The rapid expansion of the electric vehicle market, particularly in China EV sectors, has heightened the demand for reliable charging infrastructure. As a key component, charging cables must exhibit superior flexibility, durability, and electrical performance to withstand frequent bending and high-current operations. In this context, the design of stranded conductors—specifically the lay ratio—plays a critical role in determining the overall cable quality. The lay ratio, defined as the ratio of the lay length to the pitch circle diameter, influences conductor roundness, flexibility, resistance, and material efficiency. Through theoretical analysis and experimental validation, this study aims to establish an optimal lay ratio range for stranded conductors used in electric vehicle charging cables, ensuring they meet the rigorous demands of China EV applications while balancing cost and performance.
Stranding is a fundamental process in manufacturing flexible conductors for electric vehicle charging cables, typically applied to conductors with cross-sections up to 10 mm² or larger stranded wires. The lay ratio ($m_{th}$) is a pivotal parameter, calculated as $m_{th} = h / D’$, where $h$ is the lay length and $D’$ is the pitch circle diameter. This ratio directly affects the helical angle ($\alpha$), as expressed by $m_{th} = \pi \tan \alpha$. A smaller lay ratio enhances flexibility and tightness but risks conductor deformation, increased resistance due to longer single-wire paths, higher material consumption, and reduced production efficiency. Conversely, a larger lay ratio may prevent these issues but can lead to loose strands, poor contact between wires, and elevated resistance. Thus, a balanced approach combining theoretical design and experimental verification is essential for electric vehicle charging cables in China EV ecosystems.
Theoretical design of the lay ratio begins with analyzing the geometry of stranded conductors. In a stranded configuration, individual wires follow a helical path, and their cross-sections appear elliptical, with short-axis diameter $d$ and long-axis diameter $d’$ related by $d’ = d / \sin \alpha$. The theoretical lay ratio $m_{th}$ must exceed the limiting lay ratio $m_{lim}$ to ensure conductor roundness and stability. By analogy with conventional stranding, where the difference in wire count between adjacent layers ($\Delta Z_n$) is typically 6, we derive $\Delta Z_n = ( \pi D’_n – \pi D’_{n-1} ) / d’ = 2 \pi d / d’$. Substituting $d’$ gives $\alpha = \arcsin [ \Delta Z_n / (2 \pi) ]$. For $\Delta Z_n = 6$, $\alpha \approx 72.73^\circ$, and $m_{lim} = \pi \tan \alpha \approx 10.1$. Thus, the theoretical lay ratio must satisfy $m_{th} \geq 10.1$ to avoid structural defects in electric vehicle charging cables.
To validate this theoretical foundation, experimental tests were conducted on conductors of various sizes commonly used in China EV charging systems: 1.5 mm² (48 × 0.20 mm), 2.5 mm² (80 × 0.20 mm), 4.0 mm² (56 × 0.30 mm), and 6.0 mm² (84 × 0.30 mm). Using a 650-type stranding machine, conductors were produced with lay ratios ranging from 5 to 35 by adjusting the lay length via pulley changes. The DC resistance at 20°C ($R_{20}$) was measured using a double-bridge method and normalized to standard conditions. The results, summarized in Table 1, demonstrate that $R_{20}$ decreases rapidly with increasing $m_{th}$, stabilizes within a specific range, and then slightly rises. For all conductor sizes, $R_{20}$ remains low and stable when $m_{th}$ is between 11 and 25, confirming the theoretical lower limit of 10.1 and highlighting the optimal range for electric vehicle applications.
| Conductor Size (mm²) | Lay Ratio ($m_{th}$) | $R_{20}$ (Ω/km) |
|---|---|---|
| 1.5 | 5 | 13.5 |
| 1.5 | 11 | 12.1 |
| 1.5 | 15 | 11.8 |
| 1.5 | 20 | 11.9 |
| 1.5 | 25 | 12.0 |
| 1.5 | 30 | 12.2 |
| 1.5 | 35 | 12.5 |
| 2.5 | 5 | 7.8 |
| 2.5 | 11 | 7.3 |
| 2.5 | 15 | 7.1 |
| 2.5 | 20 | 7.2 |
| 2.5 | 25 | 7.3 |
| 2.5 | 30 | 7.4 |
| 2.5 | 35 | 7.6 |
| 4.0 | 5 | 4.9 |
| 4.0 | 11 | 4.6 |
| 4.0 | 15 | 4.5 |
| 4.0 | 20 | 4.5 |
| 4.0 | 25 | 4.6 |
| 4.0 | 30 | 4.7 |
| 4.0 | 35 | 4.8 |
| 6.0 | 5 | 3.2 |
| 6.0 | 11 | 3.0 |
| 6.0 | 15 | 2.9 |
| 6.0 | 20 | 3.0 |
| 6.0 | 25 | 3.1 |
| 6.0 | 30 | 3.2 |
| 6.0 | 35 | 3.3 |
In addition to electrical performance, the bending endurance of electric vehicle charging cables is crucial for China EV applications, where cables are subject to frequent movement and flexing. To evaluate this, the 6.0 mm² conductor was used to fabricate EV-EYU 5×6 type charging cables with an outer diameter of 16 mm, excluding signal wires to isolate testing effects. These cables were subjected to pendulum tests as per standard GB/T 33594-2017, with a micro-current monitoring device to detect conductor breakage. The number of swing cycles ($n_r$) was recorded for five samples at each lay ratio, and averages were computed. As shown in Table 2, $n_r$ decreases linearly from approximately 11,600 to 8,800 as $m_{th}$ increases from 13 to 25. This decline is attributed to reduced flexibility and increased inter-wire gaps at higher lay ratios, which compromise the cable’s ability to withstand repeated bending. For optimal performance in electric vehicle charging scenarios, $m_{th}$ should be limited to 20 to maintain high bending endurance.
| Lay Ratio ($m_{th}$) | Average Swing Cycles ($n_r$) |
|---|---|
| 13 | 11,600 |
| 15 | 10,900 |
| 17 | 10,200 |
| 20 | 9,500 |
| 22 | 9,100 |
| 25 | 8,800 |
The relationship between lay ratio and conductor properties can be further modeled mathematically. For instance, the DC resistance per unit length ($R$) depends on the lay ratio and material resistivity ($\rho$), approximated by $R = \rho \cdot L / A$, where $L$ is the effective length increased by stranding and $A$ is the cross-sectional area. The lay length $h$ relates to the helical path length $L_h$ via $L_h = \sqrt{h^2 + (\pi D’)^2}$, leading to a resistance increase factor $k_r = L_h / h = \sqrt{1 + (\pi D’ / h)^2} = \sqrt{1 + (1 / m_{th})^2}$. Thus, $R \propto k_r$, and minimizing $k_r$ requires maximizing $m_{th}$, but this must be balanced against flexibility. Similarly, the bending stress $\sigma_b$ in a stranded conductor under flexure can be expressed as $\sigma_b = E \cdot \delta / r$, where $E$ is the modulus of elasticity, $\delta$ is the deflection, and $r$ is the radius of curvature. A lower $m_{th}$ reduces $r$, increasing $\sigma_b$ and fatigue risk, which aligns with the experimental observations for electric vehicle charging cables.
Material efficiency is another consideration for China EV charging cable manufacturers. The mass per unit length ($M$) of a stranded conductor is given by $M = \rho_m \cdot A \cdot n \cdot k_m$, where $\rho_m$ is the material density, $n$ is the number of wires, and $k_m$ is the lay factor accounting for increased length due to stranding, $k_m = \sqrt{1 + (1 / m_{th})^2}$. As $m_{th}$ decreases, $k_m$ increases, leading to higher copper usage and cost. For example, with $m_{th} = 15$, $k_m \approx 1.002$, whereas for $m_{th} = 10$, $k_m \approx 1.005$, resulting in a 0.3% increase in material consumption. This underscores the importance of selecting a lay ratio that minimizes cost without sacrificing performance in electric vehicle applications.
In practice, the stranding process for electric vehicle charging cables involves precise control of machine parameters. The lay length $h$ is set using gear ratios or pulley systems, and the pitch circle diameter $D’$ is derived from the conductor geometry. For a concentric stranded conductor, $D’$ can be calculated as $D’ = d \cdot (n^{1/2} + \delta)$, where $n$ is the total number of wires and $\delta$ is a packing factor. The optimal lay ratio range of $m_{th} = 15$ to 20 ensures stable production with high efficiency, as it avoids excessive machine adjustments and material waste. This is particularly relevant for China EV markets, where scalability and cost-effectiveness are key drivers.
Environmental factors also influence lay ratio design for electric vehicle charging cables. In China EV operations, cables may be exposed to temperature variations, moisture, and mechanical abrasion. A tighter stranding (lower $m_{th}$) can enhance resistance to environmental stresses by reducing interstices where contaminants might accumulate. However, this must be weighed against the risk of increased resistance and reduced flexibility. Accelerated aging tests could further refine the lay ratio selection, ensuring long-term reliability for electric vehicle charging infrastructure.
In conclusion, the design of the lay ratio for stranded conductors in electric vehicle charging cables is a multifaceted optimization problem. Theoretical analysis establishes a lower limit of $m_{th} \geq 10.1$ to prevent structural instability, while experimental validation on resistance and bending endurance confirms that $m_{th}$ between 13 and 20 delivers superior performance. For China EV applications, where durability and efficiency are paramount, a lay ratio of 15 to 20 is recommended. This range ensures low DC resistance, high bending endurance, and cost-effective material usage, supporting the growth of electric vehicle adoption. Future work could explore advanced materials and stranding techniques to further enhance cable performance for the evolving demands of the electric vehicle industry.