An Analysis of the Influence of Surface Roughness and Clearance on the Dynamic Behavior of Deep Groove Ball Bearings Using Artificial Neural Networks
Abstract
:1. Introduction
2. Materials and Methods
2.1. Analysis of Measured Data
2.2. Application of the Neural Network
2.3. Organization of Data Set
2.4. Data Pre-Processing and Defining Datasets for Training, Validation and Testing
2.5. Analyzed Models of Artificial Neural Networks
2.6. Method of Training Artificial Neural Networks
2.7. Description of the Training Algorithm
2.8. Selection of Artificial Neural Network Models
3. Results and Discussion
3.1. Prediction of Quality Classes of Bearing
3.2. Influence of the Surface Roughness of the Outer Ring
3.3. Influence of the Surface Roughness of the Inner Ring
3.4. The Influence of Equivalent Surface Roughness and Radial Clearance
4. Conclusions
- The adopted models are capable of predicting the quality class for new ball bearings and can reduce time required for quality control in bearing production;
- The increase in roughness on the outer raceway causes a significant increase in the vibration level in the medium-frequency band (300–1800 Hz) and a moderate increase in the low-frequency band (50–300 Hz), whereas the change in vibration level in the high-frequency band is negligibly small;
- An increase in surface roughness on the raceway of the inner ring has a negligible effect on the amplitude of the vibration velocity in the low-frequency band, and causes a moderate increase in the medium and high band. The growth in the newly introduced parameter of the equivalent roughness of the raceway affects the moderate growth in the amplitudes of the vibration velocity in the low-frequency band. In the medium-frequency band, the model predicts global minimum vibration velocities at an equivalent roughness amplitude of 0.1 µm. In the high-frequency band, there is a slight decrease in the velocity of vibrations with an increase in the amplitude of the equivalent roughness;
- The neural network model predicted that the minimum vibration level is obtained in all frequency bands if the radial clearance has amplitude of around 20 µm and the equivalent roughness has an amplitude of around 0.05 µm.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Bearing Characteristics | Minimum Value xmin | Maximum Value xmax | Mean Value | Standard Deviation s |
---|---|---|---|---|
Gr, [µm] | 6 | 51 | 24.03 | 14.54 |
Ri/Re | 0.95 | 0.98 | 0.96 | 0.01 |
Rae, [µm] | 0.07 | 0.28 | 0.13 | 0.04 |
Rai, [µm] | 0.07 | 0.56 | 0.26 | 0.1 |
Wte max, [µm] | 0.1 | 1.97 | 0.8 | 0.32 |
Wti max, [µm] | 0.25 | 0.66 | 0.39 | 0.13 |
Wte, [µm] | 1.5 | 17.82 | 5.01 | 2.86 |
Wti, [µm] | 0.4 | 2.63 | 0.92 | 0.41 |
Bearing Characteristics | Minimum Value xmin | Maximum Value xmax | Mean Value | Standard Deviation s |
---|---|---|---|---|
Ra ekv | 0.04 | 0.14 | 0.08 | 0.02 |
Wt max ekv | 0.16 | 0.47 | 0.25 | 0.06 |
Wt ekv | 0.36 | 1.78 | 0.74 | 0.26 |
Analyzed Artificial Neural Network Models | |||||
---|---|---|---|---|---|
Technological Parameters Separately | Technological Parameters Equivalent | ||||
Training algorithm | Training algorithm | ||||
Levenberg– Marquardt | Bayesian Regularization | Scaled Conjugate Gradient | Levenberg– Marquardt | Bayesian Regularization | Scaled Conjugate Gradient |
ANN architecture | ANN architecture | ||||
One hidden layer (Number of neurons from 1 to 30) | One hidden layer (Number of neurons from 1 to 30) | ||||
Two hidden layers (Number of neurons from 1 to 30) | Two hidden layers (Number of neurons from 1 to 30) | ||||
Three hidden layers (Number of neurons from 1 to 30) | Three hidden layers (Number of neurons from 1 to 30) |
Bearing 6006 | RMS of Vibration Velocity, µm/s Class Q7 | RMS of Vibration Velocity, µm/s Class Q6 | RMS of Vibration Velocity, µm/s Class Q5 |
---|---|---|---|
Low-frequency band | 224 | 112 | 71 |
Medium-frequency band | 160 | 80 | 80 |
High-frequency band | 450 | 224 | 112 |
Test Sample 1 Rae 0.09 µm | Test Sample 2 Rae 0.072 µm | Test Sample 3 Rae 0.125 µm | Test Sample 4 Rae 0.168 µm | |||||
---|---|---|---|---|---|---|---|---|
Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | |
Low-frequency band | 80 Q6 | 105 Q6 | 60 Q6 | 103 Q6 | 73 Q6 | 108 Q6 | 97 Q6 | 83 Q6 |
Medium-frequency band | 56 Q5 | 62 Q5 | 57 Q5 | 61 Q5 | 83 Q6 | 77 Q5 | 82 Q6 | 110 Q6 |
High-frequency band | 121 Q6 | 119 Q6 | 107 Q5 | 118 Q6 | 115 Q6 | 118 Q6 | 132 Q6 | 117 Q6 |
Test Sample 1 Rai 0.073 µm | Test Sample 2 Rai 0.157 µm | Test Sample 3 Rai 0.179 µm | Test Sample 4 Rai 0.271 µm | |||||
---|---|---|---|---|---|---|---|---|
Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | Measured RMS of Vibration Velocity, µm/s, Class Quality | Predicted RMS of Vibration Velocity, µm/s, Class Quality | |
Low-frequency band | 80 Q6 | 105 Q6 | 60 Q6 | 110 Q6 | 73 Q6 | 111 Q6 | 97 Q6 | 111 Q6 |
Medium-frequency band | 56 Q5 | 71 Q5 | 57 Q5 | 71 Q5 | 83 Q6 | 78 Q5 | 82 Q6 | 84 Q6 |
High-frequency band | 121 Q6 | 113 Q6 | 107 Q5 | 115 Q6 | 115 Q6 | 116 Q6 | 132 Q6 | 117 Q6 |
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Knežević, I.; Rackov, M.; Kanović, Ž.; Buljević, A.; Antić, A.; Tica, M.; Živković, A. An Analysis of the Influence of Surface Roughness and Clearance on the Dynamic Behavior of Deep Groove Ball Bearings Using Artificial Neural Networks. Materials 2023, 16, 3529. https://doi.org/10.3390/ma16093529
Knežević I, Rackov M, Kanović Ž, Buljević A, Antić A, Tica M, Živković A. An Analysis of the Influence of Surface Roughness and Clearance on the Dynamic Behavior of Deep Groove Ball Bearings Using Artificial Neural Networks. Materials. 2023; 16(9):3529. https://doi.org/10.3390/ma16093529
Chicago/Turabian StyleKnežević, Ivan, Milan Rackov, Željko Kanović, Anja Buljević, Aco Antić, Milan Tica, and Aleksandar Živković. 2023. "An Analysis of the Influence of Surface Roughness and Clearance on the Dynamic Behavior of Deep Groove Ball Bearings Using Artificial Neural Networks" Materials 16, no. 9: 3529. https://doi.org/10.3390/ma16093529