 Open Access
 Authors : Suresh Kumar , M. L. Aggarwal , Lakhwinder Singh
 Paper ID : IJERTV8IS120293
 Volume & Issue : Volume 08, Issue 12 (December 2019)
 Published (First Online): 30122019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Stress Evaluation TechniqueCumPhysical Model for Intelligent Helical SMA Spring
Suresh Kumar1
1PhD Student,
Department of Mechanical Engineering, YMCA University of Science & Technology, Faridabad121006, Haryana, India

L. Aggarwal2
2Professor,
Department of Mechanical Engineering, YMCA University of Science &Technology, Faridabad121006, Haryana, India
Lakhwinder Singp
3Professor,
Department of Mechanical Engineering, YMCA University of Science & Technology, Faridabad121006,Haryana,India
Abstract: In this physical proposed techniquecummodel that enables the stability of intelligent helical SMA spring by defining the various working parameters before its practical implementing as an actuator. Springload values which have been also calculated by scalevalue. The presented illustration of intelligent helical spring (originally made SMA wire) and parameters included as average loadcell strain values, values of average currents, obtained values of average temperatures, atmospheric temperature changed values and applied voltage values. The various relationships as the minimum value to maximum value relationship for applied voltages and spring load values, the maximum value to minimum value relationship for applied voltages and springload values, the minimum value to median value relationship for applied voltages and springload values, the maximum value to median value relationship for applied voltages and spring load values mentioned with the help of correlations. Then, two model equations are obtained based on minimum value to maximum value & viceversa. The working parameters resulted as correlations and minimum value to maximum value & viceversa resulted as model equations during the experimentation of intelligent helical spring.
Keywords: Annealing, intelligent helical spring/SMA, normalizing, Stability, stress evaluation model.

INTRODUCTION
NiTi alloys are very famous in recently few years due to large strain setup (8%) into the internal structure in which temperature or heat used as working parameter [5]. They also are applicable in aerospace and biomedical sciences so researchers consistently focusing on bulk production with minimize costing. The actuation is mainly depends upon the set of control conditions of temperature and applied pressure with the quality of materials used. So, synthesis of NiTi vary from alloy thickness to thickness and applied different methods such as vacuum induction melting electrical are melting, HIP (Hot Isostatic Pressing), elementary power sintering, and mechanical alloying[4]. Segregation, gas absorption and crucible contamination absorption methods were old & had conventional problems [1]. In recently years,
mechanical alloying (MA) technical have been used to reduce the need of precursor materials, control of chemical composition and higher level of porosities. The NiTi compound commonly exhibits two stable phases i.e. B2 austenite phase of hightemperature structure and B19 martensite phase of lowtemperature structure. B2 is cubical crystalline structure but B19 is monoclinic crystalline structure. The shape memory behavior were firstly observed in 1932 by Olander in his study of rubber life effect in the samples of goldcadmium and in 1938 by Greninger & Mooradian in their of brass alloys (copperzinc). Many years later in 1951 Chang & Read first reported the term shape recovery. They were also working on goldcadmium alloys. In 1962 WilliamJBuebler and his coworkers at naval ordinance laboratory discovered shape memory effect in an alloy of nickel & titanium. Nowadays, these alloys are becoming the point of interest due to the special characteristics such as shape memory effect, superelasticity, high tensile strength, wear & corrosion resistance etc [2,3]. Ahmed Frikha, Patrice Cartraud, Fabien TreyssÃ¨de investigated the static behavior of helical structures under axial loads by taking into account their translational invariance and the homogenization theory [6]. Fabien TreyssÃ¨de, Ahmed Frikha, Patrice Cartraud again focused on mechanical modeling of helical structures accounting for translational invariance in his part two study. The static behavior had been addressed using a helical homogenization approach which provides the stress state corresponding to axial loads [7]. G.Machado, H.Louche, T.Alonso, D.Favier discussed the mechanical superelastic behavior of NiTi architecture tubebased NiTi materials subjected to quasi static compression was studied using two simple cellular samples. They assumed that modeling is very useful for designing and optimizing architectured materials. The superelastic behavior of two simple architecture materials based on identical tubes[8] Amir Sadjadpour and Kaushik Bhattachary suggested constitutive model for shapememory alloys that builds on ideas generated from the
micromechanical studies of the underlying microstructure as a ratedependant onedimensional thermodynamically consistent constitutive framework for the dynamic behavior of polycrystalline SMAs[9]. Ferdinando, Auricchio and Davide performed experimental tests on superelastic shapememory alloys (SMAs) show a significant dependence of the stressstrain relationship on the loadingunloading rate, coupled with a not negligible oscillation of the material temperature [10].
In present work we has used the NiTi wire with a preset conditions as prescribed by the seller and investigation objective to established physical model based on smart helical spring by using the basic electronic components such as registers, capacitors, PN diodes, transistors, rectifier and also using the electrical components such as sockets, DC supply power, transformers, cables, connectors. This work model can be measure the any helical SMA spring at any predefined condition.

MODEL PREPARATION

The proposed model comprised of the following main sub parts included as:

IronStand: Iron Stand has been used because it is made of ordinary Iron and easily availability of Ironpieces in any shape in market or marking college workshop. Further it included following parts:
Base plate with vertical column: The base plate has dimensions = 18.2X9.5X0.6 (0.6 cm represents the thickness of plate, 9.5cm represents width, whereas 18.2 cm represent length at which vertical column is welded along length). The hole represents in base plate as M7.9X0.375 (dimensions in mm).
Fig.1 (Base plate)
So it is obvious that width of plate = 9.5, the vertical column dimension = 24.4cmX0.5cm whereas 24.5cm represent vertical height of column, 2.4cm represent the width of vertical column and 0.5 cm represent the thickness of vertical column respectively. The base plate also has the threaded hole within itself which is 1.2 cm far away from width side and vertical column is welded near to the edge of plate as possible as by the tungsten arc welding m/c 400Amp. The tolerance of
Â±0.1 mm might be possible, but have no effect of such error. Cylindrical rod (vertical type): It can be seen from Fig 2, the length of rod is = 28+1+1.7 = 30.7, all dimensions are in cm. Here 28 represents the middle portion of rod &. The thread tap dimension up to 0.6 cm for 1 cm length and thread tap dimension up to 1.5cm for 1.7cm length. The diameter of middle portion (m) = 1.2 cm. The dimensions of threaded portion for both sides are M7.9 x1.25 in which outer diameter (t) = 7.9 mm
Adjustable lower plate with locking: It consists of cylindrical hollow part. The dimensions of cylindrical holow part as: length = 2.7cm, thickness = 0.7 cm, Inner diameter (i) = 1.2 cm, Outer diameter (o) = 1.2+2X0.7 = 2.6 cm.
Now for rectangular thick part, the dimensions= 11.5X2.5X0.3 (all dimension in cm), the hole dimension of this part include h = 1.2 cm. The tightened hexagonal nut also used with 0.8cm each side and having centralized hole () = 7.9mm such that M7.9×0.375. The allowance of all meshing parts varies from 0.02 to 0.04 for reading taken in mm. And the dimensions of locking plate= 3.5cmX1.9cmX3mm whereas 3 mm represent the
Fig. 2(Lower plate)
thickness of it. Threaded screw length = 1.4 cm. The Iron stand has been made with the help of drilling tool bit and drilling m/c, lathe m/c and its operation, different type of Tap holder & tap bit (threaded type) and application of tungsten arc welding 400 amp m/c also included.

Load Cell (20 Kg): It is the transducers which convert force or load into electrical signal. The various types of load cells are commercial available in markets such as Beam type, SType, Cantilever type, Tension or Compression type, Straight bar type etc[13].
Fig.3 loadcell (Pt. 1 refers for screws and pt. 2 refers for straingauges)
The straight bar load cell has been applied here; range from 0 20 kg of pressure (force) and it is single point HT sensor.
Specification asreceived: Table 1 (Temp. Sensor)
Measuring Range/ Rated capacity
020 Kg
Rated output
1 mV/V
NonLinearity
0.15 % F.S.
Recommended Excitation Voltage
12 V
Gauge factor
2 5
Metal Film/ Metal Foil
Constantan/Silicon
The Conversion of force is achieved by measuring the physical deformation of internal strain gauge. The strain gauge configured in a wheat stone bridge circuit. The strain gauges are present in terms of resistors. The load cell or HT sensor has been used here which was single point type specifications mentioned above in table1.

Temperature Sensor (LM35): A temperature sensor is a device that provides for temperature measurement through an electrical signal. So temperature value measured with respect to volt (V). It is obvious as many types of temperature sensors are available commercially in which few are RTDs, Thermocouples, Thermistors including NTC type and PTC type and semiconductor temperature sensors etc[14]. If we talk about the thermocouple & RTDs in which both are highly used as per their importance and nature of task being performed.
Fig.4(LM35)
In present practical work two LM35 have been used which is very famous due the especial features of operate range 420 volts, calibrated directly in Celsius/centigrade and low cost etc. One has been used for openatmosphere temperature during the reading and other for SMA reading. LM35 series are precision integratedcircuit temperature sensors and L35 also called precision centigrade temperature sensors whose output voltage is linearly proportional to the Celsius/centigrade temperature.
Specification asreceived: Table2 (load cell)
Operating range
420 volts
Nonlinearity
Â±1/4Â°C
(typical)
Rated range
55Â° to
+150Â°C
Selfheating
0.08Â°C (Still air only)
Linear scale factor
+10.0 mV/Â°C
Material ICs
Silicon
Colour/Body
Black
Connecting point
/ Connectors
Three (3) (A 4
20 Volts, B Output, C GND)
The LM35 has an advantage over linear temperature sensors calibrated in Â°K, as the user is not required to subtract a large constant voltage from its output to obtain convenient centigrade scaling. The LM35 does not require any external calibration.

Amplifier Circuit (Operational): The load cell had the attachment with strain gauge measuring kit which is basically amplifier circuit and this kit had setup in the work. It includes the IC7107 in which 02000 V digital panel meter using sevensegments display driver circuit as seven light emitting diodes.
IC 7107: A high performance and low power consuming integrated circuit (IC) 7107 that consists of seven segments decodes, reference voltage source, comparator and display drives as its internal circuiting[12].
Fig.5(Amplifier circuit)
Digital output value = 01999 (upto 2 volts)
No. of LED in segment = 07, Display = 7 segment drive, No. of pin = 40
Here the increment of count can be calculated using the formula = 1000 /

DC Supply: The power input in the form of direct current
has been used in this work for especially the reading of current when DC supply applied to the intelligent helical spring. The unit or component of work measured the voltages in volts on its screen and current in ampere on its screen. It also has the regulator switch in both sides of current & voltage. The coarse & final regulating switch had used to final adequate reading and gradually increasing voltage as per requirement. It includes CV screen & CC screen, CV refers to current voltage & CC for current and Coarse & fine regulating switch, Power button( On/Off switch with side fuse),Voltage
= 015 volt, Current = 05amp.Three connecting point as +ve ,
ve & ground terminal (GND)

Basic components used: In this present work the components included as Resistors(1k10k), Capacitor(1000mf/25v,1mf/63v),Diode(Electrolytic),Inductor s(coil/wound),Transistors,(3terminal)Rectifiers(BridgeIN4007
,Transformers(Setdown909) as shown in fig.5. The sets of diodes here referred to bride type rectifiers[11,12].
Fig.6(Basic components)
The final model is also shown in the below fig. 7.
Fig.7 (Final Model)

MATERIAL & MANUFACTURING OF SMA HELICAL SPRING
The material of spring wire is flexinol (trade name of NiTi alloy) which behave as smart material. The one way SMA was purchased from the thing bits electronics Pvt. Ltd. as in drawn condition. Asreceived informing about SMA in composition as 49% Nickel and 51% Titanium with one way metallic material, also produced by vacuum induction melting. The flexinol wire of dia 1.0 mm, the manufacturing of SMA helical spring used the threaded screw, end restraints and mild steel fixture with copper clamping wire. The muffle furnace is utilized for the tolerance of Â±5Â°C and muffle voltage regulator is set at 530Â°C for 45 minutes to made typical helical spring with mean coil dia. of 7.4 mm & 8 no. of turns. The annealing process was firstly applied by just switch off the muffle furnace and removing the helical spring after 24 hours and then normalized for 6 hours.
Table 3( All main observations)
Nil
Sr
. N
o.
Preset Length( L)
Volta ge Appli ed
Avg. Curre nt in wire
Atm. Temperat ure
Avg. Wir e Tem p. (0C)
Avg. Loa d Cell Stra in or GF
valu e
Sprin g load value (gm)
(cm)
(volts
)
(Amp.
)
(0C)
1
7.5
0.2
0.93
32.9
33.1
0
Nil
2
7.5
0.4
1.81
32.9
33.8
0
Nil
3
7.5
0.6
2.95
33
34.2
0
4
7.5
0.8
3.87
33
35
38.5
427.3
5
5
7.5
1
4.995
33
36.2
5
76
843.6
6
7.5
1.2
6.12
33.1
38
83
921.3
7
7.5
1.4
7.545
33.1
40.2
90.5
1004.
55
8
7.5
1.6
8.675
33
48.2
5
110.
5
1226.
55
9
7.5
1.8
9.97
33.1
58.5
117
1298.
7
10
7.5
2
10.63
5
33
64.5
128
1420.
8
For the accuracy of result, the initial LoadCell value due to the upper plate placed on loadCell without voltage maintains at zero mm
Springload value = Reading of loadCell value for an applied voltage X Scale value
7.1 Scalevalue: The scale values have been calculated with the help of steel slotted weights. The steel hanger weight was 50gm, but the slotted weights of each piece also equal to 50gm. The total 200gm weight had applied. The hanger placed on socket terminal just simply in the gap of its which is adjustable by turning the cap that present outside and behave like a nut. Placed the slotted weight of 50gm piece one by one until the weight reached firstly 100gm, then150gm and lastly 200gm.
Fig.8 (after annealed & normalized)
The parameters obtained were as 🙁 D) Mean coil Dia = 7.4 mm,(d) Wire dia = 1.0 mm,(n) No. of turns = 8,(c) Spring index = D/d=7.4,(Linitial) Initial free length of spring = 2.5 cm

EXPERIMENTAL
The NiTi SMA helical spring one end had attached with socket terminal. Although socket terminal had maintained fixed also on the top jaw of iron stand and so tightened that not tilted during the loading or unloading. The other end of SMA helical spring had maintained fixed on the movable jaw of iron stand. Preset length condition of SMA helical spring wire represents the vertical length of spring.
The Avg. scalevalue has been calculates as: Set the initial value strain for loadcell = 0 Strain value of hanger = 05
Strain value of first weight (100gm) = 09 Strain value of last weight (200gm) = 17 Table 4(For avg. scale value)
Sr N
o.
Slott ed weig ht (gm)
Hangi ng weight (gm)
Loa d Cell Strai n or GF
valu e
Atm. Temperatur e(0c)
Differe nce
value
Related value
1
0
50gm
5
32.3
5
50/05=10
2
50
100g
9
32.4
4
100/9=11.1
11
3
100
150
13
32.3
4
150/13=11.
538
4
150
200
17
32.4
4
200/17=11.
765
Avg. scale value
11.1035
Avg. scalevalue = (Relative value I+ Relative value II+ Relative value III+ Relative value IV)/4
=11.10
140
120y = 67.5x – 2.5714
140
120y = 67.5x – 2.5714

RESULTS AND DISCUSSION
100
100
RÂ² = 0.9338
RÂ² = 0.9338
y = 25.58x + 10.002
y = 25.58x + 10.002
80
80
60
40
20
0
60
40
20
0
Avg. Wire
Temperatur e
(0C)
Avg. Wire
Temperatur e
(0C)
The main data obtained in table 3, firstly the combined relationship of V, I, T, Wt and Ls were described as shown in fig.9 and corresponding table 5 showing the data.
RÂ² = 0.897
RÂ² = 0.897
Sr. No. 
V(VOLTS) 
I(AMP.) 
T(TEMP.) 
WT 
Ls 
1 
0.2 
0.93 
33.1 
0 
0 
2 
0.04 
1.81 
33.8 
0 
0 
3 
0.06 
2.95 
34.2 
0 
0 
4 
0.8 
3.87 
35 
38.5 
0.42735 
5 
1 
4.995 
36.25 
76 
0.8436 
6 
1.2 
6.12 
38 
83 
0.9213 
7 
1.4 
7.545 
40.2 
90.5 
1.00455 
8 
1.6 
8.675 
48.25 
110.5 
1.22655 
9 
1.8 
9.97 
58.5 
117 
1.2987 
10 
2 
10.635 
64.5 
128 
1.4208 
Sr. No. 
V(VOLTS) 
I(AMP.) 
T(TEMP.) 
WT 
Ls 
1 
0.2 
0.93 
33.1 
0 
0 
2 
0.04 
1.81 
33.8 
0 
0 
3 
0.06 
2.95 
34.2 
0 
0 
4 
0.8 
3.87 
35 
38.5 
0.42735 
5 
1 
4.995 
36.25 
76 
0.8436 
6 
1.2 
6.12 
38 
83 
0.9213 
7 
1.4 
7.545 
40.2 
90.5 
1.00455 
8 
1.6 
8.675 
48.25 
110.5 
1.22655 
9 
1.8 
9.97 
58.5 
117 
1.2987 
10 
2 
10.635 
64.5 
128 
1.4208 
Table 5(Data for V, I, T, Wt and Ls)
0 1 2 3
Applied votage
0 1 2 3
Applied votage
200
100
0
100
0 1 2 3
Applied voltage
Fig.9
I(AMP.)
T(TEMP.) WT
LS
Fig.10 (Minimum value to Maximum value of WT, LS)
The correlations obtained as:
Y= 67.5x2.571, R2=0.933.. (i) For WT Y= 25.58x+10.00, R2=0.897.. (i) For Ls
Here R represents the correlation coefficients.
It can be seen from the fig.9, red colour indicate the variation of WT (Avg. wire temperature) corresponding to the value against applied voltage and also blue colour indicates te variation of LS (avg. load cell strain) corresponding to the value against applied voltage in the above mention graph.
8.1 The minimum value to maximum value relationship for Avg. current in SMA wire which is measured in ampere and avg. load cell value in mm.
Table 7(data for Avg. current & GF value)
Sr. No. 
Avg. Current (Amp.) 
Avg. LoadCell Strain or GF value 
1 
3.87 
38.5 
2 
4.995 
76 
3 
6.12 
83 
4 
7.545 
90.5 
5 
8.675 
110.5 
6 
9.97 
117 
7 
10.635 
128 
Sr. No. 
Avg. Current (Amp.) 
Avg. LoadCell Strain or GF value 
1 
3.87 
38.5 
2 
4.995 
76 
3 
6.12 
83 
4 
7.545 
90.5 
5 
8.675 
110.5 
6 
9.97 
117 
7 
10.635 
128 
If we considered the minimum value to maximum value for average wire temperatures and average load cell strains readings corresponding to applied voltages as shown in table 6.
Sr. No. 
Voltage(V) 
Avg.Wire 
Avg. LoadCell Strain 
Temperature(WT) 
or GF value(LS) 

(0C) 

1 
0.8 
35 
38.5 
2 
1 
36.25 
76 
3 
1.2 
38 
83 
4 
1.4 
40.2 
90.5 
5 
1.6 
48.25 
110.5 
6 
1.8 
58.5 
117 
7 
2 
64.5 
128 
Sr. No. 
Voltage(V) 
Avg.Wire 
Avg. LoadCell Strain 
Temperature(WT) 
or GF value(LS) 

(0C) 

1 
0.8 
35 
38.5 
2 
1 
36.25 
76 
3 
1.2 
38 
83 
4 
1.4 
40.2 
90.5 
5 
1.6 
48.25 
110.5 
6 
1.8 
58.5 
117 
7 
2 
64.5 
128 
Table 6(Minimum value to Maximum value of WT, LS)
The seven readings have been considered as shown in table 7 above.
The minimum value to maximum value relationship for average wire temperatures and average load cell strains corresponding to applied voltages is shown graphically as in fig.9.
200
100
0
Avg. current(Amp.) V/s Avg. Load
Cell Strain or GF value
y = 11.475x + 6.9972 RÂ² = 0.9301
0 5 10 15
Fig.11
The correlations obtained as:
Y= 11.47x+6.997, R2=0.930 (iii)
8.2 The minimum value to maximum value relationship for applied voltage and avg. springload value measured in volts and Kg.
Table 8 (data for Voltage (Volts) & Springload value)
Sr. No. 
Voltage (Volts) 
Springload value 
1 
0.8 
0.42735 
2 
1 
0.8436 
3 
1.2 
0.9213 
4 
1.4 
1.00455 
5 
1.6 
1.22655 
6 
1.8 
1.2987 
7 
2 
1.4208 
The seven readings also have been taken again from table 3 as shown in table 8 above.
The correlations obtained as:
Y= 0.904x0.195, R2=0.829(iv) For V & Ws
8.4 The maximum value to Median value relationship for applied voltage and springload value
Table 10(data for Volts & Springload value)
Sr. No. 
Voltage(Volts) 
Springload value(WT) 
1 
2 
1.4208 
2 
1.8 
1.2987 
3 
1.6 
1.22655 
4 
1.4 
1.00455 
Springload
Springload
Here again four readings had considered as median must be 4 reading.
Voltage (Volts) V/s Springload
value(kg)
2
1.5
2
y = 0.6604x + 0.1149
RÂ² = 0.951
Voltage (Volts) V/s Springload
value(kg)
2
1.5
2
y = 0.6604x + 0.1149
RÂ² = 0.951
1
1
y = 0.7492x – 0.0285
RÂ² = 0.9338
y = 0.7492x – 0.0285
RÂ² = 0.9338
Springload
value
Springload
value
0
0
0
0
1
1
2
2
3
3
1
0.5
0
1
0.5
0
0
0
Fig.12
The correlations obtained as:
Y= 0.749x+0.028, R2=0.933. (iv)
Furthermore,
Applied voltage
Applied voltage
0.5
0.5
1
1
1.5
1.5
2
2
2.5
2.5
Fig.14
The same correlation was obtained due to no change of data but used to the find the avg. load model equation in case of maximum value to minimum value relationship for applied voltage (V) and springload value (WT).
8.3 The minimum value to Median value relationship for applied voltage and springload value
Table 9( data for Volts & WT)
Sr. No. 
Voltage(Volts) 
Springload value(WT) 
1 
0.8 
0.42735 
2 
1 
0.8436 
3 
1.2 
0.9213 
4 
1.4 
1.00455 
Four readings had considered as median in 7 values must be 4 th.
1.5
For Stressvalues of intelligent helical spring SMA Initially the spring was formed which have dimensions as:
Mean coil Dia = 7.4 mm & Wire dia = 1.0 mm, but fact is that spring deformed axially throughout according to length, so no. of turns & spring index have been changed. This 1.0 mm wire has stiffness value at room temperature, or we can say deformed position of spring in which martensite only stable phase is exist.
In present work the measured value of Initial Vertical length of spring ((Liv) = 2.5cm
Measured increased value of Final Vertical length of spring ((Lfv) = 7.5cm, Mean coil diameter = 7.4
From Table 3, 7.4/10 = 0.74 mm
Spring Index (C) = D/d = 0.74/1.0 = 0.74
Shear stress factor (Ks) = 1 +1/2C = 1 + 1/(2*0.74) = 1 + 0.676 = 1.676

Resultant Stress (rs) calculation:
We know that experimental helical spring behave like as an compression spring as at applied voltages the currents passes
springload
springload
1
0.5
0
y = 0.9046x – 0.1959
RÂ² = 0.8295
0 0.5 1 1.5
Appiled voltage
Fig.13
throughout wire and try to became full helical spring so forced imparted direction towards the each other or we can say lower end of wire try to move in upper direction and upper end of wire try to move in downward direction. Imaginary resultant stress equations (irs) have been calculated from data mentioned in experimental work based on voltages & springloads values of intelligent helical spring SMA.
From the given Table 3, The Minimum and maximum Spring load values referred to the forth reading for the 0.80 volts and 10th reading for the 2.00 volts.
The Imaginary resultant stress (irs) can be calculated as:
= (8 x Load x Spring Index x Ks ) / ( x d2).. (i)
Where
load is denoted by F or W in Newton or kg, Spring Index is denoted by C,
Shear stress factor is denoted by Ks, Wire dia. is denoted by d
Mean coil dia. Is denoted by D
For the Minimum Resultant stress value
Again from Table 1, applied voltage =0.80volts and correspondingly given value of
Springload value = 427.35 gm = 427.35/1000 kg = 0.42735kg
Spring Index (C) = 0.74
Shear stress factor (Ks) = 1.676 Using value equal to 22/7 Wire diameter = 1.0mm
Here, substituting the values in equation no. (i), we get
= (8 x Load x Spring Index x Ks) / ( x d2)
= (8 x 0.42735 x 0.74) / (22/7*1.02)
= 2.529912/3.142875 = 0.804967 0.805 (v)
For the Maximum Resultant stress value
In above mention row, applied voltage =2.0volts and correspondingly given value of
Springload value = 1420.80 gm = 1420.80/1000 kg = 1.4208kg
Now again considering, Spring Index (C) = 0.74 Shear stress factor (Ks) = 1.676
Using value equal to 22/7 Wire diameter = 1.0mm
Here, substituting the values in equation no. (i), we get
= (8 x Load x Spring Index x Ks) / ( x d2)
This equation is based on Avg. load relation for Min. value to median value and max. value to median value:
Let considering,
Load equation (ZI) = Min. value to median value Load equation (ZII) = Max. value to median value Avg. Load (ZAL) = [(ZI) + (ZII)]/2
= (0.904x0.195+0.660x+0.114)/2
= (1.564x0.081)/2
ZAL = 0.782x0.0405
Again we can write for onedimensional deflection
(Fs) = ZAL = 0.782x0.0405.(viii)
Imaginary deflections (X1, X2, .) Experimental calculations used the final length Linitial = 2.5cm = Initial free length of SMA
Lfinal = 7.5cm = final free length of SMA =Preset length of SMA spring
Deflection (X1) = Lfinal – Linitial = 7.5 2.5
First deflection (X1) = 5.0cm (data included) Linitial = 2.5cm = Initial free length of SMA
Lfinal = 6.5cm = final free length of SMA =Preset length of SMA spring
Deflection (X2) = Lfinal – Linitial = 6.5 2.5
Second deflection (X2) = 4.0cm (data not included) Deflections =X1=5.0 & X2=4.0 , must be equal to the Height(H) of weight/ load falling according to the gravity in one direction, so we can write
Height of Falling load(P)= Deflections =X1 or X2(ix)
(If initial height not considered)
These above (vii),(viii) &(ix)equations help to find the work done in springs(Ws) which to bear the calculated Load fr , For example, in spring, Work done of single spring(one dimensional loading only)
Ws = (Fs).
Ws = (Fs).
= (k. ).
= (k. ).
= (8 x 1.4208 x 0.74) / (22/7*1.02)
= 8411136/3.142875 = 2.6762255 2.676 .. (vi)
(The minimum resultant stress value and maximum resultant stress value were obtained as Imaginary Resultant Stress (rs))

Model Equations
This model equation based on data mention in Experimental work as:
1. First model equation
This equation is based on Avg. load relation for Min. value to max. value or viceversa:
Let considering,
Load equation (YI) = Min. value to max. value Load equation (YII) = Max. value to min. value Avg. Load (YAL) = [(YI) + (YII)]/2
= (0.749x+0.749x)/2(0.0.28+0.028)/2
YAl = 0.3745x0.014
In helical spring, Spring force (Fs) = – k.
If the onedimensional deflection of spring in which represents the deflection of spring and k represents the spring constant, so we can write
(Fs) = YAl = 0.3745x0.014(vii)
1. Second model equation
= 1k/2[(initial)2 (final)2]
Work done by two springs (onedimensional loading)
Ws1 = (k1 + k2).d (for IIrl condition) Ws1 = (1/k1 + 1/k2).d (for series)
For New design of helical spring necessary parameters are d(wire dai.), D(mean coil dia.) and P(load simply knowing k and calculated load (P)= YAl= ZAL. The resultant shear stress also calculated with or without considering the stress concentration in inside fibre of coil.
Above three equations also help to find P.E of falling load(P),

of falling load(P) and also which types of damping of load (P) required during falling (all in onedimensional loading only).
CONCLUSIONS
This Physical model enables the stability of intelligent helical SMA spring by defining the various working parameters before its practical implementing as an actuator. It also enables to the design of single spring or no. of springs based on the SMA. It includes

The various relationships with the help of correlations for the minimum value to maximum value relationship for applied voltages and spring
load values,, the maximum value to minimum value relationship for applied voltages and springload values, the minimum value to median value relationship for applied voltages and springload values, the maximum value to Median value relationship for applied voltages and springload values as equations iii, iv, v and vi are evaluated.

The model equations are based Imaginary resultant stresses for data available for 1.0mm wire as


Equation vii is based on Avg. load relation for Min. value to max. value or viceversa:

Equation vii is based on Avg. load relation for Min. value to median value and max. value to median value.
This prescribed work will be helpful to researchers as an alternative to evaluate SMA helical spring working parameters or SMA running condition helical spring/wire before implementing in the form of actuator in any system.
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