TABLE OF CONTENTS |
Taking into account that the curvature radius of bearings usually is bigger than the distance between their inner surface and the ultrasonic transducer, it is possible to model the bearing as a set of plane layers (Fig.1).
Fig.1. Analyzed structure water-babbitt-metal and reflected ultrasonic pulses | |||||
Table 1. The values of the reflection coefficients K_{i } in the good adhesion and the delamination cases | |||||
Reflected pulse number | |||||
0 | 1 | 2 | 3 | 4 | |
Good adhesion | |||||
Brass | 0.9225 | 0.0287 | -0.0080 | 0.0022 | -0.0004 |
Steel | 0.9225 | 0.0449 | -0.0125 | 0.0035 | -0.0006 |
Delamination | |||||
no diff. | 0.9225 | -0.1490 | -0.1375 | -0.1268 | -0.1170 |
Due to mismatch of acoustic impedances multireflections of ultrasonic pulses inside the babbitt layer take place. In Fig.1 I_{0} is the amplitude of the pulse reflected by the interface water - babbitt, I_{1}, I_{2}, I_{3} ... are the amplitudes of the multireflected pulses in the babbitt layer. Corresponding coefficients for these pulses can be expressed in terms of acoustic impedances and are equal
K_{0} = K_{wb}^{R} K_{1} = K_{wb}^{T} x K_{bm}^{R} x K_{bw}^{T} K_{i} = K_{i-1} x K_{bm}^{R} x K_{bw}^{R} I = 2,3,.... | (1) |
where superscripts denotes reflection (R) or transition (T), subscripts - material and direction (e.g. 'wb' - water/babbitt). The values of these coefficients are presented in Table 1. Acoustic impedances are taken from [2] and are for babbitt 24.8·10^{6} kg/m^{2}s, brass - 36.64·10^{6} kg/m^{2}s, steel - 46.02·10^{6} kg/m^{2}s.
From the data presented in Table 1 follows that in the case of delamination the pulses reflected inside the babbitt layer are decaying much less. The second difference is that the pulses reflected by a delamination are of an opposite polarity than the pulse reflected by the inner surface of a bearing. In the case of a good adhesion only even multireflected signals are of the opposite polarity.
The reflection coefficient K_{bm}^{R} can be expressed in terms of the ratio of the pulse amplitudes I_{0}, I_{1} or I_{1}, I_{2}. In the first case
(2) | |
assuming that K_{wb}^{T},K_{bw}^{T},K_{wb}^{R} are measured beforehand. In the second case | |
(3) |
Of course, if only the amplitude will be taken into account in both cases we shall loose the information about the sign of the reflection coefficient. Hence, the reflectivity of the interface babbitt/ metal can be evaluated from the measured ratios of the amplitudes of ultrasonic pulses reflected inside the babbitt layer and the coefficients K_{wb}^{T},K_{bw}^{T},K_{wb}^{R}.
Fig.2. The dependence of the integral reflection coefficient from the ratio
of delaminated area and ultrasonic beam crossection area |
The minimal detectable delamination area depends on the ultrasonic beam crossection area at the boundary babbitt/ metal. If the area of delaminated zone is less than the beam crossection area, the total reflected signal is the result of interference of the signals reflected from delaminated and perfectly bonded zones. In this case the amplitude of the reflected signal can be obtained from the integral reflection coefficient
_{}^{R} = S_{D} K_{1}^{d} + (S_{B} - S_{D}) x K_{1} (4)
where S_{D} is the delamination area in the beam crossection region, S_{B} is the total ultrasonic beam crossection area, K_{1}^{d} is the total reflection coefficient in the case of delamination, K_{1} is the total reflection coefficient for the pulse reflected by the boundary babbitt/metal. Note, that the reflection coefficients K_{1}^{d} and K_{1} can be positive or negative depending on the acoustic impedances of media at the particular point of the boundary. The dependence of the _{} from the ratio of delaminated and perfectly bonded covered by an ultrasonic beam is presented in Fig.2.
The minimal detectable area can be determined setting threshold level equal to 2I_{1 } for the first reflected pulse I_{1 } when a polarity of the signal is not taken into account. The minimal detectable area in this case will be approximately 0.48 / 0.58S_{B} . Using the second reflected signal I_{2 } the sensitivity can be higher and, correspondingly, minimal detectable area is approximately 0.2S_{B} . When the delaminated area covers only a part of the beam crossection region the amplitude of the first reflected pulse I_{1} can be less then the amplitude of the second reflected pulse I_{2} . This can be used as an indication that the delaminated zone does not cover the beam crossection completely.
A coverage can be evaluated taking into account that in the case of a disk transducer the ultrasonic beam spot on the boundary has a circular shape with the diameter very close to the diameter of transducer. So the maximal scanning step allowing to cover a whole surface of a bearing is equal to , where d_{t } is the transducer diameter.
The most conservative approach in the calculations of a total delamination area is to assume that at each scanner position, where the delamination was detected, the area of the delamination is equal to the area of the rectangle with the sides corresponding to scanning steps in both directions.
In order to achieve a higher accuracy of the estimation of delaminated areas it is necessary to perform scanning with a smaller step and to take into account that on the delamination edges only a part of ultrasonic beam crossection is covered by the delamination zone[2].
Fig.3. Structure of ultrasonic system for NDT of journal bearings |
The electronic unit consists of the pulse generator, the amplifier, the high speed data acquisition card with the 40MHz A/D converter, the scanner control card (SCC) and the special parallel interface for communication with the computer power supply block.
The two coordinate scanner possess two stepping motors. The minimal scanning step in the vertical direction along the axis of a bearing is 0.1mm and around the circumference is 1.8°. The test tank filled with water is used to place bearings during testing. The tank has special holders and centering mechanism enabling positioning of the bearings with an accuracy about 1 mm.
Heavily damped ultrasonic transducers with the central frequency 10MHz and the diameter 5mm are used for radiation and reception of short ultrasonic pulses. The duration of emitted ultrasonic signals is about one period. The original software have been developed to control the whole testing process. It is implemented in multiwindows mode enabling to create a convenient user interface form. The test results can be presented in the usual A,B,C scan modes with a selected option of signal processing. The bearing testing report contains a spatial distribution of delaminated zones and their total area .
The test results are presented in Fig.4 and 5. Fig.4 shows the C-scan image of the bearing. The dark areas correspond to delamination zones. There is one large defective zone near the upper edge of the bearing which shows that this bearing can not be used. The few smaller delaminated spots, shown in the middle of the image, most likely occurred during manufacturing of the bearing. The B-scan presented in Fig.5 indicates typical reverberations in the babbitt layer in the case of delamination.
Fig.6. presents C-scan image of steel shaft ceramic coating delamination which was induced by explatation.
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