Investigation of a shape memory alloy releasable mechanism applied in space environment

Abstract

Though the conventional pyrotechnic fastener mechanisms are widely used in spacecraft for their reliable releasable-fastening function, they still have several unavoidable problems: physical shock, high maintenance cost, to name a few. This paper introduces a new type of smart releasable mechanism based on a Shape Memory Alloy (SMA) spring and its corresponding heating apparatus. To obtain the high heating efficiency and increase the response speed, the SMA spring is transitionally fit with the heating apparatus shell instead of directly heating by electric current. As soon as the heating apparatus begins to work, the SMA spring will provide an un-locking force to release the fastening device within the standard time, which also realizes the similar releasable-fastening function comparing with the conventional pyrotechnic fastener mechanisms. In order to ensure the reliability of space products, the heating apparatus is composed of two identical ceramic heating elements which can be controlled independently or synchronously. Finally, the experimental results clearly show that, under the satellite power supply at the constant value of 28 V, the SMA spring can reach the desired 30 N unlocking force within 93 s and 51 s by single or dual heating elements, respectively. The maximal output force can even be increased as large as 40 N under the limited volume of the releasable mechanism.

Keywords

Releasable mechanism shape memory alloy spring actuator heating apparatus

1. Introduction

Releasable fastening devices are commonly used in aerospace vehicles to achieve some basic functions, for instance to interconnect mutually adjacent structures which must subsequently be quickly and reliably disconnected [1]. Normally, these joint separate mechanisms are realized by means of pyrotechnically actuated fasteners. However, they will lead to physical shock and vibration due to the detonation, which may destroy sensitive instruments. Moreover, pyrotechnic fasteners are not capable of repeated use, they are not suited for some repeated applications.

Shape Memory Alloy (SMA) is widely concerned as an important actuator in the field of smart materials and structures, for its shape memory and superplastic effects [2,3]. The SMA usually has large output force and displacement comparing with the other functional materials [4], it has been therefore widely applied in aerospace [5–7], medicine [8,9] and other fields. Consequently, SMA driving release mechanisms are being proposed to replace the pyrotechnic fastener. National Aeronautics and Space Administration (NASA) already presented a releasable fastening apparatus based on SMA actuator many years ago. In its detailed embodiment, the SMA actuator was mounted within a portion of the housing for displacing the piston structure by transition of the SMA actuator between martensite and austenite states. Smith et al. developed three releasing nut mechanisms for small satellites based on SMA wires, they have the advantages of fully resettable, reusable and even shock-less [10]. Tak et al. also developed a separation device activated by a SMA spring actuator comprised of a deformation module, blockers and release springs [11]. Liu et al. also designed a similar release mechanism for Synthetic Aperture Radar (SAR) antenna. The SMA wire based release mechanism would be shrunk as soon as it was powered, the rolling arm inside was then rotated into a certain angle and removed the lock [12].

As the mechanisms mentioned above, SMA actuators are usually heated directly by passing an electric current through itself. However, its ultra-low resistance greatly reduces the heating power that may cause the long-time response [13]. Another approach is to heat SMA externally by liquid mediums or solid coatings [14]. However, liquid mediums are not suitable for space environment due to the limitations of shock and weight. Solid coatings might be destroyed and affect the heating performance of SMA, especially in the case of large deformation. In this paper, a SMA spring is specially proposed to drive the releasable mechanism. The heat conduction instead of heat convection and/or radiation is presented to control the SMA spring. Moreover, a novel heating apparatus transitionally fits with the SMA spring was also proposed.

2. The principle of the SMA releasable device

The operating principle of the releasable device as well as its structure diagram is shown in Fig. 1. The SMA spring is in the form of detwinned martensite and transitionally fit with the heating apparatus shell. Because the SMA releasable device is applied in aerospace structures, two identical heating elements A and B are integrated into the shell, to improve the reliability of the heating apparatus as high as possible. The identical elements can be controlled to heat independently or synchronously. A simulated fastening device is installed ΔD₁ above the heating apparatus shell. It is worthy of note that this article mainly focuses on the SMA actuator utilized in the releasable process, the fastening mechanism is then replaced by a simple force-unlocking device, where the unlocking force can be measured by a dynamometer.

Fig. 1.

Schematic of the proposed mechanism (1, SMA spring; 2, heating apparatus shell; 3, base of heating apparatus shell; 4, simplified fastening device; 5, heating element A; 6, heating element B; 7, heat conductive adhesive) and its releasable process: a, initial state; b, just before the releasable state; c, releasable process; d, after the releasable state.

At the initial state, Fig. 1(a), the SMA spring has not been heated and still in the form of detwinned martensite. Hence the spring is in a free state without the output of force and deformation. The mechanism maintains the fastening state. As soon as the power is on, the heating element starts to work, the heat is then transferred to the SMA spring through the heat conductive adhesive, leading to the free extension of the spring. During this process, the SMA transforms from detwinned martensite to austenite. When the spring reach the simulated fastening device, the residual strain existed in the SMA spring will be converted to thrust, which starts the releasable process. As soon as the output force exceeds the tolerance limit of the fastening force F_m, the SMA spring releases the fastening device immediately. Almost all the detwinned martensite in the SMA spring is transformed to austenite, see Fig. 1(c).

After the releasable process, the heating power is off. The SMA spring may transform from austenite to detwinned martensite due to the decreasing temperature. It is noted that the fastening device can be designed to connect with the releasable mechanism, so there is no pollution of abandoned object.

Since the heating apparatus and the SMA spring are not completely contact, only part of the SMA spring starts to phase transition in the first place. The other part un-contacted with the heating apparatus will begin to phase transition during the stage of heating conduction. Due to the heat conducting time and energy dissipation, there exists a hysteresis for spring deformation response to the heating apparatus.

3. Theoretical model

The law of heat conduction, also known as Fourier’s law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. The heat flow rate is then given $\begin{eqnarray}\displaystyle Q=-kA\frac{dT}{dx} & & \displaystyle\end{eqnarray}$ (1) where, Q is the amount of heat transferred per unit time; k is the thermal conductivity of material, A is the cross-sectional surface area, dT∕dx is the temperature gradient along the x-direction. From the equation, it is known that the transmitted heat is proportional to the thermal conductivity k and to the cross-sectional surface area A. The temperature of the SMA spring T₁ can be derived by Fourier’s law $\begin{eqnarray}\displaystyle \frac{Q}{A_{c}}=k\frac{dT}{dx}=k\frac{T_{2}-T_{1}}{D_{wire}} & & \displaystyle\end{eqnarray}$ (2) where A_c is the contact area between the spring and the heating apparatus, D_wire is the diameter of the SMA wire, T₂ is the temperature of the heating apparatus. The average temperature of the SMA spring T_avg could be approximated as $\begin{eqnarray}\displaystyle T_{avg}=\frac{1}{2}(T_{1}+T_{2}). & & \displaystyle\end{eqnarray}$ (3)

According to the one-dimensional constitutive model of Brinson [15], the SMA elastic modulus E is related to the martensite volume fraction φ, expressed as Eq. (4), where E_M, E_A are the elastic modulus of the martensite and austenite, respectively. $\begin{eqnarray}\displaystyle E({\varphi})=E_{A}+{\varphi}(E_{M}-E_{A}). & & \displaystyle\end{eqnarray}$ (4)

To simplify the theoretical model, the influence of stress on martensite content is ignored here. According to the phenomenological model theory [15], the martensite content is then given in Eq. (5), where T_a1, T_a2 are the start and finish transition temperatures of austenite, respectively. $\begin{eqnarray}\displaystyle {\varphi}=\left\{\begin{array}{@{}ll@{}}1 & T_{avg}\leq T_{a1}\\ 1-{\displaystyle \frac{T_{avg}-T_{a1}}{T_{a2}-T_{a1}}} & T_{a1}<T_{avg}<T_{a2}\\ 0 & T_{avg}\geq T_{a2}.\end{array}\right. & & \displaystyle\end{eqnarray}$ (5)

The free status of the spring is in the form of austenite, the whole length is L₁. Due to the plastic deformation, the spring will rebound to L₃ after compacted (L₂), the SMA is in the form of martensite. The length of plastic deformation L_s is defined as the difference between L₁ and L₃. When the heating apparatus is being powered, at the beginning stage, the SMA spring is extending freely until it reaches the simplified fastening device. The formula of its elongation $L_{s}^{\prime }$ can be expressed, and the magnitude of the un-locking force can also be represented. $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle L_{s}\prime =L_{s}(1-{\varphi}\prime )\end{eqnarray}$ (6) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle F_{\mathit{UL}}=k({\varphi})[L_{s}(1-{\varphi})-L_{s}\prime ]=\frac{E({\varphi})D_{wire}^{4}}{8D_{spring}^{3}N}[L_{s}({\varphi}\prime -{\varphi})]\end{eqnarray}$ (7) where φ′ is the current martensite volume fraction, N represents the number of the spring coils, D_spring represents the spring pitch diameter size.

4. Simulated and experimental performance

4.1. SMA spring and its simulated performance

For space releasable mechanism, the volume of SMA spring should be as small as possible, but the produced unlocking force should be large enough. In addition, the speed of the spacecraft is very fast during the launch process, which would generate a lot of heat due to the air friction. Low austenitic finish transition temperature may lead the SMA spring to release in advance. But high austenite start transition temperature also increases the complication of the unlock process. For these reasons, the design requirements of the SMA spring are listed in the follows:

1. The component material of the SMA spring should be Ni-50-Ti;

2. The external diameter and coil number of the SMA spring should be less than 10 mm and 15 mm respectively, while the diameter of the SMA wire should be larger than 1 mm;

3. The austenite start transition temperature is about 333 K;

4. The unlocking force of the SMA spring can exceed the tolerance limit of the fastening device F_m, and the releasable duration should be within acceptable limits.

Finally, Table 1 gives the design parameters of the SMA spring.

Table 1
Parameters of the proposed SMA spring

Variables Value

Elastic stiffness of the austenite EA 70 × 10³ MPa

Elastic stiffness of the martensite EM 30 × 10³ MPa

Poisson’s ratio (equal for both phases) 0.33

Thermal expansion coefficient SMA 22.0 × 10⁻⁶ K⁻¹

Density 6720 kg/m³

Stress influence coefficient for SMA −0.35 MPa/K

Austenite start transition temperature T_a1 336 K

Austenite finish transition temperature T_a2 343 K

Variables	Value
Elastic stiffness of the austenite EA	70 × 10³ MPa
Elastic stiffness of the martensite EM	30 × 10³ MPa
Poisson’s ratio (equal for both phases)	0.33
Thermal expansion coefficient SMA	22.0 × 10⁻⁶ K⁻¹
Density	6720 kg/m³
Stress influence coefficient for SMA	−0.35 MPa/K
Austenite start transition temperature T_a1	336 K
Austenite finish transition temperature T_a2	343 K

A finite element simulation software named ABAQUS is used to analyze the performances of the SMA spring here. According to the parameters given in Table 1, a one-dimensional constitutive model is established. In addition, the hardening constants E (φ) should also be specified. The procedure for the determination of the SMA spring variables will be briefly described below.

Figure 2 shows the simulation boundary condition settings of the SMA spring. Traction-free boundary condition in the radial direction is applied. The bottom end of the spring is fixed, and a simulated fastening device is installed ΔD₁ above the top of the spring. The force F_m is therefore 0 for a period until the spring touches the fastening device. By using a thermodynamic constitutive model for the shape memory materials, the fastening force F_m can be calculated in the simulation software.

Fig. 2.

SMA spring: a, finite element model; b, boundary conditions.

To improve the reliability of the SMA releasable device, two heating elements which can operate independently or synchronously are specially designed in the device. The detailed description will be given in the next subsection. Consequently, the simulations of the output force are considered both in the single and dual heating elements. As shown in Fig. 3, the output force F_m under the different spring wire diameters are respectively illustrated. At the beginning, there is no output force, because the extension of the SMA spring is less than ΔD₁ and cannot touch the fastening device (constraint). As soon as the SMA spring reaches the constraint, the output force F_m increases with the heating time until the martensite has been completely transformed to austenite. From the figure, it is clearly seen that the maximal force strongly depends on the wire diameters d of the spring, the larger value of d will get the higher releasable force. Figure 4 shows the output force curves as a function of simulated heating time in the case of dual heating elements, as expect, the response time is about half of the previous response. It is worth of not that, though the maximal releasable force is almost proportional to the value of the spring wire diameter, considering the volume of the device and the practical engineering requirements, the wire diameter of 1.4 mm is a suitable value.

Fig. 3.

Output force as a function of simulated heating time in case of single heating element.

Fig. 4.

Output force as a function of simulated heating time in case of double heating elements.

Fig. 5.

Schematic diagram and photo of the heating apparatus (1, wires; 2, shell base; 3, pouring sealant; 4, shell; 5, heating element; 6, retrofit acid ester adhesive; 7, heating element; 8, retrofit acid ester adhesive; 9, plug).

Fig. 6.

Output force as a function of simulated heating time in case of single heating element.

4.2. Experimental test of the SMA spring performance

According to the size of the proposed SMA spring and the detailed application, the designed heating apparatus are finally given in Fig. 5. The length of the shell should be a little bit larger than l₃, make sure the SMA spring can be sufficiently heated and maintain the extended path. The heating apparatus shell is transitionally fitted with the SMA spring to ensure the high heating efficiency. Although this fitting approach leads the friction between the shell and the spring, it could be ignored comparing with the output force generated by the SMA spring.

In the experimental testing platform, we select a dynamometer probe to measure the unlocking force, a switching power supply whose output is a 28 V DC voltage is chosen to power the heating elements. By the different wiring, the heating elements can operate independently or synchronously. The experimental results are then shown in Fig. 6 and Fig. 7. When only a single of heating element works, the output force is 0 within 60 s, this is because the thermal transfer exists a lag between the SMA spring and the heating element. As soon as the SMA spring reaches the probe, the force increases up to 30 N within 33 s. At this moment, the martensite has not been completely transformed to austenite, and the maximal output force of the SMA spring can reach as high as 40 N.

If both heating elements work synchronously, the experimental unlocking force is shown in Fig. 7. At the beginning, there is still no output force due to the free extension, which is the same as in the case of single heating element, but the duration is much shorter. As soon as the SMA spring reaches the dynamometer probe, the output unlocking force can increase up to 30 N within 26 s. Moreover, the maximal output force of the SMA spring is still 40 N.

5. Conclusion

A novel kind of smart SMA releasable mechanism applied in space environment is proposed in this paper. The releasable mechanism is mainly composed of a SMA spring and a heating apparatus. The SMA spring was selected on the requirements of space release device, e.g. small volume, large output force. A simplified mechanical model for SMA spring was established. Moreover, the heating elements, the materials of the heating apparatus and so on were also specially selected. According to the experimental results, it can be found that under the stable DC power supply of 28 V, the SMA spring can get the maximal output force of 40 N, and it can obtain the 30 N unlocking force within 51 s. Anyway, ongoing works still need to improve this response time as short as possible.

Fig. 7.

Output force as a function of simulated heating time in case of double heating elements.

Footnotes

Acknowledgements

This work was supported by the National Natural Science Foundations of China (Grant No. 51705251).

Author contributions

K. Bian and C. Zhou contributed equally.

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