2 FLEXURE HINGES OR ELASTIC HINGES IN SERIES (LEAF SPRING)

Construction Design & Examples

INTRODUCTION

2 Elastic hinges or flexure hinges in parallel form a reinforced leaf spring and can be used in monolithic structures to be able to have relative motion or displacement. This sheet elaborates on the design of these flexure hinges to acquire the desired stiffness for your suspension.

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Usage

Used as a stiff alternative (C_x) for a leaf spring. Note that stiffness in other directions increase as well.

Geometric & motion characteristics

L_P=\frac{L_0+L_{RF}}{2}

\beta =\frac {h}{D}

L_{RF}^\# =L_P-\sqrt{(h-T)(T-h-2D)}

_{\#\ If\ hinge\ geometry\ is\ of\ shape\ 1\ or\ 3}

u_z=\frac{F_z}{C_{Bz}}

u_x^{\ast }=\frac{1}{2} \ast \frac {u_z^2}{L_P}

* s-shape and if u_z << L

u_x^{\ast \ast }=\frac{u_z^2}{L_P}}

** c-shape and if u_z << L

\theta _y^{\ast \ast \ast }{\approx}\frac{u_z}{L}

*** s-shape and if u_z << L

\theta _y^{\ast \ast \ast \ast }{\approx}\frac{u_z}{2L}

**** c-shape and if u_z << L

Stiffness at point B

C_{Bx}=\frac{6EbT\sqrt{\beta }}{25T+6L_{RF}\sqrt{\beta }}

C_{Bys-shape}=\frac{2ETb^3\sqrt{\beta }}{25TL^2_P+L^3_{RF}\sqrt{\beta }}

C_{Byc-shape}=\frac{ETb^3\sqrt{\beta }}{50TL^2_P+L^3_{RF}\sqrt{\beta }}

C_{Bzs-shape}=\frac{93ET^3bh^2\sqrt{\beta }}{500T^3L^2_P+93h^2L^3_{RF}\sqrt{\beta }}

C_{Bzc-shape}=\frac{93ET^3bh^2\sqrt{\beta }}{2000T^3L^2_P+93h^2L^3_{RF}\sqrt{\beta }}

K_{Bx}=\frac{Eb^3T^3\sqrt{\beta }}{42.6T^3\left (1.2+\frac {D}{h})\right + 6L_{RF}b^2(1+\nu )\sqrt{\beta }}

K_{By}=\frac{Ebh^2T^3\sqrt{\beta }}{\frac {129T^3}{6}+12L_{RF}h^2\sqrt{\beta }}

K_{Bz}=\frac{ETb^3\sqrt{\beta }}{50T+12L_{RF}\sqrt{\beta }}

Stress

Determinative for the stroke \theta _y:

\sigma _{max}^{\ast }=0.58E\sqrt{\beta }\ast \theta _y

* s-shape

\sigma _{max}^{\ast \ast }=0.58E\sqrt {\beta }\ast \frac {\theta _y}{2}

**c-shape

2 Elastic hinges in series and in s-shape deformation

2 elastic hinges in series and in s-shape deformation.

Versions with equal h, Cx and Ky
2 Elastic hinges in series shape 1-3
2 Elastic hinges in series shape 4-6

This page uses QuickLaTeX to display formulas.