6.4.2 Contact Physics – Formulas
- Constriction resistance
- $R_e = \rho/2a$
(Single spot contact according to Holm; circular touching spot between clean contact surfaces)
- $R_e = \rho/2Na$
(Multi-spot contact according to Holm without influence between the N individual spots)
- $R_e = \rho/2 x \sum a_i + 3 \pi \rho /32N^2 x \sum \sum (s_ij) i \neq j$
(Multi-spot contact according to Greenwood considering the influence between the spots)
- Contact resistance
- $R_K = R_e + R_f$
- Path resistance
- $R_d = R_b + R_K$
- Contact resistance and contact force
- $R_K = 280\rho \sqrt[3]{E (F_K \cdot r)} $
(According to Holm model for film-free spherical contact surfaces with plastic deformation of the contact material; Fk < 1 N for typical contact materials)
- $R_K = 9000 \rho \sqrt{ H/ F_K}$
(According to Holm model for film-free spherical contact surfaces with plastic deformation of the contact material; Fk > 5 N for typical contact materials)
- Dynamic contact separation (without considering magnetic fields caused by the current path)
- $F_A \approx 0,8 xl^2$
(Rule of thumb with FA in N and l in kA)
- Contact voltage and max. contact temperature
- $T_kmax \approx 3200 U_K$
- Contact resistance at higher contact forces (according to Babikow)
- $R_K = cF_k^{-m}$
For FK between 10 and 200 N
c = material dependent proportionality factor
m = shape dependent exponent of the contact force
| Material combination | c |
|---|---|
| Copper - Copper | (0.08 bis 0.14) x 10-3 |
| Aluminum - Aluminum | (3 bis 6,7) x 10-3 |
| Brass - Brass | 0.67 x 10-3 |
| Steel – Silver | 0.06 x 10-3 |
| Steel – Copper | 3.1 x 10-3 |
| Steel – Brass | 3.0 x 10-3 |
| Contact shapes | m |
|---|---|
| Flat – Flat | 1 |
| Pyramid – Flat | 0.5 |
| Sphere – Flat | 0.6 |
| Sphere – Sphere | 0.5 |
| Multi-strand brush - Flat | 1 |
| Current bar (Busbar) contact | 0.5 - 0.7 |