LEAF SPRING / FLEXURE – REINFORCED

Construction Design & Examples

INTRODUCTION

Flexures or leaf springs can be used for play and friction free motion. A downside is stiffness and to minimize the needed force, the flexures are made slender and thin. Smart reinforcement of flexures and leaf springs can help to keep the needed motion-force minimal while the flexure or leaf spring is made thicker, which is beneficial for its carrying stiffness and easier to manufacture which will decrease the manufacturing costs.

 

This sheet helps you to design such a reinformcement and also the analytical derivation is given (see downloads).

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Design parameters

\lambda =\frac{L_s}{L_0}
0<\lambda <\frac {1}{2}

\gamma =\frac t T
0<\gamma <1

L_P=L_{RF}+L_s=(1-\lambda )L_0

Deformation characteristics

u_z=\frac {F}{C_z}
u_x=\frac{u_z^2}{2L_0(1-\lambda )}

S-shape stiffness

C_x=\frac {1}{2\lambda (1-\gamma )+\gamma }\ast \frac {Etb}{L_0}
C_y=\frac {1}{2\lambda (4\lambda ^2-6\lambda +3)(1-\gamma)+\gamma }\ast \frac {Etb^3}{L_0^3}
C_z=\frac {1}{2\lambda (4\lambda ^2-6\lambda +3)(1-\gamma ^3)+\gamma ^3}\ast \frac {Ebt^3}{L_0^3}
K_x=\frac {1}{2\lambda (1-\gamma ^3)+\gamma ^3}\ast \frac {Gbt^3}{3L_0}
K_y=\frac {1}{2\lambda (1-\gamma ^3)+\gamma ^3}\ast \frac {Ebt^3}{12L_0}
K_z= \frac {1}{2\lambda (1-\gamma )+\gamma }\ast \frac {Etb^3}{12L_0}

Force limits

F_{x buckle}=\frac {1}{3} \frac{\pi ^2Ebt^3}{(2L_s)^2} or F_{x buckle}=\frac {1}{12}\frac{\pi ^2EbT^3}{L_{RF}^2}
Whichever buckles first: First eq. if: \frac {1}{\lambda ^2}<\frac {1}{\gamma ^{3(1-2\lambda )^2}}

Leaf spring - Reinforced
Design guidelines

Keep

\frac {1}{10}<\lambda <\frac {1}{3}

and

\frac {1}{10}<\gamma <\frac {1}{2}

Typical

\lambda =\frac {1}{6}

and

\gamma =\frac {1}{5}

Then:

C_x = 2.1\ast \frac {Etb}{L_0}

C_y=1.3\ast \frac{Etb^3}{L_0^3}

C_Z=1.4\ast \frac {Ebt^3}{L_0^3}

F_{x buckle}=\frac {1}{3} \frac{\pi ^2Ebt^3}{(2L_s)^2}

K_x=3.0\ast \frac{Gbt^3}{3L_0}

K_y=3.0\ast \frac{Ebt^3}{12L_0}

K_z=2.1\ast \frac {Etb^3}{12L_0}

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