Rocket engine gear defect monitoring method

• US 6,526,356 B1
• Filed: 06/19/2001
• Issued: 02/25/2003
• Est. Priority Date: 06/19/2001
• Status: Expired due to Fees

• Current Assignee: Aerospace Corporation
• Original Assignee: Aerospace Corporation
• Inventors: DiMaggio, Samuel J., Sako, Brian H.
• Primary Examiner(s): NGHIEM, MICHAEL P
• Application Number:
  US09/884,719
• Publication Number:
  US 20030028332A1
• Time in Patent Office: 616 Days
• Field of Search: 702/35, 702/183, 702/185, 702/75, 702/76, 702/77
• US Class Current: 702/35
• CPC Class Codes: F05B 2260/96 Preventing, counteracting or reducing vibration or noise
• CPC Class Codes: G01M 13/02 Gearings; Transmission mechanisms
• CPC Class Codes: G01M 13/028 Acoustic or vibration analysis

Abstract

Vibration and tachometer measurements are used to assess the health of rotating equipment to compute and store two sided cepstrum parameters used to compare the engine performance to a class of engines for determining out-of-family performance indicating the healthy or defective nature of the engine under test. The cepstrum parameter can be viewed after static test firing of a rocket engine and analyzed for changes in the cepstrum parameter further indicating defect growth during static test firing. Engine-to-engine comparisons of vibration-related parameters can be used to provide information on abnormal gear behavior. The cepstrum is defined as the inverse discrete Fourier transform of the logarithm of two-sided autospectral density. The test method is an effective screen for determining defective rocket engine components during preflight static testing.

Claims

1. A method of generating a cepstrum parameter from a vibration signal and a periodic speed signal from a moving part of a machine, the method comprising the steps of:

receiving the vibration signal and the periodic speed signal from the moving part of the machine,

transforming the vibration signal into a Fourier spectrum vibration signal,

calculating a two-sided autospectral density from the Fourier spectrum vibration signal,

logarithmically converting the two-sided autospectral density into a logarithmic autospectral density,

inverse transforming the logarithmic signal into a cepstrum vibration signal,

generating a time signal from the periodic speed signal, and

determining the cepstrum parameter from the cepstrum signal at a time indicated by the time signal.

2. The method of claim 1 wherein,

the vibration signal is recorded as a data record x(t) divided into n_d contiguous segments of length T with each record segment x_m(t) represented in digital form with a sampling interval of Δ t, by N data values {x_mn} where n=0, . . . , N−

1 and m=1, . . . , n_d where discrete Fourier components of an mth record are defined for discrete frequencies f_k=k/T=K/NΔ

t by an X_m Fourier transform equation of $X_m<br><br>\left(f_k\right)=\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{n=0}{\overset{N-1}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>x_{\mathrm{mn}}<br><br>{\mathrm{<br><br>}}^{\frac{-\mathrm{j2}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{kn}}{N}},k=-\frac{N}{2}+1,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>},\frac{N}{2}$

where X_m(f_k) is the Fourier spectrum vibration signal.

3. The method of claim 1 wherein,

the two-sided autospectral density is calculated from a two-sided autospectral density equation of $S_{\mathrm{xx}}$

(fk)=1nd

T

 



∑

m=1nd

 





Xm

(fk)

2,k=-N2+1,…



 

,N2

where S_xx(f_k) is the two-side autospectral density.

4. The method of claim 1 wherein,

the logarithmic autospectral density is logarithmically converted from the the two-side autospectral density, the logarithmic autospectral density being a logarithm in base ten of the two-side autospectral density using a logarithmic equation of log[S_xx(f_k)] for k=−

(N/2)+1, . . . , N/2.

5. The method of claim 1 wherein,

the logarithmic autospectral density is inversely Fourier transformed into the cepstrum vibration signal using a two-sided cepstrum equation of $C_{\mathrm{yy}}$

(τ

n)=

-i

{log

 

[Syy

(fk)]}=Δ



 



f

∑

k=-N2+1N2

 



{log

 

[Syy

(fk)]}

 





j2

 



π



 



knN,

n=-N2+1,…



 

,N2

where C_yy(τ

_n) is the cepstrum vibration signal.

6. The method of claim 1 wherein the time signal generating step comprises the steps of:

detecting a movement speed signal from the periodic speed signal,

averaging the movement speed signal into an average movement speed signal, and

inverting the average movement speed signal into the time signal.

7. The method of claim 1 wherein,

the cepstrum vibration signal is in a periodic time domain,

the time signal is a value identifying a point in the periodic time domain for sampling detection a value of the cepstrum vibration signal for generating the cepstrum parameter.

8. A method of determining a defect in a machine having a moving part, the method comprising the steps of:

operating the machine during run time for producing vibrations from the moving part, the moving part moving at a periodic rate,

receiving vibration signals from the vibrations,

receiving tachometer signals indicating the periodic rate of the periodic movement of the moving part,

acquiring the vibration signals and the tachometer signals,

storing the vibration and tachometer signals,

retrieving the vibration and tachometer signals,

converting the vibration and tachometer signals into digital form and into converted vibration signals and converted tachometer signals, respectively,

transforming the converted vibration signals into a Fourier spectrum vibration signal,

calculating a two-sided autospectral density signal from the Fourier spectrum vibration signal,

logarithmically converting the two-sided autospectral density signal into a logarithmic autospectral density signal,

inverse transforming the logarithmic autospectral density signal into a cepstrum vibration signal,

detecting a speed signal from the converted tachometer signals,

averaging the speed signal into an average speed signal,

inverting the average speed signal into an average periodic time value signal,

detecting the cepstrum vibration signal at the average periodic time value signal for providing a cepstrum parameter for the machine,

repeating all of the steps for a plurality of like machines for defining a base line, and

determining when the cepstrum parameter for the machine is outside the base line for indicating the defect of the machine.

9. The method of claim 8 wherein,

the vibration signals and the tachometer signals are synchronized in time during the run time,

the cepstrum vibration signal and the average periodic time value signal are synchronized in time, and

the average periodic time value signal has an average periodic time value for locating the cepstrum parameter as a value of the cepstrum vibration signal at a time point corresponding to an instance in time during the run time.

10. The method of claim 8 wherein,

the vibration signals and the tachometer signals are synchronized in time during the run time,

the cepstrum vibration signal and the average periodic time value signal are synchronized in time, and

the average periodic time value signal has a average periodic time value for locating the cepstrum parameter as a value of the cepstrum vibration signal at a time point corresponding to an instance in time during the run time,

the method further comprising the step of:

repeating all of the method steps a plurality of times for generating a respective plurality of cepstrum parameters for the machine.

11. The method of claim 8 wherein,

the vibration signals and the tachometer signals are synchronized in time during the run time,

the cepstrum vibration signal and the average periodic time value signal are synchronized in time,

the average periodic time value signal has a average periodic time value for locating the cepstrum parameter as a value of the cepstrum vibration signal at a time point corresponding to an instance in time during the run time,

the method further comprising the steps of:

repeating all of the steps a plurality of times for generating a set of cepstrum parameters for the machine, and

comparing the test set of cepstrum parameters to the base line for determining when the test set of cepstrum parameters are within the base line for indicating a proper operation of the machine and for determining when the test set of cepstrum parameters are outside the base line for indicating the defect of the machine.

12. The method of claim 8 wherein,

the vibration signals and the tachometer signals are synchronized in time during the run time, and

the cepstrum vibration signal and the average periodic time value signal are synchronized in time, and

the average periodic time value signal has a average periodic time value for locating the cepstrum parameter as a value of the cepstrum vibration signal at a time point corresponding to an instance in time during the run time,

the method further comprising the steps of:

repeating all of the method steps a plurality of times for generating a respective plurality of cepstrum parameters for the machine as a test set of cepstrum parameters,

repeating all of the method steps a plurality of times for the machine for generating a respective plurality of cepstrum parameters through the run time as a test set of cepstrum parameters, and for generating a plurality of cepstrum parameters as a plurality of sets of cepstrum parameters respectively for the plurality of like machines for generating the base line, and

comparing the test set of cepstrum parameters to the base line of cepstrum parameters, the base line of cepstrum parameters indicating a healthy operating range for determining when the test set of cepstrum parameters are within the base line for indicating a proper operation of the machine and for determining when the test set of cepstrum parameters are outside the base line for indicating a defective operation of the machine indicating the defect.

13. The method of claim 8 wherein,

the machine is a rocket engine,

the moving part is a set of gears coupled to a rotating shaft of the rocket engine, and

the tachometer signal indicates the periodic rotation of the rotating shaft.

14. A method of determining a defect in a rocket engine having a gear box enclosing a rotating shaft with gears coupled to the rotating shaft, the method comprising the steps of:

operating the rocket engine during run time for producing vibrations from the gear box, the rotating shaft moving at a periodic rate,

receiving vibration signals from the vibrations of the gear box,

receiving tachometer signals indicating the rate of the periodic rotation of the rotating shaft,

acquiring the vibration signals and the tachometer signals, the vibration signals and the tachometer signals are synchronized in time,

recording the vibration and tachometer signals,

playing back the vibration and tachometer signals,

converting the vibration and tachometer signals into digital form into converted vibration signals and converted tachometer signals, respectively,

transforming the converted vibration signals into a Fourier spectrum vibration signal,

calculating a two-sided autospectral density signal from the Fourier spectrum vibration signal,

logarithmically converting the two-sided autospectral density signal into a logarithmic autospectral density signal,

inverse transforming the logarithmic autospectral density signal into a cepstrum vibration signal,

detecting a speed signal from the converted tachometer signals,

averaging the speed signal into an average speed signal,

inverting the average speed signal into an average periodic time value signal,

detecting the cepstrum vibration signal at the average periodic time value signal for providing a cepstrum parameter, the cepstrum vibration signal and the average periodic time value signal are synchronized in time, the average periodic time value signal has an average periodic time value for locating the cepstrum parameter as a value of the cepstrum vibration signal at a point during the run time,

repeating all of the repeating steps a plurality of times for a plurality of like rocket engines for generating sets of cepstrum values for generating a base line of normally operating rocket engines for the plurality of like rocket engines over the run time, and for generating a respective plurality of cepstrum parameters for the rocket engine as a test set of cepstrum parameters, and

comparing the test set of cepstrum parameters to the base line of normally operating like rocket engines for determining when the test set of cepstrum parameters are within the base line for indicating a proper operation of the rocket engine under test and for determining when the test set of cepstrum parameters are outside the base line for indicating a defective operation of the rocket engine under test indicating the defect.

15. The method of claim 14 further comprising the step of:

storing the base line of cepstrum parameters for the plurality of like rocket engines.

16. The method of claim 14 wherein,

the vibration signals are generated from accelerometers disposed on the gear box, and

tachometer signals are generated from a magnetic transducer disposed on the gear box.

17. The method of claim 14 wherein,

the rocket engine is a liquid propellant rocket engine.

18. The method of claim 14 wherein,

the averaging step averages time displacements between peaks of the tachometer signals, the peaks occurring at the periodic rate of the rotating shaft, the periodic rate corresponding to the revolution rate of the shaft, the average speed signal being a rotation rate value of the periodic rate.

19. The method of claim 14 wherein,

the ceptrum vibration signal detecting step detects a cepstrum peak value of the cepstrum vibration signal at a periodic time associated with the inverse of the average rotation rate of the shaft, and

the cepstrum peak value tending to increase in value as the defect in the gear box progressing towards failure of the rocket engine.

20. The method of claim 14 wherein,

the defect is a gear tooth defect of the gear.