Analysis Of Lissajouss

Lissajous figures also called Bowditch curve, pattern produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. First studied by the American mathematician Nathaniel Bowditch in 1815, the curves were investigated independently by the French mathematician Jules-Antoine Lissajous in 1857–58. Lissajous used a narrow stream of sand pouring from the base of a compound pendulum to produce the curves. When using an oscilloscope, we can plot one sinusoidal signal along the x-axis against another sinusoidal signal along the y-axis, the result is a Lissajous figure. The oscilloscope displays a two dimensional representation of one or more potential differences. The plot is normally of voltage on the y-axis against time on the x-axis, making the oscilloscope useful for displaying periodic signals. This paper provides a broad review of the state of the art in Lissajous curve techniques, with particular regard to rotating machinery. Lissajous figure is a subject too wide-ranging to allow a comprehensive coverage of all of the areas associated with this field to be undertaken, and it is not the authors' intention to do so. However, a general overview of the broader issues of Lissajous curve is provided, it tells us about the phase difference between the two signals and the ratio of their frequencies, and several of the various methodologies are discussed. The experimental technique used Oscilloscopic with Rotor Rig; the display is usually a CRT or LCD panel which is laid out with both horizontal and vertical reference lines we can demonstrate the waveform images on an oscilloscope. The objective of this paper is to provide the reader with an insight into recent developments in the field of Lissajous curve, with particular regard to rotating machines. The subject of it in rotating machinery is vast, including the diagnosis of items such as rotating shafts, gears and pumps. When x-y mode is turned on, the second channel is displayed along the x-axis rather than the time base. For sine waves, this produces a Lissajous Figure from which it is possible to tell the phase difference between the two signals. Lissajous (pronounced LEE-suh-zhoo) figures were discovered by the French physicist Jules Antoine Lissajous. He would use sounds of different frequencies to vibrate a mirror. A beam of light reflected from the mirror would trace patterns which depended on the frequencies of the sounds. Lissajous' setup was similar to the apparatus which is used today to project laser lightshows. Before the days of digital frequency meters and phase-locked loops, Lissajous figures were used to determine the frequencies of sounds or radio signals. A signal of known frequency was applied to the horizontal axis of an oscilloscope, and the signal to be measured was applied to the vertical axis. The resulting pattern was a function of the ratio of the two frequencies. Lissajous figures often appeared as props in science fiction movies made during the 1950's. One of the best examples can be found in the opening sequence of the outer limits TV series. ("Do not attempt to adjust your picture-we are controlling the transmission.") The pattern of criss-cross lines is actually a Lissajous figure. The Lissajous Lab provides you with a virtual oscilloscope which you can use to generate these patterns. (You will control the horizontal. You will control the vertical.) The applet also allows you to apply a signal to modulate the hue of the trace, so you can create colourful designs. Source: http://www.shvoong.com/exact-sciences/physics/2415122-analysis-lissajous/#ixzz2zD36HUNW