Measurement of torsional vibration to detect angular misalignment through the modulated square wave of an encoder

One of the widely used processes to measure torsional vibration focuses on the analysis of a square signal from a device set in the machine shaft. The tools used for this purpose usually consist of a toothed wheel connected to an appropriate transducer, of an electromagnetic or optic type, which provides a square wave signal. If the rotation velocity is constant, the signal pulses are the same width, but when the velocity changes, the width of the pulses changes too, lengthening or shortening its width, resulting in a frequency modulated signal. When the shafts of the machines are misaligned angularly, the average speed changes due to variable torque action, so that spectral features of modulated signal show frequency components that are explained by the Bessel Functions. This work shows that these components are caused by a carrying (constant average speed) and a modulator signal (variable turning speed) between the harmonics surrounding the central frequency. Besides, it may also test their relationship with the presence of angular misalignment in the coupled-machine shafts. In addition, an iterative method is applied to construct the frequency spectral diagram of the induced square signal, once the appropriate modulation indices of the Bessel functions have been calculated. To compare and validate the method, different bench tests have been performed using pulse signal and laser interferometry. (paper)