Analysis and Characterization of Expansion Force in Cylindrical Lithium Cells

1. Why Cylindrical Cell Expansion Matters

Although radial swelling of a steel shell cylindrical cell is small (microns), internal volume changes still occur from:

• SEI growth, gas generation, and side reactions (irreversible volume increase);

• Reversible lattice changes during lithiation/delithiation (small elastic volume changes);

• Mechanical particle fracture and electrode redistribution.

These internal changes affect cell internal stress, contact between the jelly-roll and shell, and long-term safety and capacity retention. Quantifying expansion behavior in cylindrical pressure cells helps manufacturers optimize cell design, pre-loading, and thermal/mechanical management.

2. Test Information

2.1 Experimental Equipment

Equipment: IEST SWE2100 in-situ swelling testing system (constant-gap mode), as shown in Figure 1.

Procedure overview: Remove the metal can in controlled dry conditions, extend the tabs, rewrap with flexible film, place the core between ceramic plates, and use SWE2100 to measure expansion force vs state of charge (SOC). This procedure preserves the internal structure while enabling an analog measurement of the steel shell’s mechanical constraint.

Figure 1. Schematic diagram of the IEST SWE2100 in-situ swelling testing system, used in constant-gap mode to measure cylindrical cell expansion force.

3. Result Analysis

3.1 Expansion Analysis of Cylindrical Cells

Under the action of internal pressure \(P_i\), a cylindrical cell‘s steel shell is subjected to three primary stresses (Figure 2):

• \(\sigma_a\): Axial stress affecting cell height.

• \(\sigma_r\): Radial stress acting perpendicular to the shell surface.

• \(\sigma_t\): Circumferential stress causing changes in shell perimeter.

Figure 2. Cylindrical cell steel shell stress decomposition into axial (σ_a), radial (σ_r), and circumferential (σ_t) components under internal pressure.

Using thick-walled cylinder shear stress theory, the three stresses were calculated for a sample 3665 cylindrical lithium cell (inner diameter = 17.7 mm, outer diameter = 18.0 mm). Under an assumed internal pressure of 1.0 MPa, results showed:

• \(\sigma_r\) = -0.1 MPa

• \(\sigma_t\) = 52.6 MPa

• \(\sigma_a\) = 26.2 MPa

\[\sigma_r = \frac{p_i r_i^2 – p_0 r_0^2}{r_0^2 – r_i^2} – \frac{r_i^2 r_0^2 (p_i – p_0)}{r^2 (r_0^2 – r_i^2)} \qquad \text{(1)}\]

\[\sigma_t = \frac{p_i r_i^2 – p_0 r_0^2}{r_0^2 – r_i^2} + \frac{r_i^2 r_0^2 (p_i – p_0)}{r^2 (r_0^2 – r_i^2)} \qquad \text{(2)}\]

\[\sigma_a = \frac{p_i r_i^2 – p_0 r_0^2}{r_0^2 – r_i^2} \qquad \text{(3)}\]

\[\varepsilon_t = \frac{\sigma_t – \nu \sigma_a}{E} \qquad \text{(4)}\]

\[\Delta r = 2r \cdot \varepsilon_t \qquad \text{(5)}\]

Ignoring the influence of \(\sigma_r\), the change in shell diameter is obtained by combining the stress-strain law of the steel shell (Formula ④) with the circumference formula (Formula ⑤). Assuming an elastic modulus \(E = 210\) GPa and a Poisson’s ratio \(\nu = 0.3\) for the steel shell, the calculated radial expansion is approximately \(9.4\ \mu\mathrm{m}\) at full charge (internal pressure \(P_i = 1.2\) MPa). Returning to the fully discharged state (\(P_i = 1.0\) MPa), the radial expansion is approximately \(7.7\ \mu\mathrm{m}\) — giving a charge-discharge radial expansion swing of approximately \(1.7\ \mu\mathrm{m}\) for this 3665 cell format.

Calculated charge-discharge deformation for other common cylindrical battery cell formats under this same method is shown in Table 1. Across formats, there is essentially no measurable radial expansion of the cylindrical cell during charging and discharging at the micron scale predicted by this model. In practice, the internal pressure after formation may not reach 1.0 MPa, and some cell formats are formed before final sealing — meaning actual deformation is typically smaller than the calculated values in Table 1.

Thickness variations are particularly pronounced in flexible pouch cells with aluminum-plastic film shells, where measurements are easily achieved. However, due to the structural rigidity of the hardshell body, cylindrical cells exhibit much smaller diameter expansion (~0.1%), making reversible and irreversible diameter changes difficult to observe directly. Nonetheless, irreversible layer growth — such as the SEI layer and Li plating — alongside gassing from side reactions that increases internal shell pressure, means the cell core inside the shell does expand and contract during charging and discharging, even though the shell itself barely moves. Understanding the mechanical processes occurring inside a sealed cylindrical pressure cell requires suitable measurement methods to record and analyze parameters such as electrode thickness and component volume change.

Evaluating the structural characteristics of a cell typically uses methods such as X-ray imaging, computed tomography, neutron imaging, and ultrasound imaging to obtain comprehensive information on strain, stress distribution, and structural strength. While powerful, these techniques are generally restricted to offline diagnostic use due to the need for specialized equipment, high cost, and the inevitable interference high-energy sources can cause during battery operation.

3.2 Characterization of the expansion force of cylindrical cells

Given that cylindrical cells are essentially non-expanding in the radial direction, they cannot be monitored directly from the outside of the cell. The expansion changes in Table 1 are comparable to the controlled fluctuations of ±1μm in the constant gap mode of IEST in-situ swelling analysis system (SWE2100), so the SWE2100 equipment can be used to simulate the binding of the cylindrical cell shell on the core, thus realizing the characterization of the expansion force of the cylindrical cell.

The pre-testing process is shown in Figure 4: in a glove box or dry room, the outer steel shell is removed, the tabs are extended, and finally the cell core is re-encapsulated with flexible aluminum-plastic film.

Figure 4. Pre-treatment flow for a cylindrical cell: steel shell removal, tab extension, and re-encapsulation in flexible film for SWE2100 testing.

During the test, the cell core is placed directly in the test chamber between two ceramic plates. The test software (MISS2.1) is configured to constant-gap mode, monitoring expansion force as a function of SOC in situ (Figure 5).

Figure 5. Expansion force vs SOC for different cylindrical cell models, measured by the SWE2100 in constant-gap mode.

This method primarily monitors the deformation process of the cylindrical cell during charging and discharging. As shown in Figure 6, cylindrical cells — unlike the flexible aluminum-plastic film shells of pouch batteries — have rigid metal shells that impede the release of stresses generated by internal expansion. Non-uniform contact between the metal shell and the internal jelly-roll leads to tiny loose-contact regions, resulting in uneven stress distribution. In the early stages of cycling (new batteries), the volume expansion mechanism follows Figure 6a: the cell surface is initially relatively circular, and the internal stress distribution transfers to the metal case when the cell is fully charged, creating a non-uniform expansion pattern. Due to the structure of the wound cell core, radially protruding expansion produces shrinkage depressions on the metal case. As cycling proceeds, accumulating irreversible expansion permanently fixes and reinforces this peak-valley structure, bringing the case into closer contact with the interior, as shown in Figure 6b.

Figure 6. Schematic of the volume change mechanism in fresh (a) and aged (b) cylindrical lithium cells, showing how non-uniform stress distribution between the steel shell and jelly-roll core evolves with cycling.^[1]

4. Recommendations for Manufacturers and Test Labs

• Use IEST SWE2100 constant-gap testing to quantify cylindrical cell expansion force during development and incoming quality checks.

• Combine mechanical force measurements with imaging (X-ray CT, ultrasonic) for a full picture of internal evolution in cylindrical pressure cells.

• When designing can thickness and geometry for a steel shell cylindrical cell, consider not only peak internal pressure but also cumulative irreversible expansion over the cell’s life.

• For high-expansion chemistries (e.g., silicon-rich anodes), exploit the cylindrical can’s mechanical constraint and use expansion force data to select appropriate preloads and venting strategies.

5. Summary

This study demonstrates that the SWE2100 in-situ swelling analysis system, operating in constant-gap mode, offers an effective solution for characterizing expansion force in cylindrical lithium cells. By simulating the mechanical binding effect of the steel shell, this approach enables accurate assessment of internal stresses and deformation behavior during cycling — even though direct external measurement of cylindrical pressure cell diameter change is impractical at the sub-10-μm scale predicted by thick-walled cylinder theory.

The methodology provides valuable insights for the development and optimization of cylindrical cells, particularly for applications involving high-expansion materials. It also supports safety evaluations and enhances understanding of mechanical processes within rigid steel shell cylindrical cell configurations.

6. References

[1] W.X. Jiang, H.R. Li, S.C. Wang, S.S. Wang, W. Wang, Dynamic Volume Imaging by Observing the Breathing of Cylindrical Lithium-Ion Batteries during Cycling,

7. FAQs