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Modeling and Experimental
Study of a Two Modes Excitation
Travelling Wave Piezoelectric
Miniature Robot
Presented by:
Hass...
2
Travelling Wave Piezoelectric
Miniature Robot
18-20 June2012 Actuator 12
It is a mobile robot that can I move using piez...
3
Planning
I. Introduction
II. Operation principle
III. Modeling of the robot
IV. Description of the prototype
V. Optimal ...
4
Introduction
18-20 June2012 Actuator 12
The standing wave is expressed by : Us(x,t) = A*cos(kx)cos(wt)
The traveling wav...
5
Introduction
18-20 June2012 Actuator 12
[G.H. Kim]: Linear Ultrasonic Traveling Wave Motor
6
Operation principle
18-20 June2012 Actuator 12
Beam structure
Piezoelectric patches
Traveling wave generation
7
Modeling of the robot
18-20 June2012 Actuator 12
 Euler-Bernoulli assumptions for a beam structure
 Linear constitutiv...
8
Description of the prototype
18-20 June2012 Actuator 12
1
23
Prototype (1: Signal generator, 2: power amplifiers and 3: ...
918-20 June2012 Actuator 12
Why is it 11.3 kHz ?
10
Optimal operating frequency (1/5)
18-20 June2012 Actuator 12
n
Mode
shape
Frequency
fn (kHz)
fn+1 (kHz)
f
(kHz)
Wave
pr...
11
Optimal operating frequency(2/5)
18-20 June2012 Actuator 12
n
Mode
shape
Frequency
fn (kHz)
fn+1 (kHz)
f
(kHz)
Wave
pro...
1218-20 June2012 Actuator 12
Experimental verification
13
Optimal operating frequency (4/5)
18-20 June2012 Actuator 12
Pure standing wave Pure traveling wave Superposition of mo...
1418-20 June2012 Actuator 12
Experimental measurements
Robot speed versus embedded mass
on a smooth glass flat surface
Rob...
1518-20 June2012 Actuator 12
Robot speed versus embedded mass
1618-20 June2012 Actuator 12
Summary
The developed FE model and designing procedure have
been validated experimentally.
...
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Travelling Wave Piezoelectric Miniature Robot

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Modeling and Experimental Study of a Two Modes Excitation Travelling Wave Piezoelectric Miniature Robot

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Travelling Wave Piezoelectric Miniature Robot

  1. 1. Modeling and Experimental Study of a Two Modes Excitation Travelling Wave Piezoelectric Miniature Robot Presented by: Hassan HARIRI LGEP Laboratoire de Genie Electrique de Paris Electrical engineering laboratory of Paris Supervised by: Pr. Yves Bernard Pr. Adel Razek
  2. 2. 2 Travelling Wave Piezoelectric Miniature Robot 18-20 June2012 Actuator 12 It is a mobile robot that can I move using piezoelectric actuators by generating a traveling wave motion on it. How we can generate a traveling wave on a limited volume ?
  3. 3. 3 Planning I. Introduction II. Operation principle III. Modeling of the robot IV. Description of the prototype V. Optimal operating frequency VI. Experimental measurements VII. Summary and future work 18-20 June2012 Actuator 12
  4. 4. 4 Introduction 18-20 June2012 Actuator 12 The standing wave is expressed by : Us(x,t) = A*cos(kx)cos(wt) The traveling wave is expressed as : Up(x,t) = A*cos(kx-wt) Using a trigonometric relation, the second expression can be transformed as: Up(x,t) = A*cos(kx)cos(wt)+ A*cos(kx-pi/2)cos(wt-pi/2) Traveling wave Standing wave How we can generate a traveling wave on a limited volume ?
  5. 5. 5 Introduction 18-20 June2012 Actuator 12 [G.H. Kim]: Linear Ultrasonic Traveling Wave Motor
  6. 6. 6 Operation principle 18-20 June2012 Actuator 12 Beam structure Piezoelectric patches Traveling wave generation
  7. 7. 7 Modeling of the robot 18-20 June2012 Actuator 12  Euler-Bernoulli assumptions for a beam structure  Linear constitutive relations  Hamilton Principle Variational equation governing the mechanical and piezoelectric part of the system Finite Element Method FEM Variational equation in matrix form, taking into account the damping behavior of the real system H. Hariri, Y. Bernard, A. Razek, ’’Finite element model of a beam structure with piezoelectric patches using RL shunt circuits’’, AC2011, 14th International Conference on active systems for dynamics markets, Darmstadt, Germany, 2011,pp.124-131
  8. 8. 8 Description of the prototype 18-20 June2012 Actuator 12 1 23 Prototype (1: Signal generator, 2: power amplifiers and 3: robot body) Material/ Ref Dimensions (mm) Weigh t (g) Piezoelectric patche Noliac/ WAE NCE41 35 × 17 × 0.27 1.5 Beam Aluminum 180 × 17 × 0.5 3.5 Adhesive Epoxy 2013 0.2 Xp1=24 mm, Xp2= 126 mm
  9. 9. 918-20 June2012 Actuator 12 Why is it 11.3 kHz ?
  10. 10. 10 Optimal operating frequency (1/5) 18-20 June2012 Actuator 12 n Mode shape Frequency fn (kHz) fn+1 (kHz) f (kHz) Wave propagation direction 15 9 10.3 9.6 16 10.3 11.8 11 17 11.8 13 12.4 18 13 14.3 13.6 Two modes excitation Simulation
  11. 11. 11 Optimal operating frequency(2/5) 18-20 June2012 Actuator 12 n Mode shape Frequency fn (kHz) fn+1 (kHz) f (kHz) Wave propagation direction 15 9 10.3 9.6 16 10.3 11.8 11 Traveling wave on the beam length: superposition of modes (15 & 16) on the left, (16 & 17) on the right Simulation
  12. 12. 1218-20 June2012 Actuator 12 Experimental verification
  13. 13. 13 Optimal operating frequency (4/5) 18-20 June2012 Actuator 12 Pure standing wave Pure traveling wave Superposition of modes 15 & 16 Superposition of modes 16 & 17 Superposition of modes 17 & 18 Superposition of modes 18 & 19 Simulation
  14. 14. 1418-20 June2012 Actuator 12 Experimental measurements Robot speed versus embedded mass on a smooth glass flat surface Robot speed versus applied voltage on a smooth glass flat surface for different applied voltageSpeed versus mechanical load
  15. 15. 1518-20 June2012 Actuator 12 Robot speed versus embedded mass
  16. 16. 1618-20 June2012 Actuator 12 Summary The developed FE model and designing procedure have been validated experimentally. The robot has an optimal operating frequency equal to 11.3 kHz, travelling at 131.5 mm/s at 30 V amplitude without embedded mass.  It can provide 432 µW (7.2 mN, 60 mm/s), at 30 V amplitude. Future work  Developed to obtain a MDOF.  Improve the robustness of the robot.  Working in different medium displacement Miniaturize, embedded electronics, autonomous & cooperative use.

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