Effects of Vibration on the Electrical Performance of Lithium-Ion Cells Based on Mathematical Statistics
Abstract
:1. Introduction
2. Experimental Method
2.1. Determination of Sample Size
2.2. Test Electrical Performance
2.2.1. The Program Design of Cell Sample Test
2.2.2. Measuring the 1C Discharge Capacity
2.2.3. Measurement Uncertainty of DC Resistance
2.3. Design of Vibration Test
3. Experimental Results
3.1. Effect of Vibration on 1C Discharge Capacity
3.1.1. Probability Density Function of Capacity Samples
3.1.2. Cumulative Distribution Function of Capacity Samples
3.1.3. Kolmogorov–Smirnov (K–S) Test for 1C Capacity Distribution
3.1.4. Comparison for Capacity Distribution of Samples before and after Vibration
3.2. Effect of Vibration on DC Resistance
3.2.1. Parameters Estimation Based on Samples before Vibration
Estimation of Confidence Interval for the Population Mean
Estimation of Confidence Interval for the Population Standard Variation
3.2.2. Hypothesis Testing for Samples after Vibration
Hypothesis Testing for the Internal Resistance Mean μ after Vibration
Hypothesis Testing for the Resistance Standard Variation after Vibration
4. Consistency Analysis
4.1. Feature Extraction
4.1.1. Peaks Value of Incremental Capacity (IC) Curves Phase Transformation
4.1.2. Ratio of Potentio-Charge Capacity to Galvano-Charge Capacity
4.1.3. Discharge Curve
4.2. Feature Calculation
4.3. Consistency Analysis Based on Hierarchical Clustering Method
4.3.1. Clustering Tree
4.3.2. Inconsistent Coefficient
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Test Conditions Vibration Spectrum | Test Conditions State of Charge (StableOC) (%) | Normal Test Accel. (g rms) | Normal Test Time (h) | Normal Test Cumul. Time (h) |
---|---|---|---|---|
Vertical 1 spectrum | 75 | 1.9 | 0.15 | 0.15 |
Vertical 1 spectrum | 75 | 0.95 | 3.5 | 3.65 |
Vertical 2 spectrum | 75 | 1.9 | 0.15 | 3.8 |
Vertical 2 spectrum | 75 | 0.95 | 3.5 | 7.3 |
Vertical 3 spectrum | 75 | 1.9 | 0.15 | 7.45 |
Vertical 3 spectrum | 75 | 0.95 | 3.5 | 10.95 |
Test Condition | DC Internal Resistance | ||||||
---|---|---|---|---|---|---|---|
Pre-Test | 38.03 | 39.47 | 39.07 | 39.67 | 37.40 | 38.47 | 38.00 |
36.80 | 36.60 | 36.37 | 38.23 | 37.40 | 37.83 | 36.80 | |
37.40 | 37.12 | 36.73 | 36.92 | 36.16 | 36.64 | 36.79 | |
36.23 | 34.93 | 37.56 | 37.27 | 36.66 | 36.67 | 37.61 | |
36.10 | 36.52 | 35.69 |
Test Condition | DC Internal Resistance | ||||||
---|---|---|---|---|---|---|---|
Post-Test | 37.63 | 38.87 | 38.67 | 38.63 | 37.40 | 38.43 | 38.03 |
35.57 | 37.83 | 37.20 | 38.43 | 37.83 | 38.87 | 37.20 | |
38.03 | 38.23 | 37.60 | 38.83 | 36.60 | 37.43 | 37.63 | |
36.57 | 36.17 | 39.20 | 42.44 | 38.72 | 38.52 | 40.09 | |
38.43 | 38.50 | 37.13 |
Sample Number | Capacity (mAh) | DC Resistance (mΩ) | q | A (Vs) | P1 (V) | P2 (V) | P3 (V) |
---|---|---|---|---|---|---|---|
1 | 2984.2 | 38.03 | 0.2073 | 12576.5 | 3.615 | 3.648 | 4.15 |
2 | 2967.1 | 39.47 | 0.2061 | 12498.8 | 3.624 | 3.644 | 4.126 |
3 | 2987.9 | 39.07 | 0.1975 | 12582.7 | 3.617 | 3.647 | 4.129 |
4 | 2930.4 | 39.67 | 0.2083 | 12364.4 | 3.64 | 3.66 | 4.127 |
5 | 2964.1 | 37.40 | 0.2021 | 12488.5 | 3.622 | 3.654 | 4.126 |
6 | 2965.7 | 38.47 | 0.2050 | 12491.7 | 3.622 | 3.654 | 4.128 |
7 | 2977.9 | 38.00 | 0.2038 | 12570.6 | 3.619 | 3.651 | 4.165 |
8 | 2978.7 | 36.80 | 0.1970 | 12559.1 | 3.622 | 3.656 | 4.129 |
9 | 2978.2 | 36.60 | 0.2070 | 12567.5 | 3.612 | 3.646 | 4.137 |
11 | 3002.8 | 36.37 | 0.2016 | 12666.4 | 3.606 | 3.651 | 4.129 |
12 | 2993.4 | 38.23 | 0.2024 | 12621.0 | 3.616 | 3.658 | 4.134 |
13 | 2974.7 | 37.40 | 0.2015 | 12540.5 | 3.61 | 3.655 | 4.123 |
14 | 3023.8 | 37.83 | 0.1953 | 12739.2 | 3.614 | 3.655 | 4.132 |
15 | 2982.7 | 36.80 | 0.2018 | 12582.8 | 3.606 | 3.653 | 4.134 |
16 | 3015.6 | 37.40 | 0.1975 | 12722.3 | 3.61 | 3.647 | 4.134 |
17 | 2986 | 37.12 | 0.2032 | 12584.3 | 3.6 | 3.647 | 4.147 |
18 | 2964.3 | 36.73 | 0.2063 | 12503.1 | 3.599 | 3.636 | 4.141 |
19 | 3001 | 36.92 | 0.1962 | 12637.8 | 3.596 | 3.642 | 4.123 |
20 | 2997.1 | 36.16 | 0.1972 | 12638.3 | 3.6 | 3.646 | 4.14 |
21 | 2986.2 | 36.64 | 0.1971 | 12588.7 | 3.601 | 3.635 | 4.142 |
22 | 2985.7 | 36.79 | 0.2003 | 12579.5 | 3.602 | 3.648 | 4.133 |
23 | 2980.9 | 36.23 | 0.2000 | 12577.5 | 3.596 | 3.655 | 4.134 |
24 | 2990.7 | 34.93 | 0.1922 | 12610.3 | 3.586 | 3.648 | 4.136 |
25 | 2979.1 | 37.56 | 0.2076 | 12564.5 | 3.607 | 3.644 | 4.139 |
26 | 2987.2 | 37.27 | 0.2033 | 12586.6 | 3.603 | 3.638 | 4.136 |
27 | 2988 | 36.66 | 0.1990 | 12587.7 | 3.602 | 3.648 | 4.132 |
28 | 3000.4 | 36.67 | 0.1950 | 12646.5 | 3.6 | 3.65 | 4.139 |
29 | 2997.4 | 37.61 | 0.1983 | 12626.9 | 3.607 | 3.651 | 4.141 |
30 | 2985.7 | 36.10 | 0.2007 | 12574.7 | 3.596 | 3.646 | 4.134 |
31 | 3045.4 | 36.52 | 0.1908 | 12836.2 | 3.6 | 3.636 | 4.134 |
32 | 3064.6 | 35.69 | 0.1852 | 12928.2 | 3.587 | 3.637 | 4.136 |
Sample Number | Capacity (mAh) | DC Resistance (mΩ) | q | A (Vs) | P1 (V) | P2 (V) | P3 (V) |
---|---|---|---|---|---|---|---|
1 | 2925.9 | 37.63 | 0.2222 | 12331.6 | 3.646 | 3.677 | 4.151 |
2 | 2907.4 | 38.87 | 0.2200 | 12240.2 | 3.657 | 3.685 | 4.127 |
3 | 2927.6 | 38.67 | 0.2117 | 12320.8 | 3.651 | 3.678 | 4.133 |
4 | 2854.1 | 38.63 | 0.2228 | 12036.6 | 3.689 | 3.708 | 4.143 |
5 | 2913.9 | 37.40 | 0.2157 | 12264.1 | 3.655 | 3.684 | 4.141 |
6 | 2913.4 | 38.43 | 0.2208 | 12256.3 | 3.656 | 3.686 | 4.133 |
7 | 2920.5 | 38.03 | 0.2190 | 12319.9 | 3.651 | 3.682 | 4.153 |
8 | 2930.2 | 35.57 | 0.2116 | 12340.4 | 3.643 | 3.673 | 4.12 |
9 | 2904.3 | 37.83 | 0.2226 | 12241.4 | 3.632 | 3.664 | 4.157 |
11 | 2923.8 | 37.20 | 0.2151 | 12306.2 | 3.626 | 3.655 | 4.134 |
12 | 2902.2 | 38.43 | 0.2189 | 12210.9 | 3.638 | 3.657 | 4.13 |
13 | 2890.3 | 37.83 | 0.2174 | 12160.1 | 3.631 | 3.663 | 4.124 |
14 | 2951.9 | 38.87 | 0.2114 | 12403.4 | 3.637 | 3.664 | 4.116 |
15 | 2908.9 | 37.20 | 0.2200 | 12251.6 | 3.628 | 3.662 | 4.123 |
16 | 2962.1 | 38.03 | 0.2134 | 12469.3 | 3.623 | 3.654 | 4.129 |
17 | 2927.7 | 38.23 | 0.2226 | 12328.9 | 3.634 | 3.679 | 4.144 |
18 | 2873.7 | 37.60 | 0.2277 | 12121.6 | 3.635 | 3.672 | 4.135 |
19 | 2926.9 | 38.83 | 0.2147 | 12307.9 | 3.628 | 3.661 | 4.127 |
20 | 2926.6 | 36.60 | 0.2157 | 12324.9 | 3.633 | 3.676 | 4.142 |
21 | 2912.2 | 37.43 | 0.2169 | 12260.4 | 3.635 | 3.678 | 4.131 |
22 | 2915.5 | 37.63 | 0.2207 | 12268.4 | 3.638 | 3.671 | 4.134 |
23 | 2911.3 | 36.57 | 0.2189 | 12274.7 | 3.629 | 3.663 | 4.151 |
24 | 2933.2 | 36.17 | 0.2089 | 12362.1 | 3.617 | 3.651 | 4.124 |
25 | 2890.7 | 39.20 | 0.2218 | 12189.4 | 3.621 | 3.658 | 4.138 |
26 | 2915.9 | 42.44 | 0.2185 | 12273.4 | 3.628 | 3.658 | 4.132 |
27 | 2915.2 | 38.72 | 0.2104 | 12264.9 | 3.623 | 3.654 | 4.113 |
28 | 2923.1 | 38.52 | 0.2059 | 12301.2 | 3.623 | 3.666 | 4.11 |
29 | 2907.4 | 40.09 | 0.2136 | 12227.2 | 3.636 | 3.676 | 4.144 |
30 | 2909.9 | 38.43 | 0.2166 | 12239.0 | 3.621 | 3.668 | 4.127 |
31 | 2979.8 | 38.50 | 0.2049 | 12537.5 | 3.623 | 3.659 | 4.111 |
32 | 3016.2 | 37.13 | 0.1977 | 12699.5 | 3.611 | 3.647 | 4.125 |
Cell Sample Condition | The Inconsistent Coefficient of Different Classes | ||||
---|---|---|---|---|---|
Class 5 | Class 4 | Class 3 | Class 2 | Class 1 | |
Pre-Test | 2.22 | 2.51 | 2.74 | 3.22 | 2.95 |
Post-Test | 1.30 | 2.31 | 2.60 | 3.44 | 3.10 |
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Zhang, L.; Ning, Z.; Peng, H.; Mu, Z.; Sun, C. Effects of Vibration on the Electrical Performance of Lithium-Ion Cells Based on Mathematical Statistics. Appl. Sci. 2017, 7, 802. https://doi.org/10.3390/app7080802
Zhang L, Ning Z, Peng H, Mu Z, Sun C. Effects of Vibration on the Electrical Performance of Lithium-Ion Cells Based on Mathematical Statistics. Applied Sciences. 2017; 7(8):802. https://doi.org/10.3390/app7080802
Chicago/Turabian StyleZhang, Lijun, Zhansheng Ning, Hui Peng, Zhongqiang Mu, and Changyan Sun. 2017. "Effects of Vibration on the Electrical Performance of Lithium-Ion Cells Based on Mathematical Statistics" Applied Sciences 7, no. 8: 802. https://doi.org/10.3390/app7080802
APA StyleZhang, L., Ning, Z., Peng, H., Mu, Z., & Sun, C. (2017). Effects of Vibration on the Electrical Performance of Lithium-Ion Cells Based on Mathematical Statistics. Applied Sciences, 7(8), 802. https://doi.org/10.3390/app7080802