A New Approach to the Design of Helical Shape Memory Alloy Spring Actuators

Hindawi Publishing Corporation
Smart Materials Research
Volume 2011, Article ID 167195, 5 pages
doi:10.1155/2011/167195
Esuff Khan and SivakumarM. Srinivasan
               A New Approach to the Design of Helical Shape Memory Alloy Spring Actuators

1. Introduction

Shape memory alloys (SMAs) are smart materials which undergo solid-to-solid phase transformations under thermomechanical loading exhibiting special intrinsic properties such as the pseudoelasticity and the shape memory effect (SME). The shape memory effect of SMAs provides possibilities of using it as actuators [1].Unlike other known actuators, the SMA actuators are nonlinear in behavior because of the nature of SMA as a material. This paper presents a simple procedure for the design of helical SMA spring actuators, taking into account their nonlinear behavior and the introduction of hard stops. SMAs generally exist in two phases: austenite, a hightemperature phase, and martensite, a low-temperature phase. Martensite is soft in nature, can undergo finite deformations during loading, and leaves residual strains when unloaded. During loading, the stress and strain response is essentially linear until it reaches a critical stress value. At this critical stress value, it could enter into transformation zone where twinned martensite gets converted to detwinnedmartensite, undergoing large strains for small stress increments. This strain is called the transformation strain. At any point, if the temperature is increased well beyond the austenite temperature, the SMA recovers the residual strain

(phase transformation from martensite to austenite), producingan actuation stroke. During this phase transformation process of an SMA, large loads and/or displacements can be generated in a relatively short period of time making this component an interesting mechanical actuator. Because of such remarkable properties, SMAs have found a number of applications in different areas [2]. Han et al. [3] showed how SMA spring actuator can be used to enhance the buckling capacity of columns. Lee and Lee [4] explored the application of SMA spring actuator in active catheter medical device. Spinella and Dragoni [5] showed that the actuator performance can be improved by using the hollow SMA springs. They proved that by emptying the inefficient material from the wire center, the hollow section features a lower mass, lower cooling time, and lower heating energy than its solid counterpart for given strength, stiffness, and deflection. Thus, it becomes necessary to design the SMA actuator appropriate to an application to allow for efficient performance. In literature, the design approaches proposed so far haveassumed a linear mechanical response for both martensite

and austenite [2–6]. Essentially transformation induced change in modulus is assumed in these approaches to be responsible for the stroke in the actuator. Waram’s design approach [6] for SMA spring is one such popular design approach that considers mainly the modulus difference between the martensite and austenite phases in the design.The reason for such a design approach being popular could be that in the transformation region, SMA undergoes large strains for small increment of stress value. In addition, allowing high deformations that occur in this transformation regime may render degradation in its functional as well as structural performance. In Waram’s design, the martensite phase strain is restricted in design to allow for a very good fatigue life. The stroke obtainable from such designs is low compared to that which can be achieved by allowing for transformation strains. Also, it should be stressed that unlike in most other actuators, the material of SMA actuators is nonlinear in mechanical response beyond a critical stress. The response beyond this stress is involved in the effective actuator action and that could make the design complex because of the nonlinearity involved. In this paper, we propose an approach which can utilize the partial transformation strain into the spring design. Transformation strain is considered to be restricted by using the external hard stop, so that only partial detwinning takes place during loading. By including the partial transformation strain into the design, the actuation capacity of SMA helical spring may improve without compromising significantly on its fatigue life. In this paper, the design parameters are analyzed with the consideration of transformation strains. The nonlinear

behavior of martensite phase is idealized as an elastoplastic response to reduce the complexity in the formulation and is compared with the traditional linear approach. Linear approach is first presented in the next section (Section 2).Then, the nonlinear analysis and design approach is discussed in Section 3. The comparison between the two approaches based on different design parameters is made in Section 4 before making concluding remarks on the need for nonlinear approach to the design of helical SMA springs.

2. Linear Approach (Waram’s Design )

In the standard design procedure, the aim is to arrive at the wire diameter, d, the spring diameter, D, and the number of turns, n, for a spring that will deliver the required force, P, and a stroke, S, in a full actuation cycle. The appropriate values of shear moduli, Gh, in the hot and, Gl , in the cold states, the maximum allowable shear stress, τc, in the austenitic state, and the limit on shear strain, γ, in the cold state are the input parameters in this design procedure. Theprocedure is described below [6], in brief.The maximum shear stress allowable in the austenitestate, τc, provided from fatigue considerations puts a constraint on maximumallowable force on the spring, Pmax. The shear stress in the wire and the force on the spring can be related using

 it is possible to find out the required wire diameter of the spring given the maximum allowable design load.

The number of coils (n) can be calculated by

                                   

 allowable shear strain difference Δγ = (γl − γh) where γl is the maximum low-temperature martensite shear strain allowable and γh is the high temperature shear strain.

The deflection of the spring (δ) in hot or cold state, assuming the material to be elastic is given by  

 where P is the force exerted by the spring and G, the rigidity or shear modulus in the appropriate state.

The stiffness (K) can be calculated as

                                                            

 Conclusions

The design parameters are analyzed in the paper with the consideration of transformation strains in the design of SMA actuator springs. An idealized nonlinear behavior of SMA is used to reduce the complexity in the formulation and is compared with the traditional linear approach. Additionally, external hard stops are assumed in the analysis to constrain for allowable total transformation strain that is closely associated with the fatigue life of the spring. While the required wire diameter for the same actuation force is lower when nonlinear behavior is considered, the number of turns needs is higher for the same stroke. It is shown that the effect of transformation strain can be taken into account in the design procedure modified for the nonlinear behavior of the SMA spring. New simplified relations are also obtained for higher strain values. Further studies have to be carried out to quantitatively define the fatigue-sensitive problems associated with the transformation strain.