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Design of shape memory alloy actuated intelligent parabolic antenna for space applications To cite this article: Sahil Kalra et al 2017 Smart Mater. Struct. 26 095015
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Smart Materials and Structures Smart Mater. Struct. 26 (2017) 095015 (14pp)
https://doi.org/10.1088/1361-665X/aa7468
Design of shape memory alloy actuated intelligent parabolic antenna for space applications Sahil Kalra1, Bishakh Bhattacharya1 and B S Munjal2 1 2
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India Space Applications Centre, Indian Space Research Organization, India
E-mail:
[email protected] Received 1 February 2017, revised 12 May 2017 Accepted for publication 22 May 2017 Published 9 August 2017 Abstract
The deployment of large flexible antennas is becoming critical for space applications today. Such antenna systems can be reconfigured in space for variable antenna footprint, and hence can be utilized for signal transmission to different geographic locations. Due to quasi-static shape change requirements, coupled with the demand of large deflection, shape memory alloy (SMA) based actuators are uniquely suitable for this system. In this paper, we discuss the design and development of a reconfigurable parabolic antenna structure. The reflector skin of the antenna is vacuum formed using a metalized polycarbonate shell. Two different strategies are chosen for the antenna actuation. Initially, an SMA wire based offset network is formed on the back side of the reflector. A computational model is developed using equivalent coefficient of thermal expansion (ECTE) for the SMA wire. Subsequently, the interaction between the antenna and SMA wire is modeled as a constrained recovery system, using a 1D modified Brinson model. Joule effect based SMA phase transformation is considered for the relationship between input voltage and temperature at the SMA wire. The antenna is modeled using ABAQUS based finite element methodology. The deflection found through the computational model is compared with that measured in experiment. Subsequently, a point-wise actuation system is developed for higher deflection. For power-minimization, an auto-locking device is developed. The performance of the new configuration is compared with the offset-network configuration. It is envisaged that the study will provide a comprehensive procedure for the design of intelligent flexible structures especially suitable for space applications. Keywords: active shape control, SMA actuator, reconfigurable space antenna, smart antenna system (Some figures may appear in colour only in the online journal) Nomenclature
D (x )
Elastic modulus as function of Martensite volume fraction
Martensite phase of SMA
FSMA
Force applied by the SMA wire to the structure
Ac Af
Cross section area of SMA wire Austenite finish temperature
K KP, KI, KD
Conductive heat coefficient Proportional, Integral and Derivative gains
As Asur
Austenite start temperature Surface area of SMA wire
L Mf
Length of SMA wire Martensite finish temperature
E(T)
Experimentally calculated elastic modulus
Ms
Martensite start temperature
A-phase
Austenite phase of SMA
M-phase
0964-1726/17/095015+14$33.00
1
© 2017 IOP Publishing Ltd Printed in the UK
Smart Mater. Struct. 26 (2017) 095015
R Rw
Radius of curvature of the structure
T
Temperature
Ta T0
Ambient temperature Initial temperature
V ey
Voltage Input Offset distance of the SMA wire from structure
SMA Wire Resistance
h
Convective heat coefficient
k tF, tI
Equivalent stiffness of the structure at a point Final and initial time intervals
xf , f
Free displacement, strain
sb
Blocking stress
sr o
Recovery stress
aec , ac
Thermal expansion at T > As, T < As Martensite phase volume fraction
x
S Kalra et al
Initial strain
q
Angle between tangent to structure and horizontal axis
a
Angle between Force, F and horizontal axis
Figure 1. A 200 mm parabolic SMA actuated antenna (adapted from
de Weck and Miller (1998)).
Weck and Miller (1998). In this experiment, SMA wires were fixed on the base of the antenna in order to achieve large displacements, as shown in figure 1. A simplified lumped body approach was used to model SMA. A finite element (FE) approach was used for prediction of deformation in the antenna. The arrangement of SMA wire could only produce displacement up to 3 mm at six points in the periphery of the antenna. Lan et al (2007) used hinges actuated with SMA to deploy a parabolic antenna. Hinges were provided such that large displacement can be achieved with relatively small change in the length of SMA wires. However, this research was limited to only the deployment of the antenna structure. Sreekumar et al (2007) have given a critical review of SMA actuators for industrial robots. One of the specific applications relevant to the antenna deformation discussed in this paper is self reconfigurable robots, where pulley based TiNiCu SMA wire actuators are used for generation of large displacement. Banerjee et al (2010) modeled the stiffeners of antenna segments as cantilever beams and calculated the tip deflections with varying offsets using SMA actuators. The study concluded that the offset was directly proportional to the tip displacement up to a certain level, and then saturated beyond a certain limit of the offset. Jacobs et al (2012) used SMA ribbon and various type of SMA honeycombs for actuation in the deployment of cellular antenna structure. Chawla et al (2014) studied the shape control of antenna with SMA actuators. A genetic algorithm was used to reduce the error between the targeted and obtained displacements using two objective functions: (i) energy minimization and (ii) error (difference between the desired and current shape) minimization. They used SMA meshing in the back of the antenna. Even though this arrangement was effective for shape control, the maximum deflection obtained was small.
1. Introduction Large flexible structures have diverse applications today including inflatable and deployable structures, satellite communication antennas, remote arm manipulators etc. Some of these structures are designed to vary their geometric and/or mechanical properties to satisfy structural as well as functional requirements. In recent years, design of adaptive antenna systems has attracted the attention of many researchers: Gupta et al (2005), Iyer et al (2008), Munjal et al (2008, 2007, 2008), de Weck and Miller (1998), Washington (1996), Yoon and Washington (1999). These systems possess a unique capability, due to which the radiation pattern can be reinforced in a particular direction or manipulated based on communication requirements. In the early attempts at shape adaptation, active truss members with conventional electromagnetic/hydraulic/pneumatic linear actuators were used. Harris corporation (1986) discussed a truss based deployable hoop column antenna driven by cables. The proposed antenna, with a diameter of only one meter, could functionally outperform an antenna with 15-meter diameter. With the introduction of integrated smart structures for antenna design, further advantages were gained in terms of light weight, compactness, low power consumption, and fast response. Washington (1996) mounted PolyVinylidene Fluoride (PVDF) film at the back of an antenna to control the shape. Neural network based control was adopted to handle geometry and material non-linearities. However, the direct application of shape memory alloy (SMA) wire for adaptive shape control in parabolic antennas was first suggested by de 2
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To achieve larger displacement of the structure, SMA wire mesh based offset network and point by point actuation systems are considered. FE simulations of the structure are performed with a mesh of four noded shell elements. Thereafter, using the FE based static stiffness matrix, shape control of the structure is achieved. In the following section, we discuss the SMA wire characterization required to determine the parameters needed for ECTE model. Section 3 discusses modelling of the antenna structure with SMA actuators. Section 4 discusses the SMA wire mesh network based shape control of antennas in the experimental setup. Section 5 discusses point by point Antenna actuation employing a locking device. Performance of the two actuation systems is compared. Thereafter, in section 6 conclusions are drawn, along with a discussion of future scope of work.
Figure 2. Heat flow variation versus temperature in SMA wire (diameter = 375 μm).
2. SMA wire characterization with ECTE modeling
Yoon (2002) mentioned that in space, the usability of an antenna can be increased by mechanically reconfiguring its shape on an hourly basis. The optimal number of PZT actuators required for a desired shape was calculated. Their experiments have shown the feasibility of controlling electromagnetic radiation patterns with the help of PZT actuators, where a maximum displacement of 20 mm was achieved in the antenna reflector. Review of the literature confirms that SMA based actuation is feasible today for adaptive antenna systems. SMA has the advantages of large force generation, robustness, compactness and low power requirement in comparison to other actuators. However, there is a need for integrated design of SMA based systems with their host structures, to achieve desirable functional requirements. It is also observed that the maximum displacement obtained using SMA actuators is smaller than that from PZT based actuation systems. Also, continuous actuation is required to control the shape of the antenna. Thus, there is scope for the design of better SMA based actuation systems, along with an auto-locking mechanism to save power. In the present study, shape control of a C-band parabolic space antenna reflector actuated by SMA wire is considered. Such reflectors are generally used as a medium between two ground stations for space communication. A typical signal bandwidth of 3.5–8.0 GHz is used with an antenna with 1 m diameter. A similar configuration is adapted in the present work. The present paper deals systematically with the design of an SMA based antenna actuation system. We first begin with the selection of SMA wire, by developing an appropriate mathematical model of the system. The ECTE, Brinson and lumped mass thermo-electric schemes are used simultaneously to model the empirical relationship between the displacement of the antenna structure, temperature and input voltage to the SMA wire. SMA material characterization including determination of transformation temperatures (Mf , Ms, As and Af) and elastic modulus (EA and EM) is required for ECTE modeling.
The phase transformation of SMA between Ms and Af can be modeled as an equivalent negative coefficient of thermal expansion (ECTE) aec since the wire shrinks due to heat initiated phase transformation. This behavior of SMA can be easily modeled in FE once we have the information of ECTE and elastic modulus (ac (T ), E(T)). This kind of modeling technique was first proposed by Turner (2000), and subsequently used by many researchers for the analysis of SMA composites: Turner and Patel (2004), Han et al (2007), Sippola et al (2007). Equation (1) represents the free strain ( f ) produced in the SMA wire while heating which is typically considered as 3 to 5% of its total length (depending upon the configuration of SMA). aec in the equation is calculated from equation (2) with a pre-strain value.
f = =
xf = a c (T - T0) L T
òA
a ec (t ) dt
T < As T > As
(1 )
s
The relationship between ac and sr is given in the equation (2) T
òA
s
a ec (t ) dt = -
sr (T , 0) E (T )
(2 )
The parameters E(T), sr (T , 0 ) are obtained from experiments for the SMA wire of diameter 375 μm. Necessary experiments to determine these variables are explained in the following subsections. 2.1. Determination of Phase transition temperatures
Differential Scanning Calorimeter (DSC) test is performed using PerkinElmer equipment on SMA HT375 sample (wire diameter 375 μm) to obtain the phase transformation temperatures. Although these details are generally provided by the manufacturer, the test is performed for validation of data. The sample is subjected to heating from 0 °C to 130 °C at the 3
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Figure 4. Recovery stress variation with temperature in SMA wire.
Figure 3. SMA force generation upon cyclic loading.
recovery stress of 510 MPa. This value of sr (T , 0 ) is further used to calculate aec (T ) following equation (2). The same test can be used for the determination of As and Af at different stress levels. Assuming linear interpolation in figure 4, the Af at given recovery stress can be interpolated by using equation (3). This equation is used further to calculate Af at given recovery stress value (sr ).
rate of 10 °C per minute. The sample is held for a minute and then cooled to 0 °C at the same rate. A similar test is performed for 20 cycles on stress free material. Figure 2 shows the consolidated results considering all the cycles. The Austenite transformation in the first cycle occurred at higher temperature (As = 82.9, Af = 87.5 C) than in consecutive cycles. The reason for initial higher transformation temperature could be some amount of pre-strain existing in the wire. The observed values from the experiments after first cycle onwards are Mf = 47.5 C , Ms = 57.9 C, As0 = 76 C and Af 0 = 82.2 C. It may be noted that the shape control problem considered in this case is related to very low cycle of actuation. It is envisaged that there will be some drift in the temperatures, which will be compensated by the PID controller. However, in real life application, this issue will arise and further modification of the design will be necessary in the direction of Hu et al (2002), Zhang et al (2016).
A fs = A f0 + ms T - T1 1 = m= 2 s2 - s1 CA
(3 )
where m represents the approximate slope of line in figure 4. In order to compare ‘m’, two representative points are chosen from the figure. Accordingly, T2 = 130 C, T1 = 100 C, s2 = 430 MPa , s1 = 190 MPa . 2.3. Variation of elastic modulus (E) versus temperature (T)
The tensile test is conducted on a Tinius Olsen machine with a loading rate of 0.6 mm min–1 and at various temperatures. In the 1st, 2nd and 3rd cycle, the specimen is loaded up to 30 N, 60 N and 90 N respectively and unloaded. The elastic modulus (E) is obtained from the test. Figure 5 shows a typical tensile test result at room temperature used for the determination of the elastic modulus. Similar tests are carried out at various temperatures. The variation of E over the temperature range 25–160 C is shown in figure 6. E(T) and sr (T ) are used to calculate the coefficient of thermal expansion using equation (2). The values of E(T) and aec (T) (shown in figure 6) are later used in FE analysis to define the material property of SMA.
2.2. Block recovery stress in SMA wire
For this test, fresh SMA wire of gauge length 50 mm is constrained to move between the cross heads of the tensile testing machine. The voltage is then increased from 0–10 V with increment of 0.5 V, implying incremental rise in temperature. For the first cycle, the force achieved was about 38N (sr = 340 MPa); thereafter, from the subsequent cycles, the force value starts to diminish as shown in figure 3. Since, the recovery stress value (340 MPa) in the first cycle is less than syield = 550 MPa , some amount of initial strain which was set by the supplier starts decreasing as the number of cycles increases. Hence, to use SMA wire as actuator for constrained recovery application, a specific amount of initial strain (up to 5%) has to be supplied after each cycle. The force required to produce the initial strain is called cooling force. A detailed discussion about this force will be provided in section 2.4. A pre-strain of 8% is known to produce recovery stress close to the yield stress of 550 MPa in Nitinol (Cross et al, 1969). From our experiments on SMA wire (as shown in figure 4), it is evident that the pre-strain has produced a
2.4. SMA actuator selection for constraint recovery applications
SMA actuators are generally used in wire or spring form for constraint recovery applications. After some actuation cycles of the SMA materials, relatively low displacement is obtained from the actuator if the required cooling force is not provided. 4
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For the selection of appropriate SMA actuator for the parabolic reflector of 1-meter diameter, the stiffness contribution at individual control points (CPs) on structure (k) is measured by loading each CP with dead weights and measuring the deflection using a single point laser sensor as shown in figure 8. The force to deflection ratio is found to be equal to 400 N m–1 up to a deflection of 25 mm (refer figure 9). No major difference in the stiffness value between the eight CPs was recorded, since the structure is symmetric. This range of deflection is considered within elastic range. Selection of SMA actuator is carried out based upon this stiffness value and the maximum displacement requirement (20 mm) at the CP. The results are shown in table 1 which shows 310 and 375 μm wires are good candidates for the antenna system. We have finally chosen 375 μm wire, due to the availability of sufficient heating and cooling force to produce an intended deflection of 25 mm in the structure.
Figure 5. Tensile testing results for four cycles in SMA wire.
3. SMA modeling with constraint structure A simple constraint recovery model for SMA actuator is shown in figure 10, where a bias spring is actuated using SMA wire. Let x be the displacement produced in the structure when increasing the temperature of SMA from As to T. The corresponding stress (σ) generated in SMA is expressed in equation (5). For temperature less than As, the stress is considered as zero. The parameters necessary to calculate σ are obtained from experiments described in section 2. These are: • Phase transition temperatures (Ms, Mf , As , Af ) • Variation of Elastic modulus (E) with temperature (T) and • Variation of CTE (aec ) with temperature (T) Consequently, the 1D Brinson model (Brinson 1993) and ECTE models are used simultaneously to predict the displacement of the antenna structure with respect to the input voltage. The stresses in SMA are calculated using the ECTE model, which is further used for calculating the approximate strain/displacement of the structure. The prestress term of the Brinson model (si - 1) is considered to be equal to the elastic strain ( kAL ) in the structure. The temperatures range from Martensite start to Austenite finish are considered (Ms < T < Af ) as the actuating phase. Accordingly: if T As, aec (T ) is taken from figure 6, otherwise a (T )≈0. Using the Brinson model,
Figure 6. E and α variation with temperature in SMA wire.
At zero stress, the removal of heat from SMA transforms the A-phase to twinned M-phase (as explained in figure 7). A small amount of cooling force is required to bring SMA back to the detwinned M-phase. No residual stress is generated when cooling force is provided, as this force is used for transferring the detwinned M-phase of SMA to twinned M-phase. This change between twinned phase to detwinned phase is also called strain offset in the material. Not only the cooling force, but also the actuation wire should be selected in such a way that while transforming to A-phase the material does not cross the safe stress limit. This may lead to permanent strain development within the material, and hence it will not be useful for larger number of cycles with the same displacement. The safe stress in SMA is generally chosen to be one third of the maximum blocking stress. Accordingly, the safe heating stress is taken as 172 MPa and cooling stress as 70 MPa.
si - si - 1 = (E (xi )(i - i - 1) + Q (Ti - Ti - 1) + W (x )(x si - x si - 1)
(4 )
where, Q(s and T ) can be considered from phase diagram, W(x ) = - L E (x ) and L is the maximum recoverable strain.
5
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Figure 7. A schematic representation of SMA actuator design.
Figure 9. Force deflection plot for a typical CP of 1 m diameter
antenna.
Considering temperature increment (Ti - Ti - 1) to be very small, and constants xi , xsi , xTi are calculated as follows. For Ti > As and CA (Ti - Af ) < si - 1 < CA (Ti - As )
Figure 8. Test setup used for the stiffness calculation of each CP.
where stress (s (T )) in Brinson model is replaced by CTE (α) Ti E (x i ) k L (L a ec (Ti ) dT ) + i As L Ac For Ti > Ti - 1 Ti - 1 E (xi - 1) k L (L si - 1 = a c (Ti - 1) dT ) + i - 1 As L Ac otherwise k L si - 1 = i - 1 Ac
si =
ò
⎤ ⎡ xi - 1 s (cos ⎢aA (Ti - As - i - 1 ) ⎥ + 1) ⎣ 2 CA ⎦ xs x si = x si - 1 - i - 1 (xi - 1 - xi ) xi - 1 xT xTi = xTi - 1 - i - 1 (xi - 1 - xi ) . xi - 1 xi =
ò
6
(5 )
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is provided in equation (10). Based on our experimental model, the following constants are used for the analytical solution of equation (10). Voltage = 7 V, cp = 322.384J kg– 1 °C, hc = 75 W m–2 °C, ρ = 6500 kg m–3, d=375 μm. This model is further used to predict the displacement of the 3D Antenna structure. V 2 (t ) Rw
(t ) - Ta) = hA sur (T Convective Heat loss
Power Supplied 4 (t ) - T 4 ) + rVc dT + + s p rad A (T a dt Radiative Heat loss Specific Heat
(T (t ) - Ta) dx KAsur + rVdH + l dT
Figure 10. Constraint for SMA actuator at each CP.
sscr
For Ti > Ms + CM (Ti - Ms) < si - 1 < scr f + CM (Ti - Ms )
xs i =
1 - xs i - 1 2
xTi = xTi - 1 -
cos
s scr
xTi - 1 1 - xs i - 1
For Ti < Ms and x si =
1 - x si - 1 2
xTi = DT -
conductive heat loss
T = Ta +
(xs i - xs i - 1) .
cos (
n
A2
i
1 2
å t ti
(9 )
(et1ti - et1ti ) e
s
(10)
h A
where t1 = rcVcsur , t2 = rVcp Rw P Figure 11 shows a typical temperature profile. The chosen voltage profile is based upon equation (10). For structural analysis, equations (5) and (10) are jointly used to calculate the strain (ò), Martensite phase fraction (xs) for a given temperature profile. The results are shown for different values of structural stiffness (k = 0, 100, 400 N m– 1 ). The plots (figures 13–15) show the temperature, strain and martensite volume fraction (xs) profiles for given voltage inputs (figure 12) in the SMA at a given structural stiffness. It can be seen that for lighter structures (k = 0 or 100 N m–1) the strain in the first cycle is about 0.05%, and for rest of the cycles strain recorded is very small (about 1% for k = 100 N m–1). Such structures are unable to provide sufficient cooling force to the SMA and hence complete conversion of Austenite to Martensite does not take place. However, for the stiffer structures the transformation from A-phase to M-phase takes place very smoothly and repeatable strain behavior can be seen for each cycle. It may also be noted that with further increase of structural stiffness, the corresponding strain will be very small representing the blocking strain condition.
(6 )
< si - 1
