Difference between revisions of "Contact Spring Calculations"

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</figure>
 
</figure>
 
The influence of the dimensions can be illustrated best by using the single side fixed beam model <xr id="fig:Oneside_fixed_contact_bending_spring"/><!--(Fig. 6.20)-->. For small deflections the following equation is valid:
 
The influence of the dimensions can be illustrated best by using the single side fixed beam model <xr id="fig:Oneside_fixed_contact_bending_spring"/><!--(Fig. 6.20)-->. For small deflections the following equation is valid:
−
:$F = \frac{3 \cdot E \cdot J}{L^3} $
+
:<math>F = \frac{3 \cdot E \cdot J}{L^3} </math>
  
 
where J is the momentum of inertia of the rectangular cross section of the beam
 
where J is the momentum of inertia of the rectangular cross section of the beam
−
:$J = \frac{B \cdot D^3}{12}$
+
:<math>J = \frac{B \cdot D^3}{12}</math>
  
 
For springs with a circular cross-sectional area the momentum of inertia is
 
For springs with a circular cross-sectional area the momentum of inertia is
−
:$J=\pi D^4/64$
+
:<math>J=\pi D^4/64</math>
−
:$D= Durchmesser$
+
:<math>D= Durchmesser</math>
  
 
To avoid plastic deformation of the spring the max bending force σ<sub>max</sub> cannot be exceeded
 
To avoid plastic deformation of the spring the max bending force σ<sub>max</sub> cannot be exceeded
−
:$\sigma_{max} = \frac{3 \cdot E \cdot D}{2L^2}\cdot_{max}$
+
:<math>\sigma_{max} = \frac{3 \cdot E \cdot D}{2L^2}\cdot_{max}</math>
  
 
The stress limit is defined through the fatigue limit and the 0.2% elongation limit resp.
 
The stress limit is defined through the fatigue limit and the 0.2% elongation limit resp.
−
:$\times_{max} = \frac{2 \cdot L^2}{3 \cdot D \cdot E}R_{p0,2}$
+
:<math>\times_{max} = \frac{2 \cdot L^2}{3 \cdot D \cdot E}R_{p0,2}</math>
  
 
<br />and/or<br />
 
<br />and/or<br />
−
:$F_{max} = \frac{B \cdot D^2}{6L}R_{p0,2}$
+
:<math>F_{max} = \frac{B \cdot D^2}{6L}R_{p0,2}</math>
  
  
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Deflection
 
Deflection
−
:$ \times = \frac{F}{2 \cdot E \cdot J}L^3$
+
:<math> \times = \frac{F}{2 \cdot E \cdot J}L^3</math>
  
  
−
:$= \frac{6 \cdot F}{E \cdot B}\cdot \frac{L^3}{D^3}$
+
:<math>= \frac{6 \cdot F}{E \cdot B}\cdot \frac{L^3}{D^3}</math>
  
  
 
Max. bending force
 
Max. bending force
−
:$\sigma_{max}= \frac{18 \cdot F \cdot L}{B \cdot D^2}$
+
:<math>\sigma_{max}= \frac{18 \cdot F \cdot L}{B \cdot D^2}</math>
  
 
<li>'''Trapezoidal spring'''</li>
 
<li>'''Trapezoidal spring'''</li>
  
 
Deflection
 
Deflection
−
:$ \times = \frac{F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \cdot J}$
+
:<math> \times = \frac{F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \cdot J}</math>
  
  
−
:$\times= \frac{12 \cdot F}{(2 + B_{min} /B_{max})}\cdot \frac{L^3}{E \cdot B \cdot D^3}$
+
:<math>\times= \frac{12 \cdot F}{(2 + B_{min} /B_{max})}\cdot \frac{L^3}{E \cdot B \cdot D^3}</math>
  
  
 
Max. bending force
 
Max. bending force
−
:$\sigma_{max}= \frac{18 \cdot F \cdot L}{(2 + B_{min} /B_{max}) \cdot B_{max} \cdot D^2 }$
+
:<math>\sigma_{max}= \frac{18 \cdot F \cdot L}{(2 + B_{min} /B_{max}) \cdot B_{max} \cdot D^2 }</math>
 
</ul>
 
</ul>
  
 
==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:Berechnung_von_Kontaktfedern]]
 +

Revision as of 21:37, 20 September 2014

Contact Spring Calculations

One side fixed contact bending spring

The influence of the dimensions can be illustrated best by using the single side fixed beam model Figure 1. For small deflections the following equation is valid:

F = \frac{3 \cdot E \cdot J}{L^3}

where J is the momentum of inertia of the rectangular cross section of the beam

J = \frac{B \cdot D^3}{12}

For springs with a circular cross-sectional area the momentum of inertia is

J=\pi D^4/64
D= Durchmesser

To avoid plastic deformation of the spring the max bending force σmax cannot be exceeded

\sigma_{max} = \frac{3 \cdot E \cdot D}{2L^2}\cdot_{max}

The stress limit is defined through the fatigue limit and the 0.2% elongation limit resp.

\times_{max} = \frac{2 \cdot L^2}{3 \cdot D \cdot E}R_{p0,2}


and/or

F_{max} = \frac{B \cdot D^2}{6L}R_{p0,2}


  • Special Spring Shapes
    • Triangular spring

      • Deflection

      \times = \frac{F}{2 \cdot E \cdot J}L^3


      = \frac{6 \cdot F}{E \cdot B}\cdot \frac{L^3}{D^3}


      Max. bending force

      \sigma_{max}= \frac{18 \cdot F \cdot L}{B \cdot D^2}
    • Trapezoidal spring

      • Deflection

      \times = \frac{F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \cdot J}


      \times= \frac{12 \cdot F}{(2 + B_{min} /B_{max})}\cdot \frac{L^3}{E \cdot B \cdot D^3}


      Max. bending force

      \sigma_{max}= \frac{18 \cdot F \cdot L}{(2 + B_{min} /B_{max}) \cdot B_{max} \cdot D^2 }

    References

    References

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