Pres eucome 2016_v3

ITIA-CNR

Model and analysis of a novel piezo-electric rotational motor based on deformation wave precession

Marco Leonesioa, Nicola Caua,b, Giacomo Bianchia, Paolo Bonfigliob

aCNR Institute of Industrial Technology and Automation (ITIA), Milan, ItalybPhiDrive srl, Vimercate (MB), ItalyEUCOMES 2016 20th-23rd of September 2016, Nantes, France

from research . to market

NFare conclusisoni FIR 2001 w w w.fir.de

ContentsMotivation and objectivesOperating principleKinematic behaviour at steady stateModelling approachConditions for motionCharacteristic curveConclusions

EUCOMES 2016 20th-23rd of September 2016, Nantes, France

NMotivation and objectivesThe need for small, powerful motors continues to grow, often combining a greater miniaturization with higher precision (medical and aerospace sectors): piezo actuated motors match this increasing demand. (*)

A new promising piezo-motor concept has been patented by Bonfiglio & Cau in 2015 (**)

This work is aimed at providing a model to support the preliminary design phase of the above-mentioned piezo-motor concept.(*) M.S. Vijaya, Piezoelectric Matrials and devices Applications in Engineering and Medical Sciences, 2013, CRC Press, Taylor and Francis Group.

(**) Bonfiglio, Paolo, Cau, N. Motor with linear actuators, PATENT EP2875577 (A1), 2015-05-27 (2015)


NOperating principle

Motor Inactive preloadedSteady state stepping

First motion step on pn1

60


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H1) The ring slides on one pin at once, at each step (assured by command law):H2) At steady state, at each step the deformation wave moves of 120 (assumption):

H3) Initial condition:

Kinematic behaviour at steady state

: sliding displacement of the ring over the pin m at the step n

Solution:


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Kinematic behaviour at steady state


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6 nodes ring FEMModelling approach


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Modelling approachPiezos stiffness

Coulombian friction between pins and ring

No friction between piezos and ring ( low friction coatings or rollers)


NConditions for motion

Motor functioning foresees a sequence of steps in which the ring slides on a single pin while sticking on the other two.

The motor is supposed to exert a torque Cext, that is equivalent to consider 3 tangential components at pins point equal to

The motor is studied in the condition of ring incipient motion, i.e., the instants when the system, previously in static equilibrium, undergoes a small variation in external forces and starts to move. Since the accelerations and velocities are still infinitesimal, equations of static equilibrium can be assumed to hold, with an infinitesimal error.

Incipient motion on PIN 3where is the coulombian friction coefficient


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Conditions for motion

Expliciting the terms

where

P3P2P1Cext=0d1=d2=d3=0R=15mm, E=210GParing height: h=6mm ring width: b=2mm Kpz=66N/m=0.2=0.025mmpmax=0.012mm

Solution locus


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Cext= -6Nmd1=d2=d3=0

Cext= -6Nmd1=1/3*S=0.0017mmd2=2/3*S=0.0034mmd3=S=0.0050mmSolution locus corresponding to the motion against the torque shrinks, the other expands.Solution locus corresponding to the motion against the torque translates toward higher piezo displacements on p2.Effect of external torqueEffect of sliding displacement


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Effect of frictionEffect of sliding displacementIncreasing friction, the solution locus enlarges, but moves towards higher values of piezo displacements. Namely, higher torque can be transmitted, but by more performant piezos. Increasing piezos maximum range, the solution locus enlarges. Namely, higher torques can be transmitted. Cext= -6Nmd1=d2=d3=0 from 0.2 to 0.4Cext= -6Nmd1=d2=d3=0pmax from 0.012 to 0.1 = 0.4


NCharacteristic curveConsidering the steady state periodic motion, the limiting condition happens at the end of the step, when the maximum ring deformation occurs.

During this stepping phase pins 1 and 2 must be in stiction while the tangential reaction on the ring sliding clockwise at pin 3 (T5) must be negative:

Selecting a 3-uple [p1, p2, p3,], the last equation becomes a straightline in the plane Text S, that becomes a segment when limited by the other two inequalities. By scanning a proper mesh in the space of piezo displacements, it is possible to obtain the characteristic curve of the motor.(N.B.: Given the commutation frequency of piezo


NCharacteristic curve

-2000-1500-1000-5000500100015002000External Torque (motor