Difference between revisions of "Contact Physics – Formulas"

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m (Reverted edits by Doduco Redaktion (talk) to last revision by Teitscheid)
(Tag: Rollback)
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*'''Constriction resistance'''  
 
*'''Constriction resistance'''  
: $R_e = \rho/2a$
+
: <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)
: $R_e = \rho/2Na$
+
: <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)
: $R_e = \rho/2 x \sum a_i + 3 \pi \rho /32N^2 x \sum \sum (s_ij) i \neq j$
+
: <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)
  
 
*'''Contact resistance'''
 
*'''Contact resistance'''
: $R_K = R_e + R_f$
+
: <math>R_K = R_e + R_f</math>
  
 
*'''Path resistance'''  
 
*'''Path resistance'''  
: $R_d = R_b + R_K$
+
: <math>R_d = R_b + R_K</math>
  
 
*'''Contact resistance and contact force'''
 
*'''Contact resistance and contact force'''
: $R_K = 280\rho \sqrt[3]{E (F_K \cdot r)} $
+
: <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)
: $R_K = 9000 \rho \sqrt{ H/ F_K}$
+
: <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)
  
 
*'''Dynamic contact separation''' (without considering magnetic fields caused by the current path)  
 
*'''Dynamic contact separation''' (without considering magnetic fields caused by the current path)  
: $F_A \approx 0,8 xl^2$
+
: <math>F_A \approx 0,8 xl^2</math>
 
(Rule of thumb with F<sub>A</sub> in N and l in kA)
 
(Rule of thumb with F<sub>A</sub> in N and l in kA)
  
 
*'''Contact voltage and max. contact temperature'''
 
*'''Contact voltage and max. contact temperature'''
: $T_kmax \approx 3200 U_K$
+
: <math>T_kmax \approx 3200 U_K</math>
  
 
*'''Contact resistance at higher contact forces (according to Babikow)'''  
 
*'''Contact resistance at higher contact forces (according to Babikow)'''  
: $R_K = cF_k^{-m}$
+
: <math>R_K = cF_k^{-m}</math>
 
For F<sub>K</sub> between 10 and 200 N<br/>
 
For F<sub>K</sub> between 10 and 200 N<br/>
 
c = material dependent proportionality factor<br/>
 
c = material dependent proportionality factor<br/>

Revision as of 11:33, 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