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→6.4.7 Contact Spring Calculations
</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:
:<math>F = \frac{3 \cdot E \cdot J}{L^3} \cdot </math>
where J is the momentum of inertia of the rectangular cross section of the beam
:<math>J = \frac{B x \cdot D^3}{12}</math>
For springs with a circular cross-sectional area the momentum of inertia is
To avoid plastic deformation of the spring the max bending force σ<sub>max</sub> cannot be exceeded
:<math>\sigma_{max} = \frac{3 x \cdot E x \cdot D}{2L^2}x_\cdot_{max}</math>
The stress limit is defined through the fatigue limit and the 0.2% elongation limit resp.
:<math>x_\times_{max} = \frac{2 x \cdot L^2}{3 x \cdot D x \cdot E}R_{p0,2}</math>
<br />and/or<br />
:<math>F_{max} = \frac{B x \cdot D^2}{6L}R_{p0,2}</math>
Deflection
:<math>x \times = \frac{F}{2 x \cdot E x \cdot J}L^3</math>
:<math>= \frac{6 x \cdot F}{E x \cdot B}x \cdot \frac{L^3}{D^3}</math>
Max. bending force
:<math>\sigma_{max}= \frac{18 x \cdot F x \cdot L}{B x \cdot D^2}</math>
<li>'''Trapezoidal spring'''</li>
Deflection
:<math>x\times = \frac{F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E x \cdot J}</math>
:<math>x\times= \frac{12 x \cdot F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \times B \times D^3}</math>
Max. bending force
:<math>\sigma_{max}= \frac{18 x \cdot F x \cdot L}{(2 + B_{min} /B_{max}) x \cdot B_{max} x \cdot D^2 }</math>
</ul>
==References==
[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]
