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The second is that the number of available displacements is reduced from 8 to 4. This makes the analysis of the data become more difficult. In particular, when the blade vibration frequency is an integer multiple of the sampling rate, the number of available displacements can be reduced to 1. This decrease determines that uniform sampling is unsuitable to measure synchronous vibrations. Figure 2. (a) The uniform sampling; (b) The non-uniform sampling. Conversely, an alternative non-uniform sampling occurs by using Lapatinib in vitro eight non-equally mounted probes. As shown in Figure 2b, it is also a sum of eight periodically uniform sample streams. However, in this way, the time interval between successive samples is not constant for all samples, i.e., t3 ?t2 �� t2 ?t1. Eight points on the vibration waveform are different from each other, so that enough available information can be provided to monitor synchronous vibrations. In fact, it allows measurement of both types of blade vibrations with a reduced number of probes. Except for the above drawback of uniform selleck sampling, one should attach importance to another fact. That is, in practice, probes are hardly equally spaced in the outer casing due to minimal manufacturing tolerances. Reference [18] has investigated the frequency spectrum of such uniform BTT data. The results indicate that in this way, BTT sampling acts like non-uniform sampling. Thus, it is quite necessary to apply non-uniform BTT sampling to address the drawbacks of uniform sampling. 3.?Mathematical Model of the Non-Uniform BTT Sampling 3.1. Representation of Blade Tip Displacements As shown in Figure 1, BTT samples are acquired from I probes mounted circumferentially around a rotor with K blades. An additional probe r is mounted in front of the shaft as a reference sensor. There is a white marker line milled on the shaft, so that the reference sensor can measure the once-per-revolution signal. The relative angular position in the casing between probe 0 and probe i(0 �� i Liothyronine Sodium one will have ��k = ��0 +2��k/K,k �� 0,1,��,K?1 where generally ��0 =0. The concept of the BTT method is to measure the arrival time of the tip of a vibrating blade as it passes a probe. The expected blade arrival times for a single non-vibrating blade at any probe are determined by the rotation speed, blade tip radius and angular position of the probe. When there are vibrations, any deviations from these expected arrival times indicate blade vibrations with respect to the hub. These deviations are recorded by each probe to calculate a time-series of blade tip displacements and further used to analyze blade vibration characteristics.