.
This paper discusses an approach for characterizing the dynamic behavior of a friction damper. To accomplish this, the deflection of the damper is measured as a function of an applied force for a range of amplitudes, normal loads, and excitation frequencies. The resulting hysteresis curves are used to generate curves of nonlinear stiffness and damping as a function of the amplitude of motion. A method of presenting this information in a dimensionless format is demonstrated. This format allows direct comparisons of the nonlinear stiffness and damping of actual dampers with that often used in analytical models to compute the dynamic response of frictionally damped turbine blades. It is shown that for the case of a damper with a spherical head significant differences exist between the actual behavior of the damper and that often assumed in simple analytical models. In addition, Mindlin’s analysis of a sphere on a half space is used to estimate the damper’s stiffness as well as its theoretical hysteresis curves. The hysteresis curves are then used to determine dimensionless stiffness and damping curves. The results compare favorably with those found experimentally.
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