Development Results of a Nitinol (NiTi) Angular Actuator

Abstract

Shape memory alloys are key to sustainable technology and future industries, with one of the most remarkable materials at present being Nitinol (NiTi), which is known to have unique driving properties and applications, working in extreme conditions and capable of being applied in specific actuation tasks. In this context, this work presents an actuator prototype using versatile springs composed of nickel–titanium to produce angular displacements, beginning with contextual findings on the latest trends and opportunities for solutions in the field of Nitinol (NiTi) devices. Considering the research and industry concerns regarding shape memory materials and the need for research, design, and innovation in the development and investigation of various prototypes of Nitinol-based (NiTi) actuators, the functionalities, physical design, and static/dynamic performance of this newly proposed angular actuator offer strong potential. This work also presents and discusses the results of both experimental model testing and an analytical model simulation within MATLAB and Simulink R2022b.

1. Introduction

At present, there is an increasing need to adapt, with increasing demands for products that are more efficient and robust, as the optimized results of human activity.

Since industry strives for innovative solutions and materials to be used in actuators, one type that is in high demand nowadays is shape memory alloy actuators; as an example, Nitinol (NiTi) actuators can be produced in multiple configurations and models depending on the alloy shape, allowing various devices and equipment to make use of them.

The contribution of this paper consists of the analysis of a physically built prototype capable of angular actuation that exploits the thermo-mechanical properties of nickel–titanium alloy, which was tested in our laboratory. Its experimental/analytical model, along with the corresponding practical/simulation results, are presented in this paper, as well as a discussion conducted to confirm the applicability of the assembly.

2. State of the Art

An investigation carried out on the basis of shape memory materials led to the analysis of the specialized literature consisting of Nitinol (NiTi) research, referring to its various shapes and forms, for the purpose of highlighting the latest trends in nickel–titanium forms, applications, devices, and equipment through bibliometric networks.

This also involved some of the development results of recent prototypes of angular actuators built with Nitinol-based (NiTi) actuation springs.

The included research was obtained through filtering articles found on the public platform of Web of Science, focusing on nickel–titanium publications in the following areas:

• Materials science—multidisciplinary (medical/orthopedics/robotics);
• Engineering—multidisciplinary (electrical/electronic/industrial/manufacturing/aerospace).

The choice of the Web of Science database is relevant due to its complexity and wide variety of articles of high quality; here, articles were selected from the domain of Nitinol (NiTi) devices and equipment, for which there have been multiple analyses involving a large number of investigations, encompassing up to 155 articles reflected in the refences [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155].

Overall, the investigation is structured into 14 topics, first underlining the topic of Nitinol (NiTi) and then the state of the art, followed by a theoretical analysis revealing the analyzed articles, including their relevance for implemented systems. This is followed by the resulting bibliometric networks, linked from a temporal perspective, and then a research framework with a design proposal and modeling assumptions, as well as experimental modeling, experimental results, analytical modeling, and analytical results. Then, based on this, further discussion and concluding remarks are given, as well as future directions.

First, the applications of nickel–titanium memorized springs are presented as candidates for the construction of a protype device in the form of an angular actuator, followed by a discussion of the identified trends and opportunities, which are addressed in order to determine the future directions of this research.

Using classification methods, the main forms of nickel–titanium used are highlighted, as well as their main applications and domains, which highlights the most innovative concepts developed around the world by various institutes and laboratories over the last six years.

A collection of .RIS files (for the articles [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155]) was gathered and used in the VOSviewer 1.6.20 software environment [156] to generate a linking visualization based on the bibliometric networks, density, and an overlay visualization map.

The VOSviewer 1.6.20 software environment [156] uses network data to generate multiple types of bibliometric maps, and these can be visualized and explored for more detailed analyses, providing access to every element identified in the map. Moreover, they can be recreated by any individual using the same software, under the condition that the same inputs and rules are applied.

The advantages of such an analysis are as follows:

• To provide specific content;
• To observe connections and similitudes among articles;
• To guide the content of research, in a novel path, in its study area;
• To explore the evolution of a certain topic over time.

3. Theoretical Analysis over Development Concerns

Every selected article mentions a single form or multiple forms of Nitinol (NiTi) of different structures and compositions, projected to have certain characteristics to respond mostly to thermal or electrical triggering.

Nickel–titanium has a wide variety of applications preferred due to its shape memory property, activated based on temperature change, as well as due to the large range of temperature response and good mechanical stress resistance, corrosion resistance, and no toxicity, all depending on the individual alloy percentages of the nickel and titanium.

Next, there are three classifications considered, respectively: the first one is the classification after the generalized main objective, then, the one after that, the used form of the Nitinol (NiTi), and then, the one after that, the main domain of application.

3.1. Classification After the Generalized Main Objective

Firstly, we identified the most common objective of all the analyzed articles, and then, these are simplified and integrated into one of the seven categories, along with the references that they address, according to

Table 1. Classification after the generalized main objective.

Generalized Main Objective	References
To improve a device fabrication	[5,153]
To fabricate new Nitinol (NiTi) alloys	[4,23,150,154]
To test models/strategies on a controlled device based on nickel–titanium	[9,21,27,44,143,144,148,149,155]
To build a new device/equipment/application/model	[17,18,32,33,70,81,82,85,105,131,136,139,140,147,151,152]
To improve the characteristics of an already existing devices/equipment/applications/models/processes	[1,2,3,7,8,10,15,20,28,31,38,59,63,72,80,104,106,107,121,127,130,132,134,135,137,141,142,146]
To study/test devices/equipment/applications	[22,25,29,37,39,40,41,42,53,54,68,75,83,87,90,94,95,96,98,101,102,103,117,118,121,122,123,126,129,138,145]
To study/test the Nitinol (NiTi) alloy	[6,11,12,13,14,16,19,24,26,30,34,35,36,43,45,46,47,48,49,50,51,52,55,56,57,58,60,61,62,64,65,66,67,69,71,73,74,76,77,78,79,84,86,88,89,91,92,93,97,99,100,116,119,120,125,128]

.

From the total of 155 articles, 38% are focused on studying and testing the Nitinol (NiTi) alloy on different levels: the dynamic fracture performances, evolution during cooling and heating on the molecular level, martensite variant reorientation process, torsion and bending deformation modes, capturing of the shear strain field, etc.

A percentage of 21% of the researchers are focusing on studying/testing the device/equipment/applications, such as the lattices/stents, micro-electro-mechanical systems applications, welding, actuators, biomedical devices, electrochemical micromachining, chips, power laser actuation, cement mortar beams, and so on.

Another 19% of them worked to improve the characteristics of already existing devices/equipment/applications/model/process on medical robots, reduction in the surface defects, reversible bending on electrical actuators, and effectiveness of the Auricchio model; minimize hysteresis; lower prices; obtain useful transformation temperatures; improve spring actuation performance, wastewater recovery, and adhesion increase; etc.

Moreover, another 10% of them worked on building a new device/equipment/applications/model like the following: ankle rehabilitation robots, applications on the material behavior and lifespan, the development of additive manufacturing, micropump diaphragms, form fit connections, 3D models, and numerical simulation.

A reduced percentage of articles, 6.13% of them, are concerned with testing models/strategies on devices based on nickel–titanium, such as the following: the Auricchio model, numerical model, Three-Dimensional Phenomenological Constitutive model, and Diffraction Computed Tomography. The smallest percentage, 1.36% and 2.72% of the works, focused on developing a new alloy of Nitinol (NiTi), respectively, to improve the fabrication of devices using it.

3.2. Classification After the Nitinol (NiTi) Form

Secondly, a classification is conceived to provide a clear image over the most used form of nickel–titanium materials, as shown in Figure 1, where are listed 19 forms of Nitinol (NiTi).

3.3. Classification After the Application Domain

Lastly, the most frequent concerns are processed into a classification list, comprising most active domains with relevant applications for nickel–titanium integration:

• Medical:

  ▪

  Medical condition detectors; vessel insertions; vascular/valvular stents; muscular and bone implants; orthodontic wires and arches; root canal files; and minimally invasive surgical devices (including guided needles).

• Engineering:

  ▪

  Actuators; rotary actuators; thermal bimorph actuators; dynamic actuators; driven actuators (open-loop and closed-loop); and phenomena triggers.

• Civil Engineering:

  ▪

  Damping assemblies; lightweight structures; beams; grates; lattice; and foils.

• Robotics:

  ▪

  Artificial muscles; bionic effectors; and micro-actuators.

• Automotives:

  ▪

  Actuators; drives; and micro-electro-mechanical systems.

• Seismology:

  ▪

  Seismic stabilizers, and corrective equipment.

On the other hand, a bibliometric investigation would give a visual perspective using networks visualizations based on the most used and studied elements in the field. On a broader approach, the drawn links exhibit all of the most occurring items in the titles and abstracts of the selected articles (the more precise and specific content, the better the accuracy), for the establishment of interests, thematics, and concerns among the connections that emerge.

4. Bibliometric Analysis over Recent Studies

4.1. Interests, Connections, and Concerns Visualization

Thousands of elements are presented under multiple perspectives and environments, which slowly evolve under the name of development and evolution in science; therefore, Figure 2 highlights 480 items, which can be found at least five times in the analyzed articles (framing only 110 out of 155 that meet the term occurrence filtering criteria).

In the next findings are highlighted, among a variety of usages, the various types and characteristics of the actuators developed using Nitinol (NiTi), which has the property to change its shape to the memorized form when activated thermally or electrically, and then, after inactivation, it returns to the initial state.

Since nickel–titanium is an alloy that depends on the report of nickel and titanium to rewind to its memorized shape at a certain temperature, it can be identified as the normal type, or the superelastic/pseudoelastic type, in shapes such as the following: wires (ultra-fine, round, or flat), plates (flat or waved), springs (helical, micro, flat, or torsion), or rods.

Overall, the performance metrics that characterize an actuator are the force, speed, energy efficiency, and acceleration, followed by durability, operating conditions, volume, and mass (as shown in Figure 3), in combination with other properties like robustness, weight, and other details, for which a specific actuation element may be selected for a certain task.

As for examples of smart materials, there are various mentions like Ni-Ti (nickel–titanium), Fe-Mn-Si (iron–manganese–silicon), Cu-Al-Ni (copper–aluminum–nickel), and so on, but the items related to Nitinol (NiTi alloy, NiTi, etc.) (Figure 3) occurs the most times among the selected papers.

4.2. Temporal Analysis

Researchers are always discussing the evolution of development, and, then analyzing it through a filter over the past; therefore, in 2019, at least 20 papers refers to nickel–titanium, and they compile subjects such as the actuator performance increase [82], nanomechanical testing [83], biomedical applications [84], Voronoi-based reconstruction [85], uniaxial loading [86], SMA/Kapton composites [87], thermal–mechanical cycling training [88], anisotropic compressive strength [89], actuation systems [90], adhesion work [91], and so on.

From 2020, 24 identified articles highlight self-centering energy-dissipation braces [58], micromechanical strain partitioning [61], two-step phase transition [62], novel NiTi smart structures [65], post heat treatment methods [67], machining accuracy [68], critical loading conditions [71], graded materials [73], non-recoverable strain [76], bionic manipulator [78], e-mobility [81], among others. Darker green dots (as shown in Figure 4) indicate more specific items like fiber, actuator, application, voltage, martensitic transformation, and layer, among others, to help sustain the developed system.

In 2021, 28 papers refer to the decay of Ni₄Ti₃ and Ni₃Ti precipitates [31], micro-electro-mechanical-system [33], cyclic shear loading [34], torsional loading [35], interfacial shear strength [38], welding [40], the elastocaloric effect [42], lath martensites and dislocations [46], biocompatibility [47], etc.

From 2022, there were observed 30 works of research about wire electrical discharge machining [3], Ni₄Ti₃ precipitates [4], soft actuators [7], micro-electro-mechanical systems [10], X-ray diffraction [12], high accuracy [16], vacuum environment [19], lattices/stents [22], elastocaloric air cooler [23], scanning and light beam deflection [25], critical energy release rate [26], low-speed drive system [28], superelasticity/pseudoelasticity of nickel–titanium shape memory alloy [29], and yield surface [30]. Others focus on more precise things like soft robotics, viscosity, and thermal control, which are highlighted with brighter green dots (Figure 4).

In 2023, there were published 20 articles with a focus on actuators [116,117,118,120], vibration dampers [119], micro-actuators [121,123], lightweight actuators [122], Nitinol (NiTi) experimenting stands [124,125], temperature regulation to increase performance [120,126,128], high-loaded shape memory alloy actuators [127], haptic wearable devices [133], independent actuation [130], and so on.

Last year (2024), there was a focus on actuators, robotics, origami structures [137], structural elements [138], deep-sea manipulation [139], heat engines [140], nickel–titanium texturing in single or two layers [141], twisting wrist actuators [143], actuators for payloads displacement [145], the servomechanism of a rotator-type joint [147], flapping-wing micro-aerial vehicles [152], photoactuators [153], etc.

5. Research Decision

The summarized knowledge offers a broader perspective over the research landscape surrounding Nitinol (NiTi) and its applications, particularly in actuators, as evidenced by linking visualizations, temporal analyses, and key terms, while this investigation highlights the growing interest in shape memory alloys, especially nickel–titanium, across major fields.

The same literature describes the Nitinol (NiTi) hysteresis, thermo-mechanical behavior, and actuation performance, providing critical insights into the material’s thermo-mechanical behavior and performance metrics, insights that directly inspire the design and testing of the angular actuators. It offers valuable context for understanding the nickel–titanium potential in dynamic, temperature-driven applications, such as the angular actuation observed in developed actuator under heating and cooling cycles.

The identified trends and perspectives, in particular, the focus on testing models of Nitinol-based (NiTi) devices, suggests that such dynamic modeling is an essential step to address the limitations in reproducibility and performance that are demanded in the research and industry field. The temporal analysis shows a growing interest in performance metrics like displacement speed, which can be observed, and then modeled to predict, through simulation, the actuator’s response under thermal cycling and dynamic loading.

These analyses over the technical concerns provide a foundation for interpreting the angular displacement as a manifestation of the martensitic transformation or elastic recovery, thus linking the theoretical background with the revealed data.

The exposed demands, like the increasing focus on actuator thermal cycling, dynamic behavior, and evolving applications, aligns closely with the revealed experimental model and test in Section 8 and Section 9, for which a Nitinol (NiTi) spring-based angular actuator is developed and tested. This integration sets the stage for Section 10 and Section 11 which reveals the analytical modeling and simulation of the dynamic behavior of the same prototype of nickel–titanium spring-based angular actuator, as a function of time, using MATLAB and Simulink R2022b software environment [157].

6. Design Proposal

6.1. Opportunity

Regarding the previously revealed networks of interests grouped in Figure 2, of the detailed links in Figure 3, or of the frequent concerns in Figure 4, they highlight and confirm the relevant thematics for the treated scientific subjects (“actuator”, “shape memory alloy”, and “nitinol”), together with the emphasized terms (“system”, “mechanism”, “temperature”, “force”, “model”, and “application”), in association with the predominant period of demand (from 2018 to 2024), underlining the scientific potential (it is proven that the Nitinol is a tool in actuality, which is becoming increasingly popular, used in various forms and combinations of actuators), so that interest in the choice made is stimulated by the multitude of constructive variants of the ensembles of which it can be a part and within which it can be studied.

6.2. Problem

Regarding the cited sources of scientific knowledge, they discuss various solutions, but it is not certain whether they can simultaneously provide a repetitive angular thermo-mechanical actuation, developing a sufficiently useful force, at a wide angle and for each control position, through constructive simplicity and being able to be reproduced whenever necessary; thus, each technical problem could be improved by a new solution.

6.3. Objective

The main target is to achieve a solution different from the existing ones, in the form of an actuator with an angular displacement as wide as possible, with two-way movement (in two directions), which develops a relevant force, being permanently tensioned, based on thermo-mechanical actuation that can be repeated, in such a way that its dynamic behavior (output response—displacement) can be mathematically described as a function of a variable on which the actuation phenomenon depends (input reference—temperature), which can subsequently be used for various applications.

6.4. Novelty

The solution presents novelty by transforming the linear displacement of a thermo-mechanical actuation spring into angular displacement. Solving this technical gap in a different way from other existing solutions, or those capable of similar results, this approach combines different constructive elements and ensures the proposed functionality, while not being possible to be compared in terms of construction and performance with the existing solutions.

7. Modeling Assumptions

Intelligent materials with shape memory properties like those made of metallic alloys such as nickel–titanium exhibit a characteristic of state change (martensite or austenite), respectively, of temperature-sensitive mechanical actuation (e.g., straining or relaxation), around the constructive transformation temperature [158], with a transition cycle with a hysteresis loop (as shown in Figure 5). These actuation springs are used as elements of an actuator; although this characteristic underlies the generic dependence between the input quantity and the output quantity, its representation can be influenced by the constrictive particularities (frictional forces, mechanical stresses, angular stresses, non-uniformities, etc.) [159,160].

At the same time, the connection between the physical heating/cooling speed and the mechanical actuation speed can be considered ideal since the temporal differences in reaction between temperature and force are negligible. The displacement can be practically modeled only in the form of a temperature-dependent predictive curve/fitting function [161,162].

Such simple links/relationships, in the form of interpolated lookup tables or approximate mathematical models, can be candidates for constituting simulation models regarding the analytical behavior of the actuator for different simulation scenarios of thermal actuation (with natural/forced heating/cooling, a variable rate of variation, and the consequent behavioral response), hence the possibility of mathematical association and analytical study [163].

Additionally, according to the parameters and constructive properties of the available actuation spring (and considering their modification with an additional margin of ±25%) and according to various mathematical models (e.g., Newton, Lumped—single stage, Lumped—multiple stage, Brinson, Tanka, and Liang and Rogers) (for which, as is appropriate, any other/unknown parameters can be approximated based on generic variants with the same base characteristics). For the numerical approximation of the heating or cooling duration, and, respectively, the actuation speed upon contraction or relaxation, its behavior can be anticipated.

Therefore, in a scenario of instantaneous immersion in water at a temperature of 90 °C, it can be mathematically anticipated that the thermal/mechanical transition takes at most 6 s (in the worst case), until the actuation spring reaches a temperature of 86.75 °C (approx. 95% heated), and, for a scenario of instantaneous exposure to air at a temperature of 20 °C, the thermal/mechanical transition takes at most 600 s (in the worst case), until the actuation spring reaches a temperature of 28.25 °C (approx. 95% cooled) in the case of mechanical tension with a force of up to 10 N.

Depending on the needs, the transition times can be forcibly reduced and the actuator performance maximized, the heating phenomenon can be increased through the electrical power supply, and the cooling phenomenon can be increased through ventilation, hence the importance of the mathematical availability of a temperature-dependent displacement function.

8. Experimental Model Regarding the Nitinol (NiTi) Spring-Based Angular Actuator

8.1. Actuation Element

The nickel–titanium alloy is the emerging point in the following experiments; thus, multiple samples were purchased in form of usual Nitinol (NiTi) springs (as shown in Figure 6), for which the prototype of angular actuator is based on a 50%-Ni and 50%-Ti actuation spring for assuring actuation in form of angular displacements.

Nitinol (NiTi) springs are resistant to damp environments or chemicals without degrading rapidly and are also corrosion resistant, while they can be made from both usual and elastic Nickel-Titanium. Nitinol (NiTi) springs are used in various fields including medical devices (such as stents and guide wires), robotics, and aerospace. Their ability to adapt and recover after deformation makes them valuable in complex systems.

The properties below consist of the characteristics and parameters of the Nitinol (NiTi) element used in the construction of the actuator, also considered for some of the modeling assumptions:

• Composition: 50%-Ni, 50%-Ti;
• Total mass: approx. 6 g;
• Total length: 45 mm (clamped) + 30 mm (reserve) = approx. 75 mm;
• Total turns: 34 (clamped) + 24 (reserve) = 58;
• Wire diameter: approx. 1.2 mm;
• Diameter of the coil: approx. 6 mm;
• Stretching capacity: 4×;
• Transition temperature: 45 °C (active state above transition temperature).

8.2. Constructive Description

The prototype assembled for testing has the role of experimentally validating the angular actuation functionality, with an anticipated hysteresis characteristic, on which the actuator construction leaves its mark.

The actuator in Figure 7 consists of a Nitinol (NiTi) spring (15), with an effective clamped length of 45 mm, connected to a compensation steel spring (6), a spring clamping system (11), and a spring contraction and tension monitoring system. A rotation axis for actuation is assured by the turning rod (16), on which the adjustable bolt (17) is installed for gripping mechanical loads (if any is used), as well as two fixed pillars (14), to hold the steel and nickel–titanium springs, all mounted perpendicular to the base plate (13).

In the construction of the angular actuator experimental model in Figure 8, we used a heat-resistant vessel (1), in which the actuator sits submerged in immersion medium (3). The immersion liquid (3.5 L of tap water) is heated by heating resistance (2), mounted on the rim of the thermal vessel. The temperature variation is measured with a thermometer (5), attached to a holder (8), and a protractor (9), for visualizing the angle of displacement of the indicator needle (10), mounted on the holder (7). The indicator needle is located at the end of its holder (4), which is clamped to the support plate (18).

The Nitinol (NiTi) actuation spring (black—lower) is memorized so that, at a temperature above the transformation temperature of 45 °C, it contracts (becomes active), and, at temperatures lower than this value, it is flexible and stretches (becomes inactive), due to the counterforce of metallic spring (silver—upper), returning to its initial shape.

It should be mentioned that the Nitinol (NiTi) actuation spring has a 30 mm reserve length (12) from which the system can be adjusted.

8.3. Operation Description

The operation tests are based on the experimental model presented above, in which the actuator is positioned in the heat-resistant vessel (1), which creates a favorable operating environment by holding the immersion fluid (3.5 L of tap water). Using the heating resistance (2), the temperature of water will be controlled to observe the behavior of turning rod (16), at different thermal stages and equilibrium positions, changed due to the contracted/stretched actuation spring (15), while the steel spring (6) is tensioned/released.

Firstly, the heating resistance (2) is introduced in the immersion medium (3), for heating and contraction/tensioning of the active part (15) of the actuator, and mechanical tensioning of the passive part (6).

Secondly, the heating resistance (2) is taken out of the immersion medium (3), for cooling and stretching/releasing of the Nitinol (NiTi) spring (15), and mechanical releasing of the steel spring (6).

Ambiental temperature at the time of the experiment was measured to be 20 °C.

A change in temperature to 30 °C is considered as the first observable point to producing an angular actuation, but, also above the temperature of 90 °C, the actuation spring will no longer move. Even if the immersion liquid (3.5 L of tap water) temperature is raised to 95 °C, there is no further angular reaction after this threshold.

Several displacement positions of the Nitinol (NiTi) spring-based angular actuator are shown in Figure 9, the initial position at 0° and maximum displacement at 158°.

9. Experimental Results

A scenario for practical testing was chosen to highlight the practical functionality of the angular actuator, in accordance with the role that the designed prototype must fulfill.

It is noted that the turning rod and adjustable bolt is free of any mechanical loads, being driven by the assembly between the actuation spring and compensation spring, while it constitutes a point of forces in balance, displaced when driven due to the rebalancing of the compensation tension which exercises a linear mechanical stress on the actuation spring, both contributing to a wide angular movement of a near-zero mechanical load at the level of the rotation axis.

For data acquisition, the experimental model is ready to be submerged in water; then, by transferring the thermal energy and varying its temperature, the provided thermo-sensitive Nitinol (NiTi) spring causes the actuator to actively contract or inactively stretch, as seen from the angular displacement it produces.

9.1. Functional (Static) Testing Results

Figure 10 shows the characteristic of actuator displacement as a function of the heating temperature. The amount of displacement is relatively small between 20 °C and 60 °C, but the displacement visibly increases with temperature. A jump occurs between 70 °C and 80 °C, when the displacement increases from 43° to 150°. The characteristic emphasizes the sudden displacement that the actuator makes when the immersion fluid (3.5 L of tap water) reaches a temperature of 70 °C, causing a displacement of 107°. At 90 °C, the displacement reaches 158°. Even if the temperature is raised to 95 °C, the maximum displacement angle remains the same.

Figure 11 shows the characteristic of the angular displacement of the actuator as a function of the cooling temperature, which shows a constant change in the angular displacement of the actuator down to a temperature of 60 °C at which the spring of nickel–titanium contracts, suddenly returning to a position indicating 35°, followed by continuous cooling with frequent displacement jumps due to the uneven actuator grip with the turning rod until it reaches the initial displacement of 20°.

It should be noted that a more representative mechanical characteristic would be the force arm developed at the turning rod level when the compensation spring keeps it in its initial position (cooled position) or when the actuation spring brings it to its final position (heated position) separate from the existing linear force with which the actuation spring is tensioned by the compensation spring.

9.2. Additional (Dynamic) Testing Observations

Additionally, for an instantaneous immersion test in water at a temperature of 90 °C, it was observed that the (wet) actuation spring heats up and changes its shape in approx. 2–3 s. For an instantaneous exposure test in air at a temperature of 20 °C, it was observed that the (dry) actuation spring cools down and returns to its original shape in approx. 250–350 s (and, for the attempt where it is forcedly cooled with air—not quantifiable, in approx. 17–23 s). In each case, they are mechanically tensioned with a force of up to 10 N.

10. Analytical Modeling Regarding the Nitinol (NiTi) Spring-Based Angular Actuator Based on Experimental Data

The model for the simulation has the role of analytically validating the experimental functionality with the observed characteristic of hysteresis, specific to the constructive variant of the actuator, for which it is expressed through the approximated mathematical model (with an approximation error) instead of the alternative of an interpolated lookup table (with an interpolation error).

10.1. Methodology

The experimental results from Section 9, such as the angular displacement versus heating and cooling temperature characteristics (Figure 10 and Figure 11) can be leveraged to develop a simulation framework that reveals a time-dependent response of the built prototype.

A numeric method like polynomial approximation would enable the analytical representation of the angular actuator’s behavior in continuous time facilitating analytical studies and dynamic analysis enlightening the dependency of the actuator’s displacement versus temperature, a capability that is possible by manipulating dependent equations within the MATLAB and Simulink R2022b software environment [158], further addressing the need for a deeper connection between experimental and analytical modeling.

Therefore, the approach consists of using the method of equation-based polynomial approximation over the acquired data points from the experimental model to describe its equivalent approximative behavior model where there is an approximative displacement–temperature relationship (e.g., the polynomial approximation of order 6 of the points in Figure 10 and Figure 11). It is modeled mathematically within an equivalent simulation model under the MATLAB and Simulink R2022b software environment [157], capable of revealing complementary analytical results for various scenarios underlining the Nitinol (NiTi) spring-based angular actuator dynamic behavior under time-varying thermal conditions.

10.2. Mathematical Model

As for the development of an equivalent simulation model through mathematical modeling, it consists of an alternating switch between use of the Equation (1) of the fitting curve in Figure 10 for increasing temperature scenarios, or of the Equation (2) of the fitting curve in Figure 11 for decreasing temperature scenarios, for which the displacement is obtained with the MATLAB Function, as a variation of the temperature [157]:

y_{1 (heating)} = 5⁻⁹x⁶ − 2⁻⁶x⁵ + 0.0004x⁴ − 0.0255x³ + 0.9295x² − 16.028x + 103.38

(1)

y_{2 (cooling)} = −1⁻⁸x⁶ + 5⁻⁶x⁵ − 0.0007x⁴ + 0.0553x³ − 2.0421x² + 36.672x − 255.4

(2)

This pair of equations is designed to be used only for the simulation of temperature-dependent displacements in time like the various displacement-temperature study scenarios for an ideal and approximative case, on the basis of the Nitinol (NiTi) actuation spring standalone temperature (as it is, without being related to any thermodynamic phenomenon that can affect it, such as heat transfer, which shall be considered in the reference form of the temperature evolution in time, used to represent these two equations).

11. Analytical Results

A scenario for the theoretical simulation was chosen in order to highlight the connection between the functional (static) and additional (dynamic) experimental observations, in the form of the behavior that the designed prototype can exhibit in different situations, as an immediate reaction to the delayed modification of the reference parameter.

For static data generation, additional mathematical processing is carried out for enriching the representation of experimental results so that, by assuring an interpolated lookup table of the existent data, it can serve as a finer reference for static behavior for the output comparison of equivalent-approached models.

For dynamic data generation, the equivalent simulation model is ready for running under relevant scenarios, so that, by imposing a well-modeled time-dependent temperature, this gives the actuators dynamic behavior for active contraction or inactive stretching, as seen from the approximative angular displacement.

11.1. Static Simulation Comparison Under Different Approaches

Figure 12 shows the characteristic of actuator displacement as an estimation of the heating/cooling temperature. The evolution of displacement is predicted by computing the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), and the fine filling of each thermal cycle dataset.

11.2. Dynamic Simulation Behavior Under Approximative Approach

Figure 13 shows the characteristic of actuator displacement as a function of the heating temperature. The amount of displacement is in accordance with the variation form/speed of the temperature and point-by-point behavior as described by the polynomial approximation of order 6 in Equation (1), specific for the heating cycle.

Figure 14 shows the characteristic of actuator displacement as a function of the cooling temperature. The amount of displacement is in accordance with the variation form/speed of the temperature and point-by-point behavior as described by the polynomial approximation of order 6 in Equation (2), specific for the cooling cycle.

12. Further Discussions

The paper presents the development outcomes of a prototype of the angular actuator that uses a spring of nickel–titanium for actuation, beginning with the contextual finding of the latest trends and opportunities for solutions in the sphere of Nitinol (NiTi) devices.

The experimental behavior of the angular actuator upon forced heating, then the natural cooling of the spring made of nickel–titanium in water, is visible in Figure 15, which is obtained by the polynomial approximation of order 6 of the gathered experimental results.

Analyzing the heating displacement curve, it can be observed that, in the range between 20 °C and 30 °C, the displacement in relation to the temperature increase occurs slowly and at insignificant values. After the temperature of 30 °C, the actuator changes its behavior, as an increased rate displacement occurs linearly up to the temperature of 75 °C, as, for every increase in temperature by 10 °C, a displacement of 30° occurs. After the temperature of 70 °C, it can be observed that the displacement stabilizes, with its variation with temperature being very small.

It is concluded that, at the temperature of 90 °C, the maximum angle of displacement of 158° and the reaching of the memorized shape happen in a time of approx. 45 min (force heating of 3.5 L of tap water submerging the actuator), as well as the return from the temperature of 90 °C to that of 20 °C and the achieving of the initial position, which happens in approx. 200 min (natural cooling of 3.5 L of tap water submerging the actuator), reaching the stretched shape.

The analytical behavior of the angular actuator upon heating in an exponential growth manner, then cooling in an exponential decay behavior, both related to the transitory response of the thermal state change phenomenon in a plausible scenario of dynamic behavior, is visible in Figure 16. The figure was obtained by switching between the use of Equation (1) or the use of Equation (2) as appropriate and according to the transient reference.

Analyzing the overall displacement evolution, the approximative behavior expresses the experimental functionality approximated by the corresponding analytical model in Equations (1) and (2) so that the angular reaction is noticeable beginning with a delay after the increasing/decreasing of the temperature followed by a higher variation speed in time but finishing with a hastening before the stabilization of the temperature.

It is concluded that the analytical behavior approximatively matches the experimental behavior, although the reaction time can be only as fast or as slow as the temperature growth or decay time-variation that is chosen, never exceeding its variation duration.

13. Conclusive Notes

13.1. Notes over Research

The research on the development of the angular actuator, presents novelty by analyzing the connection trends between research subjects. We introduce interest in an attractive material in various technical subjects in the search of newly prototyped/studied solutions for which it is proposed to join it to the existing knowledge, revealing a constructive form (yet undocumented) of Nitinol-based (NiTi) angular actuators for compatible applications, susceptible to be adapted into specific ones. Moreover, the performances of both models (experimental and analytical) are shown, with the possibility of customization being a useful aspect in the scientific contribution at a global level.

This research is essential for researchers demanding to experiment/simulate alternatives starting from a basic version of an angular actuator which meets the trends and needs of development and research constituted as a favorable ensemble of elements validated experimentally and analytically, so, by reproducing or changing the study conditions, it can serve as the starting point in the decision to design different, more complex, or higher performing actuators.

13.2. Notes on Design

In relation to the functionality offered by the solution, that of a thermally induced, natural, or forced angular actuation, the authors state that it manifests in light of the research circumstances and the constructive particularities presented. Even if, due to its simplicity, it may not be considered an innovative activity in the sense of the patentability criteria of such solutions, the constructive form shall be useful at least in related fields where research and innovation also take into account generic prototypes to compose personalized constructive variants for specific applications of the nature of the one proposed and studied by us.

13.3. Notes over Functionality

Due to the constructive form of the disclosed angular actuator and from the combination method of the elements with actuation capabilities which were assembled, tested, and observed for how they behave, through the connection with the experimental data acquired from the experimental model and approximately reproduced by the disclosed analytical model, the authors point out the basic functionality initially proposed of thermally ensured angular displacement (through a heating/cooling process, whatever it may be) ensured by this actuator prototype that involves the use of nickel–titanium.

13.4. Validation of Experimental Model

The prototype assures a full actuation stroke of 158°, which is able to exhibit a movement while resisting under an internal mechanical tension of up to 10 N, linearly dependent on the angular position of the actuator. At an actuation radius of 7.5 mm, manifested under an internal tensioning angle of 35°, the movement transmitted over the turning rod may fluctuate with each actuation because the coils of the actuation spring are unevenly distributed on the friction surface of the turning rod. Due to this fact, they do not ensure a perfectly identical mechanical coupling from one actuation to another.

13.5. Validation of Experimental Results

We support the fact that the angular displacement as a function of temperature developed by the actuator, from those observed, is manifested in accordance with the experimental data, which validates those anticipated.

The functional (static) experimental results which express the fact that the angular displacement is dependent on the temperature of the actuator/the environment in which it is located are assessed as having a relative error up to ±5%, being the result of averaging the measurements of five distinctive actuations performed under the same scenario.

Even though, in this case, the obtained data points are considered to be precise, the interpolation of these data can be achieved by different methods (LINEAR, SPLINE, CUBIC, AKIMA, and PCHIP). It has been shown that a close representation of the visible behavior can be obtained through the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation method.

Additional (dynamic) experimental observations which complete the fact that the angular displacement constitutes an immediate reaction to the delayed change in the temperature of the actuation spring due to thermal transfer are considered to have a relative error in accordance with the range of absolute values specified.

13.6. Validation of Analytical Model

The simulation assures an approximate transposition of the experimental model into an analytical model; although it constitutes the closest mathematical function that could be fitted to approximately reproduce the angular position of the actuator depending on the temperature of the actuating spring, it can still be adjusted to be more precise.

13.7. Validation of Analytical Results

We support the fact that the thermally controlled angular actuation of the actuator, approximated by the mathematical model from those demonstrated, is manifested as closely as possible to the experiments carried out and to the experimental data on the basis of which it was created, with the mention that it is malleable in parameterization through the variables of which it is composed, unlike the equivalent of interpolation, that would stay at the basis for completing lookup tables without a mathematical foundation, but with a close reproduction of the described behavior.

The static analytical results describe the fact that the angular displacement is dependent on the actuator temperature, but the only error that can be appreciated arises from the difference between the approximate analytical results and interpolated experimental results as shown in Figure 17.

It turns out that the error of the evolution of the mathematical model underlying the approximate analytical results compared to the behavior of the experimental model underlying the interpolated experimental results is approx. 33% for the fitting curve of the heating displacement phenomenon and approx. 27% for the fitting curve of the cooling displacement phenomenon, against the prediction.

Even though, in this case, the involvement of mathematical modeling makes the simulated output data points always comply with the input simulation scenario since it approximates a close form of an experimental behavior enriched the most by interpolation, for this has shown that a well-approximated mathematical model can be obtained by a polynomial function of the sixth degree.

The dynamic analytical results highlight the fact that the behavior constitutes an immediate reaction (with a correct variation form, of the sigmoidal type) to the delayed change in the reference parameter (with a correct variation form, of the exponential type), which is appreciated as having a correct dynamic representation.

13.8. Conclusion

The extensive usage of the presented angular actuator is achievable due to its constructive simplicity and functionality of general utility, whose performance can be reproduced whenever necessary due to the fully disclosed experimental model and analytical model. Depending on the specific needs in the field, offering industrial applicability both for a wide spectrum of applications and for the spectrum of interests identified in the bibliometric concluded investigation, it raises future scientific curiosity.

Since temperature variation generates reversible structural transformations in the actuation spring of nickel–titanium between the martensite and austenite phases, thus producing a significant angular displacement, this makes the proposed design suitable for the following applications in power engineering:

• Automatic drives (for integration into solar collectors or concentrators, which actuates a valve or piston when the fluid reaches a preset temperature threshold);
• Automated conditioning circuits (for opening loops for secondary cooling/heating and activating air/water mixing valves);
• Thermal valves: cooling in turbines, thermal plants, pumps, etc.;
• Ventilation blades: thermal power plants, solar panels, greenhouses, etc.;
• Overheat protection systems can release pressure at critical temperatures.

14. Future Directions

This research is rooted in the previous studies and research from our laboratory, such as devices with intelligent materials [108,161,162] used in energetics, special actuators [102], electro and thermomechanical actuators [109,159,163], linear heliothermic actuators [110], and electromechanical micropump [111,160], but we also used Nitinol (NiTi) to study its lifespan [18] and to develop special actuators and materials with shape memory [112], clutch-type thermocoupling [113], nickel–titanium-operated micropump [114], a locking system [115], and electric mobility [155], and we hope it will result in the development of newer devices and equipment with applications in electrical engineering.

In future research, the form of the nickel–titanium alloy that is appropriate for each applicability domain can be identified, as there are certain connections between the type of the implied material, its related elasticity and durability, and the shapes used in certain applications.

The future of research in this area is taking fast steps and the trends are always going to change. The industry has a sustained interest in research that uses smart materials as an alternative for the usual ones. Future directions may lead to deeper and more precise research in the field of Nitinol-based (NiTi) devices.