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Расчет и проектирование электромеханических логических элементов с использованием проволоки из сплава с памятью формы
M. Geetha, K. Dhanalakshmi
Национальный технологический институт, Тируччираппалли, 620015, Индия
В статье предложена конструкция электромеханических логических элементов на основе шарнирных переключателей, приводимых в действие проволокой из сплава с памятью формы. Проведено их физическое моделирование и тестирование. Логические элементы микроэлектромеханических систем, приводимые в действие электростатическими, пневматическими и электротермическими переключателями, используются в качестве альтернативы традиционным логическим схемам для работы в агрессивных условиях, например ионизирующих излучений и высоких температур. Аналогичное применение находят логические элементы микрооптоэлектромеханических систем на основе электротермических переключателей. В автомобилестроении актуальной задачей является разработка пусковых механизмов для рычажных и стыковочных элементов. Работа исполнительного механизма обусловлена ограничениями и сложностью конструкции конкретного устройства. В настоящей работе предложено решение по упрощению конструкции логических элементов с механическим приводом на основе шарнирных переключателей, приводимых в действие проволокой с памятью формы. Проведена оценка работы шарнирных переключателей с проволокой из сплава с памятью формы путем расчета минимального тока, необходимого для срабатывания проволочного механизма без задержки переключения, с учетом переходных процессов при переключении режимов ВКЛ/ВЫКЛ для статического входа. Рассмотрены функциональные возможности базовых электромеханических логических элементов с шарнирным переключателем на основе проволоки с памятью формы.
Ключевые слова: сплав с памятью формы, переключатель ВКЛ/ВЫКЛ, шарнирный переключатель, электромеханический, логические элементы
DOI 10.24411/1683-805X-2019-15012
Structural design and realization of electromechanical logic elements using shape memory alloy wire actuator
M. Geetha and K. Dhanalakshmi
Department of Instrumentation and Control Engineering, National Institute of Technology, Tiruchirappalli, 620015, India
This paper presents the design, physical modelling and testing of electromechanical logic elements using shape memory alloy (SMA) wire actuated hinged beam switches. Microelectromechanical system logic devices actuated by electrostatic, pneumatic and electrothermal actuation mechanisms are used as alternatives to the conventional logic systems for harsh operating conditions such as ionizing radiations and high temperature. Microoptoelectromechanical system logic device actuated by electrothermal cantilevers can be used in the same applications. Mechanical logic units using linkages and joints in automobiles require an appropriate actuation mechanism. The actuation mechanism used in each case is inherent to typical limitations and design complexity. This work contributes to the evolution of the mechanical logic design architecture to present simplicity to the logic system, involving SMA actuated hinged beam switches. The performance of the SMA hinged beam switch is evaluated by assessing the minimum current required for the actuation of the SMA to reduce the switching delay; also the switching transients during ON and OFF are observed for a static input. The functionality of basic electromechanical logic elements composed using SMA hinged beam switch is verified.
Keywords: shape memory alloy, ON/OFF switching, hinged beam based configuration, electromechanical, logic elements
1. Introduction
Utilization of the classical logic devices has exponentially increased as a consequence of its excellent performance in speed, size, energy efficiency and cost. In spite, an alternate is required in specific situations where these
most popular logic devices would not be able to perform. When such an alternate for a conventional logic system is thought, the underlying trend is to make the new technology also meet out the challenges laid by the win-win scenario. It is a hard shell to break; but still, an attempt is made to
© Geetha M., Dhanalakshmi K., 2019
achieve a computing technology adapting to the specific requirements through the shape memory alloy (SMA) technology, i.e., the conceptual design and experimental validation of an SMA actuated electromechanical logic element. The unconventional mechanical logic devices use switching like its conventional counterpart, to realize the logic states which deployed different types of actuation mechanisms like electrostatic, electrothermal and pneumatic wherein the movement of the gate electrode towards the source and drain (resembling the conventional design), variation in the thermal coefficients of the bimetals and, variation of the air pressure are respectively their principles of operation for switching.
The advancement and growth of technology are prominently guided with the development of unconventional systems in addition to the improvement in the conventional systems in all ventures. As well, the development of logic elements in an unconventional technology becomes inevitable in places where the traditional technology fails and is not applicable. Hence, the need for implementation of the logic functionalities using an alternative technology is felt [1-3]. Mechanical logic elements are designed using moving mechanical components like levers, joints, and gears to realize the operations of a typical conventional logic element; the logic levels are represented as two finitely separated positions of the links. They are capable of handling force, displacement, and logic simultaneously. These logic devices designed in macro- and microdomains are suitable for operation in environments such as with strong electromagnetic fields or high radiations and high temperature [2-4] and can find applications in automobile industry and robotics. The drawback of the mechanical logic devices is that the linkages and joints are highly sensitive to geometry and therefore should have high dimensional accuracy. An alternative that can shun this shortcoming and moreover involve feasibility of control using electrical input could be brought about by realizing the electromechanical version. Microoptoelectromechanical system (MOEMS) logic devices are actuated by electrothermocantilevers [5]; they require a dedicated optical waveguide for the transmission of light which complicates the design and fabrication, further affects the size.
In classical logic systems, switching is the fundamental mechanism used to realize the operation of logic elements. Furthermore, in unconventional systems too, the switching principle is retained to realize logic functionalities with an appropriate actuation mechanism to perform switching. To compete with the size and component density featured by the classical logic system, microelectromechanical system (MEMS) technology supports the development of unconventional logic systems to incorporate the switching mechanism which can feasibly adopt various types of actuation mechanisms [6, 7]. Though the unconventional (mechanical) logic systems would emerge as an alternative to the classical systems where the latter is not applicable, nevertheless the former too will suffer its limitations. Literature
reports about the realization of a switching mechanical logic elements through electrothermal actuators, pneumatic actuators and electrostatic actuators [1, 4, 5]. The performance/ characteristics of these actuation mechanisms reveal the following limitations: thermal actuation consumes higher power and has a slower response time, electrostatic actuators require high actuation voltage and also has only a limited operating range and, pneumatic actuators are beneficial only till certain values of air pressure, compressibility of air and has a poor performance at slow speed of operation. A patent published in 2013 is about another unconventional meso-scale mechanism for omnidirectional steering using mechanical logic gate synchronizers [8]. To circumvent the difficulties with the aforementioned conventional actuation mechanisms, mechanical actuators driven by electrical input is preferable, for which piezoelectric actuator using electrostatic principle is the explicitly available option owing to its ease of fabrication in MEMS technology. The concept of electromechanical actuation based on SMA actuated hinged beam switch could be encouraging to realize the logic functionalities with enhanced operating conditions in SMA unlike the piezoelectric.
Only a few literatures are available on the design and implementation of mechanical logic elements. Papers [1, 2] demonstrated the design and development of micro-mechanical AND gate using flexures to transmit motion and force and a micropneumatic actuator is used to drive the device. MEMS logic gates based on electrostatic actuation of a microcantilever for NAND and NOR logics have been proposed in [4]. The concept of a circuit breaker in microscale with an SMA actuated cantilever as a normally closed temperature-sensitive switch to protect the device [5, 9] described the fabrication and characterization of microoptoelectromechanical AND, OR, XOR logic gates developed using electrothermo actuated cantilevers working as ON/OFF switches.
Logic elements generally involve two levels of input and output namely low and high logic levels. To realize logical constructs in physical devices, the use of switches that has the two states ON and OFF is inevitable and therefore a switching mechanism becomes the fundamental building block, be it the conventional or unconventional logic systems. The use of shape memory alloy for switching is suitable since by nature it has the advantage of possessing two different phases of crystal structure that can represent the two-level logic. In addition, the shape memory effect/ actuation cycle of SMA inherently is related to the switching functionality. This feature also enables to configure the mechanism as a hinged beam switch.
Shape memory alloys are adaptive materials which have the ability to return to a predetermined shape when heated. When SMA is cold, or in its martensitic phase it has very low yield strength and can be deformed to any new shape, which is retained until there is an increase in temperature. When heated above its transformation temperature, the crystal structure changes from martensitic to austenitic phase
and return to its original shape. This solid to solid phase transformation of SMA facilitates the realization of the two logic levels of the logic element.
Shape memory alloys can be engineered to be able to perform repetitive actuation in microcomponents and mac-rodevices. The multiphysics behaviour of SMA allows the conversion of electric or thermal energy to a mechanical force for actuator applications and, the change in electrical resistance during actuation for sensor applications. The resistivity of SMA is the factor that promotes Joule heating and henceforth makes electromechanical actuation possible, likewise change in electrical resistance promotes self-sensing as well, its high work density makes SMA an excellent choice for electromechanical actuation in situations requiring large force and displacement.
It is proposed to explore the features of SMA in a different orientation to realize the two logic levels of the digital domain. The ability of repetitive actuation of configured SMA has the advantages of offering two stable states to represent the logic levels with good repeatability. Use of SMA hinged beam switches would be the right approach to realize the logic functionalities. Since the SMA is actuated by means of joule heating, the design and realization of basic and derived logic elements using SMA are perceived as electromechanical logic elements and are presented in this article. Logic 0/1 is realized from the position (open/ close) of SMA hinged beam in the electromechanical logic elements such as NOT, AND, OR, NAND and NOR accommodative to change in logic states.
2. Design and working of electromechanical logic functions
The electromechanical actuation mechanism employs SMA actuated hinged beam arrangement as a switch. The bistable phases of SMA which is the fruition of its non-linearity are exploited to realize the two-state logic. Here SMA is configured to produce a minimum displacement through a minimum actuation current just to enable ON and OFF of a switch; hence, the low-speed response which is its integral demerit is thus overruled. Further, low driving voltage, noiseless actuation, and simplicity in mechanism makes it a factual choice for realizing a logic element rather than other actuators.
2.1. The basic building block of SMA actuated electromechanical logic element for switching
The basic building block of the electromechanical logic element is an SMA wire actuated hinged beam arrangement which acts as a switch [9]. The switch is configured with a flexible member, the hinged beam (5 x 1.5 x 0.4 cm3) and a point of contact on a fixed beam. The hinged beam is displaced by the actuation of an SMA wire (commercially available nitinol from Dynalloy Inc. of 100 mm length and 0.15 mm diameter) which is connected between the free end/tip of beam and its hinged end through the hub posts. The switch is positioned on the posts placed on the cent-
roidal axis of an I shaped structural support and the entire structure is made up of acrylic. The surface of both fixed and hinged beams are coated with copper strips to be able to make/break contact thereby enable normally opened (NO) or normally closed (NC) condition depending on the architecture and operation of the logic elements. The structural modelling is done in CATIA with the above specifications and shown in Fig. 1.
The hinged beam is displaced through the actuation of joule heated SMA wire while its cooling occurs through free convection in air. Being the primary component of the switch, the hinged beam also provides the required passive bias force to reset the SMA wire at its low temperature which is an added benefit. On applying current to the pre-stressed SMA wire, it contracts thus regaining its original shape and dislodges the hinged beam vertically, to make or break the contact corresponding to the structure of each logic function. During actuation, if the hinged beam establishes a contact in the switch, then it is initially in the NO condition, or if it breaks a contact, the switch is initially in the NC condition. When a connection is established between the fixed beam and hinged beam then the output of the arrangement is at logic 1, else if there is no connection, then the output is at logic 0.
2.2. The logic elements
The architecture of the electromechanical logic elements is derived using the basic building block which is the SMA wire actuated hinged beam arrangement working as a switch. The configuration of the logic elements such as NOT, AND, OR, NAND and NOR are physically realized for two inputs, and their logic conditions are verified.
Fig. 1. CATIA 3D model of the SMA actuated hinged beam switch: normal (a) and projected view (b) (color online)
2.2.1. NOT logic element
The structure of the NOT logic element is similar to that of the basic hinged beam switch as shown in Fig. 1, thereby its functionality. The functionality is achieved by a single hinged beam switch which is in the normally closed position. A DC supply of +5V (Vi) is constantly applied to the copper strip of the fixed beam. When the SMA wire is energized with a current of 200 mA (logic 1) it contracts, thus moving the hinged beam upwards during when the contact is disconnected from the supply and the output voltage Vo = 0. When the SMA wire is not energized (logic 0), the switch remains in the normally closed position and output Vo = +5V (logic 1).
2.2.2. AND logic element
The configuration of the AND logic element is made of two hinged beam switches connected in series as shown in Fig. 2 and both are in the normally open condition. The input and output voltages of the switches are Vi1, Vi2, Vo1 and Vo2 respectively. The second switch get its DC supply from the first switch when the contact gets established. When the SMA wire is energized, the input is logic 1 else the input is logic 0. If the input to both the switches is logic 0, the switches remain in the open condition and Vo2 = 0. If any one of the inputs is logic 1, one of the switches alone closes and the other is open and hence Vo2 = 0. If both the SMA hinged beam switches are energized, a contact is established between both the switches, making Vo2 = 1.
2.2.3. OR logic element
In this arrangement two normally open SMA hinged beam switches is connected in parallel as shown in Fig. 3. When any of the inputs are at logic 1 a connection is established between Vi and Vo, accordingly Vo = 1. Also when both the SMA wires are energized, both the switches are closed there by Vo = 1.
2.2.4. NOR logic element
The construction of the NOR logic element is as shown in Fig. 4 is similar to that of the AND logic element but for the switches being normally closed. Hence when both the inputs are at logic 0, Vo = 1, else the output Vo = 0.
Fig. 2. 3D model of AND logic element in CATIA (color online)
Fig. 3. CATIA 3D model of OR logic element (color online)
2.2.5. NAND logic element
In this logic element the arrangement of hinged beam switches is similar to that of OR logic element, whereas both the switches are in the normally closed condition. Output Vo = 1 when either or both inputs at logic 0 and when both the inputs are at logic 1, Vo = 0. The model is shown in Fig. 5.
3. Evaluation of the electromechanical logic structural element
The actuation system of the basic electromechanical logic element comprising of the hinged beam, a flexible integral and an SMA wire for electrical actuation, is formulated in two dimensions to obtain its structural performance and the thermo mechanical behaviour. The elevation of the assembly is shown in Fig. 6.
3.1. Structural analysis of the SMA actuated hinged beam
The structural performance is presented in terms of the forces acting on the structure, the moment and the deflection of the beam. Consider a hinged beam of length L actuated by an SMA wire of length l, whose initial length in the
Fig. 4. CATIA 3D model of NOR logic element (color online)
SMA wire
Fig. 5. CATIA 3D model of NAND logic element (color online)
prestrained state is . The SMA wire is held as shown in Fig. 7 with lj as the height of the SMA tip post and l2 as the height of the SMA hub post. The maximum deflection of a beam with rectangular cross section, loaded at the centre is given by
8 =
PL2 48EI '
(1)
where E is the Young's modulus, I is the moment of inertia of the beam, L is the length of the beam and P is the weight loaded on the beam. The moment of inertia of such a beam can be calculated by
I=
bd_ 12
(2)
where b is the width of the beam and d is the thickness of the beam.
The moment is obtained by integration [10] and is expressed as a function of beam rotating angle 9:
I (6) =
bd[b2 (1 - cos (28) + d2(1 + cos (29))] 12 '
(3)
Various forces acting on the beam and the SMA wire are as shown in the Fig. 8. The solution for the above equations can be obtained by resolving the forces acting in the system. Applying the equilibrium conditions along the X and Y directions:
F1 = Px c0s
) + Py sin (
F2 = Py cos 9- Px sin 9, Px = P cos ^ and P = Psin
SMA wire
(4)
(5)
(6)
......._ ■ ^^
L L/4
Fig. 7. Schematic of the SMA actuated hinged beam (color online)
where ^ is the angle of inclination of the SMA wire with the horizontal axis in the deformed condition, Fj, F2 are the resultant forces in the beam at the hinged end, Px, Py are the component forces of the SMA wire due to the shape memory effect, and 9 is the angle of rotation of the hinged beam. The deflection of the beam depends upon the force and angle of inclination of the SMA wire.
The moment of the beam at the point O can be calculated by applying the equilibrium condition for the moment as shown in Fig. 9:
M0 + Px cos 9(lj) + Py sin 9(lj) = 0, (7)
M o =-Px cos 9(lj) -Py sin 9(lj). (8)
From the expressions (4) and (5) it is evident that the resultant forces depend on the rotating angle of the beam 9. The deflection of the beam can be changed by varying 9. The deflection is achieved by using SMA wire clamped between the supports as shown in the Fig. 7. The SMA wire is actuated by joule heating. As the SMA wire shrinks in length, it pulls the beam from its initial position. Thus the deflection of the beam is achieved with the change in the rotation angle 9. Considering maximum deflection of the beam, the rotation angle is given by
(9)
cos 9 =
l +12 sin 9
Differentiating 9 gives its rate of change as
9' =_l_.
L sin 9+ lj cos 9
(10)
Px cos 9
Fig. 6. Front view of the SMA hinged beam (color online)
Fig. 8. Resolving forces (color online)
Fig. 9. Resolving moment (color online)
The strain in the SMA wire is given by l - l
(11)
where lt is the prestrained length of the SMA wire. The change in 0 is associated with the strain rate e of the SMA wire, thus 0' is rewritten as
0' =-^-. (12)
L sin 0 +11 cos 0
The deflection of the beam 8 can be calculated if the value of 0 is known, which is evident from the Eqs. (1) and (3). For a known strain e of the SMA wire, the change of rotation of the beam 0' can be found using Eq. (12).
3.2. Thermomechanical analysis of the SMA actuated hinged beam switch
The electrothermomechanical behaviour of an electrically driven SMA actuated hinged beam which is used as a switching element is formulated. The front view and the schematic of the SMA actuated hinged beam switch is as shown in Figs. 6 and 7, respectively. To characterize the function of the SMA actuated hinged beam as a switching element, the main factors of interest are the deflection of the hinged beam and the amount of actuation current to the SMA wire.
The one-dimensional heat transfer equation of SMA wire with Joule heating and natural cooling [11] is given by the expression
dT (t)
«c„
dt
= vi - h Aç[T (t) - Ta],
(13)
where m = pud2l/4 is the mass of the wire, p is the density of the wire in kg/m3, Cp is the specific heat capacity in J/kg K, h c is the heat convection coefficient for ambient cooling condition in W/m2 K , Ta is the ambient temperature in °C, i is the current in the wire in A, Ac is the convective surface area of the wire m2, v is the potential difference across the wire in V.
The transfer function of equation (13) is given by
T ( s ) P ( s )
l/( mCp)
s + ( hc Ac)/(mCp)
+ T.
(14)
The step response is given by vi
T = -
- + Ta.
(15)
hc 4(1 - tT)
The temperature of the wire is controlled indirectly by varying the intensity of the current flowing through it. The corresponding shape change starts in the wire when the temperature just crosses the austenite start temperature A and ends up with the austenite finish temperature Af. The switching requires to make/break the contact. To establish any of these conditions, it is sufficient to merely displace the hinged beam rather than to establish/maintain the maximum deflection for which a maximum safe current may not be essential. Therefore the current which induces the initial change in shape at As is chosen to achieve the minimum deflection of the hinged beam. Since a minimum current is used to operate the switch, it enables the logic element to work at reduced operating voltages thereby conserving energy. Use of minimum current helps ensures in immediate cooling of the SMA wire during the cycle thus enhancing the switching speed, and results in reduced hysteresis.
3.3. Electromechanical switch
The configuration of the electromechanical switch is the combination of the hinged beam and the SMA wire for actuation. During the OFF (input at logic 0) condition of the switch, the SMA wire is in the prestrained condition. It is in the martensitic state, just held to the structure and holds the hinged beam in its original position. During the ON condition (input at logic1), the SMA wire is energized through Joule heating. The temperature of the wire increases; at A the austenite start temperature the wire contracts henceforth generating stress which induces a force P on the beam and displaces it. The maximum deflection of the hinged beam is achieved when the SMA wire attains a maximum temperature through Joule heating and strains to a maximum limit, which is considered to be the logic 1 state of the electromechanical logic element and is given by
8 =_pA_
max 4bd[b2 (1 - cos (20) + d2 (1 + cos (20)] and at the logic 0 state the deflection 8 = 0.
(16)
LCD display
Power supply
Logic and control
Gate I/O Physical model of the logic element
Current drive
User input
When a current i flows through the SMA wire, then P = vi.
Fig. 10. Experimental set up block diagram
Fig. 11. Circuit diagram for displacement and delay measurement of NOT logic
4. The physical model of the electromechanical logic element
The hardware and experimental facility is developed to verify the operation and performance of the electromechanical logic elements.
4.1. Development of the hardware
The basic block diagram of the experimental set up is as shown in Fig. 10. A microcontroller is used to automate the process of analyzing the input-output characteristics of the electromechanical logic element by interfacing with the drive current circuit. It is also used to control the current supplied to the SMA wire and to measure the displacement of the hinged beam and its transients for various excitation currents [12]. The basic experimentation is the verification of logic functionalities by applying step signal corresponding to logic 0 and logic 1, to the SMA wire. The circuit diagram to measure the delay and displacement of NOT logic functionality and, the drive current circuit are shown in Figs. 11 and 12, respectively.
4.2. Verification of the logic functions
In case of NOT operation, the switch is initially in the 'normally closed' position. The input is given to the copper strip of the fixed beam and the output is measured at the copper strip on the hinged beam; these two points are connected to the I/O pins of the microcontroller. The state of the switch (ON/OFF) is identified by following a check for continuity. When the input to SMA wire is at logic 0, a connection persists between the fixed beam and the hinged beam of the arrangement ensuring the connectivity between the I/O pins of the microcontroller and hence a buzzer is switched ON indicating logic 1 output. When a step signal
for logic 1 is given to the SMA wire, it contracts to dislodge the connection between the fixed beam and the hinged beam. Therefore the connectivity check fails and the buzzer is not operated, thereby indicating the logic 0 output. Thus the operation of a basic electromechanical switching element and the truth table of the NOT logic functionality is verified (Table 1). Similarly, the structures of the other logic elements such as OR, AND, NAND and NOR are designed using basic hinged beam switch; the corresponding truth tables are verified.
4.3. Implementation of NOT logic function in a circuit breaker application
NiTi shape memory alloy based mechanisms are nowadays being used for many mechatronic instrumentation [13].This application reports a normally closed circuit breaker mechanism based on an SMA actuated hinged beam as shown in Fig. 13. It operates on the principle of a NOT logic function. The circuit breaker is placed in the power
Fig. 12. Drive current circuit
Table 1
Truth tables of NOT, OR, AND, NAND and NOR logic elements
Logic levels of the input and output
Input Output
Logic 0 0 mA Logic 0 0 V
Logic 1 200 mA Logic 1 5 V
NOT logic
Cases Input 1, mA Input2, mA Output, V
1 0 5
2 200 0
OR logic
1 0 0 0
2 0 200 5
3 200 0 5
4 200 200 5
AND logic
1 0 0 0
2 0 200 0
3 200 0 0
4 200 200 5
NAND logic
1 0 0 5
2 0 200 5
3 200 0 5
4 200 200 0
NOR logic
1 0 0 5
2 0 200 0
3 200 0 0
4 200 200 5
line of the circuit under test. When the current flowing through the SMA wire increases beyond the safe limit (logic 1 input to the NOT logic), temperature of the wire increases above the threshold level, actuating the hinged beam, disconnecting the current path to the circuit under test until the temperature drops. When the temperature is reduced to the normal level (logic 0 input to the NOT logic) the connection between the power line and circuit is established through the bias spring. The specifications of the wire are chosen to match the current ratings of the circuit under test.
5. Performance evaluation
The performance of the electromechanical logic elements shall be assessed from its transient behaviour (in terms of the speed of response), since it is this initial response of
the logic element that characterizes the switching speed. The instantaneous change in logic states corresponding to the given inputs is a demanding feature of any logic element for every repetition and change in input.
5.1. Switching transients
Though the functionalities of the electromechanical logic elements are verified through the truth tables, it is essential to possess fast switching transients to be applicable. Switching transient is defined as the time the logic element takes to switch to the new output. The SMA wire can withstand a safe heating current (maximum) of 410 mA as per its geometry. If the safe heating current is given to the SMA wire, it undergoes a maximum strain with maximum displacement. If in continuation, when logic 0 input is given, the SMA wire will take a considerable amount of time to cool and return to its original state and, be ready for the next cycle. This lapsed time is beyond the acceptable limits of the switching speed; but can be reduced provided the displacement is made minimal by actuating it with a minimum current, which also conserves the energy. Therefore reducing the switching transient is considered to be an essential aspect of the basic SMA hinged beam switch.
5.1.1. Measurement of the optimum switching current
From the above discussion, it is clear that the switching transients of the SMA hinged switch can be reduced if its heating and cooling time is chosen to be the minimum. Drive current circuits are designed as per the circuit shown in Fig. 12 to produce various currents from 200 to 280 mA in steps of 20 mA to be given as the logic 1 input to the SMA wire and the corresponding displacements of the hinged beam are measured; from which the optimum switching current (minimum current corresponding to the minimum displacement that can be maintained) is determined. The procedure adopted is by capturing the displacement of the hinged beam for various currents as video images using Nikon Coolpix T900 SLR camera in full HD (1920x 1080) of resolution at 30 frames per second and processing it. The video is given as input to a windows desktop application designed in Visual C++ environment to measure the displacement and provides output data as a text report file as shown in Table 2, as well a graph is plotted between the
1—SMA wire
2—hinged beam
3—copper contacts
4—Vi Vo
•• 2 , __j 3
Fig. 13. Conceptual illustration of NOT logic in a circuit breaker
Table 2
Displacement of the hinged beam for varying amplitudes of Joule heating
Current, mA Displacement, ^m
Heating phase Cooling phase
200 640 720
220 1368 1502
240 2180 2412
260 2998 3380
280 3618 3618
excitation current and output displacement which is shown in Fig. 14. The image is processed by an edge detection procedure to identify the two ends of the SMA wire, and the displacement of the hinged beam in each frame is evaluated from the time of the video input and the frame rate. The optimum switching current of200 mA produces a minimum displacement of 640 jum during the ON time and 720 jm during the OFF time.
5.1.2. Measurement of the delay
Delay has not been taken as an influencing parameter in the reported literature on mechanical logic gates, but it makes no meaning if a logical element takes a considerable amount of time to switch between its states. Propagation delay is defined as the time the signal takes to traverse from the input to the output of the logic element.
This delay includes the time lapsed during the ON and OFF switching process which corresponds to the time inclusive of the displacement during actuation and the restraining of the SMA wire.
The microcontroller is programmed to measure the lapsed time whenever a contact is made or broken between the fixed beam and hinged beam to evaluate the delay of the logic element. As explained earlier, the SMA hinged beam switch is initially in the 'normally closed' position. For the first state of the truth table when logic 0 input is given, the fixed beam and hinged beam are in contact and,
continuity exists indicated by the beep sound of the buzzer. For the next state of the truth table when a 200 mA current signal is given through the microcontroller as a logic 1 pulse to the SMA wire, it contracts and displaces the hinged beam from its contact with the fixed beam. The continuity check fails indicated by a break in the beep sound of the buzzer. The microcontroller is programmed to measure the time between the current given to the SMA wire and the time at which the hinged beam displaces, and it is measured as the ON delay. The input is now disconnected and the hinged beam is allowed to return to the original position, corresponding time lapsed is the OFF delay. The process is repeated for 100 cycles and the average ON time and OFF time delay are found to be 1.1 ms and 1.08 ms respectively. The delay can further be reduced if the mechanical arrangement of the structure is optimized.
5.2. Effect of hysteresis
A hysteresis loop is formed when the temperature of the SMA wire is changed cyclically from martensitic phase to austenitic phase through Joule heating. This transformation is called as the thermally induced transformation [14], at constant stress. The transformation thus occurred in the SMA wire used for the actuation of electromechanical logic element with the geometry of 100 mm length and 0.15 mm diameter through Joule heating is as shown in Fig. 14. Another case is the stress induced transformation [14] that occurs at a constant temperature when also a hysteresis cycle is formed.
This case of transformation is obtained for the SMA wire with the above said geometry under uniaxial loading in COMSOL as shown in Fig. 15. In both the cases, hysteresis occurs as the austenite to martensite transformation occurs over a different temperature range or stress levels than the martensite to austenite transformation resulting in a nonlinear behaviour of the material. From Figs. 14 and 15 it can be noticed that the hysteresis width of the thermally induced transformation through Joule heating is less than that of the stress-induced transformation. The reduced hysteresis width is an indication of the suitable design of the
Current,
Fig. 14. Displacement of hinged beam during Joule heating
Fig. 15. The axial stress-strain curve of SMA wire in COMSOL
mechanical structure of the SMA wire actuated switch and the choice of a minimal current for minimal displacing actuation thus reducing the cooling time of the SMA wire. Thus nonlinearity could be avoided by proper choice of structural design and optimal operating conditions.
6. Conclusion
The nonlinear characteristic of SME facilitates the bistable phases of SMA permitting the realization of the two logic states thereby, the design of electromechanical logic elements such as NOT, OR, AND, NAND and NOR. The physical design of electromechanical logic elements is accomplished using SMA actuated hinged beam switch. The structural modelling of the logic elements is done in CATIA V5. Physical models with the respective arrangement of the hinged beam switches are constructed, and the logical operation of the elements are verified. The SMA hinged beam is used as an ON/OFF switch to make or break contact with the copper strip of the fixed beam and that of the hinged beam to realize logic 0 or logic 1 states indicated by the position of the SMA hinged beam. The truth tables of NOT, OR, AND, NOR and NAND logic elements are verified. The displacement of the hinged beam switch for various actuation currents of the SMA are found, and the optimum current for minimum displacement is obtained to reduce the switching transient of the hinged beam switch and thus reduce the ON/OFF delay of the logic element. The ON/ OFF delay thus measured is about 1.1 ms and 1.08 ms respectively for the minimum actuation current of200 mA. This delay can be reduced by optimizing the design of the structure in the mesoscale, and further by realizing in microscale. The axial stress and strain hysteresis curve for the SMA wire is obtained in COMSOL. The displacement of the hinged beam for various actuation currents is plotted, and the minimum actuation current is found to reduce the cooling time of SMA which results in the reduced switching transients.
The logic element designed based on SMA actuated electromechanical principle exhibits satisfactory performance, since it does not depend on the geometry, friction between the joints and flexures etc. unlike the mechanical logic elements do. SMA technology is also compatible and appropriately fit in environments of high temperature and hazardous radiations for the design of mechanical logic elements. The mechanical logic elements can find appli-
cations in instrumentation in the field of automobile. The mechanism of omnidirectional steering [8] implemented in automobiles through mechanical logic gates can now be thought of replacing by these electromechanical logic elements. The circuit breakers implemented using mechanical AND gates does not facilitate automatic restoration of power after the fault is rectified. This can be made possible with SMA based logic elements and the system can be fully automated.
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Received 02.10.2019, revised 02.10.2019, accepted 09.10.2019
Сведения об авторах
Muthuveeran Geetha, Research Scholar, National Institute of Technology, India, [email protected] Kaliaperumal Dhanalakshmi, Dr., Prof., National Institute of Technology, India, [email protected]
