The Thermal Error Estimation of the Machine Tool Spindle Based on Machine Learning
Abstract
:1. Introduction
2. Methodology
2.1. Spindle Running-in Setup
2.2. Feature Temperature Measurement
2.3. Thermal Error Measurement
2.4. Training Data and Validation Data
2.5. Thermal Error Modeling by Machine Learning
2.5.1. Gaussian Process Regression (GPR)
- Use the “Import Data” to import the training data sets and the testing data sets;
- Choose the “Machine Learning and Deep Learning” variety in the App toolbar, and then use the “Regression Learner”;
- Choose a training data set, set the thermal error data to response, set the temperature data to predictors, and set “validation” to prevent the model from overfitting;
- Choose the Exponential of Gaussian Process Regression, one can use “Advanced” to adjust the training parameters;
- Click “Export Model”, input testing data set to the model to get a response, get mean error and accuracy by calculating the true value, and predicted value based on the testing data set.
2.5.2. Random Forests (RF)
3. Results
3.1. Thermal Error Model Based on Gaussian Process Regression
3.2. Thermal Error Model Based on Random Forest
3.3. Feature Temperature Points Selection by Pearson Correlation Coefficient (PCC)
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
References
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Specification of the Temperature Sensor Probe | Specification of the Laser Displacement Meter | ||
---|---|---|---|
Sensor type | PT1000 (A class) | Sensor type | Keyence LK-055 |
Accuracy (°C) | ±(0.15 ± 0.002|t|) | Reference distance (mm) | 50 |
Measurement range (°C) | −50 to 300 | Measurement range (mm) | ±10 |
Excited current limit (mA) | ≤5 | Light source | Red semiconductor laser |
Thermal response (s) | ≤0.3 @ air | Wave length (nm) | 655 |
Package material | Stainless steel 304 | Light spot diameter (μm) | 50 × 2000 |
Protection level | IP 65 | Linearity | ±0.02% |
Repeatability (μm) | 0.025 | ||
Sampling time (μs) | 20 | ||
Package material | Al | ||
Protection level | IP 67 |
Data Group | Data Set | Speed (rpm) |
---|---|---|
Training group | T5000,1, T5000,2, T5000,3 | 5000 |
T6000,1, T6000,2, T6000,3 | 6000 | |
T7000,1, T7000,2, T7000,3 | 7000 | |
T8000,1, T8000,2, T8000,3 | 8000 | |
Tvar,1, Tvar,2, Tvar,3 | 5000→6000→7000→8000 | |
Validation group | V5000,1, V5000,2, V5000,3 | 5000 |
V6000,1, V6000,2, V6000,3 | 6000 | |
V7000,1, V7000,2, V7000,3 | 7000 | |
V8000,1, V8000,2, V8000,3 | 8000 | |
Vvar,1, Vvar,2, Vvar,3 | 5000→6000→7000→8000 |
No. F. Pt. 1 | ME2 (μm) | RMSE3 (μm) | R2 * | Accuracy |
---|---|---|---|---|
2 | 1.6423 | 1.7481 | 0.9884 | 88.92% |
3 | 1.6128 | 1.6860 | 0.9888 | 89.09% |
4 | 1.5960 | 1.7098 | 0.9888 | 89.19% |
5 | 1.5595 | 1.6805 | 0.9889 | 89.45% |
6 | 1.5769 | 1.6759 | 0.9894 | 89.38% |
7 | 1.5458 | 1.6557 | 0.9899 | 89.57% |
8 | 1.5374 | 1.6734 | 0.9906 | 89.64% |
9 | 1.5145 | 1.6539 | 0.9905 | 89.71% |
10 | 1.5160 | 1.6573 | 0.9910 | 89.62% |
No. F. Pt. 1 | ME 2 (μm) | RMSE 3 (μm) | R2 * | Accuracy |
---|---|---|---|---|
2 | 1.5728 | 1.6633 | 0.9914 | 89.41% |
3 | 1.5730 | 1.6656 | 0.9909 | 89.41% |
4 | 1.5273 | 1.6402 | 0.9905 | 90.49% |
5 | 1.5167 | 1.6474 | 0.9901 | 89.61% |
6 | 1.5125 | 1.6417 | 0.9902 | 89.62% |
7 | 1.5140 | 1.6495 | 0.9898 | 89.61% |
8 | 1.5129 | 1.6482 | 0.9899 | 89.62% |
9 | 1.5130 | 1.6490 | 0.9898 | 89.62% |
10 | 1.5181 | 1.6506 | 0.9898 | 89.60% |
Paper | M. L. Model * | F. Pt. Selection * | No. F. Pt. * | ME * | RMSE * | R2 * | Accuracy * |
---|---|---|---|---|---|---|---|
This paper | RF ** | PCC *** | 4 | 1.5273 | 1.6402 | 0.9905 | 90.49% |
GPR ** | PCC | 4 | 1.5960 | 1.7098 | 0.9888 | 89.19% | |
[16] | DCM ** | IGM *** | 4 | 3.62 | - | - | - |
[17] | Mallows’ Cp | CC *** | 4 | - | - | 0.982 | 89% |
[19] | MLR ** | FCM *** | 4 | 1.8 | - | - | - |
[20] | MLR | KHM *** | 3 | - | 6.9690 | 0.9356 | 90.86% |
[21] | GI ** | - | 9 | - | 2.4928 | - | 93% |
[22] | LS ** | SRCC *** | 11 | - | - | - | 85% |
[23] | RBF ** | CC | 5 | - | 2.4 | - | 75% |
[29] | BNN ** | FCM | 3 | 1.741 | 1.998 | 0.807 | 74.1% |
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Chiu, Y.-C.; Wang, P.-H.; Hu, Y.-C. The Thermal Error Estimation of the Machine Tool Spindle Based on Machine Learning. Machines 2021, 9, 184. https://doi.org/10.3390/machines9090184
Chiu Y-C, Wang P-H, Hu Y-C. The Thermal Error Estimation of the Machine Tool Spindle Based on Machine Learning. Machines. 2021; 9(9):184. https://doi.org/10.3390/machines9090184
Chicago/Turabian StyleChiu, Yu-Cheng, Po-Hsun Wang, and Yuh-Chung Hu. 2021. "The Thermal Error Estimation of the Machine Tool Spindle Based on Machine Learning" Machines 9, no. 9: 184. https://doi.org/10.3390/machines9090184