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Contact Physics – Formulas

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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


References