# Applications of Operational Modal Analysis in Gearbox and Induction Motor, Based on Random Decrement Technique and Enhanced Ibrahim Time Method

^{*}

## Abstract

**:**

## 1. Introduction

^{TM}, was also used for validation proposes. The measured object was a four-stage centrifugal compressor. The identification of the of shaft harmonics were based on the values of the enhanced kurtosis analysis, However, the harmonics eliminations were not clear.

## 2. Methods and Procedure Analysis

#### 2.1. Experimental Modal Analysis (EMA)

#### 2.2. Random Decrement Technique (RDT)

#### 2.3. Correlation Function Estimation (CFE)

#### 2.4. Enhance Ibrahim Time Method (EITM)

_{n}are the continuous time resonances, $a$

_{n}are the mode shapes, and ${\mu}_{n}$ are the discrete resonances. The following equation describes the Hankel matrix [1]:

_{1}), it can be expressed as [1]:

_{2}can be expressed with a delay of two time steps:

#### 2.5. Measurement Set Up and Procedure Analysis

_{1}had 17, E

_{2}had 40, E

_{3}had 13, and E

_{4}had 27 teeth, respectively.

## 3. Analysis and Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The analysis procedure for Random Decrement Technique [4].

**Figure 2.**Experimental set up for gearbox’s measurements: (

**a**,

**b**) show the set of the spur gears, (

**c**) denotes the gearbox’s top view, and (

**d**) shows the gear box and mounted accelerometers.

**Figure 3.**Experimental set up for an induction (

**a**) motor and (

**b**) gearbox, placed for a free–free condition and excited by an impedance hammer.

**Figure 6.**Force and vibration signals in the time-domain: (

**a**) the impedance hammer’s force; (

**b**) vibration response.

**Figure 9.**Comparison of the induction motor’s regenerated FRFs, with varying speeds (1800, 2400 and 3000 rpm).

**Figure 10.**Comparison of the induction motor’s FRFs, with five modes at varying speeds (1800, 2400, and 3000 rpm).

**Figure 12.**Comparison of the gearbox’s FRFs, with eight modes at varying speeds (1800, 2400, and 3000 rpm).

Mode Number | |||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |

EMA [Hz] | 8 | 59 | 165 | 326 | 534 |

OMA [Hz] | - | 59 | 165 | 326 | 535 |

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**MDPI and ACS Style**

Castro, G.; Zurita, G.
Applications of Operational Modal Analysis in Gearbox and Induction Motor, Based on Random Decrement Technique and Enhanced Ibrahim Time Method. *Appl. Sci.* **2022**, *12*, 5284.
https://doi.org/10.3390/app12105284

**AMA Style**

Castro G, Zurita G.
Applications of Operational Modal Analysis in Gearbox and Induction Motor, Based on Random Decrement Technique and Enhanced Ibrahim Time Method. *Applied Sciences*. 2022; 12(10):5284.
https://doi.org/10.3390/app12105284

**Chicago/Turabian Style**

Castro, Gabriel, and Grover Zurita.
2022. "Applications of Operational Modal Analysis in Gearbox and Induction Motor, Based on Random Decrement Technique and Enhanced Ibrahim Time Method" *Applied Sciences* 12, no. 10: 5284.
https://doi.org/10.3390/app12105284