Difference between revisions of "Contact Spring Calculations"

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===6.4.7 Contact Spring Calculations===
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[[File:One side fixed contact bending spring.jpg|right|thumb|One side fixed contact bending spring]]
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Fig. 6.20:
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One side fixed contact bending spring<br />
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L = Length of spring<br />
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E = Modulus of elasticity<br />
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B = Width of spring<br />
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F = Spring force<br />
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D = Thickness of spring<br />
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x = Deflection<br />
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max = maximum bending force
  
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The influence of the dimensions can be illustrated best by using the single side fixed beam model (Fig. 6.20). For small deflections the following equation is valid:
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:<math>F = \frac {3 x E x J}{L^3} x</math>
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where J is the momentum of inertia of the rectangular cross section of the beam
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:<math>J = \frac {B x D^3}{12}</math>
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For springs with a circular cross-sectional area the momentum of inertia is
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:<math>J=\pi D^4/64</math>
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:<math>D= Durchmesser</math>
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To avoid plastic deformation of the spring the max bending force σ<sub>max</sub> cannot be exceeded
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:<math>\sigma _{max} = \frac {3 x E x D}{2L^2}x_{max}</math>
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The stress limit is defined through the fatigue limit and the 0.2% elongation limit resp.
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:<math>x _{max} = \frac {2 x L^2}{3 x D x E}R_{p0,2}</math>
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<br />and/or<br />
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:<math>F _{max} = \frac {B x D^2}{6L}R_{p0,2}</math>
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<li>'''Special Spring Shapes'''</li>
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<ul>
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<li>'''Triangular spring'''</li>
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Deflection
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:<math>x = \frac {F}{2 x E x J}L^3</math>
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:<math>= \frac {6 x F}{E x B}x \frac{L^3}{D^3}</math>
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Max. bending force
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:<math>\sigma _{max}= \frac {18 x F x L}{B x D^2}</math>
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<li>'''Trapezoidal spring'''</li>
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Deflection
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:<math>x= \frac {F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E x J}</math>
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:<math>x= \frac {12 x F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \times B \times D^3}</math>
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Max. bending force
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:<math>\sigma _{max}= \frac {18 x F x L}{(2 + B_{min} /B_{max}) x B_{max} x D^2 }</math>
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</ul>
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==References==
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[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]

Revision as of 14:28, 2 April 2014

6.4.7 Contact Spring Calculations

One side fixed contact bending spring

Fig. 6.20: One side fixed contact bending spring
L = Length of spring
E = Modulus of elasticity
B = Width of spring
F = Spring force
D = Thickness of spring
x = Deflection
max = maximum bending force

The influence of the dimensions can be illustrated best by using the single side fixed beam model (Fig. 6.20). For small deflections the following equation is valid:

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

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

J = \frac {B x 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 x E x D}{2L^2}x_{max}

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

x _{max} = \frac {2 x L^2}{3 x D x E}R_{p0,2}


and/or

F _{max} = \frac {B x D^2}{6L}R_{p0,2}


  • Special Spring Shapes
    • Triangular spring

      • Deflection

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


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


      Max. bending force

      \sigma _{max}= \frac {18 x F x L}{B x D^2}
    • Trapezoidal spring

      • Deflection

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


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


      Max. bending force

      \sigma _{max}= \frac {18 x F x L}{(2 + B_{min} /B_{max}) x B_{max} x D^2 }

    References

    References

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