Contact Physics – Formulas

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; F_k < 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; F_k > 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 F_A 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 F_K 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

References

References