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'''  
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*'''Constriction resistance''' <math><br />R<sub>e</sub> = \rho/2a</math>
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: <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)
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: <math>R_e = \rho/2Na</math>
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<math>R<sub>e</sub> = \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)
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: <math>R_e = \rho/2 x \sum a_i + 3 \pi \rho /32N^2 x \sum \sum (s_ij) i \neq j</math>
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<math>R<sub>e</sub> = \rho/2 x \sum a<sub>i</sub> + 3 \pi \rho/32N² x \sum \sum (s<sub>ij</sub>) 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'''
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*'''Contact resistance''' <br />R<sub>K</sub> = R<sub>e</sub> + R<sub>f</sub>
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: <math>R_K = R_e + R_f</math>
 
  
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*'''Path resistance'''  
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*'''Path resistance''' <br />R<sub>d</sub> = R<sub>b</sub> + R<sub>K</sub>
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: <math>R_d = R_b + R_K</math>
 
  
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*'''Contact resistance and contact force'''
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*'''Contact resistance and contact force''' <math><br />R<sub>K</sub> = 280D ³ E(F · r) K</math>  
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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 \rho \sqrt{ H/ F_K}</math>
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<math>R<sub>K</sub> = 9000 D H/ FK</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)  
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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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: <math>F_A \approx 0,8 xl^2</math>
 
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(Rule of thumb with F<sub>A</sub> in N and l in kA)
 
  
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*'''Contact voltage and max. contact temperature'''
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*'''Contact voltage and max. contact temperature''' <br />T<sub>kmax</sub> 3200 U<sub>K</sub>
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: <math>T_kmax \approx 3200 U_K</math>
 
  
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*'''Contact resistance at higher contact forces (according to Babikow)'''  
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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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: <math>R_K = cF_k^{-m}</math>
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For F<sub>K</sub> between 10 and 200 N
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For F<sub>K</sub> between 10 and 200 N<br/>
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c = material dependent proportionality factor
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c = material dependent proportionality factor<br/>
 
 
m = shape dependent exponent of the contact force
 
m = shape dependent exponent of the contact force
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{| class="twocolortable scalable" style="text-align: left; font-size: 12px; width:45%;"
 
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|-
 
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!Material combination
 
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!c
 
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|-
 
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|Copper - Copper
 
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|(0.08 bis 0.14) x 10<sup>-3</sup>
 
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|-
 
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|Aluminum - Aluminum
 
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|(3 bis 6,7) x 10<sup>-3</sup>
 
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|-
 
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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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|-
 
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|Steel – Copper
 
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|3.1 x 10<sup>-3</sup>
 
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|-
 
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|Steel – Brass
 
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|3.0 x 10<sup>-3</sup>
 
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|}
 
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{| class="twocolortable scalable" style="text-align: left; font-size: 12px; width:45%; "
 
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|-
 
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!Contact shapes
 
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!m
 
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|-
 
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|Flat – Flat
 
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|1
 
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|-
 
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|Pyramid – Flat
 
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|0.5
 
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|-
 
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|Sphere – Flat
 
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|0.6
 
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|-
 
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|Sphere – Sphere
 
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|0.5
 
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|-
 
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|Multi-strand brush - Flat
 
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|1
 
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|-
 
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|Current bar (Busbar) contact
 
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|0.5 - 0.7
 
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|}
 
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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]]
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[[de:Formeln_aus_der_Kontaktphysik]]
 

Revision as of 18:12, 26 March 2014

6.4.2 Contact Physics – Formulas

  • Constriction resistance <br />R<sub>e</sub> = \rho/2a

(Single spot contact according to Holm; circular touching spot between clean contact surfaces) R<sub>e</sub> = \rho/2Na (Multi-spot contact according to Holm without influence between the N individual spots) R<sub>e</sub> = \rho/2 x \sum a<sub>i</sub> + 3 \pi \rho/32N² x \sum \sum (s<sub>ij</sub>) i \neq j (Multi-spot contact according to Greenwood considering the influence between the spots)

  • Contact resistance
    RK = Re + Rf
  • Path resistance
    Rd = Rb + RK
  • Contact resistance and contact force <br />R<sub>K</sub> = 280D ³ E(F · r) K

(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<sub>K</sub> = 9000 D H/ FK (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)
    FA 0,8 x I2(Rule of thumb with FA in N and I in kA)
  • Contact voltage and max. contact temperature
    Tkmax 3200 UK
  • Contact resistance at higher contact forces (according to Babikow)
    RK = cF -m K

For FK between 10 and 200 N c = material dependent proportionality factor m = shape dependent exponent of the contact force

References

References

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