Method and Apparatus for Structural Actuation and Sensing in a Desired Direction

Technical Field

The present invention is directed to the directional attachment of an actuator/sensor to a substrate. More specifically, the present invention is directed to the directional attachment of an actuator/sensor to a substrate such that it is possible to actuate/sense strains in the substrate in a desired direction, regardless of the passive stiffness properties of the substrate, actuator element, or sensor element.

Background Art

Currently, a structure can only be actuated by a piezoelectric, magnetostrictive, thermally actuated lamina (including bimetallic) or shape memory alloy (SMA) elements isotropically, which means that a twist or torsional deflection can be produced in the structure if and only if it is fully attached and extension-twist or bending-twist coupled. The same holds true for sensing; currently, a structure must be fully attached and extension-twist coupled or bending-twist coupled to piezoelectric, magnetostrictive, thermally actuated lamina (including bimetallic) or shape memory alloy (SMA) sensors aligned to sense the twist through the amount of extension or bending. Figure 7 shows two fully attached actuator/sensor elements 10 attached to a substrate 30 in a bending-twist coupled arrangement. Figure 8 shows two fully attached actuator/sensor elements 10 attached to a substrate 30 in an extension twist coupled arrangement. Thus, these arrangements do not allow twist or torsional deflections in a substrate to be actuated or sensed regardless of the

passive structural properties of the substrate.

Coupling actuator/sensor elements to structures has been shown to be particularly useful in controlling and reducing vibration in several types of aeronautical and aerospace structures. Applications include vibration suppression in space trusses, dynamic control of camber and twist for gust alleviation and flutter suppression on fixed wing surfaces. Vibration suppression in rotorcraft could also be enhanced through the use of intelligent actuators because current methods of vibration reduction in rotorcraft or helicopters do not address some of the vibration inducing phenomena that occur in actual helicopters including differences in individual blade tracking and magnitude and locations of dynamic stall. Because the unsteady bending moments in a rotor blade are several orders of magnitude greater than present intelligent actuators can impart, direct manipulation of the rotor blade and bending is currently not feasible. However, through blade twist manipulation many types of vibration reduction methods can be employed including suppression of blade vibrational modes, in flight tracking and dynamic stall reduction through small amplitude pitch oscillation, as well as higher harmonic control (HHC) and individual blade control (IBC) .

Implementation of dynamic blade twist requires the introduction of torsional forcing to orthotropic or quasi- orthotropic blade structures such as uncoupled composite or aluminum blades. Since nearly all composite rotor blades in use today have such characteristics, a method of torsional forcing must be developed. Many types of intelligent actuation devices, including piezoelectric actuators, in production today are incapable of imparting this torsional forcing due to their quasi-isotropic nature.

Therefore, these systems do not allow the coupling of actuators/sensors to rotor blades in such a way that the behavior of the actuators/sensors is anisotropic.

Through classical laminated plate theory, the 5 principles of directional attachment can be examined. Assuming the actuator/sensor is isotropic or quasi- isotropic, as most suitable actuator/sensor materials are, it is not possible to directly actuate or sense strains that arise from torsional deformations.

10 For an isotropic material, the longitudinal modulus, E _L , the transverse modulus, E _τ , and the Poisson's ratios, v _LT , v _TL , are equal. Utilizing the mathematical analysis given in "Mechanics of Composite Materials", Jones, R.M. , published by Hemisphere Publishing Company, New York, N.Y.,

15 1975, the reduced stiffnesses (in tensor notation) as given by equation 2.61 in Jones, 1975, are as follows:

(1)

■Eim = reduced stiffness in longitudinal direction (GPA, MSI) 0 £ ₂₂₂₂ = reduced stiffness in transverse direction (GPA, MSI) ■E ₁₁₂₂ ⁼ reduced coupling stiffness (GPA, MSI)

■E ₁₂₁₂ ⁼ shear modulus (GPA, MSI)

For isotropic actuator/sensor elements, from equations

1, -Eim = £ _{2222 *} ^{If tne} actuator/sensor element is rotated to a particular angle with respect to the laminate or substrate, the rotated reduced stiffnesses are given by equations 2.80, Jones 1975, as follows:

li li

1111 ^" E* _nl Cos ø 2 ' ^; (E ^C '*1122+2E* )Sin 2 2 ⁺ ^12i2 ^iW θCos Θ Ec* ₂₂₂ -Sin Θ n 2 2 U

2222 ^" E ^C *l 1 _j Sin Θ + 2(E* ₁₂₂ +2E* ₂₁₂ )Sin ΘCos Θ + E* ₂₂₂ Cos θ

^E 1122 ⁼ ^ ^E * ₁₁ +E* ₂₂₂ -4E* ₂₁₂ )Sin 0Cos ² β + E* ₁₂₂ (Sin ø+Cos ø) (E ^c, *l ₁₁ +E ₂₂₂₂ -2E* ₁₂₂ -2E* ₂₁₂ )Sin OCos Θ + E* ₂₁₂ (Sin Θ+Cos ©)

^• 1112 ^' (E» ₁₁ -E* ₁₂₂ -2E* ₂₁₂ )SinθCos ³ θ + (E* ₁₂ ,-E* ₂₂₂ +2E* ₂₁₂ )Sin ³ 0Cosø

!21 (E* ₁₁ -E* ₁₂₂ -2E* ₂₁₂ )Sin ^J OCosO + (E* ₁₂₂ -E* ₂₂ .,+2E* _{2I 2} )SinθCos ³ θ

(2)

From equations 2, for an isotropic actuator/sensor element, it is seen that the rotated reduced stiffnesses are the same as the non-rotated stiffnesses and Eι ₁₁₂ = £ ₂ 212

= 0. Accordingly, the rotation angle has no effect on an actuator/sensor material that is completely integrated into or attached to a substrate. The strain energy in a beam demonstrates the relationship between the passive structure or substrate (laminate, lam.) and the actuator/sensor (a/s) as follows:

1am

^e 11 longitudinal extension strain (M/M, IN/IN) ^e 22 transverse extension strain (M/M, IN/IN) ^C °12 shear strain (M/M, IN/IN) ^κ °ll longitudinal bending (RAD/M) ^κ °22 transverse bending (RAD/M) ^κ °12 twist (RAD/M)

N = number of plys, k = individual ply, z = distance through the thickness, as given in Jones, 1975.

For piezoelectric crystals, the strain actuation matrix is composed of actuation voltages, E _x , and charge coefficients, d _χx , and according to equation 29 from a paper titled "Development of Piezoelectric Technology for Applications in Control of Intelligent Structures" by Crawley, E.F. et al. presented at the American Control Conference, June 1988, are related to the actuation strain matrix by,

0 0 0 0 '15 0

[e?., 22"12 11 22 ^■ 12- [E. lE'-.2E'-3,] 0 0 0 d 1,5 0 0, (4)

'31 '31 '33 0 0 oi

E = charge across crystal in longitudinal direction (V) E ₂ = charge across crystal in transverse direction (V) E ₃ = charge across crystal in thickness direction

(V) d ₃₁ = transverse charge coefficient

(μ strain/ _(V/mm) ) d ₃₃ = direct charge coefficient (μ strain/, _v / _mm) ) d ₁₅ = shear coupling charge (μ strain/, _v /nim ₎ )

Similarly, for a piezoelectric sensor, the strain sensing matrix is composed of sensing voltages, V _χ , and voltage coefficitntε, g _χχ .

(5)

V _χ = potential across crystal in longitudinal direction

V ₂ = potential across crystal in transverse direction V ₃ = potential across crystal in thickness direction g ₃₁ = transverse voltage coefficient g ₃₃ = direct voltage coefficient g ₁₅ = shear coupling voltage

For practical purposes, the only voltages that can be

actuated or sensed are through the thickness of the actuator/sensor element (E ₃ d ₃₁ , V ₃ g ₃₁ ) because of the lead attachment area, equations 6 and 7 follow:

r ^L _ε °11ε ^E °22 _ε °12 _K 11 κ„2,2 *,1,2] ^J s= [ ^l E,3d,31, E ₃ 3d ₃ ³ ₁ ¹ 0 0 ^{0 0] (} 6 ⁾

ΓL _P ^ε Oιι _P ^ε O22 _E ^ε Oi2 _K κ _{n K} κ ₂ 2 [ ^L V„3g ^& -3,i V,3g°3-,i 0 0 0 0] ⁽ 7 ⁾

From equations 1 through 7, the only types of actuation/sensing that current (isotropic) types of fully attached actuator/sensor elements can actuate/sense are longitudinal extension, e ⁰ ^, lateral extension, e° ₂ , longitudinal bending, κ , and lateral bending, κ ₂₂ - For the fully attached, isotropic actuator/sensor, e° ₁₁ cannot be distinguished from e° ₂₂ ' ^{and κ} ιι cannot be distinguished from κ ₂₂ . The shear strain, e° ₁₂ , and the twist, κ ₁₂ , cannot be actuated or sensed at all.

Disclosure of the Invention

Accordingly, one object of the present invention is to provide a novel system of directionally attaching of an actuator/sensor to a structure in which it is possible to sense a strain in the structure or actuate the structure in a desired direction, regardless of the passive stiffness properties of the structure, actuator element, or sensor element.

Another object of the present invention is to attach an actuator/sensor to a structure such that torsional and bending deflections can be actuated/sensed.

Yet a further object of the present invention is to

-8-

attach an actuator/sensor to a structure such that the actuator/sensor behaves in an anisotropic way.

These and other objects are achieved according to the present invention by providing a new and improved apparatus, system and method for actuating or sensing strains in a substrate, including at least one actuator/sensor element having transverse and longitudinal axes, wherein the actuator/sensor element is attached to the substrate in such a manner that the stiffness of the actuator/sensor element differs in the transverse and longitudinal axes of the actuator/sensor element.

Brief Description of the Drawings

A more complete appreciation of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:

FIGURE la and lb represents first and second embodiment of a directionally attached actuator/sensor and substrate;

FIGURE 2(a-h) represents alternative techniques of a directionally attached actuator/sensor;

FIGURE 3 represents a third embodiment of a directionally attached actuator/sensor;

FIGURE 4 represents a side view of the embodiment of FIGURE 3;

FIGURE 5 represents an end view of the embodiment of

FIGURE 3 .

FIGURE 6 represents an aeronautical element utilizing particular actuator/sensors of piezoelectric crystals which are directionally attached;

FIGURE 7 represents a bending-twist coupled actuator/sensor element and substrate; and

FIGURE 8 represents an extension-twist coupled actuator/sensor element and substrate.

FIGURE 9 represents a feedback control system for use with a directionally attached actuator/sensor system.

Best Mode for Carrying Out the Invention

Referring now to the drawings wherein like reference numerals designate identical or corresponding parts throughout the several views and more particularly to FIGURE 1(a) thereof, in which a first embodiment of a directionally attached piezoelectric actuator/sensor of the present invention is shown.

The present invention can operate utilizing piezoelectric, magnetostrictive, shape memory alloy (SMA) and thermally actuated lamina (including bimetallic) actuator/sensor elements, and in a preferred embodiment utilizes piezoelectric actuator/sensor elements.

The present invention can operate in a preferred embodiment utilizing conventional stamped and extruded piezoelectric elements. Conventional stamped piezoelectric elements, however, have been found to be about 1.5 times more effective than extruded piezoelectric elements.

Furthermore, the present invention is operable on any substrates which actuator/sensor elements are conventionally coupled to such as aluminum, graphite/epoxy composites, etc. Furthermore, conventional circuitry can be used to generate and apply to the actuator element actuation signals, or to sense signals produced by the element in the detection of strains occurring in a substrate.

The present invention utilizes a system of directional attachment of an actuator or sensor element onto a substrate such that strains can be sensed or generated in a desired direction, independent of the passive stiffness and geometric properties of the substrate, actuator or sensor material. In this way, an isotropic actuator/sensor element is attached to a substrate in such a way that its behavior is anisotropic. To achieve these results the present invention utilizes a partial attachment system as shown in FIGURE 1(a), in which a portion of the actuator/sensor is made inactive in one strain (i.e., the transverse strain) and is made active in the other strain (i.e., the longitudinal strain). As shown in Figure l, an actuator/sensor 10 is attached to a substrate 30 only in the area defined as the area of attachment 20. This area of attachment can take on an area in the range of approximately the central 1/5 to 3/4 of the actuator/sensor element. In a preferred embodiment, the area of attachment will occupy approximately the central 1/3 (third) of the width of the actuator/sensor and substrate and run the entire length of the actuator/sensor.

FIGURE 1(b) represents an inverse ellipse partial attachment pattern which the area of attachment between the actuator/sensor and substrate can take on to achieve the same results as that of FIGURE 1(a).

The actuator/sensor elements can be attached to the substrate using conventional surface bonding techniques utilizing a bonding agent such as M-Bond 200~ manufactured by The Loctite Co. (through M-Line Products) or a conventional epoxy. Another way to attach the actuator/sensor elements is by embedding the actuator/sensor elements into the substrate.

Figures 2(a-h) detail other possible partial attachment systems. Figure 2(a) shows the inverse elipse pattern described in Figure 1(b) above and Figure 2(b) shows the central third attachment pattern described in Figure 1(a) above. As shown in Figure 2(c) the bonding agent may also be only applied to the piezoelectric element at its edge portions in its traverse axes. As shown in Figure 2(d) the actuator/sensor element need only be rigidly attached at its transverse axes edges. As shown in Figure 2(e-h), the actuator/sensor element can be embedded in the substrate utilizing any of the above cited patterns so long as the edges in the transverse axes are rigidly attached and the edges in the longitudinal axes are flexibly attached.

The flexible attachment areas and rigid attachment areas can be effectuated by the manner in which the actuator/sensor element is either placed on the surface of the substrate on embedded into the substrate. That is, with reference to Figures 2(e-h), the actuator/sensor elements will be embedded into a slot in the substrate. The size of the slot in the substrate can be manipulated to provide the flexible and rigid attachment areas. That is, if the size of the slot in the substrate is chosen such that the actuator/sensor element fits snugly in the slot in the longitudinal direction and loosely in the slot in the

transverse directions, then the rigid (snug) and flexible (loose) attachments as shown in Figures 2(e-h) will be effectuated. The slot in which the actuator/sensor element is embedded then must be slightly larger than the actuator/sensor element in the transverse direction, allowing enough extra space for the actuator/sensor element to expand and just large enough in the longitudinal direction to allow the actuator/sensor element to fit into the slot. Thus, by the actuator/sensor element fitting snugly in the substrate in the longitudinal direction and loosely in the substrate in the transverse direction, a rigid attachment in the longitudinal direction and a flexible attachment in the transverse direction will be effectuated. As to Figure 2(d), the manner in which the actuator/sensor element is placed on the surface of the substrate can also effectuate a rigid attachment at its transverse axis edges. This can be accomplished, for example, by placing the actuator/sensor element between two rigid members which extend above the surface of the substrate, or in any other conventional manner.

The embodiments shown in FIGURES 1 and 2 operate such that when the actuator/sensor element becomes active, stress is rapidly distributed to the free edges in the longitudinal strain. In this way, the embodiments of FIGURES l and 2 operate such that the unattached sides of the actuator/sensor element contribute to the longitudinal stiffness of the element and therefore make the actuator/sensor element impart more longitudinal than transverse stiffness to the substrate. In this way, the end effect is that the stiffness of the actuator/sensor as seen from the substrate is greater in the longitudinal direction than it is in the transverse direction.

FIGURES 3-5 show a second system of attaching an

actuator/sensor to a substrate in such a way that the same results as described with reference to FIGURES 1 and 2 are achieved. The system of FIGURES 3-5 achieves these results by increasing the aspect ratio and bond line thickness of the actuator/sensor element to the point where the finite amount of shear lag present in the bond line significantly reduces the transverse stiffness of the element. The aspect ratio is defined as L _a / _B /W _a / _S and the bond line thickness is shown as B _τ in Figures 3-5. The aspect ratio should take on values greater than 10:1 and the bond line thickness should be approximately the same as the actuator/sensor element thickness. The greater the aspect ratio the more improved the performance and the aspect ratio should ideally be infinite. Also, the bond line thickness will need to be optimized in each individual application but generally will be approximately the same thickness as the actuator/sensor element. FIGURES 3-5 detail exaggerated deflections of the bonding material to illustrate the finite shear lag in longitudinal and transverse directions. The effective length of the actuator/sensor Le reflects the effective length of the actuator that actually produces strain in the substrate or the length of the sensor that actually has strain produced in it by the substrate. In the system of FIGURES 3-5 the ratio of the effective length of the actuator/sensor Le divided by the actual length La/s should be approximately equal to one. Furthermore, in this preferred embodiment Le/La should be a factor of 2 or more greater than the width effectiveness ratio, We/Wa. By tailoring the thickness of the bond line and attachment area, the transverse shear lag can produce the beneficial effect of further reducing the effective width of the actuator/sensor while maintaining a high effective length.

One further approach to achieving the results of the

directional attachment of the present invention is to utilize a system which combines the partial attachment technique of FIGURES 1 and 2 with the transverse shear lag techniques of FIGURES 3-5.

Since directional attachment effectively reduces the stiffnesses of the actuator/sensor, E _Ta/ , _B ≠ E _La , _B . From equations 1 the reduced stiffnesses, E* _lllla / _B ≠ E* _2222a / _B and from equations 2, the rotated reduced stiffnesses are not equal to the non-rotated values with E _1112a / _S * 0, E ₂₂ i2a/ _B ^≠ 0. The resulting actuation/sensing stiffness matrix is fully populated. With the implementation of directional attachment, equation 3 takes the form of equation 8.

ev, *?2. dl ^κ l l ^C 22 a/s 1a,τ.

(8)

Equation 8 shows that through directional attachment, any mode of strain can be forced/detected if the actuator/sensor is sensitive to just one or two extensional strains: e° _1:L and/or e° ₂₂ . Most types of sensor/actuator materials are isotropic and sensitive in just this way. And as demonstrated by equations 4 through 7, actuator/sensor elements are particularly well suited for directional attachment.

Figure 6 shows one implementation of directionally attaching actuator/sensor elements onto an aeronautical member such as an airfoil or rotor blade.

In a preferred embodiment, those actuator/sensor elements are piezoelectric elements, but may also be magnetostrictive, shape memory alloys or thermally actuated lamina (including bi-metallix) elements. As shown in Figure 6 a plurality of piezoelectric elements 10, as represented by the dark lines, are attached to an aeronautical member 50 at an angle, which may be, for example, 45°. The piezoelectric elements 10 are attached n one of the above-described techniques, that is, utilizing either of the partial attachment systems detailed in Figures l or 2, the system detailed in Figures 3-5 or a combination of the above two systems. Utilizing one of the above-described directional attachment techniques the piezoelectric elements 10 will behave in an anisotropic way and thus are able to impart a torsional deflection or sensing to the aeronautical element. This torsional deflection or sensing can then be implemented for such reasons as vibration reducing, in-flight tracking blade and dynamic stall reduction. Attaching the piezoelectric elements 10 at a 45° to the aeronautical member 50 allows the piezoelectric elements 10 to maximize the torsional deflection imparted or sensed to or from the aeronautical

member 50. However, the angle of the piezoelectric elements can take on any value dependent on the amount of torsional deflection to be actuated or sensed. It is noted that the spacing of the piezoelectrical elements in this configuration is important. If the spacing is too large, then the effective density is reduced. If the spacing is too small, then capillary action may draw the bonding agent between the piezoelectric elements. If the bonding agent accumulates between the crystals, then the directionality is destroyed as the behavior of the piezoelectric elements becomes quasi-isotropic; and accordingly, twist and torsional deflection cannot be actuated or sensed. In this prefered embodiment, the proper spacing is approximately lO il. (1 mil. = .001") and should at least exceed 5 mil. to avoid drawing the bonding agent between the piezoelectric elements through capillary action.

As noted, the directional attachment techniques of the present invention may have many applications such as actuation and sensing of rotor blade and aircraft wing twist and bending distribution, actuation and sensing of space-based structures including space-trusses, targeting/sensing apparatus and weapons platforms, torque actuation and sensing, including simultaneously actuating and sensing high frequency variations in torque and bending loads, and use in Multi-mode accelerometers.

As previously noted, the utilization of the directionally attached actuator/sensor elements can be accomplished in several ways, each being slightly different than the others as the different types of actuator/sensor aterials behave differently.

For directionally attached pizoelectric elements, a voltage is applied across the surfaces of the elements.

Specifically, for piezoelectric crystals, voltage potentials ranging from 100 to 20,000 V/mm of crystal thickness are used for actuation, depending on the specific type of crystal. The voltage signal can be steady-state, time-variant, or impulse. Each of the types of actuations will produce specific deflections as prescribed by the manufacturers. If the directionally attached piezoelectric crystals are used for sensing, an impulsive, steady-state or time-variant structural strain will produce voltages across the crystal faces according to the manufacturers data. These sensed voltages or actuated strains can be used alone (for structural actuation only or structural sensing only) or simultaneously in a feedback loop arrangement. For the piezoelectric sensor/actuator element, actuation and sensing can be accomplished at the same time through the measurement of the voltage and impedance of the crystal. The aeronautical member or rotor blade shown in Figure 6 can utilize the feedback loop arrangement shown in Figure 9.

As shown in Figure 9, two signals, a first signal Fexternal which represents the external forces acting on the aeronautical member, and a second signal Fpiezo which represents the force applied to the aeronautical member by the piezoelectric elements, act on the aeronautical memeber as represented by the adder 100. Thus these forces both act on the aeronautical member simultaneously to be thus combined. The difference between these two signals Fexternal and Fpiezo is a signal represented as Fnet in Figure 9 which is then input into the feedback loop. This signal Fnet represents a signal to be cancelled by the feedback loop. That is, this signal Fnet is to be cancelled to eliminate any displacement in the aeronautical member 50. The particular transfer function of the aeronautical member will vary from one aeronautical member

to the other and is represented in Figure 9 as box 110, Blade Structure. The signal Fnet then, which will be a function of the specific blade structure of the aeronautical member as represented by box 110, can be represented by a function of three signals, displacement X, velocity ' , and acceleration X", as shown in Figure 9. In the present case, it is the displacement X of the aeronautical member which is to be cancelled. Thus, the piezoelectric sensor 120 will sense the displacement in the aeronautical member and output it as a voltage signal represented as V _x in Figure 9. This signal V _x then will be fed into a signal conditioner 130. The specifics of the signal conditioner 130 will vary from application to application and any conventional signal conditioner which acts in such piezoelectric circuits may be employed, such as a PCB Brand Model 482A04. The signal output from the signal conditioner 130 will then be fed into an amplifier 140 which multiplies the signal by k. The output from this amplifier 140 will then be applied to the piezoelectric actuators 150. A certain force will then be imparted onto the piezoelectric actuators as represented by Fpiezo in Figure 9. In this way, Fpiezo will approach Fexternal and consequently Fnet will be minimized.

For directionally attached magnetostrictive actuator/sensor elements, the actuation and sensing characteristics are similar to those of the piezoelectric, but accomplished through the use of a magnetic field. The magnetic field is generated (most frequently) through the use of electrical current passing through wires near-by or surrounding the magnetostrictive element. The magnetic field causes the element to expand which induces structural strains. For sensing, structural strains induce the magnetostrictive element to create a magnetic field which is sensed by electrical wires adjacent to the element. The

control loop arrangement is similar to that shown in Figure 9 can be employed utilizing magnetostrictive elements, but with an intermediate magnetic field. Again, the magnetostrictive elements can be used for sensing alone, actuation alone, or actuation and sensing at the same time.

For the actuation of the directionally attached shape- memory-alloys, strains can be induced by the use of a thermal, electrical, or electro- hermal triggers. No sensing is currently feasible with the use of shape-memory alloys.

For the actuation of directionally attached bimetallic or, more generally, thermally actuated lamina, thermal changes or gradients must be applied to the laminate to produce strains. Two or more materials that have different coefficients of thermal expansions can be directionally attached so as to impart orthotropic actuation loads. Sensing cannot currently be accomplished by the use of thermally actuated lamina. Metal structures are particularly amendable to this form of directional attachment.

Obviously, numerous additional modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.