Difference between revisions of "Contact Physics – Formulas"
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| − | + | ===<!--6.4.2-->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; 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%;" | ||
|- | |- | ||
| − | + | !Material combination | |
| − | + | !c | |
| − | |||
| − | |||
| − | |||
|- | |- | ||
| − | | | + | |Copper - Copper |
| − | | | + | |(0.08 bis 0.14) x 10<sup>-3</sup> |
|- | |- | ||
| − | | | + | |Aluminum - Aluminum |
| − | | | + | |(3 bis 6,7) x 10<sup>-3</sup> |
| − | |||
| − | |||
| − | |||
|- | |- | ||
| − | | | + | |Brass - Brass |
| − | | | + | |0.67 x 10<sup>-3</sup> |
| − | |||
| − | |||
| − | |||
|- | |- | ||
| + | |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 |
