10.1111/j.1460-2695.2007.01149.x Torsion response of a cracked stainless steel shaft C. J. LISSENDEN 1 ∗ , S. P. TISSOT 1 , M. W. TRETHEWEY 2 and K. P. MAYNARD 3 1 Department of Engineering Science and Mechanics, 2 Department of Mechanical Engineering, 3 Applied Research Laboratory, Penn State, University Park, PA 16802, USA Received in final form 26 December 2006 ABSTRACT Pump shafts used for power generation are susceptible to fatigue cracking while often in near-continuous operation. Technology based on torsional vibration is under develop- ment for condition-based assessment of shaft health. The focus of this paper is on the relationship between a crack, which propagated due to bending loads, and the torsional stiffness of the shaft. An analytical method to determine the compliance associated with a crack has been implemented for a semi-elliptical surface crack. A 3-D finite element model of a shaft section with a crack has also been used to predict the effect of a crack on stiffness. Fatigue cracks were seeded in shafts on a three-point bend apparatus. A benchtop test rig was constructed to evaluate the torsional natural frequencies of a cracked shaft system. Quasistatic torsional stiffness tests indicated that crack closure has an effect on the results. A torsional finite element model of the benchtop test rig indicates that the first torsional natural frequency is reduced by the propagation of a crack. The reduction in torsional stiffness of the shaft inferred from the natural frequency results is in reasonable agreement with the quasistatic results and the model predictions. Keywords semi-elliptical surface crack, torsional stiffness, natural frequency, condition- based monitoring. INTRODUCTION The growth of fatigue cracks in rotating components in the power generation industry, especially pump shafts, is a significant economic and safety concern. 1 Fatigue cracks typically initiate at stress concentrators due to some com- bination of thermal, bending and torsional loads. In many cases the equipment is required to operate continuously for extended periods of time, highlighting the impor- tance of on-line structural health monitoring. The mea- surement of vibrational response features can be used to monitor structural damage, such as that due to a fatigue crack because crack growth decreases structural stiffness, which changes the vibrational characteristics. The work presented herein was undertaken in response to the occur- rence of fatigue cracks in reactor coolant pump shafts for nuclear power plants. In this case, the crack apparently ini- tiates at a pinhole due to thermal loading and then prop- agates due to bending stresses. These cracks have been observed to propagate as either a semi-elliptical surface ∗ Correspondence: C. J. Lissenden. E-mail: [email protected] crack or a circumferential crack. Shaft deflection-based vibration monitoring systems were ineffective in provid- ing an early warning to the plant operators. Recent work has shown the potential of torsional vibration monitoring to detect structural damage. 2,3 Laboratory tests have shown the ability to detect tor- sional natural frequency changes as successively deeper seeded faults were placed in shafts and a model bladed disk assembly. 3 However, effective prognostics require the change in torsional natural frequency to be related to the change in the shaft’s structural state (i.e., fatigue crack size). If the crack geometry can be related to the change in torsional stiffness, the shaft’s health can be directly as- sessed from the observed torsional vibration signature fea- tures. Previous work 4,5 has examined the effects of tor- sional stiffness for cuts with straight fronts, but cuts are not necessarily representative of the effects that a fatigue crack has on a shaft’s torsional stiffness. The difference is primarily due to the surface contact associated with crack closure present for a fatigue crack, but not for a cut. The effect of fatigue cracks on torsional stiffness has not been thoroughly investigated until very recently by Vaziri and Nayeb-Hashemi, 6,7 who consider circumferential cracks. 734 c 2007 The Authors. Journal compilation c 2007 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 30, 734–747
Torsion response of a cracked stainless steel shaft
May 20, 2023
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