Kunio Asai

Mechanical Approach for Predicting Fretting Fatigue Strength

Stress distribution at the contact edge is known to have a dominant influence on fretting fatigue strength. Stresses acting on the contact surface are tangential stress and compressive stress. In the present study, fretting fatigue strengths of 12 Cr steel specimen under two different mean stresses have been predicted based on the generalized tangential stress range - compressive stress range diagram. The generalized tangential stress range - compressive stress range diagram was obtained by carrying out fretting fatigue tests and finite element analysis using various steel specimens with various geometries of contact pad from the previous studies. The predicted fretting fatigue strengths were in good agreement with the experimental results.

Evaluation of Friction Damping in Dovetail Root Joints Based on Dissipation Energy on Contact Surfaces

It is necessary to increase and estimate friction damping at contact interfaces to reduce vibratory stresses in turbines. The hysteresis behavior between tangential contact force and relative displacement should be precisely estimated to improve the accuracy of fiction-damping estimates. There is a difficulty in establishing a general model of hysteresis because tangential contact stiffness depends on many parameters, such as normal contact force, contact geometry, surface roughness, and wear status. We discuss a procedure to empirically calculate friction damping in dovetail root joints using the tangential contact stiffness estimated from measured natural frequencies and the micro-slip model whose coefficients were experimentally obtained from special fretting tests. Instead of the multi-harmonic balance methods, we calculated the friction damping on the basis of the energy dissipation at contact surfaces to discuss the effects of the tangential contact stiffness on several physical values, i.e., tangential and normal contact forces, natural frequency, and micro-slip. In our model, the linear forced response analysis was conducted by taking into consideration the non-linearity between the tangential contact force and the relative displacement by defining the actual and imaginary tangential contact stiffness. We confirmed that the numerically calculated damping ratios are quantitatively in very good agreement with the measured ones under different contact angles, input gravity levels, and contact forces. This indicates that if the tangential contact stiffness is accurately estimated, friction damping with our method can be precisely estimated under different test conditions. We also showed that the estimated tangential contact stiffness for dovetail root joints are smaller than those obtained by the fretting tests at high input gravity. This is probably because the contact interface partially separates during a cyclic loading in the former case; this results in the decrease of the contact area and contact stiffness.Copyright

Experimental Verification of Friction Behaviors Under Periodically-Varied Normal Force by Developing a Two-Directional Friction Test System

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.Copyright

Experimental Validation of Fretting Fatigue Strength and Fretting Wear Rate at Contact Surface of Turbine-Blade-Shroud Cover

In continuously coupled blade structures, fretting fatigue and wear have to be considered as supposed failure modes at the contact surface of the shroud cover, which is subject to steady contact pressure from centrifugal force and the vibratory load of the blade. We did unique fretting tests that modeled the structure of the shroud cover, where the vibratory load is only carried by the contact friction force, i.e., a type of friction. What was investigated in this study are fretting fatigue strength, wear rate, and friction characteristics, such as friction coefficient and slip-range of 12%-Cr steel blade material. The friction-type tests showed that fretting fatigue strength decreases with the contact pressure and a critical normal contact force exists under which fretting fatigue failure does not occur at any vibratory load. This differs from knowledge obtained through pad-type load carry tests that fretting fatigue strength decreases with the increase of contact pressure and that it almost saturates under a certain contact pressure. Our detailed observation in the friction-type tests clarified that this mechanism was the low contact pressure narrowing the contact area and a resulting high stress concentration at a local area. The fretting wear rate was explained by the dissipated energy rate per cycle obtained from the measured hysteresis loop between the relative slip range and the tangential contact force. It was found that the fretting wear rate is smaller than the wear rate obtained by one-way sliding tests, and the former is much smaller than the latter as the dissipated energy decreases. Finally, to prevent fretting fatigue and wear, we propose an evaluation design chart of the contact surface of the shroud cover based on our friction-type fretting tests.

Corrosion Fatigue Life Evaluation Method for the Bladed Disk Attachments of Low-Pressure Steam Turbine

The mechanism of disk cracking was investigated and an evaluation method for its failure occurrence rate was developed. It was found that the disk cracking was caused by the corrosion pit growth, the superposition of the multiple vibration modes, and the increase in the scatter of the natural frequency due to the interface condition change after long-term operation. The effects of several uncertainties on the failure occurrence rate were examined and the values of the uncertainties were obtained by solving the inverse problem according to the failure analysis; the examined uncertainties were the standard deviation of the natural frequency and the stimulus ratio. It is recommended to perform the replica inspection by removing the blades and to take the proper maintenance actions based on the remaining life evaluations because relatively small corrosion pits can cause crack initiation. It was found that a continuous cover blade is superior to the conventional tenon-shroud-type grouped blade because the former reduces resonance points in the interference diagram and eliminates any tangential modes which are main contributors for the disk cracking.Copyright