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## Section 2, Basic Understanding of the Sine Wave Representation of Vibration

Note: Most people in vibration control do not need to understand this section in order to do effective vibration analyses. It has been added only for those who want to understand "why" the angle of phase indicates as it does. If your past training makes this section unnecessary, simply use phase angle for balancing or vibration analysis.

For a circle, assume the 0° and 360° positions are placed at the "3:00 o'clock" position. Also assume that degrees increase in the clockwise direction. Mentally cut the circle at the 0°/360° point and stretch it out in a horizontal line with 0° at the left end and 360° at the right end.

Now assume that the circle with the vector represents constant deflection due to the centrifugal force resulting from unbalance. Notice that at the start, with the vector at 0°, the vertical component of this force is 0. At 30°, the vertical component is larger and extended to where it crosses the 30° line. Continue this process for each 30° rotation. Notice that a wave is formed, called a sine wave. (Most readers have studied sine waves at some time in their education. However, for some this was left out. Sine waves could easily be demonstrated on either an oscilloscope or on most vibration instruments capable of displaying vibration amplitude vs time.) (The illustration being developed uses a pure sine wave. As other frequencies are also included, the sine wave is no longer "pure" and is no longer referred to as a "sine wave." Instead, the proper words become "time waveform.")

Although most people new to vibration recognize the meaning of vibration amplitude, they are not necessarily as aware that all vibrations have phase. Phase is usually measured as an angle between one point on a circle, as compared to another point. Usually, for instruments that use strobelights, the angular position for the reference mark is arbitrary, such as would be for a shaft key or a painted mark. Therefore, phase becomes meaningful only when comparing the position of the reference mark when the pickup is moved from one position to another (or when used for balancing, comparing phase from one balancing "run" to another). For instruments that display phase digitally, phase is measured as the angle between the vibration "high spot" and the position of the applied light responsive phase mark (usually tape). Some instruments use the "low spot."

To the plot, add the factor of time. As the deflection vector rotates, it takes time to get from one angular position to the other. If it takes 1/30 of a second to rotate one complete revolution, it then rotates at 1800 rpm.

However, for simplicity, imagine that the deflection force is rotating very slowly. Assume in this case, that the force is rotating once per second or 60 times per minute. The single cycle can then be laid out in units of time rather than just units of degrees. (Zero time will start out at 0° and the full cycle of 360° will be completed in one second.)

Notice in Fig. 4 that the vertical vibration reaches a maximum negative amount after the vector rotates 90°, or after 1/4 of a second elapses from the start. It will reach its maximum magnitude in the positive direction, when it rotates 270° after 3/4 of a second. This assumption is only to enable easy mental visualization. Actual timing for phase response varies with different types of instruments.

Now, assume that the vibration has a phase indication, either with a readout in degrees or through the flashing of a strobelight. Since phase via a strobelight is easier to portray graphically, it will be used for this example. If digital or meter readout in degrees is preferred, then place a reference mark at the "degree" position.

The strobelight flash lasts only about one ten thousandths of a second and, therefore, for all practical purposes it is out for all the time after the start of any cycle until 3/4 of a second elapses. With the strobe flashing at once per revolution, the rotor will appear as if it is not rotating. (Refer back to the rotor's reference mark.) As the light, in this case, flashes after 3/4 of a cycle has expired (270°), then the reference mark or key should appear to be "standing still at the 7:00 o'clock position.

Textbook Index

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