A Novel Data-Driven Feature Extraction Strategy and Its Application in Looseness Detection of Rotor-Bearing System
Abstract
:1. Introduction
2. Data-Driven Feature Extraction
3. Data-Driven Feature Extraction of Pedestal Looseness in Rotor-Bearing System
3.1. Dynamic Modelling of a Rotor-Bearing System with Pedestal Looseness
3.2. Influence of Looseness Stiffness on Vibration Response
3.3. Data-Driven Fault Feature Extraction
4. Experimental Verification
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Values |
---|---|
Shaft diameter at left bearing/mm | 55 |
Shaft diameter at disc/mm | 55 |
The span between two bearings l/mm | 800 |
Coupling cantilever length lc/mm | 165 |
The span between the right bearing and disc l/mm | 164.5 |
Elastic modulus of shaft E/Pa | 2.07 × 1011 |
Poisson’s ratio υ | 0.3 |
Density ρ/kg/m3 | 7850 |
Horizontal and vertical stiffness of left bearing kbl/N/m | 1 × 107 |
Horizontal and vertical damping of left bearing cbl/N·s/m | 1 × 104 |
Horizontal and vertical stiffness of right bearing kbr/N/m | 2 × 108 |
Horizontal and vertical damping of right bearing cbl/N·s/m | 2 × 105 |
No. | kf2 = 1 × 109 N/m | kf2 = 1 × 108 N/m | kf2 = 5 × 107 N/m | kf2 = 1 × 107 N/m |
---|---|---|---|---|
1 | u(k − 4) [−1.81 × 10−6] | y(k − 1) [2.91] | y(k − 1) [2.84] | y(k − 1) [2.71] |
2 | u(k − 3) [5.21 × 10−6] | y(k − 2) [−3.77] | y(k − 2) [−3.57] | y(k − 2) [−3.37] |
3 | y(k − 1) [2.77] | y(k − 3) [3.27] | y(k − 3) [3.00] | y(k − 3) [2.91] |
4 | y(k − 2) [−2.09] | y(k − 4) [−2.31] | y(k − 4) [−2.05] | y(k − 4) [−2.09] |
5 | y(k − 3) [−5.32] | y(k − 5) [1.21] | y(k − 5) [9.76 × 10−1] | y(k − 5) [1.13] |
6 | u(k − 6) [−3.89 × 10−6] | y(k − 6) [−3.29] | y(k − 6) [−2.22 × 10−1] | y(k − 6) [−3.28] |
7 | y(k − 6) [−3.71 × 10−1] | u(k − 1) [1.83 × 10−2] | u(k − 1) [3.11 × 10−4] | u(k − 6) [2.33 × 10−3] |
8 | y(k − 5) [8.29 × 10−1] | u3(k − 1) u(k − 5) [3.78 × 10−9] | u3(k − 1)u(k − 6) [4.87 × 10−10] | u3(k − 6) [1.02 × 10−6] |
9 | [9.36 × 10−8] | [−3.01 × 10−3] | [−6.12 × 10−3] | [−6.58 × 10−2] |
10 | u(k − 2) [3.39 × 10−6] | u(k − 1)u(k − 2) [−1.31 × 10−5] | u(k − 1)u(k − 2) [4.42 × 10−6] | u(k − 1)u(k − 2)y(k − 1) [−1.91 × 10−5] |
11 | y(k − 4) [8.60 × 10−2] | u(k − 6) [7.26 × 10−2] | u3(k − 1) [1.46 × 10−7] | u2 (k − 6) [3.83 × 10−4] |
12 | u(k − 5) [−1.11 × 10−6] | u(k − 1)u(k − 3) [1.60 × 10−5] | u2(k − 1) y(k − 1) [−1.71 × 10−5] | u2(k − 5) [−3.73 × 10−4] |
13 | u(k − 1) [8.14 × 10−7] | u(k − 1)u2(k − 2)u(k − 4) [−4.14 × 10−9] | u(k − 1)u(k − 4)y(k − 2) [1.28 × 10−5] | u3(k − 1)y(k − 1) [1.67 × 10−7] |
14 | y3(k − 6) [−8.43 × 10−9] | u(k − 5) [−9.05 × 10−2] | u(k − 6)y2(k − 1) [−2.13 × 10−4] | u(k − 1)y(k − 1) [3.30 × 10−4] |
No. | Normal | Weak | Serious |
---|---|---|---|
1 | u(k − 1) [−3.58] | y(k − 1) [1.17] | u(k − 6) [−1.51 × 10−1] |
2 | y(k − 4) [5.24 × 10−2] | y(k − 2) [−3.58 × 10−1] | y(k − 1) [9.21 × 10−1] |
3 | y(k − 1) [5.96 × 10−1] | u(k − 1) [−5.61 × 10−1] | y(k − 2) [2.14 × 10−1] |
4 | y(k − 2) [−2.24 × 10−1] | u(k − 6)y(k − 1) [−6.66 × 10−3] | u(k − 2)u(k − 6)y(k − 2)y(k − 6) [6.34 × 10−7] |
5 | u(k − 2)u(k − 4)u(k − 6) [−2.08 × 10−2] | u(k − 4)y(k − 1) [9.08 × 10−3] | u(k − 1)u(k − 5)y(k − 2)y(k − 5) [−1.44 × 10−6] |
6 | y4(k − 6) [1.02 × 10−7] | u(k − 5)u2(k − 6)y(k − 1) [−4.73 × 10−8] | u2(k − 5)y(k − 5) [1.33 × 10−4] |
7 | u(k − 6)y3(k − 4) [−8.85 × 10−8] | u4(k − 6) [2.43 × 10−6] | u2(k − 1)u(k − 4) [−4.68 × 10−5] |
8 | y(k − 2)y(k − 6) [3.71 × 10−3] | y4(k − 1) [−3.89 × 10−7] | u(k − 3)y2(k − 2) [4.46 × 10−5] |
9 | y3(k − 1)y(k − 6) [9.41 × 10−8] | u(k − 1)y3(k − 1) [2.16 × 10−7] | u(k − 1)u2(k − 6)y(k − 6) [7.85 × 10−7] |
10 | u(k − 2)u2(k − 5) [2.07 × 10−2] | u3(k − 4) [9.76 × 10−5] | y(k − 3) [−1.91 × 10−1] |
11 | y(k − 3) y(k − 4)y2(k − 6) [−5.02 × 10−7] | y(k − 3)y3(k − 6) [−1.55 × 10−7] | u2(k − 2) [1.72 × 10−3] |
12 | u(k − 5)y2(k − 1)y(k − 4) [6.67 × 10−7] | u3(k − 1)y(k − 6) [−3.55 × 10−6] | u(k − 3)u(k − 6)y2(k − 6) [7.15 × 10−7] |
13 | u(k − 1)y(k − 4)y(k − 6) [8.57 × 10−5] | u(k − 5)y(k − 2)y(k − 6) [−3.84 × 10−5] | u(k − 2)u(k − 6)y(k − 4)y(k − 5) [−1.15 × 10−7] |
14 | y(k − 1)y2(k − 5) [2.39 × 10−6] | u(k − 3)u3(k − 6) [−2.99 × 10−6] | u(k − 3)u(k − 6)y(k − 6) [−3.52 × 10−5] |
15 | y(k − 1)y(k − 3)y2(k − 6) [1.72 × 10−7] | u2(k − 1)y(k − 1)y(k − 6) [−2.37 × 10−6] | u2(k − 1)u2(k − 5) [−1.62 × 10−6] |
16 | u(k − 4)y(k − 1)y(k − 6) [−6.14 × 10−5] | y(k − 3) [−2.14 × 10−1] | u(k − 1)u(k − 6)y(k − 2)y(k − 4) [1.94 × 10−6] |
17 | y2(k − 3)y(k − 5) [1.30 × 10−5] | u(k − 2)y3(k − 1) [−1.62 × 10−6] | y(k − 4) [−2.10 × 10−1] |
18 | u(k − 6)y(k − 3) [−3.28 × 10−3] | u2(k − 1)y(k − 5) [1.18 × 10−5] | y4(k − 3) [−2.405065 × 10−8] |
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Zhao, Y.; Lin, J.; Wang, X.; Han, Q.; Liu, Y. A Novel Data-Driven Feature Extraction Strategy and Its Application in Looseness Detection of Rotor-Bearing System. Mathematics 2023, 11, 2769. https://doi.org/10.3390/math11122769
Zhao Y, Lin J, Wang X, Han Q, Liu Y. A Novel Data-Driven Feature Extraction Strategy and Its Application in Looseness Detection of Rotor-Bearing System. Mathematics. 2023; 11(12):2769. https://doi.org/10.3390/math11122769
Chicago/Turabian StyleZhao, Yulai, Junzhe Lin, Xiaowei Wang, Qingkai Han, and Yang Liu. 2023. "A Novel Data-Driven Feature Extraction Strategy and Its Application in Looseness Detection of Rotor-Bearing System" Mathematics 11, no. 12: 2769. https://doi.org/10.3390/math11122769
APA StyleZhao, Y., Lin, J., Wang, X., Han, Q., & Liu, Y. (2023). A Novel Data-Driven Feature Extraction Strategy and Its Application in Looseness Detection of Rotor-Bearing System. Mathematics, 11(12), 2769. https://doi.org/10.3390/math11122769