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'''
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: <math>R_e = \rho/2a</math>
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 +
Re = D/2a
 
(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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Re = D/2Na
 
(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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Re = D/2 x E ai + 3B D/32N² x E E (sij) i = j
 
(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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als bild?
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: <math>R_K = R_e + R_f</math>
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 +
 
 +
*'''Contact resistance''' <br />RK = Re + Rf
  
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*'''Path resistance'''  
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*'''Path resistance''' <br />Rd = Rb + RK
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: <math>R_d = R_b + R_K</math>
 
  
 
*'''Contact resistance and contact force'''
 
*'''Contact resistance and contact force'''
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: <math>R_K = 280\rho \sqrt[3]{E (F_K \cdot r)} </math>
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R = 280D ³ E(F · r) K K
 
(According to Holm model for film-free spherical contact surfaces with plastic
 
(According to Holm model for film-free spherical contact surfaces with plastic
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deformation of the contact material; F<sub>k</sub> < 1 N for typical contact materials)
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deformation of the contact material; F < 1 N for typical contact materials) k
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: <math>R_K = 9000 \rho \sqrt{ H/ F_K}</math>
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RK = 9000 D H/ FK
 
(According to Holm model for film-free spherical contact surfaces with plastic
 
(According to Holm model for film-free spherical contact surfaces with plastic
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deformation of the contact material; F<sub>k</sub> > 5 N for typical contact materials)
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deformation of the contact material; F > 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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: <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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*'''Dynamic contact separation''' (without considering magnetic fields caused by the current path)
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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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FA 0,8 x I²
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: <math>R_K = cF_k^{-m}</math>
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(Rule of thumb with F in N and I in kA)
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For F<sub>K</sub> between 10 and 200 N<br/>
 
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c = material dependent proportionality factor<br/>
 
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m = shape dependent exponent of the contact force
 
  
 +
*'''Contact voltage and max. contact temperature''' <br />T kmax 3200 UK
  
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{| class="twocolortable scalable" style="text-align: left; font-size: 12px; width:45%;"
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*'''Contact resistance at higher contact forces (according to Babikow)'''
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|-
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R = cF -m K K
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!Material combination
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For F between 10 and 200 N K
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!c
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c = material dependent proportionality factor
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|-
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m = shape dependent exponent of the contact force
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|Copper - Copper
 
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|(0.08 bis 0.14) x 10<sup>-3</sup>
 
−
|-
 
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|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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|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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|-
 
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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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|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==
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[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]
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[[Application Tables and Guidance Data for the Use of Electrical Contacts#References|References]]
−
 
 
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[[de:Formeln_aus_der_Kontaktphysik]]
 

Revision as of 14:24, 8 January 2014

6.4.2 Contact Physics – Formulas

  • Constriction resistance

Re = D/2a (Single spot contact according to Holm; circular touching spot between clean contact surfaces) Re = D/2Na (Multi-spot contact according to Holm without influence between the N individual spots) Re = D/2 x E ai + 3B D/32N² x E E (sij) i = j (Multi-spot contact according to Greenwood considering the influence between the spots)

als bild?


  • Contact resistance
    RK = Re + Rf
  • Path resistance
    Rd = Rb + RK
  • Contact resistance and contact force

R = 280D ³ E(F · r) K K (According to Holm model for film-free spherical contact surfaces with plastic deformation of the contact material; F < 1 N for typical contact materials) k RK = 9000 D H/ FK (According to Holm model for film-free spherical contact surfaces with plastic deformation of the contact material; F > 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 F in N and I in kA)

  • Contact voltage and max. contact temperature
    T kmax 3200 UK
  • Contact resistance at higher contact forces (according to Babikow)

R = cF -m K K For F between 10 and 200 N K c = material dependent proportionality factor m = shape dependent exponent of the contact force

References

References

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