Difference between revisions of "Contact Spring Calculations"

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(→‎6.4.7 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:One side 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:One side fixed contact bending spring"/> (Fig. 6.20). For small deflections the following equation is valid:
−
:<math>F = \frac{3 \cdot E \cdot J}{L^3} \cdot </math>
+
:<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
−
:<math>J = \frac{B x D^3}{12}</math>
+
:<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
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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
−
:<math>\sigma_{max} = \frac{3 x E x D}{2L^2}x_{max}</math>
+
:<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.
−
:<math>x_{max} = \frac{2 x L^2}{3 x D x E}R_{p0,2}</math>
+
:<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 />
−
:<math>F_{max} = \frac{B x D^2}{6L}R_{p0,2}</math>
+
:<math>F_{max} = \frac{B \cdot D^2}{6L}R_{p0,2}</math>
  
  
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Deflection
 
Deflection
−
:<math>x = \frac{F}{2 x E x J}L^3</math>  
+
:<math> \times = \frac{F}{2 \cdot E \cdot J}L^3</math>  
  
  
−
:<math>= \frac{6 x F}{E x B}x \frac{L^3}{D^3}</math>
+
:<math>= \frac{6 \cdot F}{E \cdot B}\cdot \frac{L^3}{D^3}</math>
  
  
 
Max. bending force
 
Max. bending force
−
:<math>\sigma_{max}= \frac{18 x F x L}{B x D^2}</math>  
+
:<math>\sigma_{max}= \frac{18 \cdot F \cdot L}{B \cdot D^2}</math>  
  
 
<li>'''Trapezoidal spring'''</li>
 
<li>'''Trapezoidal spring'''</li>
  
 
Deflection
 
Deflection
−
:<math>x= \frac{F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E x J}</math>
+
:<math> \times = \frac{F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \cdot J}</math>
  
  
−
:<math>x= \frac{12 x F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \times B \times D^3}</math>
+
:<math>\times= \frac{12 \cdot F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \times B \times D^3}</math>
  
  
 
Max. bending force
 
Max. bending force
−
:<math>\sigma_{max}= \frac{18 x F x L}{(2 + B_{min} /B_{max}) x B_{max} x D^2 }</math>
+
:<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]]

Revision as of 14:45, 30 April 2014

6.4.7 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 (Fig. 6.20). 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})}\times \frac{L^3}{E \times B \times 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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