Bending Force and Tonnage Calculations for Heavy Copper Busbar Plates

In industrial power distribution and switchgear manufacturing, forming thick copper busbars requires massive forces. When bending heavy copper plates—such as $100 \times 10 \text{ mm}$ or $120 \times 12 \text{ mm}$ profiles—understanding the mechanical requirements is critical.

Calculating the Bending Force (Tonnage) ensures that:

1. The machinery is never overloaded, protecting hydraulic pumps and structural monoblock cast frames from fatigue.
2. The V-die tooling is correctly specified to prevent premature cracking of the copper’s outer fibers.
3. The spatial alignment remains locked, ensuring high angular repeatabilities under continuous operation.

For mid-to-high volume switchboard assembly, planning these forces is essential. This paper analyzes the formulas and practical calculations for air bending high-conductivity T2 copper plates using the DHAC-BB-H Dedicated Servo-Hydraulic Bending Machine or the bending station of our 3-in-1 multi-station busbar processor.

1. The Mathematical Bending Force Formula

For standard 90° air bending of sheet metal and heavy conductive bars, engineers utilize a classic beam-deflection formula modified by empirical coefficients.

The required Bending Force ($F$) is calculated as:

$$F = \frac{C \cdot \sigma_b \cdot W \cdot T^2}{1000 \cdot V}$$

Where:

• $F$ = Required Bending Force in Metric Tons (t).
• $C$ = Empirical shape/material coefficient (typically $1.5$ for standard copper air bending).
• $\sigma_b$ = Ultimate Tensile Strength of the material in $\text{N/mm}^2$ (or $\text{MPa}$). For standard half-hard T2 red copper, $\sigma_b \approx 260 \text{ MPa}$.
• $W$ = Width of the copper busbar in $\text{mm}$.
• $T$ = Thickness of the copper busbar in $\text{mm}$.
• $V$ = V-die opening width in $\text{mm}$ (typically chosen between $6T$ and $8T$ to prevent cracking).

Note: The division by 1,000 converts the output from kilonewtons ($\text{kN}$) into standard Metric Tons ($\text{t}$), which is the rating system for industrial hydraulic cylinders.

2. Practical Calculation Walkthroughs

To demonstrate how this formula operates in a real-world switchgear plant, let us calculate the required tonnage for two common B2B copper configurations:

Scenario A: Processing a $100 \times 10 \text{ mm}$ Copper Bar

• Material: Half-hard T2 Red Copper ($\sigma_b = 260 \text{ MPa}$)
• Width ($W$): $100 \text{ mm}$
• Thickness ($T$): $10 \text{ mm}$
• V-Die Opening ($V$): We select a standard $8T$ ratio, meaning $V = 8 \times 10 \text{ mm} = 80 \text{ mm}$.

Applying the formula:

$$F = \frac{1.5 \times 260 \times 100 \times 10^2}{1000 \times 80}$$

$$F = \frac{1.5 \times 260 \times 100 \times 100}{80000}$$

$$F = \frac{3,900,000}{80,000} = 48.75 \text{ Metric Tons}$$

Engineering Conclusion: To bend a $100 \times 10 \text{ mm}$ copper bar with a standard $V=80\text{mm}$ die, the hydraulic system must exert at least 48.75 Tons of press force. Our DHAC-BB-H Servo Bending Workstation provides a robust 50-to-80 Ton capacity, easily accommodating this load with a comfortable safety margin.

Scenario B: Processing a $120 \times 12 \text{ mm}$ Copper Bar (Heavy Busduct Specification)

• Material: Half-hard T2 Red Copper ($\sigma_b = 260 \text{ MPa}$)
• Width ($W$): $120 \text{ mm}$
• Thickness ($T$): $12 \text{ mm}$
• V-Die Opening ($V$): Using $V = 8T = 8 \times 12 \text{ mm} = 96 \text{ mm}$.

Applying the formula:

$$F = \frac{1.5 \times 260 \times 120 \times 12^2}{1000 \times 96}$$

$$F = \frac{1.5 \times 260 \times 120 \times 144}{96000}$$

$$F = \frac{6,739,200}{96,000} = 70.20 \text{ Metric Tons}$$

Engineering Conclusion: This heavy-duty application requires 70.2 Tons of force. Operating a standard manual 30-ton bender on this profile will lead to structural deflection, hydraulic line blowouts, and uneven bend geometries.

3. V-Die Selection & Tonnage Mapping Matrix

Choosing the correct V-die opening width is a delicate balance. A wider V-die reduces the required force but increases the minimum physical bend radius and requires a longer flat section at the ends of the bar.

The table below maps the required tonnage and minimum inner bend radii ($R_{\text{min}}$) for various material thicknesses ($T$) across a standard $100 \text{ mm}$ width of half-hard copper, assuming a standard $\sigma_b = 260 \text{ MPa}$:

4. Engineering Safe-forming Protocols

To prevent mechanical damage and surface fractures during high-tonnage bending operations:

• Grain Direction: Whenever possible, bend the copper plate perpendicular to the rolling grain direction of the metal. Bending parallel to the grain reduces ductility and can trigger micro-cracks on the outer radius.
• Die Lubrication: Apply high-viscosity stamping oil to the V-die shoulders. This reduces friction, minimizing surface scoring on the copper plate and decreasing required force by up to 5%.
• Avoid Under-Sizing V-Dies: Never attempt to bend a 10mm copper plate on a 40mm V-die ($4T$). This raises the required force exponentially ($F \propto 1/V$) and can cause catastrophic cylinder failures.

5. Advanced Closed-Loop Hydraulic Bending

On conventional hydraulic press brakes, managing springback requires constant manual adjustments due to fluid viscosity changes as temperatures rise.

The DHAC-BB-H horizontal busbar bender resolves this through a closed-loop servo-hydraulic system. Real-time pressure sensors measure the resistive load curve during the initial stroke, allowing the Siemens PLC to calculate exact yield points and automatically adjust the cylinder’s over-travel depth. This ensures a consistent ±0.2° angular precision without operator intervention.

Switchgear procurement managers can request a custom tooling engineering evaluation to submit CAD drawings and receive a detailed calculations audit for their specific copper components.

References and Standards

1. DIN EN ISO 7438 - Metallic materials - Bend test standards.
2. DIN 43671 - Design standards for electrical copper conductors.
3. CE Machine Safety Directive 2006/42/EC - Guidelines for high-pressure hydraulic metal forming systems.