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- 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 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 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 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 Introduction 18-20 June2012 Actuator 12 [G.H. Kim]: Linear Ultrasonic Traveling Wave Motor
- 6. 6 Operation principle 18-20 June2012 Actuator 12 Beam structure Piezoelectric patches Traveling wave generation
- 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 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. 918-20 June2012 Actuator 12 Why is it 11.3 kHz ?
- 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 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. 1218-20 June2012 Actuator 12 Experimental verification
- 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. 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. 1518-20 June2012 Actuator 12 Robot speed versus embedded mass
- 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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