View source for Contact Physics – Formulas

===6.4.2 Contact Physics – Formulas===

*'''Constriction resistance''' 
: <math>R_e = \rho/2a</math>
(Single spot contact according to Holm; circular touching spot between clean
contact surfaces)
: <math>R_e = \rho/2Na</math>
(Multi-spot contact according to Holm without influence between the N
individual spots)
: <math>R_e = \rho/2 x \sum a_i + 3 \pi \rho /32N^2 x \sum \sum (s_ij) i \neq j</math>
(Multi-spot contact according to Greenwood considering the influence between
the spots)

*'''Contact resistance'''
: <math>R_K = R_e + R_f</math>

*'''Path resistance''' 
: <math>R_d = R_b + R_K</math>

*'''Contact resistance and contact force'''
: <math>R_K = 280\rho \sqrt[3]{E (F_K \cdot r)} </math> 
(According to Holm model for film-free spherical contact surfaces with plastic
deformation of the contact material; F<sub>k</sub> < 1 N for typical contact materials)
: <math>R_K = 9000 \rho \sqrt{ H/ F_K}</math>
(According to Holm model for film-free spherical contact surfaces with plastic
deformation of the contact material; F<sub>k</sub> > 5 N for typical contact materials)

*'''Dynamic contact separation''' (without considering magnetic fields caused by the current path) 
: <math>F_A \approx 0,8 xl^2</math>
(Rule of thumb with F<sub>A</sub> in N and l in kA)

*'''Contact voltage and max. contact temperature'''
: <math>T_kmax \approx 3200 U_K</math>

*'''Contact resistance at higher contact forces (according to Babikow)''' 
: <math>R_K = cF_k^{-m}</math>
For F<sub>K</sub> between 10 and 200 N<br/>
c = material dependent proportionality factor<br/>
m = shape dependent exponent of the contact force


{| class="twocolortable" style="text-align: left; font-size: 12px"
|-
!Material combination 
!c
|-
|Copper - Copper 
|(0.08 bis 0.14) x 10<sup>-3</sup>
|-
|Aluminum - Aluminum
|(3 bis 6,7) x 10<sup>-3</sup>
|-
|Brass - Brass 
|0.67 x 10<sup>-3</sup>
|-
|Steel – Silver
|0.06 x 10<sup>-3</sup>
|-
|Steel – Copper
|3.1 x 10<sup>-3</sup>
|-
|Steel – Brass
|3.0 x 10<sup>-3</sup>
|}


{| class="twocolortable" style="text-align: left; font-size: 12px"
|-
!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==
[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]