design of adjustable stiffness spring

ASEMINAR

ONDESIGN OF ADJUSTABLE

STIFFNESS SPRING

ByAshton Menezes12ME63R08

CONTENTS

Why use Adjustable stiffness springs ?

Introduction

Mechanism

Mathematical Modeling

Experimental Results

Conclusion

References

WHY USE ADJUSTABLE STIFFNESS SPRINGS?

> (for isolation)If W is low, soWn should lower than W,But Wn =

Mass m is fixed so we have to decrease k , Xstatic =

For a low value of k, Xstatic is very large which is not practicable , so we use adjustable stiffness springs according to the requirement.

mk

k

gm

2WnW

In Industrial activities where robots are used; Reducing the stiffness protects the robot

against possible impacts with humans, facilitates dexterous tasks such as polishing or peg-in-hole, etc.

Low compliance deteriorates the robot’s accuracy and load capacity and makes control more difficult.

A robot able to adapt its stiffness according to the type of task or movement could maintain the advantages of both stiff manipulators and safe-dexterous compliant ones.

INTRODUCTION Variable stiffness actuators work on three principal

technologies: Electro-active polymers (EAPs)

Pneumatic artificial Muscles

Adjustable-stiffness elastic elements. Here we will focus only on adjustable stiffness elastic

elements. Adjustable-stiffness elastic elements, consists an elastic

passive element whose stiffness can be adjusted.

Above image from www.mech.vub.ac.be

INTRODUCTION An adjustable-stiffness spring has two non-linear

springs clamped at each end. The global stiffness of the system can be adjusted

by modifying the shape of the these springs.

1 & 2 - Bars where force is applied. 3 - Elastic element.

MECHANISM

1. & 2. Bars 5. C shaped element3. Leaf spring 6. Rollers4. Screw 7. Electric motor

Prototype Model

MECHANISM

If δ < δ’ thenΔX > ΔX’, for the same force F.

MATHEMATICAL MODELING

For a fixed roller position given by the aspect ratio α = The deformed shape y(x) for the leaf spring is given by the

solution of the following non-linear differential equation.

[ from the equation of curvature]

f

f

YX


Where and are both the horizontal and vertical distance between the extremes of the leaf spring, and the term EI is the flexural stiffness.

fX fY


The solution of the nonlinear differential equation is..

where the parameter a is obtained by imposing that

y( ) = 0, that is, a is numerically computed from the integral equation ..

fX


Once the deformed shapes have been obtained, the stored energy in one leaf spring is numerically computed through the expression

Therefore, the horizontal force in one leaf spring is

obtained from the first derivative of the potential energy, i.e.


Assume a spring displacement where xf is the new horizontal position of the right

extreme for a given load. Now considering all of the four leaf springs working

together, the global or equivalent force of the actuator is obtained as..

and the global stiffness as..

for a fixed value of α.

Mechanical behaviour of a leaf spring versus aspect ratio for a fixed value of yf =40.5mm

EXPERIMENTAL RESULTS Experiments were performed for different aspect ratios

of the leaf spring. For α=3.5 ( δ =60 ×10−3 m) to α=2.0 (δ = 180×10−3m), that

allows us to obtain a stiffness value k between 1000 N/m and 16,000 N/m.

As a result of the experimental test, force versus displacement values were obtained.

EXPERIMENTAL RESULTS

For α = 3.5

For α = 3.25

For α = 3.0

For α = 2.75

For α = 2.5

CONCLUSION This seminar proposes a new model of an adjustable-

stiffness spring. The proposed device has four leaf springs with non-linear

elastic deformations. The geometry of the leaf spring can be modified by means

of an electric motor that adjusts the stiffness of the spring to the desired value.

The most important characteristic is its large stiffness range (with variations greater than 1500%), and its scalability for working with very high and very low loads.

These characteristics allow the spring to be used for different purposes, like robotics, automotive engineering etc.

REFERENCES Design of an adjustable-stiffness spring: Mathematical

modeling and simulation, fabrication and experimental validation by A. González Rodríguez , J.M. Chacón, A. Donoso, A.G. González Rodríguez.

A variable stiffness vibration absorber for minimization of transient vibrations P. L. Walsh and j. S. Lamancusa. Department of Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.

Engineering Mechanics of solid by EGOR. P. POPOV, Prentice hall publication,2002.

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design of adjustable stiffness spring

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