FLEXURE ENGINEERING FUNDAMENTAL – LEAF SPRING

Construction fundamentals

INTRODUCTION

A plate flexure of ‘leaf spring’ is one of the most fundamental features in flexure engineering and can be used in monolithic structures to fix 3 DOF of an element. The plate flexure can be set in S-mode or in C-mode, dependent on other kinematic constraints. C-mode comprise different flexure stiffness and flexure motion than the S-mode. This Precision Point sheet allows you to compute these to benefit your design.

Was this helpful? Please share this with your colleagues and friends:

S-shape stiffness

C_x=\frac{12EI}{L^3}
C_y=\frac{Etb^3}{4L^3}
C_z=\frac{EA}{L} only if u_x=0
C_z=\frac{700EAI}{L(700I+u_x^2A)} for u_x{\neq}0

K_x=\frac{Etb^3}{12L}
K_y=\frac{EI}{L}=\frac{Ebt^3}{12L}
K_z=\frac{Gbt^3}{3L}=\frac{Ebt^3}{6(1+\nu )L}

S-shape motion characteristics

u_x=\frac{F_x}{C_x}
u_{xmax}=\frac{1}{3}\frac{L^2}{Et}\sigma _{max}
u_z=\frac{3}{5}\ast \frac{u_x^2}{L}

S-shape force limits

F_{z buckling}=4\frac{\pi ^2{EI}}{L^2} only if u_x=0
\sigma _{max}=\frac{M_{max}}{I}\ast\frac{1}{2}t=\frac{\frac{F_xL}{2}}{I}\ast\frac{1}{2}t=\frac{F_xLt}{4I}

dynamic movements: \sigma _{max}< fatigue stress limit

static deformation: \sigma _{max}< yield stress limit (\sigma _{0.2})

C-shape stiffness

C_x=\frac{3EI}{L^3}
C_y=\frac{Etb^3}{4L^3}
C_z=\frac{EA}{L} only if u_x=0

K_x=\frac{Etb^3}{12L}
K_y=\frac{EI}{L}=\frac{Ebt^3}{12L}
K_z=\frac{Gbt^3}{3L}=\frac{Ebt^3}{6(1+\nu)L}

C-shape motion characteristics

u_x=\frac{F_x}{C_x}
u_{xmax}=\frac{2}{3}\frac{L^2}{Et}\sigma _{max}
u_z=\frac{3}{5}\ast\frac{u_x^2}{L}

C-shape force limits

F_{z buckling}=2.045\frac{\pi ^2EI}{L^2} only if u_x=0
\sigma _{max}=\frac{M_{max}}{I}\ast\frac{1}{2}t=\frac{F_xL}{I}\ast\frac{1}{2}t=\frac{F_xLt}{2I}

dynamic movements: \sigma _{max}< fatigue stress limit

static deformation: \sigma _{max}< yield stress limit (\sigma _{0.2})

Leaf Spring S-Shape Deformation

Leaf spring in s-shape deformation: I=\frac {1}{12} bt^3

Leaf Spring C-Shape

This page uses QuickLaTeX to display formulas.