## 2 Experimental Method
### Design of Vibration Test  
Both United Nations Recommendations on the Transport of Dangerous Goods (UN) 38.3 and SAE J2380 are common standards for the cell vibration and the shock test. The UN 38.3 standard was chosen within Ref. [17]; while regulation UN 38.3 is a legal requirement, the standard is primarily focused on emulating the worst case shock load and vibration that may be experienced by the cell. Load profiles are unrepresentative of those that would be experienced by the battery during road vehicle operation [19]. However, it is noteworthy that SAE J2380 vibration profiles defined have been synthesized from actual rough road measurement data and sequenced to emulate 100,000 miles of vehicle usage. In addition, the UN 38.3, ECE Regulation 100, SAE J2380 and BS 62660 standards were analyzed within Ref. [19]; the conclusion of the SAE J2380 standard could better reflect the actual vibration of lithium-ion cells which was obtained, and therefore the SAE J2380 standard is used in this paper. The test steps of the vertical direction (i.e., the \(Z\)-axis) are summarized in Table 1, and loading curves are presented in Figure 3  
In this paper, a short-term vibration effect on the electrical properties of batteries was researched. On the premise that no resonance occurs during the vibration process, the test was carried out based on the SAE J2380 standard, but some steps in the actual process are different compared to the standard. For example, the standard requires the SOC at 100% and 20% to be complete, but a 75% SOC was used according to the literature [23]. In addition, the standard requires both \(X\)-axis and \(Y\)-axis direction to be used to conduct a certain vibration test, but it was noted within [9; 17; 21] that the \(Z\)-axis vibration displayed a greater tendency for electrical degradation. The \(Z\)-axis profile was only loaded in this paper, in order to eliminate the influence of the non-main vibration direction on the electrical performance. However, it should be noted that, even if the battery will be affected in a single vibration direction but three directions are subjected to vibration, this does not necessarily have an impact; therefore, it can be said that the contents of Refs. [21; 23] are studied in detail. In addition, the test only considers the effect of short-term vibration on the electrical performance of the cell, and the test of long-term vibration is a  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Conditions** & **Test Conditions State of** & **Normal Test** & **Normal Test** & **Normal Test** \\
**Vibration Spectrum** & **Charge (StableOC) (\%)** & **Accel. (g rms)** & **Time (h)** & **Cumul. Time (h)** \\ \hline 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 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Test schedule.  
Figure 3: Vibration spectra for random vibration test referring to Society of Automotive Engineers (SAE) J2380 standard.  
key point of further research. The definition of directions is presented in Figure 4. The \(Z\)-direction defined by the battery is in accordance with the \(Z\)-direction defined by the electric vehicle.