Elsevier

Materials & Design

Volume 30, Issue 8, September 2009, Pages 3020-3029
Materials & Design

Application of trained NiTi SMA actuators in a spatial compliant mechanism: Experimental investigations

https://doi.org/10.1016/j.matdes.2008.12.017Get rights and content

Abstract

This contribution presents the experimental investigations on the open loop behavior of a spatial compliant mechanism using trained NiTi Shape Memory Alloy (SMA) actuators. The mechanism consists of a central superelastic pillar on which a moving platform is mounted and actuated by three SMA wires. The SMA actuators have been trained by thermal cycling with constant bias force before fixing them on to the mechanism. The optimal power requirements of the actuators have been determined experimentally. Open loop time responses have been obtained by applying various voltage inputs and duty cycles to the actuators for establishing a suitable working point. Models representing the reverse transformation (heating) and forward transformation (cooling) have been obtained from experiments. The relationship between the actuation force and the tilt of the moving platform obtained with trained and untrained SMA actuators are compared. The experiments demonstrate that the results obtained with trained actuators are in close agreement with the analytical results.

Introduction

Shape memory alloys are functional smart materials characterized by shape memory and superelastic effects (SME and SE). SMAs as actuators are well known as they are silent in operation, simple to operate, light in weight, and capable of developing large strains, to mention a few. SMA actuators possess high energy density, in the order of 107 J/m3 [1], which is the highest among the presently known actuation principles. They also have drawbacks such as hysteresis effects, high power requirements and control difficulties. Inspite of all these limitations they are widely used in robotic arms, parallel mechanisms, endoscopic devices, heart valves, stents, orthodontic devices, surgical instruments etc. [2], [3]. Mostly, SMA actuators have been integrated with a rigid or a compliant structure to exploit their shape memory and superelastic effects. Earlier researches had been focused on embedding the actuator inside the structure [4], [5], [6] so as to make a composite part. This method has limitations in terms of actuation frequency in case the actuator is made to cool in ambient conditions. Another method is to fix the actuators outside the structure in order to obtain actuation at faster rates compared to the embedded system. But in all the cases, integrating the effect of SMA actuation with the response of the compliant structure is difficult due to large deflections of the structure. Also, involvement of interrelated constant and variable geometric parameters that describe the large deflection of the structure and the nonlinear behavior of the actuator makes the coupled effect complex.

This experimental work is the continuation of the theoretical analysis that was communicated in Ref. [7]. The theoretical models for the large displacement of the moving platform, based on elastica approach, were obtained for the selective actuation of one wire and two wires at a time. The large deflection expressions and the additional expressions derived from the geometric constraints of the mechanism were used to couple the effect of SMA actuation and elastica deflection. The mobility of the platform was simulated in [8] using FEM analysis. These research works were focused on the coupled effect of force developed due to SMA actuation and force required for elastica deflection of the central superelastic pillar. The available literature related to large deflection analysis of compliant mechanisms [9], [10] were formulated considering the orientation of force as fixed with respect to the tip deflection and by treating the tip moment as constant. For the mechanism under development, both the force and the moment have been considered continuously varying in orientation with tip deflection.

In order to validate the analytical results, specifically the relationship between forces and tilt angles, an experimental setup was developed as shown in Fig. 1. Three strain gauge based miniature force sensors have been designed to measure the SMA actuation force and fabricated to match the fixing arrangement of the mechanism. Carrier frequency amplifiers are used to power and acquire signals from the force sensors. A three axis MEMS based accelerometer is mounted on top of the platform to measure its static tilt angle. The SMA actuators have been powered by three individual MOSFET drivers in response to PWM signal inputs. All these mechatronic components have been integrated with a data acquisition system. The overall experimental setup is shown as a block diagram in Fig. 1c and further details are available in Ref. [11].

One-way shape memory effect (OWSME) and two-way shape memory effect (TWSME) are the two distinguishable characteristics associated with thermomechanical phase transformations of austenite to martensite and vice versa. SMA with TWSME is a better choice for actuator functions as an external force for deforming the actuator is not needed unlike the one with OWSME effect. Training is an important effect that induces TWSME in SMA actuators that are usually with OWSME so as to obtain maximum actuation force and shape memory effects. Mostly the training methods are based on thermal cycling of alternate heating and cooling under a constant mechanical load. The two important parameters that influence the training procedure are the input power required for heating and the bias force applied for deforming the actuator. The benefits that could be obtained after training the actuator are summarized below.

  • It helps to find optimal current and voltage for obtaining maximum strain and actuation force.

  • It stabilizes the effect of hysteresis [12] and hence reduces the effect of nonlinearity.

  • It induces TWSME which requires minimum bias force for initial deformation or does not require any external force. Whereas, for the actuators with OWSME, bias force is the major driving factor.

  • It aids the transformation process as it induces detwinned martensite after certain number of training cycles.

  • Training enhances fatigue property and hence life of the actuator.

  • It reduces the phase transformation temperatures [13].

  • After training, the actuator consumes less power in the case of resistive heating.

  • Irrecoverable elongation effect can be avoided [14].

In support of the above facts, authors in Ref. [15] experimentally confirmed that there is degradation in the recovery of force after 15 cycles of training. This means that, the recovery force becomes more stable after certain cycles. Also in Ref. [16], the cyclic behavior of the SMA has been extensively investigated and it was confirmed that the cyclic loading of SMA wire leads to marginal reduction in loading stress plateau due to the fatigue effect. Fatigue which results from localized slip, ultimately assist forward transformation and hence require lower levels of bias force. This effect results in the development of higher actuation forces. In Ref. [17], an SMA strip was trained under constant stress and the authors highlighted that hysteresis effect of the actuators has been stabilized after 100 cycles of repeated thermal actuation. As a special case, Huang and Toh [18] showed the flexibility of using reheat treatment to obtain TWSME in shape memory alloy which was is originally with OWSME. In Ref. [16], Ti–Ni–Cu SMA wire of 0.29 mm in diameter was trained by heating and cooling for 100 cycles under a dead weight of 10 N.

Naito et al. [19] have analyzed the influence of the loading cycle on the stress-strain relationship of pseudoelasticity of SMAs by accounting the effect of residual martensite in the thermo-mechanical model. Quasi-static experiments were conducted in Ref. [20] where Ni–Ti ribbons were slowly heated/cooled with precise control of temperature over its length and it was demonstrated that the change in the maximum load has been stabilized after 5–10 cycles of heating and cooling. Similar test was conducted in Ref. [14] with electrical resistance feed back up to 105 cycles and recorded that irrecoverable elongation can be avoided by training the SMA wire. Also in Ref. [21], TWSME was induced by alternate heating and cooling for 50 cycles under constant stress of 372 MPa and showed that the recoverable strain obtained was about 3.7%. Factors such as material composition, geometry, phase transformation temperatures, hysteresis effect, power applied and the duty cycle, bias force, and the ambient conditions [22] are the major factors that influence the dynamic behavior of SMA actuators integrated with a structure or a mechanism. However, the direct influence on the actuation behavior of SMA and the corresponding shape change are depending on the rate of heat transfer from the actuator for which a simplified one-dimensional heat transfer model is available.

The major disadvantage while using SMA as actuator is the slow response, which is generally of the order of 2 Hz or less. It mainly depends on how fast the heat is added and removed. Of the various heating and cooling methods, Joule heating combined with forced convective cooling results in higher frequency of operation. In order to understand the temperature dependent actuation of SMA, its thermo-electric response based on heat transfer dynamics needs to be evaluated. It is based on the rate at which heat is added to and removed from the actuator. The simplified one-dimensional heat transfer expression [20], [22], [23] that describes the SMA actuation for resistive heating and with ambient air cooling is expressed asmcp(dT/dt)=i2R-hA(T-Ta),heating-hA(T-Ta),coolingwhere, m = ρπd2/4 is mass of the SMA wire per unit length, ρ is density, d is diameter of the wire, cp is specific heat capacity, T and Ta are maximum temperature of the wire and ambient temperature respectively, i is the current applied, R is resistance per unit length, h is convective heat transfer coefficient for ambient cooling conditions, A = πdl is convective surface area of the wire and l is the length of the wire. The above heat transfer expression is based on the assumptions that the effect is one dimensional, the load applied to the actuator is gradual or constant, radiation effects are negligible compared to conduction mode of heat transfer, volume and area changes are insignificant, Ta, R and h remain constant, wire temperature field is spatially uniform and phase transformation temperatures are also considered as constants. The effect of heat radiation is neglected as the range of working temperature is below 200 °C [1]. Eq. (1) can be solved for maximum temperature T of the wire separately for heating and cooling process and hence the resulting expression becomesT-Ta=(Ti-Ta)exp-t/τ+i2λ(1-exp-t/τ),heating(Ti-Ta)exp-t/τ,coolingwhere, Ti is temperature of the wire at any time t, τ (time constant) = mcp/hA, and λ (current constant) = R/hA. From Eq. (2), the current required to heat the actuator to a temperature T is obtained asi(heating)=sqrt{[(T-Ta)-(Ti-Ta)exp-t/τ]/[λ(1-exp-t/τ)]}

While applying heat to the actuator, the phase transformation and the corresponding shape change starts when the temperature crosses As (austenite start) temperature and ends at Af (austenite finish temperature). In order to maintain the actuator at the actuated position, the temperature has to be maintained just above Af by the application of optimal power. The power applied to the actuator and the corresponding temperature rise have been simulated for SMA wires of diameter 200 μm, 250 μm, and 300 μm, keeping l of all wires as 105 mm which is the actual length required for the mechanism. Other parameters considered for the simulation are, h = 110 W/m2 °C, R(200 μm) = 31 Ω/m, R(250 μm)=20 Ω/m, R(300 μm) = 13 Ω/m, Af = 98 °C, T = 105 °C, Ta = 25 °C and cp = 322.384 J/kg °C. The relationship between temperature Ti and current i for various heating time (0.1 s, 0.5 s and 1.0 s) are shown in Fig. 2. It is seen that the power required to heat the wires in 0.1 s is much higher than in 0.5 s and 1.0 s for all the three wires. Hence, for the experimental work, on-times of 0.5 s and 1.0 s have been considered.

In the present work, the optimal power required for heating the actuators have been obtained experimentally as training helps to find out a threshold voltage and current beyond which the actuator gets over heated. The open-loop response has been verified experimentally using PWM signals in order to obtain maximum benefits of actuation. The details about the time response of the actuator while heating and cooling and their output functions over time are summarized and presented. Also presented is the comparison of experimental results obtained from trained and untrained actuators related to the actuation force developed and the corresponding tilt of the platform.

Section snippets

Experimental set-up used for training

The experimental set-up used for training SMA actuators before fixing with the mechanism is shown in Fig. 3. The actuator is equiatomic NiTi SMA, procured from Mondo-tronicsâ. The mechanical and electrical properties of the actuator have already been listed in the earlier work of the authors [8]. The length of the wires required for the mechanism is 105 mm and hence same length of wire is used in the training process. A constant bias force has been induced by a dead weight which produced around

Results and discussion

It is desirable to find out the optimum voltage and current need to be applied to the actuator for obtaining maximum benefits. This also helps to find out the threshold voltage and current beyond which the actuator gets over heated and below which the applied voltage is insufficient to develop the required strain. Though few of the important data have been recommended by the manufacturer of SMA wires, they have to be verified as the ambient conditions may not exactly match with the

Conclusions

This contribution presented about experimental investigations on the effect of using trained shape memory alloy wires as actuators in a spatial compliant parallel mechanism. The mechanism is smart in such a way that it exploits shape memory effect of SMA as actuator and superelastic effect of SMA as the compliant structural member possessing large deflections. The mechanism has been fabricated and integrated with three custom made miniature force sensors, a tilt sensor, three actuator drivers

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