# Thermographic Fault Diagnosis of Ventilation in BLDC Motors

## Abstract

**:**

## 1. Introduction

#### Related Work

## 2. Analyzed States of BLDC Motors

## 3. Thermographic Measurements for the BLDC

_{BLDC}

_{1}= 25 W (power of the BLDC), RAS

_{BLDC}

_{1}= 1450 rpm, RAS

_{BLDC}

_{1}= 2100 rpm (rotor angular speed), VO

_{BLDC}= 230 V/50 Hz (voltage), WE

_{FAN}= 1.6 kg (weight of the fan). The BLDC motor of the clipper has PO

_{BLDC}

_{2}= 5.4 W (power of the BLDC). The parameters of the FLIR E4 camera are as follows: temperature measuring range (−20 °C to +250 °C), resolution of images (80 × 60), its thermal sensitivity is less than 0.15 °C, and the image frequency is equal to 9 Hz. Images of 80 × 60 pixels were converted to images of 320 × 240 pixels using FLIR software. The thermal camera was vibrating in the range of 0–0.5 m/s

^{2}. Different measured thermal images were used. A movie was recorded for two devices (two fans, two clippers). The thermal imaging camera was set at the highest temperature of the analyzed state, that is, blocked ventilation of the BLDC motor at 2100 rpm. The measurements were performed after a steady state was reached so as to avoid the negative effects of transients in the damage detection method. Measurements were carried out for 30 s of operation of the motor. The parameter ε (emissivity coefficient) was equal to 0.6. The parameter ε is between 0.62–0.73 for various types of steel. Rolled sheet steel (temperature 21 °C) has an emissivity coefficient equal to 0.660. Stainless steel 303, after 42 h of heating at 527 °C (temperature 216–527 °C) has an emissivity coefficient equal of 0.620−0.730 [22]. The author selected ε = 0.6 and it was good enough for measurements. Nylon covering was used for the detection of fan faults. The nylon blocking the ventilation leads to a temperature increase (indicative of damage for many conditions), but it does not affect the thermal imaging equipment thanks to its transparency. Nylon covering was used to simulate damage, thus allowing us to implement damage detection.

## 4. The Developed Thermal Fault Diagnosis Method

#### 4.1. Common Part of Arithmetic Mean of Thermographic Images (CPoAMoTI)

- Gray-scale thermal images (256 colors, matrices 320 × 240) are grouped as training and test sets.
- Compute image of the arithmetic mean using thermal images of training set:$$clas{s}_{k}=\frac{{\displaystyle \sum _{n=1}^{n}\left|{X}_{n}\right|}}{{n}_{}},$$
**X**is the matrix of training thermal image, n is the number of training thermal images (n = 11),_{n}**class**is the arithmetic means of class with_{k}**k**index (matrix 320 × 240),**class**is the image of the arithmetic mean of training thermal images of the healthy BLDC motor at 1450 rpm,_{1}**class**is the image of the arithmetic mean of training thermal images of the healthy BLDC motor at 2100 rpm,_{2}**class**is the image of the arithmetic mean of the training thermal images of blocked ventilation of the BLDC motor at 1450 rpm,_{3}**class**is the image of the arithmetic mean of the training thermal images of blocked ventilation of the BLDC motor at 2100 rpm (4 classes for the analyzed fan)._{4} - Compute differences:
**diff**= |_{j}**class**−_{k}**class**|,_{g}**diff**is the difference of two matrices;_{j}**j**is the number of computed differences for 4 classes**j**= 6,**diff**= |_{1}**class**−_{1}**class**|,…,_{2}**diff**= |_{6}**class**−_{3}**class**|;_{4}**k**,**g**is the number of classes, for 4 classes: 1, 2, 3, 4. - Compute the following sum:$$sum\_avg={\displaystyle \sum _{j=1}^{j}\left|dif{f}_{j}\right|},$$
- Compute the value of M:M = max(
**sum_avg**),**sum_avg**. - Compute the value of m:m = p × M,
- For each training and test thermal image, compute
**C**=**TI**+**sum_avg**−**G**,**C**is the computed image;**G**is the matrix of 320 × 240, each element of matrix**G**has a value equal to m;**TI**is the training or test thermal image (matrix of 320 × 240). - In matrix
**C**, set 0 for values less than zero. The computed images are as follows: images**C1**,**C2**, …,**C44**for the training set and**C51**, …,**C290**for the test set (only for analyzed fan). - Compute image subtraction:
**d**= |_{i}**C**−_{a}**C**|,_{b}**d**is the matrix of differences between test and training thermal images (for one test image and 44 training images,_{i}**d1**,**d2**, …,**d44**are computed),**C**is the test thermal image (_{a}**C51**, …,**C290**),**C**is the training thermal image (_{b}**C1**,**C2**, …,**C44**). - Compute sums of pixel values s
_{i}for each computed matrix**d**,_{i}$${s}_{i}={\displaystyle \sum _{j=z}^{z}\left|p{v}_{z}\right|},$$_{i}is the sum of pixel values for**d**; i is the integer from 1 to 44; pv_{i}_{z}is the pixel value, z is the integer from 1 to 76,800 (320 × 240 = 76,800). - Find the lowest value of the computed sums.
- Detect the proper class of the BLDC motor.

**class**,

_{1}**class**,

_{2}**class**,

_{3}**class**are presented in Figure 15.

_{4}**sum_avg**is presented in Figure 17.

**sum_avg**is equal to 2.8784 for the considered training thermal images. This maximum is used for the equation m = p × M. The author analyzed the following p parameters: 0; 0.3; 0.5; 0.7; 0.9; 1.0. Next, step 7 was performed:

**C**=

**TI**+

**sum_avg**−

**G**. The thermal images of the healthy BLDC motor at 2100 rpm for different parameters p are shown in Figure 18.

## 5. Results of the Analysis

_{BLDC}is expressed as Equation (9):

_{BLDC}(AME

_{BLDC}) is expressed as Equation (10):

_{BLDC}

_{1}is the E

_{BLDC}for the healthy BLDC motor at 1450 rpm, E

_{BLDC}

_{2}is the E

_{BLDC}for the healthy BLDC motor at 2100 rpm, E

_{BLDC}

_{3}is the E

_{BLDC}for blocked ventilation of the BLDC motor at 1450 rpm, E

_{BLDC}

_{4}is the E

_{BLDC}for blocked ventilation of the BLDC motor at 2100 rpm.

_{BLDC}

_{5}is the E

_{BLDC}for the healthy clipper, E

_{BLDC}

_{6}is the E

_{BLDC}for blocked ventilation of the clipper.

_{BLDC}= 100% (parameter p in the range of 0–0.9). The thermographic images are very similar. However, the proposed method CPoAMoTI is good enough to correctly recognize four classes.

_{BLDC}= 100% (parameter p in the range of 0–1.0).

## 6. Discussion

^{2}. The computed results were quite good (AME

_{BLDC}= 100%) for the CPoAMoTI method. The author considered vibrations in the range of 0–0.5 m/s

^{2}for the training and test sets. Both sets were different. Thresholding of the CPoAMoTI was carried out using Equation (6). Unnecessary elements in the image (labels, temperature, scale bar) were removed. The BLDC motor was at a distance of 0.2 m from the thermal imaging camera. The distance between the thermal imaging camera and the analyzed motor, and the vibration of the thermal imaging camera have an influence on the computed results.

## 7. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Blocked ventilation of the BLDC motor at 1450 rpm (

**a**) gray-scale, (

**b**) iron scale, (

**c**) rainbow scale.

**Figure 7.**Blocked ventilation of the BLDC motor at 2100 rpm (

**a**) gray-scale, (

**b**) iron scale, (

**c**) rainbow scale.

**Figure 15.**(

**a**) Image of arithmetic mean of thermal images of the healthy BLDC motor at 1450 rpm (

**class**). (

_{1}**b**) Image of arithmetic mean of thermal images of the healthy BLDC motor at 2100 rpm (

**class**). (

_{2}**c**) Image of arithmetic mean of thermal images of the blocked ventilation of the BLDC motor at 1450 rpm (

**class**). (

_{3}**d**) Image of arithmetic mean of thermal images of the blocked ventilation of the BLDC motor at 2100 rpm (

**class**).

_{4}**Figure 16.**Computed difference: (

**a**)

**diff**= |

_{1}**class**−

_{1}**class**|, (

_{2}**b**)

**diff**= |

_{2}**class**−

_{1}**class**|, (

_{3}**c**)

**diff**= |

_{3}**class**−

_{1}**class**|. Computed difference: (

_{4}**d**)

**diff**= |

_{4}**class**−

_{2}**class**|, (

_{3}**e**)

**diff**= |

_{5}**class**−

_{2}**class**|, (

_{4}**f**)

**diff**= |

_{6}**class**−

_{3}**class**|.

_{4}**Figure 18.**Thermal image of the healthy BLDC motor at 2100 rpm (

**class**) for the parameter (

_{2}**a**) p = 0, (

**b**) p = 0.3, (

**c**) p = 0.5. Thermal image of the healthy BLDC motor at 2100 rpm (

**class**) for the parameter (

_{2}**d**) p = 0.7, (

**e**) p = 0.9, (

**f**) p = 1.0.

**Figure 19.**Computed difference

**d**: (

_{i}**a**) |test_

**class**− training_

_{2}**class**|, (

_{1}**b**) |test_

**class**− training_

_{2}**class**|. Computed difference

_{2}**d**: (

_{i}**c**) |test_

**class**− training_

_{2}**class**|, (

_{3}**d**) |test_

**class**− training_

_{2}**class**|.

_{4}State of the BLDC (Fan) | Sum of Pixel Values |
---|---|

healthy BLDC motor at 1450 rpm | 1575.6 |

healthy BLDC motor at 2100 rpm | 975.5 |

blocked ventilation of the BLDC motor at 1450 rpm | 1910.9 |

blocked ventilation of the BLDC motor at 2100 rpm | 1428.3 |

State of the BLDC | E_{BLDC} [%] |
---|---|

E_{BLDC}_{1}, healthy BLDC motor at 1450 rpm | 100 |

E_{BLDC}_{2}, healthy BLDC motor at 2100 rpm | 98.33 |

E_{BLDC}_{3}, blocked ventilation of the BLDCmotor at 1450 rpm | 100 |

E_{BLDC}_{4}, blocked ventilation of the BLDCmotor at 2100 rpm | 100 |

AME_{BLDC} [%] | |

AME_{BLDC} | 99.58 |

State of the BLDC | E_{BLDC} [%] |
---|---|

E_{BLDC}_{1}, healthy BLDC motor at 1450 rpm | 100 |

E_{BLDC}_{2}, healthy BLDC motor at 2100 rpm | 100 |

E_{BLDC}_{3}, blocked ventilation of the BLDCmotor at 1450 rpm | 100 |

E_{BLDC}_{4}, blocked ventilation of the BLDCmotor at 2100 rpm | 100 |

AME_{BLDC} [%] | |

AME_{BLDC} | 100 |

**Table 4.**Results of recognition for CPoAMoTI method (parameter p = 0–1.0) for the BLDC motor (Clipper HC5440/80).

State of the BLDC | E_{BLDC} [%] |
---|---|

E_{BLDC}_{5}, healthy clipper
| 100 |

E_{BLDC}_{6}, blocked ventilation of the clipper
| 100 |

AME_{BLDC} [%] | |

AME_{BLDC} | 100 |

Analyzed Method | MoASoID | BCAoID | CPoAMoTI |
---|---|---|---|

Type of motor | Three-phase induction motor | Commutator motor | BLDC motor |

Power of the analyzed motor | 550 W | 500 W | 25 W, 5.4 W |

Analyzed faults of the motor | electrical | mechanical | mechanical |

Temperature range of analyzed thermal images | 21–38.7 °C | 27.6–39 °C | 34.1–43.1 °C 28.7–41.9 °C |

Measurement with Vibrations | No | 0.05 m offset | Vibration 0–0.5 m/s ^{2} |

Thresholding | Binarization, 1 time | Binarization, 2 times | C = TI + sum_avg − G, negative values to 0 |

Problems with unnecessary elements in the image (label, temperature, scale bar) | Yes | No | No |

Differences | Between images of training and test sets | Between images of training and test sets | Between arithmetic means of training classes |

Number of analyzed features | 1 feature— Sum of pixels | 1 feature— Sum of pixels | Matrix 320 × 240 |

Number of analyzed classes | 3 | 3 | 4 + 2 |

Recognition | Nearest Neighbor classifier, K-means, backpropagation neural network) | Nearest Neighbor classifier and the backpropagation neural network | Difference between features (matrices C) |

Scale | Rainbow | Gray-scale | Gray-scale |

Recognition Rate (%) | 100 | 97.91–100 | 100 |

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**MDPI and ACS Style**

Glowacz, A.
Thermographic Fault Diagnosis of Ventilation in BLDC Motors. *Sensors* **2021**, *21*, 7245.
https://doi.org/10.3390/s21217245

**AMA Style**

Glowacz A.
Thermographic Fault Diagnosis of Ventilation in BLDC Motors. *Sensors*. 2021; 21(21):7245.
https://doi.org/10.3390/s21217245

**Chicago/Turabian Style**

Glowacz, Adam.
2021. "Thermographic Fault Diagnosis of Ventilation in BLDC Motors" *Sensors* 21, no. 21: 7245.
https://doi.org/10.3390/s21217245