Vibration Analysis of a Moving Probe with Long Cable for Defect Detection of Helical Tubes

Abstract

A defect detection of a heating tube installed in a power station is a very important process for avoidance of a serious disaster. The defect detection for the fast breeder reactor “Monju” in Japan is implemented by feeding an eddy current testing (ECT) probe (Isobe et al., 1995; Robinson, 1998) with a magnetic sensor, into the tube. The ECT probe (hereafter, simply called probe) is controlled so as to move in the heating tube at a constant velocity. A peculiar feature of the heating tubes in “Monju” is that each tube is mostly helical. An undesirable vibration of the probe always happened in the helical heating tube under a certain condition (Inoue et al., 2007). The vibration was considerably large and generated an obstructive noise in the signal of the magnetic sensor. It made the detection of defects difficult. Some papers reported similar problems (Bihan, 2002; Giguere et al., 2001; Tian and Sophian, 2005), but a large vibration of the probe was not involved. A key to the problem is that the noise in the signal was accompanied with the hard vibration. Several characteristics of the vibration became clear through some experiments by using a mock-up, and a countermeasure was taken by making use of the characteristics of the vibration (Inoue et al., 2007). However, an essential factor on the cause of the vibration was still unclear. Since the noise in the signal is highly correlated with the vibration, a thorough investigation of the vibration is needed. It is desirable to find out the cause of the vibration in order to remove or reduce the vibration and ensure the reliability of the inspection. In this study, the cause of the vibration is assumed to be Coulomb friction between floats, which are attached to the probe, and the inner wall of the heating tube on the basis of the experimental results. An analytical model is obtained by taking Coulomb friction into account and numerical simulation is implemented by applying a step-by-step time integration scheme. However, the analytical model has a very large number of degree of freedom. Furthermore, there are many points on which Coulomb friction acts when the probe is fed into the tube under air pressure since many floats, which are in contact with the inner wall of the heating tube, are attached to the probe. It implies that a lot of strong nonlinearities exist in the analytical model. There is no precedent for this kind of problem, and heavy computational costs are ordinarily required to carry out the numerical simulation. Sueoka et al. (1985) presented the Transfer Influence Coefficient Method (Inoue et al., 1997; Kondou et al., 1989, hereafter: TICM), which is a computational method for a dynamic