Method and system for use in analyzing vibrations of a variable speed rotating body

1. A method for analyzing vibrations of a variable speed rotating body, said method comprising:

producing a signal that is proportional to an acceleration of the rotating body;

producing a plurality of pulses using a tachometer, wherein each pulse represents a revolution of the rotating body and is indicative of a vibration sample at a rotational position of the rotating body;

converting the signal to a numeric value that is indicative of a vibrational amplitude of the rotating body;

converting the plurality of pulses to revolution time periods indicative of a rotational rate of the rotating body;

calculating an angular position of the rotating body between each pulse of the tachometer to produce a harmonic vibrational amplitude at a harmonic of the rotational rate of the rotating body; and

representing a phase of the harmonic vibrational amplitude relative to the rotational position of the rotating body.

2. A method in accordance with claim 1 , further comprising calculating an angular velocity of the rotating body based on measured time periods between each tachometer pulse.

3. A method in accordance with claim 2 , further comprising calculating a velocity of the rotating body at a start of each revolution of the rotating body based on the calculated angular velocity and an angular acceleration of the rotating body.

4. A method in accordance with claim 2 , further comprising calculating a velocity of the rotating body at an end of each revolution of the rotating body based on the calculated angular velocity and an angular acceleration of the rotating body.

5. A method in accordance with claim 1 , further comprising representing the harmonic vibrational amplitude relative to the rotational position of the rotating body in polar form.

6. A method in accordance with claim 1 , further comprising generating a plot of at least one of an acceleration, a velocity, and a displacement of the rotating body.

7. A system for use in analyzing vibrations of a variable speed rotating body, said system comprising:

at least one sensor configured to produce a signal that is proportional to an acceleration of the rotating body;

at least one tachometer configured to produce a plurality of pulses, wherein each pulse represents a revolution of the rotating body and is indicative of a vibration sample at a rotational position of the rotating body; and

a processor programmed to:

convert the signal to a numeric value that is indicative of a vibrational amplitude of the rotating body;

convert the plurality of pulses to revolution time periods indicative of a rotational rate of the rotating body;

calculate a velocity of the rotating body at a start of each revolution of the rotating body based on the calculated angular velocity and an angular acceleration of the rotating body;

produce a harmonic vibrational amplitude at a harmonic of the rotational rate of the rotating body; and

represent a phase of the harmonic vibrational amplitude relative to the rotational position of the rotating body.

8. A system in accordance with claim 7 , wherein the processor is further programmed to calculate an angular velocity of the rotating body based on measured time periods between each tachometer pulse.

9. A system in accordance with claim 7 , wherein the processor is further programmed to calculate a velocity of the rotating body at an end of each revolution of the rotating body based on the calculated angular velocity and an angular acceleration of the rotating body.

10. A system in accordance with claim 7 , wherein the processor is further programmed to calculate an angular position of the rotating body between each pulse of the tachometer to produce the harmonic vibrational amplitude.

11. A system in accordance with claim 7 , wherein the processor is further programmed to represent the vibrational amplitude relative to the rotational position of the rotating body in polar form.

12. A system in accordance with claim 7 , wherein the processor is further programmed to generate a plot of at least one of an acceleration, a velocity, and a displacement of the rotating body.

13. A processor for use in analyzing vibrations of a variable speed rotating body, said processor comprising:

a converter to convert a signal from at least one sensor to a numeric value that is indicative of a vibrational amplitude of a rotating body, wherein the signal is proportional to an acceleration of the rotating body; and

a device to convert a plurality of pulses from a tachometer to revolution time periods indicative of a rotational rate of the rotating body, wherein each pulse represents a revolution of the rotating body and is indicative of a vibration sample at a rotational position of the rotating body, the processor programmed to calculate an angular position of the rotating body between each pulse of the tachometer to produce a harmonic vibrational amplitude at a harmonic of the rotational rate of the rotating body, and represent a phase of the harmonic vibrational amplitude relative to the rotational position of the rotating body.

14. A processor in accordance with claim 13 , wherein said processor is further programmed to calculate an angular velocity of the rotating body based on measured time periods between each tachometer pulse.

15. A processor in accordance with claim 13 , wherein said processor is further programmed to calculate a velocity of the rotating body at a start of each revolution of the rotating body based on the calculated angular velocity and an angular acceleration of the rotating body.

16. A processor in accordance with claim 13 , wherein said processor is further programmed to calculate a velocity of the rotating body at an end of each revolution of the rotating body based on the calculated angular velocity and an angular acceleration of the rotating body.

17. A processor in accordance with claim 13 , wherein said processor is further programmed to represent the vibrational amplitude relative to the rotational position of the rotating body in polar form.