- Email: [email protected]
A radiant energy-powered shape memory alloy actuator
Mechatronics 14 (2004) 757–775
A radiant energy-powered shape memory alloy actuator P.V. Hull a, S.L. Canfield
a,*
, C. Carrington
b
a
b
Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN 38501, USA Marshall Space Flight Center/NASA, Flight Projects Directorate, Huntsville, AL 35812, USA
Abstract This paper will present the development of an innovative actuator using a shape memory alloy (SMA) that is powered by available radiant energy in the space environment. Currently, self-contained or tethered power supplies provide the energy source for actuators in space applications. These can be costly, heavy and require regular maintenance and/or refueling. Ideally an actuator for space applications should have a high power density, be able to operate with little interference from its power source and maintain a low operating cost. Shape memory alloys are materials that recover internal strain with the addition of heat, thus changing thermal energy to mechanical energy. Because of this, they are known as thermomechanical motors. These materials can be thermally actuated by a number of means with the primary conventional approach based on resistive heating. Radiant energy, while typically impractical for use under normal circumstances, is a significant and abundant energy source in space and can be directed to control phase transition in a SMA material. This paper will describe the development of a radiant-heat driven SMA actuator, presenting a simple actuator model and prototype. The paper will also compare this actuator against other SMA-based actuators. 2004 Elsevier Ltd. All rights reserved. Keywords: Actuator; Cylindrical concentrator; Maxwell’s relation; Radiant energy; Shape memory alloys; Space
*
Corresponding author. Tel.: +1-931-372-6359; fax: +1-931-372-6340. E-mail address: scanfi[email protected] (S.L. Canfield).
0957-4158/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2004.01.008
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1. Introduction The primary objective for this paper is to present the development of a shape memory alloy (SMA)-based actuator that makes direct use of available radiant energy in the space environment. The space environment has an abundant and endless supply of radiant energy. Harnessing this energy to power an actuator can potentially result in an efficient and cost-effective actuation device. Typical actuators for space applications require self contained or tethered power supplies, adding weight to the system as well as cost of recharging or refueling. Ideally, actuators for reoccurring or continuous applications should have a high power-to-weight density, be able to operate with little interference from their power source and be maintained at a low cost. The shape memory alloy material provides a thermomechanical motor that converts thermal energy to mechanical energy due to a material phase transition. This transition, known as the memory effect, is a cycle through the material phases, austenite and martensite. Austenite is the material phase of high temperature and low stress that exists in a cubic lattice structure; it is a rigid phase with strong crystal symmetry that is due to the face centered cubic structure. Martensite is the material phase of low temperature and high stress that exists as a distorted version of the austenite phase. The use of shape memory alloys to create actuators is common in the literature with a variety of applications demonstrated. For example, McClean et al. [1] investigates using SMAs for vibration control of large space structures. The frangibolt [2] is a commercially available device used for permanent deployment of space vehicle and payloads. Designs exist for steerable catheters for use in surgical applications [3], while SMA’s have been implemented as an anti-scaled valve [4] to monitor water temperature in a shower and prevent water flow if the temperature rises above a specified level. Forced convective heating and cooling to actuate SMAs has been demonstrated [5]. Shape memory alloys are employed to actuate microdevices, such as micro-thin film actuators [6], microfabricated hinges and microvalves [8]. These examples provide only a few of the many implementations of SMAs as actuators, and demonstrate the variety of forms used to drive this material through the transitional phases. Specifically, these examples demonstrate various modes for causing temperature transition through resistive heating [1,2,6], forced convection heating [4], forced convective heating and cooling [21] and conduction [3]. This paper will propose an alternative approach for inducing phase change in SMAs based on directed radiant heating of the actuator material. There are many benefits and potential applications for this approach. This method of heating can overcome the costs, mass and in a few cases size (for example when compared to the use of solar cells for photovoltaic power) associated with traditional power supplies by making use of available radiant energy, while at the same time reducing much of the complexity of the actuator system. Further this design may allow improved packaging, for example through the use of deployable thin-film concentrators. Potential applications for this solar driven actuator include finite control of mirrors or other devices for accurate positioning, opening and closing doors, deploying space
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appendages, and vibration control of large space structures. However, this approach will require an energy concentration system and appropriate models and control algorithms. A complete model of the radiant-heat activated SMA actuator will be developed in this paper to demonstrate its viability and evaluate its performance in space applications. This model will combine several basic parts; a material model, an environmental model, a control strategy and an engineering model for prototype construction. The concept will be developed in Section 2.1 and compared at an energy density level to other SMA actuators. The material model (Section 2.2) will characterize the functional relations between temperatures, stress and strain in the SMA and will be based on the thermodynamic model developed by Ivshin and Pence [10]. The environmental model (Section 2.3) will be based on a single degree of freedom finite element time-based thermal model that simulates an appropriate lower earth orbit environment and includes the effects of the solar concentrator. The control strategy (Section 2.4) will describe a PI control implementation for the model. Finally, a physical model (Section 3) will be described and a prototype will be constructed based on the model and engineering developments for testing and evaluation of the design. Based on the system model and prototype created, the capabilities of this solar-driven SMA actuator will be characterized and summarized (Section 3.2). Issues in practical development of such a system will be discussed.
2. Concept and model development This section focuses on modeling and design of a space actuator driven by solar radiant energy. Based on this energy source (solar), various methods of capturing and using this energy to drive the actuator were considered, as well as topology forms for the actuator. 2.1. Concept development Several topologies could be implemented in a radiant-driven SMA actuator device, including longitudinal extension of wire or ribbon, bending of beam-type elements or surface strain induced in thin film layers. The wire form actuator has the advantage of being radially symmetric while the ribbon and thin-film layers possess a high surface area to volume ratio. Likewise the beam-type actuator can provide significant angular displacements when desired. Each form depends heavily on the desired application. A linear SMA wire actuator will be discussed in detail here due to ease of implementation on an initial prototype system. Similarly, a variety of methods to concentrate solar radiant energy on the SMA were considered and evaluated on their suitability to all aspects of operation in the space environment and the ability to model and prototype. These methods include both lenses and reflectors. Lenses may provide significant advantages in weight and size (for example a thin film deployable lens or a fresnel lens). Alternatively, reflective mirrors may provide means to shield as well as concentrate energy at varying amounts while providing a higher efficiency in transferring solar radiant energy than
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a lens. Based on the evaluation of these concepts, a cylindrical concentrator was chosen for reasons including expandability, shading capabilities, lightweight and ease of prototyping. Fig. 1 shows a schematic radiant-heat activated SMA actuator and labels the elements forming the basic components of the model development. The wire actuator provides axial displacement and tensile forces at the output ends at which control force and/or displacement desired. A solar concentrator, formed as a cylindrical concentrator, encircles a portion of the wire actuator. The concentrator can also serve as a solar shield and/or radiator during cooling phases. The solar concentrator in this model is driven in a rotary fashion about the wire by a small, low-power motor. The actuator is designed to maintain the wire at the focal point of the cylindrical concentrator while varying the level of concentrated radiant heat on the wire as a function of the rotation angle relative to incident solar rays. Appropriate sensors are included in the model to determine incident solar energy directions and the actuator states. Finally, the space environment indicated in the schematic will include orbit information, radiation effects from the sun, earth and the space structure, and conductive effects to the radiating shield and the remainder of the structure. Note that one design issue that will arise when placing many of these actuators on a space structure is that each solar collector needs to be in full view of the sun (not in a structural shadow) for actuation. Discussion of this issue is beyond the scope of this paper. Power densities of various SMA actuator systems are discussed here. The merits of a radiant energy-driven actuator are based on the ability to match the force and motion capabilities of similar actuators while providing the potential for greater power density. The power densities of several SMA actuators are compared based on the method of energy storage (or extraction) and energy transfer, as shown in Table 1. This table compares various energy sources using resistive, convective and radiant
Fig. 1. Outline of this paper.
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Table 1 Summary of driving methods for SMA actuators SMA heat actuation method
Energy source for heating SMA
Specific energy of source for SMA heating (kJ/kg)
E transfer efficiency (approx.)
Power density SMA Eff (10%) (kJ/kg)
Resistive heating from battery Resistive heating from fuel cell Forced convection from combustor
Lithium battery (non-rechargeable) Hydrogen fuel cell
1000
95%, 700 (kJ/kg) 25%, 75.3 (kJ/kg) 25%, 1276 (kJ/kg)
70
Resistive heating from PV array source Radiant heating from reflector Radiant heating with thin-film lens
300 55 · 102
7.53
CH3 OH (methanol)/ CH4 (methane, butane, etc.) PV array
388a; b
13%, 65.96 (kJ/kg)
6.596
Reflected radiant heat
2286a
217.7
Magnified radiant heat
2286
95%c , 2172 (kJ/kg) 50%c , 1143 (kJ/kg)
127
114.3
a Dependent on the area density of the PV (photovoltaic) arrays or concentrators (assumed 0.074 m2 /kg for PV, 0.19 m2 /kg for concentrators). b Assumes 17% efficiency transfer of solar to electric energy. c Assumes 70% absorptivity and position tolerance.
heating. Information on specific energy values was obtained from [22,23], while approximate efficiency in energy transfer was acquired from [21]. The overall material efficiency of SMAs in converting thermal to mechanical energy used in the table is 10% as given by [22]. The radiant heating method using a reflecting solar concentrator has the potential to provide the highest power density. Actuators for space application have high costs associated with transport, assembly and maintenance, making the value of a high power density significant. For example, the transportation costs of a single kg of payload using the shuttle is on the order of $22,000 [21]. In addition, the proposed radiant-based SMA actuator may provide a minimal impact to the surrounding environment, while providing a simple actuator with a small part count improving reliability. 2.2. Material model A material model is developed to characterize the behavior (phase transition rate) of the SMA under the influence of stress and temperature. There have been several numerical approaches for modeling the properties and behavior of SMA presented in the literature. Two basic types of models developed include a thermodynamic model using Gibb’s free energy and Maxwell’s relation, and an iterative finite element model. For example, Ivshin and Pence [10], Xu et al. [13], Niezgodka and Spreckles [14] and Liang and Rogers [15] present thermodynamic models examining
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uniaxial stress and strain conditions of a SMA while Gaudenzi and Bathe [16] presents an iterative finite element model to determine the electrical and mechanical responses of the maximum induced strain of a SMA. The thermodynamic-based SMA material model developed by [10] will be adapted and used in this paper. This model has been validated and provides an approximate representation of the SMA considering uniaxial stress and strains only, which is well suited to the wire actuator considered here. In this model, Maxwell relations are used to establish the thermomechanical phase transitional behavior of the SMA during heat addition and result in equations of state that specifically govern the strain and entropy of the system as a function of stress and temperature. These governing relational equations from [10] are oSA ðT ; rÞ oeA ðT ; rÞ ¼ oT or
ð1Þ
oSM ðT ; rÞ oeM ðT ; rÞ ¼ oT or
ð2Þ
and
in which S is the entropy, T is the bulk material temperature, r is the stress on the SMA and subscripts A and M refer to austenite and martensite phases respectively. Ivshin and Pence [10] solve for strain from these equations to result in r r e ¼ ð1 aÞ ð3Þ vM ðT T0 Þ þ a vA ðT T0 Þ EM EA where EM and EA are the modulus properties associated with the martensite and austenite phases, vM and vA are the thermal expansion coefficients, a is the phase fraction (percentage of austenite), T0 is the initial temperature of the system and T is the current temperature. Thus knowing the strain and original length, the displacement is easily found. Note that Eq. (3) and therefore the actuator displacement depend on an estimation of phase fraction, a, which provides a method of defining the percentage of material in the austenite phase (following the variables defined by [10]). A material that is fully in the austenite phase, a phase resulting from high temperature, low stress and having asymmetric lattice structure has a phase fraction of a ¼ 1, while a material that is fully in the martensite phase, resulting from low temperature, high stress and displaying a deformed lattice structure, has a phase fraction of a ¼ 0. The primary problem in solving for a is that the phase transition process of changing from martensite to austenite and similarly from austenite to martensite is one that introduces a natural hysteresis (see Fig. 2a for example). If the problem can be defined as one of monotonic increase or decrease in temperature at a constant stress and from a known state, then the process state is known and can be defined by the envelope functions of Fig. 2a. However, in practice it is necessary to approximate the current phase fraction given a material state of stress or strain and temperature and the current rate of change of a with respect to time.
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Fig. 2. (a) Phase fraction plot from austenite–martensite (left) and from austenite–martensite. (b) Envelope functions for r ¼ 0–100 Mpa.
The phase fraction a must exist between two envelope functions, amin and amax . Ivshin and Pence [10] developed these envelope functions, adjusted with four fitting parameters, k1 –k4 as given in the following equations ^ amin ðbÞ ¼ 0:5 ð1 þ tanhðk3 b þ k4 ÞÞ
ð4Þ
^ amax ðbÞ ¼ 0:5 ð1 þ tanhðk1 b þ k2 ÞÞ
ð5Þ
and
with b a variable describing the relationship between entropy and strain in Maxwells’ relation as,
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bðT ; rÞ ¼ T þ
1 ðsA ðT0 Þ sM ðT0 ÞÞ
ðEM EA Þ 2 r dr 2EM EA
ð6Þ
where typical values for b range from 15 to 30 and d, the transformation strain of the displacement phase, is assigned a value of 7% as obtained from the accompanying material data sheet accompanying the material used in this work. The amin curve (Eq. (4)) is the phase fractional plot starting in the martensite phase as the temperature increases. Similarly, the amax curve is the phase fractional plot starting in the austenite phase as the temperature decreases. The fitting parameters, k1 , k2 , k3 , and k4 are material dependent and are selected to ensure that a remains within the envelope functions. Following the same procedure defined in Ivshin and Pence [10], the fitting parameters k1 , k2 , k3 , and k4 are determined in an approximate fashion through an iterative process that forces the amin and amax plots to encompass the a plot. In this process, a sinusoidal temperature function is applied to the SMA, and the fitting parameters were adjusted based on visual inspection of the envelope phase fraction plots. Initial values for the fitting parameters were obtained from Ivshin and Pence [10]. The process was performed for the material used in this work, a NiTi SMA alloy with, EA ¼ 83 GPa, EM ¼ 28–41 GPa, m ¼ 0:33, e ¼ 0:0018 and a ¼ 1:0, and resulted in the following k values, k1 ¼ 0:11;
k2 ¼ 1:4;
k3 ¼ 0:128;
k4 ¼ 3:7
ð7Þ
These fitting parameters are slightly different than [11] mainly due to the material used. The phase fraction a was first established by Ivshin and Pence [11] and the same formulation is followed for the phase fraction calculations here. To perform this approximation, first consider the time rate of change of a, and define a and amax at times tk , the point at which the first derivative of a changes from a positive to a negative value, and a and amin at time tj , the point at which the first derivative of a changes from a negative to a positive value. Approximations for a between these switching instants are then given as, aðtk Þ da P0 ð8Þ aðtÞ ¼ ðamax ðT ðtÞ; rðtÞÞÞ for amax ðT ðtk Þ; rðtk ÞÞ dt and aðtÞ ¼ 1
1 aðtj Þ 1 amin ðT ðtj Þ; rðtj ÞÞ
ð1 amin ðT ðtÞ; rðtÞÞÞ
for
da P0 dt
ð9Þ
with da describing the current path of the material within the hysteresis loop. dt A portrayal of the envelope functions that describe the inherent material hysteresis and the path followed by the phase fraction as a function of temperature and stress is given in Fig. 2a and b for the material model. This material model is then implemented for the specific material properties to be used in the prototype actuator development. An experimental hysteresis profile was generated for the SMA material used in this work and compared to the theoretical material model hysteresis profile developed here, with the results shown in Fig. 3. The correlation of the hysteresis
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Fig. 3. A hysteresis profile comparing the mathematical control model to the experimental model.
curve between the two models provides verification of the implementation of this material model. 2.3. Environmental model To continue the radiant-heat driven actuator model, the environment in space and its effects on the actuator thermal state must be characterized. This model will consider the primary effects of controlled radiant energy, directed by the concentrator, the secondary effects of earth and surrounding structure radiation and thermal conduction to connective elements in the system. The model will allow for variations in the degree of radiant energy delivered to the actuator material as a function of concentrator angle, and will also allow for complete shielding of the actuator and selective conduction to a cooling radiator. To begin the model, certain basic assumptions are formed. These include an ideal concentrator model, an even application of heat over the entire ‘‘radiant’’ length of the SMA and no loss of energy through natural or forced convection. The radiant energy into the actuator material is a combination of solar, earth and structure sources. Note that the solar component of radiation is far greater than the others, for example, the solar constant in lower earth orbit (LEO) is approximately 1340 W/m2 while the solar energy emitted from earth is approximately 20 W/m2 (21). The solar concentrator provides the means to amplify or reduce the solar radiation rate on the SMA material, and is regulated by controlling the concentrator position about the
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material. The true rate of radiant energy received by the material then is determined from the current concentrator angle and relative geometries of the radiant sources. 2.3.1. Finite element temperature model A one-dimensional time dependent finite element analysis of the actuator wire was performed to determine the state of the actuator in time under varying heat flux conditions, as provided by the solar concentrator. This model is used to implement the control strategy for the SMA actuator. The model characterizes the SMA wire actuator and a significant portion of its structural attachments to which the wire is thermally connected as a system of heat transfer elements. This model will consider external radiant heat sources from the sun, earth and the structure, and will initially ignore potential heat sources such as atmospheric drag [19]. In this manner, radiant heat flux as well as conductive heat transfer to the connecting structure is modeled. Continuing with the finite element approach, a thermal stiffness and a lumped-mass matrix for the heat conduction problem are formed for each element in the model. These are appropriately combined to result in a time dependent, first-order heat transfer equation as MT_ þ KT ¼ Q
ð10Þ
with M and K the thermal mass and thermal conductivity matrices and T and Q the nodal temperature and nodal heat flux vectors [9]. A simulation of nodal temperatures with respect to time is accomplished based on a general temporal integration scheme shown in Eq. (11), 1 1 M þ cK Tiþ1 ¼ M ð1 cKÞ Ti þ ð1 cÞQc þ cQiþ1 ð11Þ Dt Dt where the value of c determines the type of numerical integration technique as given in Cook et al. [18]. Vector Q represents the net heat flux into the system resulting from radiation [19], Q ¼ Qradiation
in
Qradiation
out
ð12Þ
with Qradiation
in
¼ a A½cx qsun þ qearth þ qstruct
ð13Þ
with a the absorptivity of the SMA wire, A the projected elemental area of the wire, cx the solar concentration ratio, and qsun , qearth , qstruct , the heat flux from the sun, earth and structure respectively and Qradiation
out
¼ As e rthermal T4
ð14Þ
where As is the elemental surface area, e the emissivity of the SMA wire, rthermal the surface tension and T the average temperature between nodes. This finite element model was verified with commercial FEA software (ANSYS).
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Effective cooling of the wire is a difficult task and in general presents the biggest obstacle in the time response of the actuator. As demonstrated in Eq. (14), the wire will cool as a simple radiator when protected from incoming heat flux. Note that additional heat sinks could be added and modeled in a similar fashion to improve the effective cooling rate. The solar concentration ratio, thermal model and material model can now be coupled to create a time simulation of the system. Starting with a specific concentration ratio and current material state, the change in material temperature over a small time step is determined from the FE temperature model (Eq. (11)). Then, the material model is invoked (Section 2.2) to determine phase-fraction values, a, of the material and subsequent strain at the new time step. The process is then repeated as the simulation moves forward in time. 2.4. Control model A simple control strategy model for the SMA actuator prototype is developed and combined with a PI (proportional, integral) feedback control, chosen primarily to reduce the response time and eliminate steady state error (the system is considered stable enough to avoid the implementation of derivative control). In general, the control strategy will need to monitor the direction of incoming radiation, concentrator orientation and the temperature of the actuator wire. Then, based on desired actuator response, the concentrator angle is controlled to modify the concentrator gain as a function of feedback motion information. The gains are adjusted using an iterative search in a routine that employs the simulation described at the end of Section 2.3.1 to represent the physical actuator. For the prototype, the concentrator and radiant source geometry is fixed, while the feedback gains are adjusted based on prototype performance, this is shown in Fig. 4. This actuator is envisioned to be a standalone system coupled with appropriate sensors and embedded control. The control technique employed in practice will then be dependent on the capabilities of the microcontroller selected. For example, if using the Motorola HC12 microcontroller, a fuzzy-logic control scheme could be naturally and efficiently implemented using built-in functions for evaluating values of membership functions and fuzzy rules.
Fig. 4. PI controller for the SMA cylindrical concentrators.
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Fig. 5. Response of actuator model tracking sinusoidal displacement.
2.5. Model response The material and environmental models with PI control are combined and used now to demonstrate the response of an ideal radiant-heat activated SMA actuator in a simulated space environment. The example here is based on a 0.038 cm diameter, 100 cm SMA wire that is used to produce a desired sinusoidal displacement function under a constant load of 7 N with amplitude of approximately 4.25 cm or 4.25% of the wire length. The model assumes that the actuator wire is exposed under a single solar concentrator, with the entire structure in a lower earth orbit. The test is run during daylight time period for full exposure to the sun. The response of the actuator and its ability to track the desired sinusoidal displacement function is observed as shown in Fig. 5. This figure demonstrates the ability of the modeled actuator to track a desired response over time. Note that departures of the model response from the specified response results from a saturation below the peak amplitude desired and to cool the system at the same rate it is heated.
3. Radiant heat actuated SMA prototype A prototype of the radiant-heat activated SMA actuator was fabricated to evaluate the actuator model and demonstrate proof of concept. The prototype was developed to operate in a laboratory environment that attempted to simulate an environment dominated by solar radiation. The prototype environment allows convective heat transfer, the most significant departure from the space environment.
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The lab prototype is shown for reference in Fig. 6, with labels for the model elements in the system. Solar energy in the prototype is provided by a pair of 500 W halogen lamps and are arranged to provide radiant energy comparable to a space environment with appropriate adjustments in the theoretical model. This radiant energy is captured by a set of cylindrical concentrators and focused onto a portion of the SMA wire. The SMA wire is constrained to lie along the focal axis of the concentrator. In addition, the cylindrical concentrators are designed to have a rotational degree of freedom about their focal axis. This allows controlled focus onto or shielding of the SMA wire from the radiant source. In the prototype design, focus providing up to 30· concentration is available. Control of the concentrator rotation is provided by a
Fig. 6. Prototype system: 1––Radiant heat source, 2––Cylindrical concentrator, 3––Displacement measurement device, 4––SMA actuator wire, 5––Positioning control system.
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small servo motor and transmission, which allows radiant energy to be focused on or shielded from the SMA wire. Control of the prototype system and data acquisition of system sensor data is performed using LabView 6 and an SC-2070 data acquisition card. The entire unit consisting of the SMA wire, concentrator and servomotor can be scaled according to the wire size and the application. For example, if the actuator forms part of the structure, the assembly support may be provided as well by the structure. For the smaller prototype developed here, a base is included to support the system, as shown in Fig. 7. A number of engineering issues were addressed in creating the prototype and are presented in the following section. Finally, a brief description of results from prototype testing is presented. 3.1. Engineering design and implementation Primary aspects in the engineering design considered here include the effects of manufacturing tolerances on concentrator placement and thermal isolation of the actuator wire. The actuator design requires the SMA actuator wire to lie along the focal axis of a cylindrical concentrator. In addition, to allow focus of and shielding from radiant energy, the concentrator must have a rotational degree of freedom. Manufacturing end mounts that capture the SMA wire along the focal axis and allow rotation around this axis performs this.
Fig. 7. Wire, concentrator, and base.
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3.1.1. Sensitivity to manufacture tolerances The end pieces are attached to the cylindrical concentrators in the prototype-using super adhesive in a rigid fixture. In general, the degree of accuracy or tolerance in manufacturing and placing these end mounts is a significant factor in the performance of the physical actuator. To observe the effects of manufacturing error, an error analysis was performed to determine the sensitivity of concentration to positioning tolerance of the wire about the focal axis. The sensitivity is considered in a geometric sense as the percent of concentrator returning incident rays to the wire. The results of this analysis are shown graphically in Fig. 8 and show the high degree of sensitivity near the focal point. This places a relatively high tolerance on locating the wire in the system and results in a trade-off between the size of concentrator needed and the degree of tolerance in manufacture. For the prototype SMA actuator, the wire is positioned to with a 0.0013 mm position and radial tolerance of the desired focal point. 3.1.2. Thermal isolation Considerations for thermal isolation were also significant in the prototype. Due to size constraints in the physical demonstrator, the radiant energy sources (halogen lamps) heated the base of the structure through conduction. In order to reduce
Fig. 8. Sensitivity of concentrator intensity.
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conductive heating of the SMA wire, the capturing elements were designed to provide significant thermal insulation to the wire. Components for thermal isolation include glass ball bearings to provide the rotational degree of freedom about the focal axis and delrin guides to capture the SMA wire. Convective heating of the prototype model also exists during testing in an ambient atmospheric laboratory environment. Several techniques could be considered to account for this additional heating. The convective heating could be avoided by testing the prototype in a vacuum chamber, or accounted for by including a convection heat source in the model for prototype. The prototype system could also be constructed such that radiant heating is the dominant factor acting on the SMA. This third technique has been employed in the prototype system. 3.2. Demonstrating the prototype Similar to the actuator model, the prototype is used to demonstrate the response of a physical model of the radiant-heat activated SMA wire in a laboratory setting. The example is based on a 0.038 cm diameter actuator with 50 cm of actuated length, to produce a sinusoidal displacement function under a steady-state load of 7 N. Note that two concentrators were used in this prototype due to the limited size of lens length available for inexpensive fabrication. The amplitude of the total contracted
Fig. 9. Response of the physical prototype under simulated task.
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length of the actuator is approximately 2.2 cm or 4.5% of the total length of the sample. The input radiant energy is constant, and held at a constant geometry relative to the SMA and concentrator. These concentrators, while capable of independent response, function under the same control strategy to track the desired displacement. Note that the desired displacement profile does not reach the maximum displacement for the SMA wire. This reduced range of actuator motion was encountered for several reasons. First, the prototype had a certain amount of inefficiency in uniformly heating the actuator material. In addition, the material used in the prototype has a phase transition temperature that was very near the maximum temperature that could be achieved by the prototype. The response however, demonstrates the ability of this device to follow a determined path of the actuator and its ability to track the desired sinusoidal forcing function are observed in Fig. 9. Note that response is similar in form to Fig. 5 in tracking the desired displacement function in time. It is also noted that the similar difficulties occur in cooling the wire in both the model and prototype. The higher frequency transients in the actuator response shown in Fig. 9 result from the measurement system and not transients in the actuator itself.
4. Conclusions This paper has proposed a means of using direct radiant energy to activate phase change in a SMA material in a controlled fashion resulting in an actuator designed for space applications. Other methods for driving SMA materials were compared based on an approximate evaluation of power density. The comparison of power density for all the heating methods discussed revealed that the radiant heating approach could possess the greatest power density directly reducing the cost for space applications. A complete model of this actuator has been developed which includes material and environmental models and a general control strategy. Experiments have been performed to verify the material model as well as the composite actuator model. It has been shown that this concept has several significant advantages over other more conventional SMA-based actuators. This advantage lies primarily in the weight savings resulting from direct use of radiant energy to activate the SMA phase change. Finally, a prototype of this actuator has been built and tested providing a system demonstration and evaluation. Evaluation of the prototype, and comparison with the actuator model are performed. The results of this comparison show a strong similarity in the trend in actuator response. The significant differences are in the lower response time, particularly in the cooling phase, for the actuator model as well as the maximum amplitude. The main constraint for the radiant heat activated SMA actuator is the cooling time (phase transition from austenite to martensite). Increasing the heat loss during the cooling cycle would result in a significant decrease the overall actuation times. Since the mathematical, control, environmental and prototype
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modeling have been demonstrated with high congruence, future work on this novel actuator will focus on the development and implementation of increased cooling capabilities.
Acknowledgements The authors express their appreciation for the help and support from John Fikes and Joe Howell in the Flight Projects Directorate at NASA/MSFC, contract number NAG8-1749 and the support of the Manufacturing Center at Tennessee Technological University.
References [1] Maclean BJ, Patterson GJ, Misra MS. Modeling of a shape memory integrated actuator for vibration control of large space structures. J Intelligent Mater Syst Struct 1991;II:72–94. [2] Johnson AD. Non-explosive separation device, US Patent Number 5,119,555, June 1992. [3] Dario P, Montesi MC. Shape memory alloy microactuators for minimally invasive surgery. In: Proceedings of SMST-94 conference, Asilomar CA, March 1994. [4] Wu MH, Ewing WA. Pilot-operated anti-scaled safety valve: design and actuator considerations. In: SMST-94 proceedings, Asilomar CA, March 1994. [5] Rediniotis OK, Lagoudas DC, Jun HY, Allen RD. Fuel-powered compact SMA actuator. In: McGowan A.-M.R., editor. Proc. SPIE, Smart Structures and Materials 2002: Industrial and Commercial Applications of Smart Structures Technologies. Vol. 4698, pp. 441–453. [6] Krulevitch P, Lee AP, Ramsey PB, Trevino JC, Hamilton J, Northrup MA. Thin film shape memory alloy microactuators. Journal of MEMS 1996;5(4). [8] Pister KSJ, Judy MJ, Burgett SR, Fearing RS. Microfabricated hinges. Sensors Actuat (A) 1992;33(3):249–56. [9] Jerman H, Dunbar M. Understanding microvalve technology. Sensors 1994:26–36. [10] Ivshin Y, Pence TJ. A constitutive model for hysteretic phase transition behavior. Int J Eng Sci 1994;32:681–704. [11] Ivshin Y, Pence TJ. A thermomechanical model for a one variant memory material. J Intelligent Mater Syst Struct 1994;5:455–73. [13] Xu G, Lougoudas DC, Wen JT, Declan H. Thermo-electro-mechanical modeling and structural response of a flexible beam with external SMA actuators. Smart Struct Mater 1995;27:503– 15. [14] Niezgodka M, Spreckles J. Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys. Math Methods Appl Sci 1988;10:197–223. [15] Liang C, Rogers CA. One-dimensional thermomechanical constitutive relations for shape memory materials. J Intelligent Mater Syst Struct 1990;V1:207. [16] Paolo G, Bathe K-J. Recent applications of an iterative finite element procedure for the analysis of electroelastic materials. Fourth International Conference on Adaptive Structures November 2–4, 1993. p. 59–70. [18] Cook RD, Malkus DS, Plesha ME. Concepts and applications of finite element analysis. 3rd ed. John Wiley and Sons; 1989. [19] Incopra F, David P. Dewitt Fundamentals of Heat and Mass Transfer. 3rd ed. John Wiley and Sons; 1990. [21] Avallone EA, Theodore III B. Mark’s standard handbook for mechanical engineers, 10th Ed.
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[22] Bar-Cohen Y, Sherrit S, Bao X, Chang Z. Ultrasonic/sonic sampler and sensor platform for in-situ planetary exploration. In: 2003 International Conference on MEMS, NANO, and Smart Systems, July 2003, Banff, Canada. [23] Energy density. Int J Hydrogen Energy, September 1996. Available from:.
A radiant energy-powered shape memory alloy actuator P.V. Hull a, S.L. Canfield
a,*
, C. Carrington
b
a
b
Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN 38501, USA Marshall Space Flight Center/NASA, Flight Projects Directorate, Huntsville, AL 35812, USA
Abstract This paper will present the development of an innovative actuator using a shape memory alloy (SMA) that is powered by available radiant energy in the space environment. Currently, self-contained or tethered power supplies provide the energy source for actuators in space applications. These can be costly, heavy and require regular maintenance and/or refueling. Ideally an actuator for space applications should have a high power density, be able to operate with little interference from its power source and maintain a low operating cost. Shape memory alloys are materials that recover internal strain with the addition of heat, thus changing thermal energy to mechanical energy. Because of this, they are known as thermomechanical motors. These materials can be thermally actuated by a number of means with the primary conventional approach based on resistive heating. Radiant energy, while typically impractical for use under normal circumstances, is a significant and abundant energy source in space and can be directed to control phase transition in a SMA material. This paper will describe the development of a radiant-heat driven SMA actuator, presenting a simple actuator model and prototype. The paper will also compare this actuator against other SMA-based actuators. 2004 Elsevier Ltd. All rights reserved. Keywords: Actuator; Cylindrical concentrator; Maxwell’s relation; Radiant energy; Shape memory alloys; Space
*
Corresponding author. Tel.: +1-931-372-6359; fax: +1-931-372-6340. E-mail address: scanfi[email protected] (S.L. Canfield).
0957-4158/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2004.01.008
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1. Introduction The primary objective for this paper is to present the development of a shape memory alloy (SMA)-based actuator that makes direct use of available radiant energy in the space environment. The space environment has an abundant and endless supply of radiant energy. Harnessing this energy to power an actuator can potentially result in an efficient and cost-effective actuation device. Typical actuators for space applications require self contained or tethered power supplies, adding weight to the system as well as cost of recharging or refueling. Ideally, actuators for reoccurring or continuous applications should have a high power-to-weight density, be able to operate with little interference from their power source and be maintained at a low cost. The shape memory alloy material provides a thermomechanical motor that converts thermal energy to mechanical energy due to a material phase transition. This transition, known as the memory effect, is a cycle through the material phases, austenite and martensite. Austenite is the material phase of high temperature and low stress that exists in a cubic lattice structure; it is a rigid phase with strong crystal symmetry that is due to the face centered cubic structure. Martensite is the material phase of low temperature and high stress that exists as a distorted version of the austenite phase. The use of shape memory alloys to create actuators is common in the literature with a variety of applications demonstrated. For example, McClean et al. [1] investigates using SMAs for vibration control of large space structures. The frangibolt [2] is a commercially available device used for permanent deployment of space vehicle and payloads. Designs exist for steerable catheters for use in surgical applications [3], while SMA’s have been implemented as an anti-scaled valve [4] to monitor water temperature in a shower and prevent water flow if the temperature rises above a specified level. Forced convective heating and cooling to actuate SMAs has been demonstrated [5]. Shape memory alloys are employed to actuate microdevices, such as micro-thin film actuators [6], microfabricated hinges and microvalves [8]. These examples provide only a few of the many implementations of SMAs as actuators, and demonstrate the variety of forms used to drive this material through the transitional phases. Specifically, these examples demonstrate various modes for causing temperature transition through resistive heating [1,2,6], forced convection heating [4], forced convective heating and cooling [21] and conduction [3]. This paper will propose an alternative approach for inducing phase change in SMAs based on directed radiant heating of the actuator material. There are many benefits and potential applications for this approach. This method of heating can overcome the costs, mass and in a few cases size (for example when compared to the use of solar cells for photovoltaic power) associated with traditional power supplies by making use of available radiant energy, while at the same time reducing much of the complexity of the actuator system. Further this design may allow improved packaging, for example through the use of deployable thin-film concentrators. Potential applications for this solar driven actuator include finite control of mirrors or other devices for accurate positioning, opening and closing doors, deploying space
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appendages, and vibration control of large space structures. However, this approach will require an energy concentration system and appropriate models and control algorithms. A complete model of the radiant-heat activated SMA actuator will be developed in this paper to demonstrate its viability and evaluate its performance in space applications. This model will combine several basic parts; a material model, an environmental model, a control strategy and an engineering model for prototype construction. The concept will be developed in Section 2.1 and compared at an energy density level to other SMA actuators. The material model (Section 2.2) will characterize the functional relations between temperatures, stress and strain in the SMA and will be based on the thermodynamic model developed by Ivshin and Pence [10]. The environmental model (Section 2.3) will be based on a single degree of freedom finite element time-based thermal model that simulates an appropriate lower earth orbit environment and includes the effects of the solar concentrator. The control strategy (Section 2.4) will describe a PI control implementation for the model. Finally, a physical model (Section 3) will be described and a prototype will be constructed based on the model and engineering developments for testing and evaluation of the design. Based on the system model and prototype created, the capabilities of this solar-driven SMA actuator will be characterized and summarized (Section 3.2). Issues in practical development of such a system will be discussed.
2. Concept and model development This section focuses on modeling and design of a space actuator driven by solar radiant energy. Based on this energy source (solar), various methods of capturing and using this energy to drive the actuator were considered, as well as topology forms for the actuator. 2.1. Concept development Several topologies could be implemented in a radiant-driven SMA actuator device, including longitudinal extension of wire or ribbon, bending of beam-type elements or surface strain induced in thin film layers. The wire form actuator has the advantage of being radially symmetric while the ribbon and thin-film layers possess a high surface area to volume ratio. Likewise the beam-type actuator can provide significant angular displacements when desired. Each form depends heavily on the desired application. A linear SMA wire actuator will be discussed in detail here due to ease of implementation on an initial prototype system. Similarly, a variety of methods to concentrate solar radiant energy on the SMA were considered and evaluated on their suitability to all aspects of operation in the space environment and the ability to model and prototype. These methods include both lenses and reflectors. Lenses may provide significant advantages in weight and size (for example a thin film deployable lens or a fresnel lens). Alternatively, reflective mirrors may provide means to shield as well as concentrate energy at varying amounts while providing a higher efficiency in transferring solar radiant energy than
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a lens. Based on the evaluation of these concepts, a cylindrical concentrator was chosen for reasons including expandability, shading capabilities, lightweight and ease of prototyping. Fig. 1 shows a schematic radiant-heat activated SMA actuator and labels the elements forming the basic components of the model development. The wire actuator provides axial displacement and tensile forces at the output ends at which control force and/or displacement desired. A solar concentrator, formed as a cylindrical concentrator, encircles a portion of the wire actuator. The concentrator can also serve as a solar shield and/or radiator during cooling phases. The solar concentrator in this model is driven in a rotary fashion about the wire by a small, low-power motor. The actuator is designed to maintain the wire at the focal point of the cylindrical concentrator while varying the level of concentrated radiant heat on the wire as a function of the rotation angle relative to incident solar rays. Appropriate sensors are included in the model to determine incident solar energy directions and the actuator states. Finally, the space environment indicated in the schematic will include orbit information, radiation effects from the sun, earth and the space structure, and conductive effects to the radiating shield and the remainder of the structure. Note that one design issue that will arise when placing many of these actuators on a space structure is that each solar collector needs to be in full view of the sun (not in a structural shadow) for actuation. Discussion of this issue is beyond the scope of this paper. Power densities of various SMA actuator systems are discussed here. The merits of a radiant energy-driven actuator are based on the ability to match the force and motion capabilities of similar actuators while providing the potential for greater power density. The power densities of several SMA actuators are compared based on the method of energy storage (or extraction) and energy transfer, as shown in Table 1. This table compares various energy sources using resistive, convective and radiant
Fig. 1. Outline of this paper.
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Table 1 Summary of driving methods for SMA actuators SMA heat actuation method
Energy source for heating SMA
Specific energy of source for SMA heating (kJ/kg)
E transfer efficiency (approx.)
Power density SMA Eff (10%) (kJ/kg)
Resistive heating from battery Resistive heating from fuel cell Forced convection from combustor
Lithium battery (non-rechargeable) Hydrogen fuel cell
1000
95%, 700 (kJ/kg) 25%, 75.3 (kJ/kg) 25%, 1276 (kJ/kg)
70
Resistive heating from PV array source Radiant heating from reflector Radiant heating with thin-film lens
300 55 · 102
7.53
CH3 OH (methanol)/ CH4 (methane, butane, etc.) PV array
388a; b
13%, 65.96 (kJ/kg)
6.596
Reflected radiant heat
2286a
217.7
Magnified radiant heat
2286
95%c , 2172 (kJ/kg) 50%c , 1143 (kJ/kg)
127
114.3
a Dependent on the area density of the PV (photovoltaic) arrays or concentrators (assumed 0.074 m2 /kg for PV, 0.19 m2 /kg for concentrators). b Assumes 17% efficiency transfer of solar to electric energy. c Assumes 70% absorptivity and position tolerance.
heating. Information on specific energy values was obtained from [22,23], while approximate efficiency in energy transfer was acquired from [21]. The overall material efficiency of SMAs in converting thermal to mechanical energy used in the table is 10% as given by [22]. The radiant heating method using a reflecting solar concentrator has the potential to provide the highest power density. Actuators for space application have high costs associated with transport, assembly and maintenance, making the value of a high power density significant. For example, the transportation costs of a single kg of payload using the shuttle is on the order of $22,000 [21]. In addition, the proposed radiant-based SMA actuator may provide a minimal impact to the surrounding environment, while providing a simple actuator with a small part count improving reliability. 2.2. Material model A material model is developed to characterize the behavior (phase transition rate) of the SMA under the influence of stress and temperature. There have been several numerical approaches for modeling the properties and behavior of SMA presented in the literature. Two basic types of models developed include a thermodynamic model using Gibb’s free energy and Maxwell’s relation, and an iterative finite element model. For example, Ivshin and Pence [10], Xu et al. [13], Niezgodka and Spreckles [14] and Liang and Rogers [15] present thermodynamic models examining
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uniaxial stress and strain conditions of a SMA while Gaudenzi and Bathe [16] presents an iterative finite element model to determine the electrical and mechanical responses of the maximum induced strain of a SMA. The thermodynamic-based SMA material model developed by [10] will be adapted and used in this paper. This model has been validated and provides an approximate representation of the SMA considering uniaxial stress and strains only, which is well suited to the wire actuator considered here. In this model, Maxwell relations are used to establish the thermomechanical phase transitional behavior of the SMA during heat addition and result in equations of state that specifically govern the strain and entropy of the system as a function of stress and temperature. These governing relational equations from [10] are oSA ðT ; rÞ oeA ðT ; rÞ ¼ oT or
ð1Þ
oSM ðT ; rÞ oeM ðT ; rÞ ¼ oT or
ð2Þ
and
in which S is the entropy, T is the bulk material temperature, r is the stress on the SMA and subscripts A and M refer to austenite and martensite phases respectively. Ivshin and Pence [10] solve for strain from these equations to result in r r e ¼ ð1 aÞ ð3Þ vM ðT T0 Þ þ a vA ðT T0 Þ EM EA where EM and EA are the modulus properties associated with the martensite and austenite phases, vM and vA are the thermal expansion coefficients, a is the phase fraction (percentage of austenite), T0 is the initial temperature of the system and T is the current temperature. Thus knowing the strain and original length, the displacement is easily found. Note that Eq. (3) and therefore the actuator displacement depend on an estimation of phase fraction, a, which provides a method of defining the percentage of material in the austenite phase (following the variables defined by [10]). A material that is fully in the austenite phase, a phase resulting from high temperature, low stress and having asymmetric lattice structure has a phase fraction of a ¼ 1, while a material that is fully in the martensite phase, resulting from low temperature, high stress and displaying a deformed lattice structure, has a phase fraction of a ¼ 0. The primary problem in solving for a is that the phase transition process of changing from martensite to austenite and similarly from austenite to martensite is one that introduces a natural hysteresis (see Fig. 2a for example). If the problem can be defined as one of monotonic increase or decrease in temperature at a constant stress and from a known state, then the process state is known and can be defined by the envelope functions of Fig. 2a. However, in practice it is necessary to approximate the current phase fraction given a material state of stress or strain and temperature and the current rate of change of a with respect to time.
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Fig. 2. (a) Phase fraction plot from austenite–martensite (left) and from austenite–martensite. (b) Envelope functions for r ¼ 0–100 Mpa.
The phase fraction a must exist between two envelope functions, amin and amax . Ivshin and Pence [10] developed these envelope functions, adjusted with four fitting parameters, k1 –k4 as given in the following equations ^ amin ðbÞ ¼ 0:5 ð1 þ tanhðk3 b þ k4 ÞÞ
ð4Þ
^ amax ðbÞ ¼ 0:5 ð1 þ tanhðk1 b þ k2 ÞÞ
ð5Þ
and
with b a variable describing the relationship between entropy and strain in Maxwells’ relation as,
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bðT ; rÞ ¼ T þ
1 ðsA ðT0 Þ sM ðT0 ÞÞ
ðEM EA Þ 2 r dr 2EM EA
ð6Þ
where typical values for b range from 15 to 30 and d, the transformation strain of the displacement phase, is assigned a value of 7% as obtained from the accompanying material data sheet accompanying the material used in this work. The amin curve (Eq. (4)) is the phase fractional plot starting in the martensite phase as the temperature increases. Similarly, the amax curve is the phase fractional plot starting in the austenite phase as the temperature decreases. The fitting parameters, k1 , k2 , k3 , and k4 are material dependent and are selected to ensure that a remains within the envelope functions. Following the same procedure defined in Ivshin and Pence [10], the fitting parameters k1 , k2 , k3 , and k4 are determined in an approximate fashion through an iterative process that forces the amin and amax plots to encompass the a plot. In this process, a sinusoidal temperature function is applied to the SMA, and the fitting parameters were adjusted based on visual inspection of the envelope phase fraction plots. Initial values for the fitting parameters were obtained from Ivshin and Pence [10]. The process was performed for the material used in this work, a NiTi SMA alloy with, EA ¼ 83 GPa, EM ¼ 28–41 GPa, m ¼ 0:33, e ¼ 0:0018 and a ¼ 1:0, and resulted in the following k values, k1 ¼ 0:11;
k2 ¼ 1:4;
k3 ¼ 0:128;
k4 ¼ 3:7
ð7Þ
These fitting parameters are slightly different than [11] mainly due to the material used. The phase fraction a was first established by Ivshin and Pence [11] and the same formulation is followed for the phase fraction calculations here. To perform this approximation, first consider the time rate of change of a, and define a and amax at times tk , the point at which the first derivative of a changes from a positive to a negative value, and a and amin at time tj , the point at which the first derivative of a changes from a negative to a positive value. Approximations for a between these switching instants are then given as, aðtk Þ da P0 ð8Þ aðtÞ ¼ ðamax ðT ðtÞ; rðtÞÞÞ for amax ðT ðtk Þ; rðtk ÞÞ dt and aðtÞ ¼ 1
1 aðtj Þ 1 amin ðT ðtj Þ; rðtj ÞÞ
ð1 amin ðT ðtÞ; rðtÞÞÞ
for
da P0 dt
ð9Þ
with da describing the current path of the material within the hysteresis loop. dt A portrayal of the envelope functions that describe the inherent material hysteresis and the path followed by the phase fraction as a function of temperature and stress is given in Fig. 2a and b for the material model. This material model is then implemented for the specific material properties to be used in the prototype actuator development. An experimental hysteresis profile was generated for the SMA material used in this work and compared to the theoretical material model hysteresis profile developed here, with the results shown in Fig. 3. The correlation of the hysteresis
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Fig. 3. A hysteresis profile comparing the mathematical control model to the experimental model.
curve between the two models provides verification of the implementation of this material model. 2.3. Environmental model To continue the radiant-heat driven actuator model, the environment in space and its effects on the actuator thermal state must be characterized. This model will consider the primary effects of controlled radiant energy, directed by the concentrator, the secondary effects of earth and surrounding structure radiation and thermal conduction to connective elements in the system. The model will allow for variations in the degree of radiant energy delivered to the actuator material as a function of concentrator angle, and will also allow for complete shielding of the actuator and selective conduction to a cooling radiator. To begin the model, certain basic assumptions are formed. These include an ideal concentrator model, an even application of heat over the entire ‘‘radiant’’ length of the SMA and no loss of energy through natural or forced convection. The radiant energy into the actuator material is a combination of solar, earth and structure sources. Note that the solar component of radiation is far greater than the others, for example, the solar constant in lower earth orbit (LEO) is approximately 1340 W/m2 while the solar energy emitted from earth is approximately 20 W/m2 (21). The solar concentrator provides the means to amplify or reduce the solar radiation rate on the SMA material, and is regulated by controlling the concentrator position about the
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material. The true rate of radiant energy received by the material then is determined from the current concentrator angle and relative geometries of the radiant sources. 2.3.1. Finite element temperature model A one-dimensional time dependent finite element analysis of the actuator wire was performed to determine the state of the actuator in time under varying heat flux conditions, as provided by the solar concentrator. This model is used to implement the control strategy for the SMA actuator. The model characterizes the SMA wire actuator and a significant portion of its structural attachments to which the wire is thermally connected as a system of heat transfer elements. This model will consider external radiant heat sources from the sun, earth and the structure, and will initially ignore potential heat sources such as atmospheric drag [19]. In this manner, radiant heat flux as well as conductive heat transfer to the connecting structure is modeled. Continuing with the finite element approach, a thermal stiffness and a lumped-mass matrix for the heat conduction problem are formed for each element in the model. These are appropriately combined to result in a time dependent, first-order heat transfer equation as MT_ þ KT ¼ Q
ð10Þ
with M and K the thermal mass and thermal conductivity matrices and T and Q the nodal temperature and nodal heat flux vectors [9]. A simulation of nodal temperatures with respect to time is accomplished based on a general temporal integration scheme shown in Eq. (11), 1 1 M þ cK Tiþ1 ¼ M ð1 cKÞ Ti þ ð1 cÞQc þ cQiþ1 ð11Þ Dt Dt where the value of c determines the type of numerical integration technique as given in Cook et al. [18]. Vector Q represents the net heat flux into the system resulting from radiation [19], Q ¼ Qradiation
in
Qradiation
out
ð12Þ
with Qradiation
in
¼ a A½cx qsun þ qearth þ qstruct
ð13Þ
with a the absorptivity of the SMA wire, A the projected elemental area of the wire, cx the solar concentration ratio, and qsun , qearth , qstruct , the heat flux from the sun, earth and structure respectively and Qradiation
out
¼ As e rthermal T4
ð14Þ
where As is the elemental surface area, e the emissivity of the SMA wire, rthermal the surface tension and T the average temperature between nodes. This finite element model was verified with commercial FEA software (ANSYS).
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Effective cooling of the wire is a difficult task and in general presents the biggest obstacle in the time response of the actuator. As demonstrated in Eq. (14), the wire will cool as a simple radiator when protected from incoming heat flux. Note that additional heat sinks could be added and modeled in a similar fashion to improve the effective cooling rate. The solar concentration ratio, thermal model and material model can now be coupled to create a time simulation of the system. Starting with a specific concentration ratio and current material state, the change in material temperature over a small time step is determined from the FE temperature model (Eq. (11)). Then, the material model is invoked (Section 2.2) to determine phase-fraction values, a, of the material and subsequent strain at the new time step. The process is then repeated as the simulation moves forward in time. 2.4. Control model A simple control strategy model for the SMA actuator prototype is developed and combined with a PI (proportional, integral) feedback control, chosen primarily to reduce the response time and eliminate steady state error (the system is considered stable enough to avoid the implementation of derivative control). In general, the control strategy will need to monitor the direction of incoming radiation, concentrator orientation and the temperature of the actuator wire. Then, based on desired actuator response, the concentrator angle is controlled to modify the concentrator gain as a function of feedback motion information. The gains are adjusted using an iterative search in a routine that employs the simulation described at the end of Section 2.3.1 to represent the physical actuator. For the prototype, the concentrator and radiant source geometry is fixed, while the feedback gains are adjusted based on prototype performance, this is shown in Fig. 4. This actuator is envisioned to be a standalone system coupled with appropriate sensors and embedded control. The control technique employed in practice will then be dependent on the capabilities of the microcontroller selected. For example, if using the Motorola HC12 microcontroller, a fuzzy-logic control scheme could be naturally and efficiently implemented using built-in functions for evaluating values of membership functions and fuzzy rules.
Fig. 4. PI controller for the SMA cylindrical concentrators.
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Fig. 5. Response of actuator model tracking sinusoidal displacement.
2.5. Model response The material and environmental models with PI control are combined and used now to demonstrate the response of an ideal radiant-heat activated SMA actuator in a simulated space environment. The example here is based on a 0.038 cm diameter, 100 cm SMA wire that is used to produce a desired sinusoidal displacement function under a constant load of 7 N with amplitude of approximately 4.25 cm or 4.25% of the wire length. The model assumes that the actuator wire is exposed under a single solar concentrator, with the entire structure in a lower earth orbit. The test is run during daylight time period for full exposure to the sun. The response of the actuator and its ability to track the desired sinusoidal displacement function is observed as shown in Fig. 5. This figure demonstrates the ability of the modeled actuator to track a desired response over time. Note that departures of the model response from the specified response results from a saturation below the peak amplitude desired and to cool the system at the same rate it is heated.
3. Radiant heat actuated SMA prototype A prototype of the radiant-heat activated SMA actuator was fabricated to evaluate the actuator model and demonstrate proof of concept. The prototype was developed to operate in a laboratory environment that attempted to simulate an environment dominated by solar radiation. The prototype environment allows convective heat transfer, the most significant departure from the space environment.
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The lab prototype is shown for reference in Fig. 6, with labels for the model elements in the system. Solar energy in the prototype is provided by a pair of 500 W halogen lamps and are arranged to provide radiant energy comparable to a space environment with appropriate adjustments in the theoretical model. This radiant energy is captured by a set of cylindrical concentrators and focused onto a portion of the SMA wire. The SMA wire is constrained to lie along the focal axis of the concentrator. In addition, the cylindrical concentrators are designed to have a rotational degree of freedom about their focal axis. This allows controlled focus onto or shielding of the SMA wire from the radiant source. In the prototype design, focus providing up to 30· concentration is available. Control of the concentrator rotation is provided by a
Fig. 6. Prototype system: 1––Radiant heat source, 2––Cylindrical concentrator, 3––Displacement measurement device, 4––SMA actuator wire, 5––Positioning control system.
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small servo motor and transmission, which allows radiant energy to be focused on or shielded from the SMA wire. Control of the prototype system and data acquisition of system sensor data is performed using LabView 6 and an SC-2070 data acquisition card. The entire unit consisting of the SMA wire, concentrator and servomotor can be scaled according to the wire size and the application. For example, if the actuator forms part of the structure, the assembly support may be provided as well by the structure. For the smaller prototype developed here, a base is included to support the system, as shown in Fig. 7. A number of engineering issues were addressed in creating the prototype and are presented in the following section. Finally, a brief description of results from prototype testing is presented. 3.1. Engineering design and implementation Primary aspects in the engineering design considered here include the effects of manufacturing tolerances on concentrator placement and thermal isolation of the actuator wire. The actuator design requires the SMA actuator wire to lie along the focal axis of a cylindrical concentrator. In addition, to allow focus of and shielding from radiant energy, the concentrator must have a rotational degree of freedom. Manufacturing end mounts that capture the SMA wire along the focal axis and allow rotation around this axis performs this.
Fig. 7. Wire, concentrator, and base.
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3.1.1. Sensitivity to manufacture tolerances The end pieces are attached to the cylindrical concentrators in the prototype-using super adhesive in a rigid fixture. In general, the degree of accuracy or tolerance in manufacturing and placing these end mounts is a significant factor in the performance of the physical actuator. To observe the effects of manufacturing error, an error analysis was performed to determine the sensitivity of concentration to positioning tolerance of the wire about the focal axis. The sensitivity is considered in a geometric sense as the percent of concentrator returning incident rays to the wire. The results of this analysis are shown graphically in Fig. 8 and show the high degree of sensitivity near the focal point. This places a relatively high tolerance on locating the wire in the system and results in a trade-off between the size of concentrator needed and the degree of tolerance in manufacture. For the prototype SMA actuator, the wire is positioned to with a 0.0013 mm position and radial tolerance of the desired focal point. 3.1.2. Thermal isolation Considerations for thermal isolation were also significant in the prototype. Due to size constraints in the physical demonstrator, the radiant energy sources (halogen lamps) heated the base of the structure through conduction. In order to reduce
Fig. 8. Sensitivity of concentrator intensity.
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conductive heating of the SMA wire, the capturing elements were designed to provide significant thermal insulation to the wire. Components for thermal isolation include glass ball bearings to provide the rotational degree of freedom about the focal axis and delrin guides to capture the SMA wire. Convective heating of the prototype model also exists during testing in an ambient atmospheric laboratory environment. Several techniques could be considered to account for this additional heating. The convective heating could be avoided by testing the prototype in a vacuum chamber, or accounted for by including a convection heat source in the model for prototype. The prototype system could also be constructed such that radiant heating is the dominant factor acting on the SMA. This third technique has been employed in the prototype system. 3.2. Demonstrating the prototype Similar to the actuator model, the prototype is used to demonstrate the response of a physical model of the radiant-heat activated SMA wire in a laboratory setting. The example is based on a 0.038 cm diameter actuator with 50 cm of actuated length, to produce a sinusoidal displacement function under a steady-state load of 7 N. Note that two concentrators were used in this prototype due to the limited size of lens length available for inexpensive fabrication. The amplitude of the total contracted
Fig. 9. Response of the physical prototype under simulated task.
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length of the actuator is approximately 2.2 cm or 4.5% of the total length of the sample. The input radiant energy is constant, and held at a constant geometry relative to the SMA and concentrator. These concentrators, while capable of independent response, function under the same control strategy to track the desired displacement. Note that the desired displacement profile does not reach the maximum displacement for the SMA wire. This reduced range of actuator motion was encountered for several reasons. First, the prototype had a certain amount of inefficiency in uniformly heating the actuator material. In addition, the material used in the prototype has a phase transition temperature that was very near the maximum temperature that could be achieved by the prototype. The response however, demonstrates the ability of this device to follow a determined path of the actuator and its ability to track the desired sinusoidal forcing function are observed in Fig. 9. Note that response is similar in form to Fig. 5 in tracking the desired displacement function in time. It is also noted that the similar difficulties occur in cooling the wire in both the model and prototype. The higher frequency transients in the actuator response shown in Fig. 9 result from the measurement system and not transients in the actuator itself.
4. Conclusions This paper has proposed a means of using direct radiant energy to activate phase change in a SMA material in a controlled fashion resulting in an actuator designed for space applications. Other methods for driving SMA materials were compared based on an approximate evaluation of power density. The comparison of power density for all the heating methods discussed revealed that the radiant heating approach could possess the greatest power density directly reducing the cost for space applications. A complete model of this actuator has been developed which includes material and environmental models and a general control strategy. Experiments have been performed to verify the material model as well as the composite actuator model. It has been shown that this concept has several significant advantages over other more conventional SMA-based actuators. This advantage lies primarily in the weight savings resulting from direct use of radiant energy to activate the SMA phase change. Finally, a prototype of this actuator has been built and tested providing a system demonstration and evaluation. Evaluation of the prototype, and comparison with the actuator model are performed. The results of this comparison show a strong similarity in the trend in actuator response. The significant differences are in the lower response time, particularly in the cooling phase, for the actuator model as well as the maximum amplitude. The main constraint for the radiant heat activated SMA actuator is the cooling time (phase transition from austenite to martensite). Increasing the heat loss during the cooling cycle would result in a significant decrease the overall actuation times. Since the mathematical, control, environmental and prototype
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modeling have been demonstrated with high congruence, future work on this novel actuator will focus on the development and implementation of increased cooling capabilities.
Acknowledgements The authors express their appreciation for the help and support from John Fikes and Joe Howell in the Flight Projects Directorate at NASA/MSFC, contract number NAG8-1749 and the support of the Manufacturing Center at Tennessee Technological University.
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