## Mechanical Properties and Nondestructive Testing of Advanced Materials

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# Characteristics Analysis and Testing of SMA Spring Actuator

**Academic Editor:**Xing Chen

#### Abstract

The biasing form two-way shape memory alloy (SMA) actuator composed of SMA spring and steel spring is analyzed. Based on the force equilibrium equation, the relationship between load capacity of SMA spring and geometric parameters is established. In order to obtain the characteristics of SMA spring actuator, the output force and output displacement of SMA spring under different temperatures are analyzed by the theoretical model and the experimental method. Based on the shape memory effect of SMA, the relationship of the SMA spring actuator's output displacement with the temperature, the stress and strain, the material parameters, and the size parameters is established. The results indicate that the trend of theoretical results is basically consistent with the experimental data. The output displacement of SMA spring actuator is increased with the increasing temperature.

#### 1. Introduction

Shape memory alloy (SMA) is known as a kind of new intelligent material. SMA may undergo mechanical shape changes at relatively low temperatures, retain them until heated, and then come back to the initial shape [1, 2]. The outstanding quality characteristics of SMA are shape memory effect (SME) and super elasticity (SE) [3]. The shape memory effect, which allows the deformed material to recover a memorized shape when heated above the transformation temperature, can be exploited effectively in microrobots, automobile, automatic adjustment devices, aerospace, home appliances and daily necessities, [4–8] and so on.

An actuator based on these materials is made up of an SMA element that works against a contrasting element (a weight or other constant force, a conventional spring, or a second SMA element). At low temperature, the contrasting element overcomes the resistance of the easily deformable SMA element. The actuator is activated by heating the SMA element above the transformation temperature. The resulting increase in stiffness enables the SMA element to overcome the resistance of the contrast, thus generating useful displacements and producing mechanical work [3, 9–11].

In this paper, we present the biasing form SMA actuator, which is able to generate displacement and force. Based on the force equilibrium equation, the output force and output displacement of SMA spring under different temperatures are analyzed by the theoretical model and the experimental method. Based on the shape memory effect of SMA, the relationship of the SMA spring actuator’s output displacement with the temperature, the stress and strain, the material parameters, and the size parameters is established. The output displacement of SMA spring actuator is increased with the increasing temperature.

#### 2. Properties of SMA

The most commonly used SMA elements for actuators are helical springs, which for this form produce a large displacement. The force that a spring of any material produces at a given deflection depends linearly on the shear modulus of the material. SMAs exhibit a large temperature dependence on the material shear modulus. The relationship between shear modulus and temperature for SMAs is given by where is the shear modulus of SMAs. is temperature and , , , and are the start and finish transformation temperatures of martensite and austenite, respectively, as shown in Figure 1. and are the shear moduli of martensite and austenite, respectively. When , in absence of stress, shear modulus of SMAs can be expressed approximately as

In the process of heating, , ; in the process of cooling, , .

When the SMA wire is heated or cooled, the heat balance equation is where is the mass density of SMA, is the specific heat, is the volume of SMA exposed in air, is the time, is the heat exchange coefficient, is the superficial area of SMA, and is the temperature of airflow.

If , when , the temperature variation of SMA wire with time is where is the initial temperature and is the time constant of SMA wire, .

If the material and structural parameters of SMA have been determined, the time constant is inversely proportional to the heat exchange coefficient. Under three different heat exchange coefficients, the temperature variation of SMA wire with the around airflow temperature is shown in Figure 2. As shown in Figure 2, in a different heat exchange coefficient, the temperature of SMA wire changes faster when the time constant is smaller and the lag of time is shorter. When the time constant is less than 2.5, the lag time is less than 2 seconds.

#### 3. Operational Principle of SMA Actuator

The SMA drive element uses the properties of low yield stress at martensitic state and returns to the high yield stress at austenite phase state when heated. Thus, the action form of a single SMA part is one-way. To obtain two-way characteristics of SMA elements, the structures of differential form and biasing from are used commonly. The differential form uses two or more SMA elements to obtain the two-way characteristics. The biasing form combines the one-way SMA with other parts to obtain two-way characteristics, shown in Figure 3, with the SMA helical spring working against a conventional steel spring (referred here as the “biasing” spring). At low temperatures, the steel spring is able to completely deflect the SMA spring to its compressed length. When increasing the temperature of the SMA spring, it expands, compressing the steel spring and moving the push rod.

#### 4. Property Analysis of SMA Spring

Relative to the free length of the spring, the SMA spring provides a large action stroke, shown in Figure 4.

The expression for shear stress in an SMA spring is described as where the axial load is , is the average diameter of the spring, represents the wire diameter, is the spring index, , and is known as the Wahl correction factor applied:

Shear stress has a relationship with shear strain which is

The stretch of spring under the load is where is the number of turns in the spring.

The relationship between compressed length and shear strain for SMA spring is given by

The wire diameter for the actuator can be obtained from (5) for acceptable values of ranging from 3 to 12:

The number of turns in the spring can be obtained from (9): where represents the stroke of the actuator and is the strain difference at high and low temperatures:

##### 4.1. The Output Force of SMA Spring under Different Temperatures

The experimental system for the output force of SMA spring versus temperature under the constraint of displacement is shown in Figure 5 and the experimental device is shown in Figure 6.

As shown in (8), when , the axial load at temperature can be expressed as

The axial load at low temperature is expressed as

When the axial displacement of SMA spring is restricted, the compressed length of SMA spring is kept as

When , the output force at temperature can be obtained from (13), (14), and (15) as

In this study, Ti-49.8at.%Ni SMA spring is used, shown in Figure 7; its start and finish temperatures of the martensitic and austenitic phase transformation are °C, °C, °C, and °C, respectively. The shear moduli of martensite and austenite are GPa and GPa, respectively. The wire diameter of SMA spring is mm, the angle of inclination is °, the diameter of SMA spring is mm, and the number of turns is . When mm, the theoretical and the experimental results of the relationship between the output force and temperatures of SMA spring are shown in Figure 8. The trend of theoretical results is basically consistent with the experimental data. The output force is increased with the rising of temperature.

**(a)**

**(b)**

##### 4.2. The Output Displacement of SMA Spring under Different Temperatures

The experimental system for output displacement of SMA spring under different temperatures is shown in Figure 9 and the experimental device is shown in Figure 10.

As shown in (9), the compressed length can be expressed as When , shear strain is

The output displacement can be obtained from (17) and (18) as

The typical SMA spring sample is shown in Figure 7; when the maximum shear strain is %, the theoretical and the experimental results of the relationship between the output displacement and temperatures of SMA spring are shown in Figure 11. The trend of theoretical results is basically consistent with the experimental data. The output displacement is increased with the rise of temperature.

#### 5. Analysis of SMA Actuator

The scheme of the proposed actuator with an SMA spring and conventional steel against spring is illustrated in Figure 3, where at low temperature the SMA spring will be compressed and when heated will extend with a pushing actuation. For the SMA actuator in Figure 3, the axial load of SMA spring has the relationship with the compressed length of SMA spring as follows: where , , and are the axial load, compressed length, and shear modulus of SMA spring at temperature , respectively; , , and are the axial load, compressed length, and shear modulus of SMA spring at low temperature, respectively; is the axial load at high temperature; and is the output displacement of SMA spring actuator:

The output displacement of SMA spring actuator can be obtained from (1), (2), (9), (20), and (21)

The experimental system for output displacement of SMA actuator under different temperatures is shown in Figure 12. The SMA helical spring works against a conventional steel spring to obtain the two-way SMA actuator. The typical SMA spring sample is shown in Figure 7. The stroke of the actuator is mm. The effect of temperature on the output displacement of SMA spring actuator is analyzed by the theoretical model and the experimental method, shown in Figure 13. The axial loads of SMA spring at low and high temperatures are N and N, respectively. The low temperature shear strain is %. As shown in Figure 13, the output displacement of SMA spring actuator is increased with the increasing temperature.

#### 6. Conclusions

The characteristics and test method of SMA spring and SMA actuator are analyzed in this paper. The output force and output displacement equations of SMA spring are derived. The output force and output displacement are increased with the rise of temperature. The relationship of the SMA spring actuator’s output displacement with the temperature is investigated theoretically and experimentally. With the increase of the temperature acting on SMA actuator, the output displacement of SMA spring actuator is increased proportionally.

#### Acknowledgments

This work was supported by the National Natural Science Foundation of China (51175532, 11272368) and by the Natural Science Foundation Project of CQ CSTC (Key Project CSTC, 2011BA4028).

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#### Copyright

Copyright © 2013 Jianzuo Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.