Balancing of a Rotating Shaft using Computed Order Tracking

The paper presents the use of Computed Order Tracking (COT) to balance rotating machines. Shaft balancing essentially requires the measurement of amplitude and phase angle of the synchronous harmonic of the vibration signal with respect to a reference keyphasor. COT provides a tool for re-sampling a constant time sampled vibration signal to constant angle sampled signal, converting the measured nonstationary vibration signal to a stationary signal. Discrete Fourier series representation of this stationary signal helps compute the amplitude and phase angle of the harmonic component of interest. The accuracy of the COT algorithm depends on the accuracy with which the zero-crossing of the keyphasor signal is measured. An increased timing resolution has been achieved by a linear interpolation of the keyphasor signal around the zero-crossing, allowing slower keyphasor sampling rates. The present implementation samples the vibration and the keyphasor sensor signals using single data acquisition system. This allows for highly simplified and cost effective hardware requirements. Least square estimation using multiple zero-crossings helps reduce errors in the re-sampling process and provide a more robust approach. In addition, for machines that might see sub-harmonic vibrations such as in the case with fluid bearings, processing the signal over multiple cycles allows computing accurate first order phase angle and amplitudes. Cubic spline interpolation is used for re-sampling the vibration signal. The primary focus is to put together a practical algorithm that could compute the first order amplitude and phase angle to carry out shaft balancing.