1. Modeling and Characterization of a Linear PiezoMotor Mustafa Arafa, Osama Aldraihem*, Amr Baz 5 th International Symposium on Mechatronics and its Applications (ISMA’08), 27- 29 May, 2008, Amman, Jordan

2. This work has been funded by King Abdulaziz City for Science and Technology (KACST) Grant # 28-115. Special thanks are due to Prince Dr. Turki Al-Saud, KACST VP, the technical monitor for his invaluable technical inputs and support. Acknowledgement

3. Outline  Concept of smart snake robots  Linear PiezoMotor  Dynamic model  Numerical and experimental methods  Results & conclusions

4. Muscle (Peizo-actuator) contracting Muscle (Peizo-actuator) extending Vertebra Concept of smart snake robots A single piezoelectric actuator is used to connect neighboring vertebra. No need for complex mechanisms, gears, or any moving parts. Yaw Pitch (a)- degrees of freedom (b) – in-plane motion (c) – out-of-plane motion

5. Concept of … Cont. Applications include: unmanned robots, surveillance, communication, laparoscopic surgery, etc. New generations will maneuver through caves & confined tunnels. Radical departure from conventional designs.

6. 1.Characterization of the Piezoelectric actuators (PEA) 2.Modeling and experimental validation of PEA dynamics 3.Optimization of topology (shape) of snake segments 4.Integrating PEA models with the dynamics of the snake structure 5.Validating theoretical predictions experimentally 6.Demonstrating experimentally the feasibility of the concept of smart snake robots with piezoelectric actuators Research objectives

7. Piezoelectric linear motor Source: Johansson, S., Bexell, M. and Jansson, A., “Fine control of electromechanical motors” US Patent No. 2004/0007944A1, 2004 PiezoMotor Construction: Drive rod Rollers Springs

8. Piezoelectric linear motor Drive rod Piezoelectric bimorphs Operating Principle: Four Piezoceramic bimorphs (Two layers). Each bimorph can be expanded, contracted and bended by applying voltages. No voltage Right layer under voltage Both layers under voltage Left layer under voltage

9. Real Operation

10. Dynamic model Bimorph: each element consists of alternating layers of active piezoelectric and electrodes, forming a multi-layer piezoceramic “d 33 bimorph”. External loads: applied electric field, axial load by drive rod, and transverse friction. 3.5 mm w 2h2h L Length, L3.5 mm Width, w3 mm Thickness, h1.35 mm Geometrical properties: 3 mm 88 layers

11. Dynamic model…Cont. Constitutive equation: For a single piezoelectric layer Piezoelectric strain constant, d eff 33 4.76 x 10 -8 m/V Elastic modulus, E63 GPa Density7600 kg/m 3 Material properties: Geometrical Coordinate Poling directions 3, x Material Coordinate Single layer Where is the effective piezoelectric coefficient

12. h M F M F U M F M F L Dynamic model…Cont. It follows that: Axial strain: Upon activation of layers, F & M develop (No Mechanical loads):

13. Dynamic model…Cont. For a statically applied field, the tip displacement is: Bending: Extension/ contraction: Trapezoidal supply voltagesTip follows rhombic trajectory a b c d x y x y L h

14. Dynamic model…Cont. Axial loading Each bimorph is loaded axially during half the drive cycle. Then, it carries no axial load and repositions itself in preparation for the next half cycle. Process keeps alternating. Axial displacements are significantly small compared to the initial compression of the preload spring. Assume that preload remains constant and is always shared by two bimorphs. Click to play

15. is coefficient of friction Transverse friction forces N/2  N/2 N/2 Lo Free-body diagram N is normal force from rollers L 0 is external load Based on experimentation, rod velocity decreases with load L 0 : v = drive rod velocity V = bimorph tip velocity v s = slip velocity

16. Transverse friction forces…Cont.  vsvs (a) Friction models (a) Coulomb For constant velocity motion: Hence a Coulomb friction model cannot be used! NOT CONSTANT (b) (b) Viscous During sticking: v s = 0  vsvs = 0 f = 0 NO DRIVING FORCE WITHOUT SLIPPING!

17. Transverse friction forces  vsvs (c) Coulomb & viscous Sticking Slipping During the stick state, the friction force can take on any value between an upper and lower limit, including zero, depending on the applied external load, and the velocity of the bimorph tips is completely transferred to the drive rod. As the applied external load increases beyond a certain limit, slipping commences, and the drive rod velocity drops.

18. Numerical & experimental methods Response to arbitrary input voltage, axial & transverse loads using FEA = structural degrees of freedom {u(t)} = vector of external loads from axial load, transverse load and bending moment acting on the bimorph tip due to the applied electric field and drive rod interaction.

19. Numerical & experimental methods Free bimorph: Input voltage as measured experimentally Supply voltage varies in a trapezoidal manner. Amplitude: 24 V; frequency: 925 Hz Every bimorph is driven by a pair of excitations that are phase shifted by 90°.

20. Input voltage and applied excitation moment for FE model Numerical & experimental methods

21. Tip displacement of bimorph Results Maximum displacement of about 1.24  m Velocity of an unloaded PiezoMotor is about 4.59 mm/s.

22. Comparison of numerical and experimental velocities Results

23. Experimental setup Experimental work Loaded bimorph Laser Sensor Piezomotor Weight Bracket Loads Piezomotor Laser sensor

24. Experimental load-velocity relationship Experimental work Experimental Fit Experimental Fit vsvs

25. Conclusions Dynamic modeling of linear piezomotor  Response to various loads and excitation schemes  Appropriate friction model is used to account for the friction between the bimorph and the drive rod  Experimental testing of piezomotor to validate theoretical model This effort aims ultimately at demonstrating the feasibility of employing this class of piezoelectric actuators in driving smart snake robots

26. Prototype

28. THANK YOU!