Difference between revisions of "Contact Physics – Formulas"

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===6.4.2 Contact Physics – Formulas===
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===<!--6.4.2-->Contact Physics – Formulas===
  
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*'''Constriction resistance''' <math>R_e = \rho/2a</math>
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*'''Constriction resistance'''  
 +
: <math>R_e = \rho/2a</math>
 
(Single spot contact according to Holm; circular touching spot between clean
 
(Single spot contact according to Holm; circular touching spot between clean
 
contact surfaces)
 
contact surfaces)
−
<math>R_e = \rho/2Na</math>
+
: <math>R_e = \rho/2Na</math>
 
(Multi-spot contact according to Holm without influence between the N
 
(Multi-spot contact according to Holm without influence between the N
 
individual spots)
 
individual spots)
−
<math>R_e = \rho/2 x \sum a_i + 3 \pi \rho/32N² x \sum \sum (s_ij) i \neq j</math>
+
: <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
 
(Multi-spot contact according to Greenwood considering the influence between
 
the spots)
 
the spots)
  
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*'''Contact resistance''' R<sub>K</sub> = R<sub>e</sub> + R<sub>f</sub>
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*'''Contact resistance'''
 +
: <math>R_K = R_e + R_f</math>
  
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*'''Path resistance''' cR<sub>d</sub> = R<sub>b</sub> + R<sub>K</sub>
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*'''Path resistance'''  
 +
: <math>R_d = R_b + R_K</math>
  
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*'''Contact resistance and contact force''' <math>R_K = 280D ³ E(F · r) K</math>  
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*'''Contact resistance and contact force'''
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: <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
 
(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)
 
deformation of the contact material; F<sub>k</sub> < 1 N for typical contact materials)
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<math>R_K = 9000 D H/ FK</math>
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: <math>R_K = 9000 \rho \sqrt{ H/ F_K}</math>
 
(According to Holm model for film-free spherical contact surfaces with plastic
 
(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)
 
deformation of the contact material; F<sub>k</sub> > 5 N for typical contact materials)
  
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*'''Dynamic contact separation''' (without considering magnetic fields caused by the current path) <br />F<sub>A</sub> 0,8 x I<sup>2</sup>(Rule of thumb with F<sub>A</sub> in N and I in kA)
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*'''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)
  
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*'''Contact voltage and max. contact temperature''' <br />T<sub>kmax</sub> 3200 U<sub>K</sub>
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*'''Contact voltage and max. contact temperature'''
 +
: <math>T_kmax \approx 3200 U_K</math>
  
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*'''Contact resistance at higher contact forces (according to Babikow)''' <br />R<sub>K</sub> = cF -m K
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*'''Contact resistance at higher contact forces (according to Babikow)'''  
−
For F<sub>K</sub> between 10 and 200 N
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: <math>R_K = cF_k^{-m}</math>
−
c = material dependent proportionality factor
+
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
 
m = shape dependent exponent of the contact force
 +
 +
 +
{| class="twocolortable scalable" style="text-align: left; font-size: 12px; width:45%;"
 +
|-
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!Material combination
 +
!c
 +
|-
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|Copper - Copper
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|(0.08 bis 0.14) x 10<sup>-3</sup>
 +
|-
 +
|Aluminum - Aluminum
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|(3 bis 6,7) x 10<sup>-3</sup>
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|-
 +
|Brass - Brass
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|0.67 x 10<sup>-3</sup>
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|-
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|Steel – Silver
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|0.06 x 10<sup>-3</sup>
 +
|-
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|Steel – Copper
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|3.1 x 10<sup>-3</sup>
 +
|-
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|Steel – Brass
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|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
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|0.5
 +
|-
 +
|Multi-strand brush - Flat
 +
|1
 +
|-
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|Current bar (Busbar) contact
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|0.5 - 0.7
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|}
 +
<div class="clear"></div>
  
 
==References==
 
==References==
 
[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]
 
[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]
 +
 +
[[de:Formeln_aus_der_Kontaktphysik]]

Revision as of 12:33, 7 February 2019

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

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