Sensors and Actuators A 140 (2007) 94–102
Wireless and distributed sensing of the shape of morphing structures W. Akl a , S. Poh b , A. Baz b,∗ a
b
Design & Production Engineering Department, Ain Shams University, Cairo, Egypt Mechanical Engineering Department, University of Maryland, College Park, MD 20742, United States Received 9 January 2007; received in revised form 14 June 2007; accepted 21 June 2007 Available online 27 June 2007
Abstract Monitoring the shape of morphing structures is essential for their effective and safe operation. However, current sensing systems such as fiber optic sensors are expensive, brittle, and unsuitable for monitoring large shape changes without being susceptible to failure or performance degradation. Therefore, a new class of sensors that does not suffer from these serious limitations is presented. The sensor system relies in its operation on a specially configured distributed network of wires that is embedded in the composite fabric of these structures. The output of the sensor network is wirelessly transmitted to a control processor to compute the linear and angular deflections, the shape, and maps of the strain distribution over the entire surface of the morphing. The deflection and shape information are vital to ascertain that the structure is properly deployed. The strain map ensures that the structure is not loaded excessively to adversely affecting its service life. The equations governing the operation of the sensor network are developed for a beam-like morphing structure using the non-linear theory of finite elements. The resulting equations will provide the sensor with its unique interpolation capabilities that make it possible to map the linear and angular deflection and strain field distribution over the entire surface of the morphing structure. The theoretical and experimental characteristics of the sensor network are determined under static and dynamic loading conditions. The results obtained are used to demonstrate the merits and potential of this new class of sensors as a viable means for monitoring the deflections of 1D morphing structures. Integration of the proposed sensor network with the supporting electronics and with arrays of flexible actuators will enable the development of a self-contained, actively controlled, and autonomously operating new generation of morphing. © 2007 Elsevier B.V. All rights reserved. Keywords: Wireless and distributed sensor network; Morphing structures; Shape monitoring
1. Introduction Considerable attention has been given to the development of a wide variety of morphing structures because of their numerous attractive attributes. For example, morphing aircraft have been considered because of their ability to perform drastically different mission roles during a single flight such as loitering and strike roles as shown in Fig. 1. In these roles, the aircraft wing changes from a high span and a large surface area for a loitering wing to a low span and a low area for a strike wing. The ability of the aircraft to morph enables the control of critical performance characteristics, such as turning radius, endurance, payload, and maximum velocity [1,2]. Furthermore, morphing aircraft have unique maneuvering capabilities which can be achieved by pulling one wing in and rolling the other
∗
Corresponding author. Tel.: +1 301 405 5216; fax: +1 301 405 8331. E-mail address:
[email protected] (A. Baz).
0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.06.026
one. Hence, considerable weight can be saved by eliminating the usual control surfaces. The motivation behind the development of such morphing configurations is biologically inspired by the multi-tasking flight capabilities of birds which tend to cover a broad range of tasks ranging from slow, near-hover flight to aggressive dives. Birds are able to achieve such a wide dynamic range missions through large shape changes to their wings. In particular, birds are able to articulate their wings in a craning motion to vary the dihedral or sweep angles (Fig. 2), wing area, wing planform, wingspan, and other parameters. These changes allow the bird to quickly transition between soaring, cruising, and descending flight. Examples of successful attempts in developing biologically inspired morphing aircraft include the AFTI/F-111 mission adaptive wing (MAW) with its variable camber wing [2], the adaptive aeroelastic wing (AAW) with twist control [3] and NASA’s hyper-elliptic cambered span (HECS) wing [4,5]. In all these attempts, the morphing aircraft exhibit tunable aerodynamic properties to suit the needs of multi-mission roles during
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Fig. 1. Biologically inspired morphing aircraft: (a) folding wings (Lockheed Martin, dihedral angle changes), (b) sliding skin (Raytheon, sweep angle changes) [1].
Fig. 2. Different strategies wing morphing of birds: (a) dihedral angle morphing (craning), (b) sweep angle morphing.
a single flight. Fig. 3 shows the complete work envelop for the AFTI/F-111 aircraft whereby the airfoil shape of the wing can be morphed to make the lift-drag characteristics compatible with the mission requirements. Similar characteristics are reported for other morphing approaches [6–9]. Apart from the distinctly different morphing approaches, all the morphing structures have in common their ability to undergo large geometrical changes while attempting to maintain dimensional accuracy in order to achieve effective operation. For example, morphing aircraft may experience 200% changes in the aspect ratio and/or 50% changes in the wing area while maintaining strict tolerances on the shape during a particular mission in order to attain the desired aerodynamic characteristics [6–11]. Accordingly, continuous monitoring of the shape of the morphing structures is necessary to ensure effective performance. The monitored shape information can then be fedback to appropriate shape control systems to achieve the desired shape while ensuring that the surfaces are aerodynamically smooth and wrinkle-free. Several attempts have already been made to monitor the shape and health of morphing structures using fiber optic sensors [12–14]. However, these attempts are still in their preliminary
stages and the fiber optics sensing systems used are expensive, rigid, and unsuitable for monitoring large shape changes without being susceptible to failure or performance degradation. Therefore, it is the purpose of this paper to present a novel class of sensors that does not suffer from the serious limitations of current sensor systems. Particular emphasis is placed on morphing structures with dihedral angle changes. 2. Sensor system 2.1. Overview The sensor system consists of a specially configured distributed network of wire sensors that are embedded in the composite fabric of the morphing structures in the form of the grids displayed in Fig. 4. Each wire sensor acts as a distributed strain gage sensor. The sensors are distributed over the surface of the morphing structure to monitor the shape along the span and the camber directions. The outputs of the sensors are wirelessly transmitted to the command unit to simultaneously compute: (a) maps of the linear and angular deflections, i.e. the shape, (b) maps of the strain distribution. The deflection and shape information are required to ascertain that the structure is properly deployed. The strain map ensures that the structure is not loaded excessively to adversely affect its service life. 2.2. Concept and modeling of the distributed sensor network
Fig. 3. Aerodynamic characteristics of AFTI/F-111 [2].
The development of the distributed sensor for monitoring the large deformation of morphing structures will be based on the work of Baz et al. [15–17] which employed networks of
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Fig. 4. Distributed sensor network.
The strain ε(x) in a wire embedded inside the beam at a distance a, from its neutral axis, can be determined from the following von Karman strain–displacement relationships [18,19]: ε = u,x + 21 (w,x )2 − aw,xx
Fig. 5. Flexible beam with distributed sensor.
distributed wire sensors to monitor small amplitudes of vibration of beams and plates. For small deflections, the sensor relies in its operation on the linear theory of finite elements to extract the transverse linear and angular deflections. But for large deflections, the sensor network will be based on the non-linear theory of finite elements to extract the transverse linear and angular deflections as well as the in-plane longitudinal deflections. The concept of the distributed network sensor can best be understood by considering the one-dimensional flexible beamlike structure shown in Fig. 5.
(1)
Fig. 5 shows also that the wire sensor is divided into N segments in order to extract N unknown degrees of freedom, i.e. nodal deflections, as will be explained later. The axial and transverse displacements, u and w, can be approximated as follows: u = {Nu }{} and w = {Nw }{}
(2)
where {Nu } and {Nw } are the classical shape functions for axial and transverse displacements, and {} is the nodal deflection vector defined as: {} = { u
Fig. 6. Wireless system.
T
w w,x }
(3)
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Table 1 Specifications of the wireless system (Microstrain Inc., Williston, VT) Strain gauge inputs Strain resolution Offset programmability Gain programmability Data acquisition modes DAS software Analog to digital (A/D) converter Data storage capacity Data logging sample rate Continuous transmission sample rate Data sample duration SG-link node input power Radio frequency (rf) transceiver carrier Range for Base station rf trigger
3 channels; with 1/4, 1/2, or full bridge ±1 microstrain typical for three wire quarter bridge installations Software programmable input offsets 5–10,000/default = 500 which represents approx. ±2000 micro-strain FS Mode 1: auto-trigger, user specified as a programmable output voltage from a specific channel; mode 2: on command from RS-232 or RF link; mode 3: transmit continually for pre-programmed time period Windows 95/98/2000/XP, PC compatible Successive approximation type, 12 bits resolution 2 MB (approximately 1 million data points) Programmable, from 32 to 2048 sweeps/second (one sweep represents one sample from all active channels) 1900 Sweeps of a single channel per second 1000 sweeps of three channels per second (3 ch. option) Programmable from 1 to 65,535 data sweeps; for 2048 sweeps per second, sample duration is 32 s 3.6 V lithium ion AA size internal battery recommended, 2400 mAh capacity standard; optional rechargeable lithium battery w/600 mAh and charger available for single channel systems 916 MHz, narrowband, FCC compliant 100 feet (30 m) typical, line of sight
Substituting Eq. (4) into Eq. (5) results in: Ls 1 {Nu,x } + {}T {Nw,x }T {Nw,x } − a{Nw,xx } Ls = 2 0 × dx{}
(6)
which can be expressed as Ls = ({g1s } + {}T [g2s ] + {g3s }){} for s = 1, . . . , N (7)
Fig. 7. Distributed sensor assembly.
where Substituting Eqs. (2) and (3) into Eq. (1) yields: ε = {Nu,x }{} + 21 {}T {Nw,x }T {Nw,x }{} − a{Nw,xx }{} (4)
Ls
1 {Nu,x }, [g2s ] dx = {g1s } = 2 0 Ls {Nw,xx } dx and {g3s } = −a
Ls
{Nw,x }T {Nw,x } dx,
0
(8)
0
The change Ls in the length of a wire segment s can be determined from: Ls Ls = ε dx (5) 0
In Eq. (7), the nodal vector {} has N degrees of freedom (DOF). For example, if the beam is mounted as a cantilever beam and is represented by one finite element, then the beam has T 3 DOF, i.e., {} = { u1 w1 w,x1 } . Hence, the wire sensor
Fig. 8. METRA box coater: (a) outside view and (b) inside view.
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Fig. 9. Photograph of morphing beam/sensor, transmitter, and receiver system.
Fig. 10. Comparison between actual and measured shapes of a morphing beam: (a) qualitative and (b) quantitative.
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must be divided into, at least, three segments such that N = 3. Then, Eq. (7) can be put into a matrix form by considering the changes of length of all the N wire segments to give: ⎛⎡
⎤ ⎡ ⎤⎞ ⎤ ⎡ {g11 } {}T [g21 ] {g31 } ⎜⎢ . ⎥ ⎢ ⎥ ⎢ . ⎥⎟ .. ⎢ ⎥ ⎢ ⎥ + ⎢ . ⎥⎟ {} {L} = ⎜ . ⎝⎣ .. ⎦ + ⎣ ⎦ ⎣ . ⎦⎠ T {g1N } {g3N } {} [g2N ] = ([G1 ] + [G2 ({})] + [G3 ]){} = [G]{}
(9)
where {} = {L1 , . . ., Ln }T . Note that the matrix equation (9) represents a set of N equations in the N unknown degrees of freedom of the vector {}. The elements of the vector {} can be computed by inverting the matrix [G]. However, such a computational process is iterative in nature as matrix [G2 ] is a function of the unknown deflection vector {}. The iterative solution of Eq. (9) is given by: {}n = ([G1 ] + [G2 ({}n−1 ) + [G3 ])−1 {L}
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2.3. Wireless system The layout of the wireless system is shown in Fig. 6. The sensor network is divided into sensor nodes (1, 2,. . ., N) which communicate with a computer-controlled base station transceiver which triggers data logging from the nodes at distances up to 30 m. Data transmission occurs at a sweep rate of 2 kHz and the transceiver stores the data in a 2 MB of memory. Each node has a unique address enabling a single host transceiver to address thousands of sensor nodes. The base station may trigger one or all nodes, sending a timing signal for millisecond network synchronization. The main characteristics of the system are given in Table 1. The wireless system relies on the AgileLinkTM software package to fully configure and communicate with the entire nodes of the system. AgileLinkTM incorporates power management, simple quality of service (QoS) tests, channel independent auto-balancing, and easily accessible node information. Each
(10)
where n is the nth iteration, and {}0 is the initial guess for the deflection vector given by: {}0 = ([G1 ] + [G3 ])−1 {L}
(11)
It is important here to note that the distributed wire sensor is in effect a distributed strain gage sensor. Such a distributed nature of the sensor has many inherent advantages. First, it makes the placement of the sensor insensitive to the location of the nodes of vibration. This of course is not the case for conventional discrete strain gages where the sensors cannot be placed at these nodes. Second, because the distributed wire sensor relies on integrating the strain along the wire segments, as described by Eq. (5), its output signal will be less noisy than that of conventional strain gages and high signal-to-noise ratios can be obtained. Third, the sensor can also detect structural failures by monitoring the failure of any wire segment. These advantages make the distributed wire sensor suitable for accurately monitoring the deflection, shape, vibration, and integrity of morphing structures. Most importantly, the proposed distributed wire sensor has unique characteristics which stem from its interpolating capabilities as can be ascertained from Eqs. (2) and (4). Hence, once the nodal deflection vector {} is computed, the deflections u and w at any location x can be easily determined using the interpolating functions [Nu ] and [Nw ] as given by Eq. (2). Also, the angular deflection θ(x), at any location x, can be computed from: θ(x) = [Nw,x ]{}
(12)
Similarly, the strain field ε can then be determined using Eq. (4). Such interpolation capabilities of the distributed wire sensor render it suitable for monitoring the entire deflection and strain fields for large structures with only a small number of wire segments. These innovative interpolation capabilities are unique to the proposed distributed wire sensor and are not available with any of the presently used sensors.
Fig. 11. Comparison between actual and measured shapes of configuration 1 of the morphing structure: (a) morphing structure, (b) shape and (c) strains.
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wireless channel is completely configurable to monitor in realtime the logged data in readable physical units. Data monitoring becomes easier as graph configurability provides robust capability for viewing real-time data and Microsoft Excel integration drastically increases the overall speed and productivity. 3. Fabrication and performance of sensor A 3 in. × 12 in. flexible morphing beam is manufactured from a polyester/Mylar film of thickness 0.030 in. with a sensor consisting of three sections deposited on the beam as shown in Fig. 7. The sensor sections are manufactured by first deposit˚ thickness directly on the Mylar ing a chromium layer of 200 A ˚ thickfilm through a mask followed by a gold layer of 915 A ness using a thermal evaporation vacuum chamber (METRA box coater) shown in Fig. 8. Note also that the different sensor sections are manufactured such that the electrical resistance of each section is 120 . This enables the use of standard Wheatstone bridge techniques for measuring the changes in the resistance (or
Fig. 12. Comparison between actual and measured shapes of configuration 2 of the morphing structure: (a) morphing structure, (b) shape and (c) strains.
the length) of each section in a manner similar to conventional strain gauges. 4. Performance of the sensor The manufactured morphing beam/sensor system is clamped in a cantilever arrangement as shown in Fig. 9 and accordingly, the shape of the beam can be determined completely using the three-section sensor. These three sections enable the computation of the three degrees of freedom (u, w, wx ) at the free end of the beam which are then used with Eqs. (2), (4), and (12) to generate the complete deflection and strain maps over the entire surface of the beam. Fig. 10a and b shows qualitative and quantitative comparisons between the actual and measured shapes of the morphing beam for two different morphing configurations. It is evident that the simple configuration of the three-section sensor is capable of
Fig. 13. Comparison between actual and measured shapes of configuration 3 of the morphing structure: (a) morphing structure, (b) shape and (c) strain.
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monitoring very complex shapes of the morphing beam. Note that the “End of Sensor” circle matches that mark shown in Fig. 7. The sensor shown in Fig. 7 is bonded to a morphing beam-like structure which consists of four segments driven by dc servomotors that are computer-controlled using dSpace control board (dSpace Inc., Novi, MI) as displayed in Fig. 11. The user inputs a desired shape of the morphing structure, the computer drives the motors to generate that shape, and the sensor monitors the shape as structure morphs from an initial shape to the desired shape. Figs. 11–13 show comparisons between the desired and the monitored shapes for three configurations of the morphing structure. Shown also on the figures are comparisons between the outputs of three strain gages, placed at equal spacing on the top surface of the morphing structure, and the strains as extracted from the distributed sensor using its interpolation capabilities. The figures show also, in a quantitative manner, that the threesection distributed sensor is capable of measuring the complex shape of the morphing beam and the strain distribution along the beam. 5. Conclusions This paper has presented a new class of sensors that can be used to simultaneously measure the shape of a wide variety of morphing and inflatable structures. The unique features of the proposed sensor include its ability to monitor linear and angular deflections, the shape, and strain distribution over the surface of the structure. The deflection and shape information are vital to ascertain that the structure is properly deployed and that its surfaces are operating wrinkle-free. The strain map ensures that the structure is not loaded excessively to adversely affect its service life. All these features are novel and are not available in any of the presently used sensing systems. With such unique features, the presented sensor can have a great impact on the safe deployment and effective operation of morphing and inflatable structures. Examples of these structures include: morphing aircraft, morphing unmanned air vehicles (UAV), solar sails, inflatable wings, large antennas, inflatable solar arrays, solar power concentrators and transmitters, sun shields, as well as planetary balloons and habitats. Acknowledgement This work has been funded by an NSF Grant (CMS DivisionCMS0625029) with Dr. Shih Liu as the Technical Monitor.
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Wael Akl completed his PhD in “Smart Foam” in Mechanical Engineering Dept. at the University of Maryland, USA in 2005. He is working as an assistant professor at Ain Shams University in Egypt. His main research interests are topology optimization, sound and vibration control, smart structures and virtual reality. He holds more than 11 international journal and conference papers. He is a founding member of the acoustical society of Egypt and an associate member of the American Society of Mechanical Engineering.
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Soon Neo Poh is an assistance research scientist at Mechanical Engineering Department, University of Maryland at College Park, MD 20742. He completed his PhD and MME in mechanical engineering at Catholic University, Washington, DC. His research interests are active and passive control of smart structures and mechanical system, vibration and acoustic testing, measurements, analysis and control. He has published over thirty papers in international and national journal and conference. Amr Baz earned his PhD in mechanical engineering from University of Wisconsin at Madison in 1973. Currently, he is professor of mechanical engineering at the University of Maryland in College Park, MD. His research
interests include active and passive control of vibration and noise and virtual reality design of smart structures. He has published more than 135 papers in referred journals and holds 6 US patents. He is fellow of the American Society of Mechanical Engineers, 1996; listed in Who’s Who of American Inventors, 1996; and recipient of Engineering Alumni Association Outstanding Faculty Research Achievement Award, 1997. Dr. Baz serves on the editorial boards of journals of Vibration and Control, Thin-Walled Structures, Vehicle Noise & Vibration, Smart Structures & Systems, Mechanics of Advanced Materials and Structures, and Advances in Acoustics and Vibration.
