Life cycle analysis of electrically actuated SMA spring using Talbot interferometry

Reena Disawal; Tameshwer Nath; Shashi Prakash; I. A. Palani

doi:10.1364/AO.57.005779

Applied Optics
Vol. 57,
Issue 20,
pp. 5779-5783
(2018)
•https://doi.org/10.1364/AO.57.005779

Life cycle analysis of electrically actuated SMA spring using Talbot interferometry

Reena Disawal, Tameshwer Nath, Shashi Prakash, and I. A. Palani

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Reena Disawal, Tameshwer Nath, Shashi Prakash, and I. A. Palani, "Life cycle analysis of electrically actuated SMA spring using Talbot interferometry," Appl. Opt. 57, 5779-5783 (2018)

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Abstract

Electrically actuated shape memory alloys (SMAs) find widespread applications in engineering and science. Such materials are known to retain/remember their state. In the stressed/deformed state, when activated by the application of a suitable excitation mechanism, such as the use of heat or potential, they return to their original unstressed state. To test their reliability, it is a standard procedure to undertake a life cycle analysis. In this paper, the life cycle analysis of a SMA spring using the Talbot interferometric technique is reported. The life cycle of the SMA spring is analyzed in terms of the displacement drift, which sets in because of the functional fatigue generated due to its repeated use. Collimated light from a He–Ne laser transmitted through a beam splitter is converged through a focusing lens onto a plane mirror attached to the spring. Backreflected light from the mirror is incident on a set of two Ronchi gratings separated by the Talbot distance, forming a moiré pattern. The resulting interferograms are analyzed using a fringe rotation mechanism. The angle of orientation is a function of displacement drift. There is deterioration in the SMA property because of repeated cycles, and the spring loses its ability to return to its original unstretched position. The values of the displacement drift generated after 1, 1000, 2000, 3000, 4000, and 5000 such cycles as measured using a Talbot interferometer are 0, 0.875, 1.275, 1.459, 1.720, and 1.859 mm, respectively. It is observed that the SMA effect deteriorates as the number of stretching/contraction cycles increases. The uncertainty analysis is also reported. The expanded uncertainty was determined to be 201.61 μm.

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Standard Uncertainty Component $u (x i)$	Source of Uncertainty	Value of Standard Uncertainty $u (x i)$ (μm)	Type	Degrees of Freedom	$c i = δ f / δ x i$	$u i (Δ d) = \| c i \| u (x i)$ (μm)	Variance ${u i}^{2} (Δ d) (μm)^{2}$
$u (Δ d)$	Displacement measurement repeatability	4.023	A	9	1	4.023	16.184529
$u (ϕ)$	Angle of orientation of fringes	115.4734411	B	$\infty$	0.0226	2.609699769	6.8105328
$u (θ)$	Angle of orientation of grating planes	115.4734411	B	$\infty$	0.5926	68.4295612	4682.6048
$u (d)$	Measurement of focal length of focusing lens [manufacturer + calibration]	835.5881929	B	$\infty$	0.0884	73.86599625	5456.1854
$u (gp)$	Grating periodicity	0.057736721	B	$\infty$	$1.00 \times 10^{- 7}$	5.77367E-09	$3.33353 \times 10^{- 17}$
$u (a v)$	Angular variation in setting grating planes	115.4734411	B	$\infty$	$1.00 \times 10^{- 6}$	0.000115473	$1.33341 \times 10^{- 8}$
$u (a)$	Air turbulence	0.000577367	B	$\infty$	1	0.000577367	$3.33353 \times 10^{- 7}$
$u (m e)$	Distortion due to mechanical mountings	0.001616628	B	$\infty$	1	0.001616628	$2.61349 \times 10^{- 6}$
$u (T)$	Temperature effect	0.000577367	B	$\infty$	1	0.000577367	$3.33353 \times 10^{- 7}$
$u (r)$	Interferometer resolution	0.0028	B	$\infty$	1	0.0028	0.00000784
$u (λ)$	Wavelength source	0.01154	B	$\infty$	1	0.01154	0.000133172
$Combined variance = (Σ u i^{2} (Δ d)) (μm)^{2}$	10161.78545
$Combined uncertainty = [(Σ u i^{2} (Δ d))] 0.5 {(μm)}^{2}$ )	100.8056817
Expanded uncertainty (μm)	201.6113633

Standard Uncertainty Component $u (x i)$	Source of Uncertainty	Value of Standard Uncertainty $u (x i)$ (μm)	Type	Degrees of Freedom	$c i = δ f / δ x i$	$u i (Δ d) = \| c i \| u (x i)$ (μm)	Variance ${u i}^{2} (Δ d) (μm)^{2}$
$u (Δ d)$	Displacement measurement repeatability	4.023	A	9	1	4.023	16.184529
$u (ϕ)$	Angle of orientation of fringes	115.4734411	B	$\infty$	0.0226	2.609699769	6.8105328
$u (θ)$	Angle of orientation of grating planes	115.4734411	B	$\infty$	0.5926	68.4295612	4682.6048
$u (d)$	Measurement of focal length of focusing lens [manufacturer + calibration]	835.5881929	B	$\infty$	0.0884	73.86599625	5456.1854
$u (gp)$	Grating periodicity	0.057736721	B	$\infty$	$1.00 \times 10^{- 7}$	5.77367E-09	$3.33353 \times 10^{- 17}$
$u (a v)$	Angular variation in setting grating planes	115.4734411	B	$\infty$	$1.00 \times 10^{- 6}$	0.000115473	$1.33341 \times 10^{- 8}$
$u (a)$	Air turbulence	0.000577367	B	$\infty$	1	0.000577367	$3.33353 \times 10^{- 7}$
$u (m e)$	Distortion due to mechanical mountings	0.001616628	B	$\infty$	1	0.001616628	$2.61349 \times 10^{- 6}$
$u (T)$	Temperature effect	0.000577367	B	$\infty$	1	0.000577367	$3.33353 \times 10^{- 7}$
$u (r)$	Interferometer resolution	0.0028	B	$\infty$	1	0.0028	0.00000784
$u (λ)$	Wavelength source	0.01154	B	$\infty$	1	0.01154	0.000133172
$Combined variance = (Σ u i^{2} (Δ d)) (μm)^{2}$	10161.78545
$Combined uncertainty = [(Σ u i^{2} (Δ d))] 0.5 {(μm)}^{2}$ )	100.8056817
Expanded uncertainty (μm)	201.6113633

Sr. No.	Number of Cycles	Angle of Orientation of Fringes (deg)	Displacement Drift (mm)
1	1	0	0
2	1000	17	0.875
3	2000	24	1.275
4	3000	27	1.459
5	4000	31	1.720
6	5000	33	1.859

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Applied Optics