Polished Technical Report: Resistance Efficiency of Bolted Copper Busbar Connections

2. Temperature Effect

Temperature rise (ΔT) induces an increment of bolt tensile force (F_supp) that depends on the difference in thermal expansion coefficients (α_a - α_b), the elastic moduli of bolt and busbar, and dimensions of the joint assembly. When α_a and α_b differ significantly—as with high-strength steel versus copper—the bolt tension can increase markedly under heating.

In the formula:

αₐ — Thermal expansion coefficient of the busbar conductor

αᵦ — Thermal expansion coefficient of the bolt

Aᵦ — Cross-sectional area of the bolt

Eᵦ — Elastic modulus of the bolt

Eₐ — Elastic modulus of the busbar

t — Thickness of the washer

a — Thickness of the busbar

A_w — Apparent area under the washer

Aₐ — Apparent area of the joint overlap region

The variation in bolt stress is directly proportional to the difference in thermal expansion coefficients (αₐ − αᵦ).
For example:

If high-strength steel bolts are used, the difference in thermal expansion coefficients is large (Δα = 5.5×10⁻⁶/°C), causing a significant increase in bolt tension.

If CW307G aluminum bronze bolts are used, the difference is very small (Δα = −0.3×10⁻⁶/°C), so the bolt tension will only decrease slightly.

3. Bolt Stress and Use of Belleville Washers

Design must ensure the maximum tensile force at any operating temperature remains below 95% of the bolt yield strength. If this limit is exceeded, the bolt may undergo plastic deformation, ultimately leading to joint loosening and failure.

When calculating bolt stress, the tensile stress area of the bolt (refer to Table 1 for specific values) should be applied, instead of the nominal bolt area.

Table 1 Typical Thread Characteristic Parameters

Use tensile stress area—not nominal diameter—when calculating bolt stress. If high-strength steel bolts are mandated, incorporate Belleville (conical spring) washers to limit thermal force increments by providing compliant displacement under expansion.

4. Slot Optimization in Overlap Region

Introducing longitudinal slots in the lap joint can reduce contact resistance by 30–40% by improving pressure uniformity and effective contact area.

The reduction in electrical resistance is attributed to this design’s ability to improve the uniformity of contact pressure at each branch of the joint, thereby increasing the contact area.

5. Recommended Bolt Arrangement and Torque

For single-sided lap joints, long-practiced layouts provide a sound starting point. Recommended torques typically apply to Grade 8.8 steel or aluminum bronze fasteners with standard coarse threads, normal surface roughness, and no added lubrication.

6. Connection Efficiency and Governing Formulas

Connection efficiency (η) is the ratio of the resistance of the conductor section including the joint (R_j) to the resistance of an equal length of straight busbar (R_b). Joint resistance comprises the streamline-effect resistance due to current path distortion and the contact resistance at the mating surfaces.

Contact resistance per unit area: R_i = Y / (a · l), where Y depends on contact pressure, a is busbar width, and l is overlap length.

Total joint resistance: R_j = R_streamline + R_i
Efficiency: η = R_j / R_b, with R_b as the straight busbar resistance for the same length.

7. Worked Examples

Example A — 50 mm × 10 mm busbar, overlap 70 mm, 2 × M12 bolts: contact pressure ≈ 10.7 N/mm², Y ≈ 3000 μΩ·mm², resistance ratio e ≈ 0.55, resulting efficiency η ≈ 1.12 (joint slightly higher resistance than straight busbar).

Example B — Redesign with 90 mm overlap and 3 × M12 bolts: contact pressure ≈ 12.5 N/mm², Y ≈ 2600 μΩ·mm², e ≈ 0.52, yielding η ≈ 0.91 (joint resistance lower than straight busbar).

8. Notes and Assumptions

The figures provided are illustrative and not drawn to scale.

The pressure–resistance curve in Figure 1 is synthetic for visualization; use laboratory or vendor data for design-critical calculations.

All formulas and values are derived from the attached source material on copper busbar joint design.

9. FAQ: Common Questions on Copper Busbar Joint Design

Q1: What is the best bolt material for copper busbar connections?
A: Aluminum bronze (CW307G) is recommended due to its similar thermal expansion to copper, which helps maintain stable contact pressure and reduces galvanic corrosion.

Q2: How does temperature affect bolt tension in busbar joints?
A: Temperature rise can increase bolt tension if the bolt and busbar have different thermal expansion coefficients. Using materials with matched coefficients minimizes this effect.

Q3: How can I reduce contact resistance in a bolted busbar joint?
A: Introducing longitudinal slots in the overlap region can improve pressure distribution and reduce contact resistance by 30–40%.

Q4: What is connection efficiency and how is it calculated?
A: Connection efficiency is the ratio of joint resistance to the resistance of an equivalent straight busbar. It is influenced by overlap length, bolt count, and contact pressure.