Difference between revisions of "Contact Physics – Formulas"

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{|
+
===<!--6.4.2-->Contact Physics – Formulas===
|'''Editor''':
+
 
|DODUCO Holding GmbH<br>
+
*'''Constriction resistance'''
Im Altgefäll 12<br>
+
: $R_e = \rho/2a$
75181 Pforzheim / Germany<br>
+
(Single spot contact according to Holm; circular touching spot between clean
Phone +49 (0) 7231 602-0<br>
+
contact surfaces)
Fax +49 (0) 7231 602-398<br>
+
: $R_e = \rho/2Na$
Mail: info@doduco.net<br>
+
(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<sub>k</sub> < 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<sub>k</sub> > 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<sub>A</sub> 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<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 scalable" style="text-align: left; font-size: 12px; width:45%;"
 
|-
 
|-
|'''Managing Directors''':
+
!Material combination
|
+
!c
Dr. Hans-Joachim Dittloff (Vorsitzender)<br>
 
Dr. Franz Kaspar<br>
 
Hajo Kufahl<br>
 
 
|-
 
|-
|'''Registration''':
+
|Copper - Copper
|HRB 710592 AG Mannheim
+
|(0.08 bis 0.14) x 10<sup>-3</sup>
 
|-
 
|-
|'''Consulting and Realisation''':
+
|Aluminum - Aluminum
|Steinbeis - Transferzentrum Unternehmensentwicklung an der Hochschule Pforzheim (SZUE)<br>
+
|(3 bis 6,7) x 10<sup>-3</sup>
Blücherstraße 32 <br>
 
75177 Pforzheim <br>
 
https://www.szue.de/
 
 
|-
 
|-
|'''Revision and German version''':
+
|Brass - Brass
|Christian Teitscheid - Teitscheid Freelance IT<br>
+
|0.67 x 10<sup>-3</sup>
Barbarastraße 22 <br>
 
47495 Rheinberg <br>
 
http://www.teitscheid-freelance.de/
 
 
|-
 
|-
 +
|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 scalable" style="text-align: left; font-size: 12px; width:45%; "
 +
|-
 +
!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
 
|}
 
|}
 +
<div class="clear"></div>
 +
 +
==References==
 +
[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]
 +
 +
[[de:Formeln_aus_der_Kontaktphysik]]

Revision as of 12:30, 10 August 2018

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

References