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Actuators are used everywhere and create controlled motion by applying the correct excitation force or torque to perform various operations in manufacturing and industrial automation. The need for faster, smaller and more efficient drives is driving innovation in drive design. Shape Memory Alloy (SMA) drives offer a number of advantages over conventional drives, including a high power-to-weight ratio. In this dissertation, a two-feathered SMA-based actuator was developed that combines the advantages of the feathery muscles of biological systems and the unique properties of SMAs. This study explores and extends previous SMA actuators by developing a mathematical model of the new actuator based on the bimodal SMA wire arrangement and testing it experimentally. Compared to known drives based on SMA, the actuation force of the new drive is at least 5 times higher (up to 150 N). The corresponding weight loss is about 67%. The results of sensitivity analysis of mathematical models are useful for tuning design parameters and understanding key parameters. This study further presents a multi-level Nth stage drive that can be used to further enhance dynamics. SMA-based dipvalerate muscle actuators have a wide range of applications, from building automation to precision drug delivery systems.
Biological systems, such as the muscular structures of mammals, can activate many subtle actuators1. Mammals have different muscle structures, each serving a specific purpose. However, much of the structure of mammalian muscle tissue can be divided into two broad categories. Parallel and pennate. In the hamstrings and other flexors, as the name suggests, the parallel musculature has muscle fibers parallel to the central tendon. The chain of muscle fibers is lined up and functionally connected by the connective tissue around them. Although these muscles are said to have a large excursion (percentage shortening), their overall muscle strength is very limited. In contrast, in the triceps calf muscle2 (lateral gastrocnemius (GL)3, medial gastrocnemius (GM)4 and soleus (SOL)) and extensor femoris (quadriceps)5,6 pennate muscle tissue is found in each muscle7. In a pinnate structure, the muscle fibers in the bipennate musculature are present on both sides of the central tendon at oblique angles (pinnate angles). Pennate comes from the Latin word “penna”, which means “pen”, and, as shown in fig. 1 has a feather-like appearance. The fibers of the pennate muscles are shorter and angled to the longitudinal axis of the muscle. Due to the pinnate structure, the overall mobility of these muscles is reduced, which leads to the transverse and longitudinal components of the shortening process. On the other hand, activation of these muscles leads to higher overall muscle strength due to the way physiological cross-sectional area is measured. Therefore, for a given cross-sectional area, pennate muscles will be stronger and will generate higher forces than muscles with parallel fibers. Forces generated by individual fibers generate muscle forces at a macroscopic level in that muscle tissue. In addition, it has such unique properties as fast shrinkage, protection against tensile damage, cushioning. It transforms the relationship between fiber input and muscle power output by exploiting the unique features and geometric complexity of the fiber arrangement associated with muscle lines of action.
Shown are schematic diagrams of existing SMA-based actuator designs in relation to a bimodal muscular architecture, for example (a), representing the interaction of tactile force in which a hand-shaped device actuated by SMA wires is mounted on a two-wheeled autonomous mobile robot9,10. , (b) Robotic orbital prosthesis with antagonistically placed SMA spring-loaded orbital prosthesis. The position of the prosthetic eye is controlled by a signal from the ocular muscle of the eye11, (c) SMA actuators are ideal for underwater applications due to their high frequency response and low bandwidth. In this configuration, SMA actuators are used to create wave motion by simulating the movement of fish, (d) SMA actuators are used to create a micro pipe inspection robot that can use the inch worm motion principle, controlled by the movement of SMA wires inside channel 10, (e) shows the direction of contraction muscle fibers and generating contractile force in gastrocnemius tissue, (f) shows SMA wires arranged in the form of muscle fibers in the pennate muscle structure.
Actuators have become an important part of mechanical systems due to their wide range of applications. Therefore, the need for smaller, faster and more efficient drives becomes critical. Despite their advantages, traditional drives have proven to be expensive and time-consuming to maintain. Hydraulic and pneumatic actuators are complex and expensive and are subject to wear, lubrication problems and component failure. In response to demand, the focus is on developing cost-effective, sizing-optimized and advanced actuators based on smart materials. Ongoing research is looking at shape memory alloy (SMA) layered actuators to meet this need. Hierarchical actuators are unique in that they combine many discrete actuators into geometrically complex macro scale subsystems to provide increased and expanded functionality. In this regard, the human muscle tissue described above provides an excellent multilayered example of such multilayered actuation. The current study describes a multi-level SMA drive with several individual drive elements (SMA wires) aligned to the fiber orientations present in bimodal muscles, which improves the overall drive performance.
The main purpose of an actuator is to generate mechanical power output such as force and displacement by converting electrical energy. Shape memory alloys are a class of “smart” materials that can restore their shape at high temperatures. Under high loads, an increase in the temperature of the SMA wire leads to shape recovery, resulting in a higher actuation energy density compared to various directly bonded smart materials. At the same time, under mechanical loads, SMAs become brittle. Under certain conditions, a cyclic load can absorb and release mechanical energy, exhibiting reversible hysteretic shape changes. These unique properties make SMA ideal for sensors, vibration damping and especially actuators12. With this in mind, there has been a lot of research into SMA-based drives. It should be noted that SMA-based actuators are designed to provide translational and rotary motion for a variety of applications13,14,15. Although some rotary actuators have been developed, researchers are particularly interested in linear actuators. These linear actuators can be divided into three types of actuators: one-dimensional, displacement and differential actuators 16 . Initially, hybrid drives were created in combination with SMA and other conventional drives. One such example of an SMA-based hybrid linear actuator is the use of an SMA wire with a DC motor to provide an output force of around 100 N and significant displacement17.
One of the first developments in drives based entirely on SMA was the SMA parallel drive. Using multiple SMA wires, the SMA-based parallel drive is designed to increase the power capability of the drive by placing all SMA18 wires in parallel. Parallel connection of actuators not only requires more power, but also limits the output power of a single wire. Another disadvantage of SMA based actuators is the limited travel they can achieve. To solve this problem, an SMA cable beam was created containing a deflected flexible beam to increase displacement and achieve linear motion, but did not generate higher forces19. Soft deformable structures and fabrics for robots based on shape memory alloys have been developed primarily for impact amplification20,21,22. For applications where high speeds are required, compact driven pumps have been reported using thin film SMAs for micropump driven applications23. The drive frequency of the thin film SMA membrane is a key factor in controlling the speed of the driver. Therefore, SMA linear motors have a better dynamic response than SMA spring or rod motors. Soft robotics and gripping technology are two other applications that use SMA-based actuators. For example, to replace the standard actuator used in the 25 N space clamp, a shape memory alloy parallel actuator 24 was developed. In another case, an SMA soft actuator was fabricated based on a wire with an embedded matrix capable of producing a maximum pulling force of 30 N. Due to their mechanical properties, SMAs are also used to produce actuators that mimic biological phenomena. One such development includes a 12-cell robot that is a biomimetic of an earthworm-like organism with SMA to generate a sinusoidal motion to fire26,27.
As mentioned earlier, there is a limit to the maximum force that can be obtained from existing SMA-based actuators. To address this issue, this study presents a biomimetic bimodal muscle structure. Driven by shape memory alloy wire. It provides a classification system that includes several shape memory alloy wires. To date, no SMA-based actuators with a similar architecture have been reported in the literature. This unique and novel system based on SMA was developed to study the behavior of SMA during bimodal muscle alignment. Compared to existing SMA-based actuators, the goal of this study was to create a biomimetic dipvalerate actuator to generate significantly higher forces in a small volume. Compared to conventional stepper motor driven drives used in HVAC building automation and control systems, the proposed SMA-based bimodal drive design reduces the weight of the drive mechanism by 67%. In the following, the terms “muscle” and “drive” are used interchangeably. This study investigates the multiphysics simulation of such a drive. The mechanical behavior of such systems has been studied by experimental and analytical methods. Force and temperature distributions were further investigated at an input voltage of 7 V. Subsequently, a parametric analysis was carried out to better understand the relationship between key parameters and the output force. Finally, hierarchical actuators have been envisioned and hierarchical level effects have been proposed as a potential future area for non-magnetic actuators for prosthetic applications. According to the results of the aforementioned studies, the use of a single-stage architecture produces forces at least four to five times higher than reported SMA-based actuators. In addition, the same drive force generated by a multi-level multi-level drive has been shown to be more than ten times that of conventional SMA-based drives. The study then reports key parameters using sensitivity analysis between different designs and input variables. The initial length of the SMA wire (\(l_0\)), the pinnate angle (\(\alpha\)) and the number of single strands (n) in each individual strand have a strong negative effect on the magnitude of the driving force. strength, while the input voltage (energy) turned out to be positively correlated.
SMA wire exhibits the shape memory effect (SME) seen in the nickel-titanium (Ni-Ti) family of alloys. Typically, SMAs exhibit two temperature dependent phases: a low temperature phase and a high temperature phase. Both phases have unique properties due to the presence of different crystal structures. In the austenite phase (high temperature phase) existing above the transformation temperature, the material exhibits high strength and is poorly deformed under load. The alloy behaves like stainless steel, so it is able to withstand higher actuation pressures. Taking advantage of this property of Ni-Ti alloys, the SMA wires are slanted to form an actuator. Appropriate analytical models are developed to understand the fundamental mechanics of the thermal behavior of SMA under the influence of various parameters and various geometries. Good agreement was obtained between the experimental and analytical results.
An experimental study was carried out on the prototype shown in Fig. 9a to evaluate the performance of a bimodal drive based on SMA. Two of these properties, the force generated by the drive (muscle force) and the temperature of the SMA wire (SMA temperature), were measured experimentally. As the voltage difference increases along the entire length of the wire in the drive, the temperature of the wire increases due to the Joule heating effect. The input voltage was applied in two 10-s cycles (shown as red dots in Fig. 2a, b) with a 15-s cooling period between each cycle. The blocking force was measured using a piezoelectric strain gauge, and the temperature distribution of the SMA wire was monitored in real time using a scientific-grade high-resolution LWIR camera (see the characteristics of the equipment used in Table 2). shows that during the high voltage phase, the temperature of the wire increases monotonically, but when no current is flowing, the temperature of the wire continues to fall. In the current experimental setup, the temperature of the SMA wire dropped during the cooling phase, but it was still above the ambient temperature. On fig. 2e shows a snapshot of the temperature on the SMA wire taken from the LWIR camera. On the other hand, in fig. 2a shows the blocking force generated by the drive system. When the muscle force exceeds the restoring force of the spring, the movable arm, as shown in Figure 9a, begins to move. As soon as actuation begins, the movable arm comes into contact with the sensor, creating a body force, as shown in fig. 2c, d. When the maximum temperature is close to \(84\,^{\circ}\hbox {C}\), the maximum observed force is 105 N.
The graph shows the experimental results of the temperature of the SMA wire and the force generated by the SMA-based bimodal actuator during two cycles. The input voltage is applied in two 10 second cycles (shown as red dots) with a 15 second cool down period between each cycle. The SMA wire used for the experiments was a 0.51 mm diameter Flexinol wire from Dynalloy, Inc. (a) The graph shows the experimental force obtained over two cycles, (c, d) shows two independent examples of the action of moving arm actuators on a PACEline CFT/5kN piezoelectric force transducer, (b) the graph shows the maximum temperature of the entire SMA wire during time two cycles, (e) shows a temperature snapshot taken from the SMA wire using the FLIR ResearchIR software LWIR camera. The geometric parameters taken into account in the experiments are given in Table. one.
The simulation results of the mathematical model and the experimental results are compared under the condition of an input voltage of 7V, as shown in Fig.5. According to the results of parametric analysis and in order to avoid the possibility of overheating of the SMA wire, a power of 11.2 W was supplied to the actuator. A programmable DC power supply was used to supply 7V as the input voltage, and a current of 1.6A was measured across the wire. The force generated by the drive and the temperature of the SDR increase when current is applied. With an input voltage of 7V, the maximum output force obtained from the simulation results and experimental results of the first cycle is 78 N and 96 N, respectively. In the second cycle, the maximum output force of the simulation and experimental results was 150 N and 105 N, respectively. The discrepancy between occlusion force measurements and experimental data may be due to the method used to measure occlusion force. The experimental results shown in fig. 5a correspond to the measurement of the locking force, which in turn was measured when the drive shaft was in contact with the PACEline CFT/5kN piezoelectric force transducer, as shown in fig. 2s. Therefore, when the drive shaft is not in contact with the force sensor at the beginning of the cooling zone, the force immediately becomes zero, as shown in Fig. 2d. In addition, other parameters that affect the formation of force in subsequent cycles are the values ​​of the cooling time and the coefficient of convective heat transfer in the previous cycle. From fig. 2b, it can be seen that after a 15 second cooling period, the SMA wire did not reach room temperature and therefore had a higher initial temperature (\(40\,^{\circ }\hbox {C}\)) in the second driving cycle compared to with the first cycle (\(25\, ^{\circ}\hbox {C}\)). Thus, compared with the first cycle, the temperature of the SMA wire during the second heating cycle reaches the initial austenite temperature (\(A_s\)) earlier and stays in the transition period longer, resulting in stress and force. On the other hand, temperature distributions during heating and cooling cycles obtained from experiments and simulations have a high qualitative similarity to examples from thermographic analysis. Comparative analysis of SMA wire thermal data from experiments and simulations showed consistency during heating and cooling cycles and within acceptable tolerances for experimental data. The maximum temperature of the SMA wire, obtained from the results of simulation and experiments of the first cycle, is \(89\,^{\circ }\hbox {C}\) and \(75\,^{\circ }\hbox { C }\, respectively ), and in the second cycle the maximum temperature of the SMA wire is \(94\,^{\circ }\hbox {C}\) and \(83\,^{\circ }\ hbox {C}\). The fundamentally developed model confirms the effect of the shape memory effect. The role of fatigue and overheating was not considered in this review. In the future, the model will be improved to include the stress history of the SMA wire, making it more suitable for engineering applications. The drive output force and SMA temperature plots obtained from the Simulink block are within the allowable tolerances of the experimental data under the condition of an input voltage pulse of 7 V. This confirms the correctness and reliability of the developed mathematical model.
The mathematical model was developed in the MathWorks Simulink R2020b environment using the basic equations described in the Methods section. On fig. 3b shows a block diagram of the Simulink math model. The model was simulated for a 7V input voltage pulse as shown in Fig. 2a, b. The values ​​of the parameters used in the simulation are listed in Table 1. The results of the simulation of transient processes are presented in Figures 1 and 1. Figures 3a and 4. In fig. 4a,b shows the induced voltage in the SMA wire and the force generated by the actuator as a function of time. During reverse transformation (heating), when the SMA wire temperature, \(T < A_s^{\prime}\) (stress-modified austenite phase start temperature), the rate of change of martensite volume fraction (\(\dot{\xi }\)) will be zero. During reverse transformation (heating), when the SMA wire temperature, \(T < A_s^{\prime}\) (stress-modified austenite phase start temperature), the rate of change of martensite volume fraction (\(\dot{\ xi }\)) will be zero. Во время обратного превращения (нагрева), когда температура проволоки SMA, \(T < A_s^{\prime}\) (температура начала аустенитной фазы, модифицированная напряжением), скорость изменения объемной доли мартенсита (\(\dot{\ xi }\)) будет равно нулю. During the reverse transformation (heating), when the temperature of the SMA wire, \(T < A_s^{\prime}\) (stress-modified austenite onset temperature), the rate of change of the martensite volume fraction (\(\dot{\ xi }\ )) will be zero.在反向转变（加热）过程中，当SMA 线温度\(T < A_s^{\prime}\)（应力修正奥氏体相起始温度）时，马氏体体积分数的变化率（\(\dot{\ xi }\)) 将为零。在 反向 转变 （加热） 中 ， 当 当 当 线 温度 \ (t <a_s^{\ prime}=”" \)=”" （应力=”" 修正=”" 奥=”" 氏体=”" 温度）=”" 时=”" 马氏体=”" 体积=”" 分数=”" 变化率=”" （\=”" (=”" \dot{\=”" xi=”" }\))=”" 将为零。<=”" b=”"> При обратном превращении (нагреве) при температуре проволоки СПФ \(T < A_s^{\prime}\) (температура зарождения аустенитной фазы с поправкой на напряжение) скорость изменения объемной доли мартенсита (\( \dot{\ xi }\)) будет равно нулю. During the reverse transformation (heating) at the temperature of the SMA wire \(T < A_s^{\prime}\) (the temperature of the nucleation of the austenite phase, corrected for stress), the rate of change in the volume fraction of martensite (\( \dot{\ xi }\)) will be equals zero. Therefore, the rate of stress change (\(\dot{\sigma}\)) will depend on the strain rate (\(\dot{\epsilon}\)) and the temperature gradient (\(\dot{T} \) ) only with using equation (1). However, as the SMA wire increases in temperature and crosses (\(A_s^{\prime}\)), the austenite phase begins to form, and (\(\dot{\xi}\)) is taken as the given value of the equation ( 3). Therefore, the rate of change of voltage (\(\dot{\sigma}\)) is jointly controlled by \(\dot{\epsilon}, \dot{T}\) and \(\dot{\xi}\) be equal to given in formula (1). This explains the gradient changes observed in the time-varying stress and force maps during the heating cycle, as shown in Fig. 4a, b.
(a) Simulation result showing temperature distribution and stress-induced junction temperature in an SMA-based divalerate actuator. When the wire temperature crosses the austenite transition temperature in the heating stage, the modified austenite transition temperature begins to increase, and similarly, when the wire rod temperature crosses the martensitic transition temperature in the cooling stage, the martensitic transition temperature decreases. SMA for analytical modeling of the actuation process. (For a detailed view of each subsystem of a Simulink model, see the appendix section of the supplementary file.)
The results of the analysis for different parameter distributions are shown for two cycles of the 7V input voltage (10 second warm up cycles and 15 second cool down cycles). While (ac) and (e) depict the distribution over time, on the other hand, (d) and (f) illustrate the distribution with temperature. For the respective input conditions, the maximum observed stress is 106 MPa (less than 345 MPa, wire yield strength), the force is 150 N, the maximum displacement is 270 µm, and the minimum martensitic volume fraction is 0.91. On the other hand, the change in stress and the change in the volume fraction of martensite with temperature are similar to hysteresis characteristics.
The same explanation applies to the direct transformation (cooling) from the austenite phase to the martensite phase, where the SMA wire temperature (T) and the end temperature of the stress-modified martensite phase (\(M_f^{\prime}\ )) is excellent. On fig. 4d,f shows the change in the induced stress (\(\sigma\)) and the volume fraction of martensite (\(\xi\)) in the SMA wire as a function of the change in temperature of the SMA wire (T), for both driving cycles. On fig. Figure 3a shows the change in the temperature of the SMA wire with time depending on the input voltage pulse. As can be seen from the figure, the temperature of the wire continues to increase by providing a heat source at zero voltage and subsequent convective cooling. During heating, the retransformation of martensite to the austenite phase begins when the SMA wire temperature (T) crosses the stress-corrected austenite nucleation temperature (\(A_s^{\prime}\)). During this phase, the SMA wire is compressed and the actuator generates force. Also during cooling, when the temperature of the SMA wire (T) crosses the nucleation temperature of the stress-modified martensite phase (\(M_s^{\prime}\)) there is a positive transition from the austenite phase to the martensite phase. the drive force decreases.
The main qualitative aspects of the bimodal drive based on SMA can be obtained from the simulation results. In the case of a voltage pulse input, the temperature of the SMA wire increases due to the Joule heating effect. The initial value of the martensite volume fraction (\(\xi\)) is set to 1, since the material is initially in a fully martensitic phase. As the wire continues to heat up, the temperature of the SMA wire exceeds the stress-corrected austenite nucleation temperature \(A_s^{\prime}\), resulting in a decrease in the martensite volume fraction, as shown in Figure 4c. In addition, in fig. 4e shows the distribution of strokes of the actuator in time, and in fig. 5 – driving force as a function of time. A related system of equations includes temperature, martensite volume fraction, and stress that develops in the wire, resulting in shrinkage of the SMA wire and the force generated by the actuator. As shown in fig. 4d,f, voltage variation with temperature and martensite volume fraction variation with temperature correspond to the hysteresis characteristics of the SMA in the simulated case at 7 V.
Comparison of driving parameters was obtained through experiments and analytical calculations. The wires were subjected to a pulsed input voltage of 7 V for 10 seconds, then cooled down for 15 seconds (cooling phase) over two cycles. The pinnate angle is set to \(40^{\circ}\) and the initial length of the SMA wire in each single pin leg is set to 83mm. (a) Measuring the driving force with a load cell (b) Monitoring wire temperature with a thermal infrared camera.
In order to understand the influence of physical parameters on the force produced by the drive, an analysis of the sensitivity of the mathematical model to the selected physical parameters was carried out, and the parameters were ranked according to their influence. First, the sampling of model parameters was done using experimental design principles that followed a uniform distribution (see Supplementary Section on Sensitivity Analysis). In this case, the model parameters include input voltage (\(V_{in}\)), initial SMA wire length (\(l_0\)), triangle angle (\(\alpha\)), bias spring constant (\( K_x\ )), the convective heat transfer coefficient (\(h_T\)) and the number of unimodal branches (n). In the next step, peak muscle strength was chosen as a study design requirement and the parametric effects of each set of variables on strength were obtained. The tornado plots for the sensitivity analysis were derived from the correlation coefficients for each parameter, as shown in Fig. 6a.
(a) The correlation coefficient values ​​of the model parameters and their effect on the maximum output force of 2500 unique groups of the above model parameters are shown in the tornado plot. The graph shows the rank correlation of several indicators. It is clear that \(V_{in}\) is the only parameter with a positive correlation, and \(l_0\) is the parameter with the highest negative correlation. The effect of various parameters in various combinations on peak muscle strength is shown in (b, c). \(K_x\) ranges from 400 to 800 N/m and n ranges from 4 to 24. Voltage (\(V_{in}\)) changed from 4V to 10V, wire length (\(l_{0 } \)) changed from 40 to 100 mm, and the tail angle (\ (\alpha \)) varied from \ (20 – 60 \, ^ {\circ }\).
On fig. 6a shows a tornado plot of various correlation coefficients for each parameter with peak drive force design requirements. From fig. 6a it can be seen that the voltage parameter (\(V_{in}\)) is directly related to the maximum output force, and the convective heat transfer coefficient (\(h_T\)), flame angle (\ ( \alpha\)) , displacement spring constant ( \(K_x\)) is negatively correlated with the output force and the initial length (\(l_0\)) of the SMA wire, and the number of unimodal branches (n) shows a strong inverse correlation In the case of direct correlation In the case of a higher value of the voltage correlation coefficient (\(V_ {in}\)) indicates that this parameter has the greatest effect on the power output. Another similar analysis measures the peak force by evaluating the effect of different parameters in different combinations of the two computational spaces, as shown in Fig. 6b, c. \(V_{in}\) and \(l_0\), \(\alpha\) and \(l_0\) have similar patterns, and the graph shows that \(V_{in}\) and \(\alpha\ ) and \(\alpha\) have similar patterns. Smaller values ​​of \(l_0\) result in higher peak forces. The other two plots are consistent with Figure 6a, where n and \(K_x\) are negatively correlated and \(V_{in}\) are positively correlated. This analysis helps to define and adjust the influencing parameters by which the output force, stroke and efficiency of the drive system can be adapted to the requirements and application.
Current research work introduces and investigates hierarchical drives with N levels. In a two-level hierarchy, as shown in Fig. 7a, where instead of each SMA wire of the first level actuator, a bimodal arrangement is achieved, as shown in fig. 9e. On fig. 7c shows how the SMA wire is wound around a movable arm (auxiliary arm) that only moves in the longitudinal direction. However, the primary movable arm continues to move in the same manner as the movable arm of the 1st stage multi-stage actuator. Typically, an N-stage drive is created by replacing the \(N-1\) stage SMA wire with a first-stage drive. As a result, each branch imitates the first stage drive, with the exception of the branch that holds the wire itself. In this way, nested structures can be formed that create forces that are several times greater than the forces of the primary drives. In this study, for each level, a total effective SMA wire length of 1 m was taken into account, as shown in tabular format in Fig. 7d. The current through each wire in each unimodal design and the resulting prestress and voltage in each SMA wire segment are the same at each level. According to our analytical model, the output force is positively correlated with the level, while the displacement is negatively correlated. At the same time, there was a trade-off between displacement and muscle strength. As seen in fig. 7b, while the maximum force is achieved in the largest number of layers, the largest displacement is observed in the lowest layer. When the hierarchy level was set to \(N=5\), a peak muscle force of 2.58 kN was found with 2 observed strokes \(\upmu\)m. On the other hand, the first stage drive generates a force of 150 N at a stroke of 277 \(\upmu\)m. Multi-level actuators are able to mimic real biological muscles, where artificial muscles based on shape memory alloys are able to generate significantly higher forces with precise and finer movements. The limitations of this miniaturized design are that as the hierarchy increases, the movement is greatly reduced and the complexity of the drive manufacturing process increases.
(a) A two-stage (\(N=2\)) layered shape memory alloy linear actuator system is shown in a bimodal configuration. The proposed model is achieved by replacing the SMA wire in the first stage layered actuator with another single stage layered actuator. (c) Deformed configuration of the second stage multilayer actuator. (b) The distribution of forces and displacements depending on the number of levels is described. It has been found that the peak force of the actuator is positively correlated with the scale level on the graph, while the stroke is negatively correlated with the scale level. The current and pre-voltage in each wire remain constant at all levels. (d) The table shows the number of taps and the length of the SMA wire (fiber) at each level. The characteristics of the wires are indicated by index 1, and the number of secondary branches (one connected to the primary leg) is indicated by the largest number in the subscript. For example, at level 5, \(n_1\) refers to the number of SMA wires present in each bimodal structure, and \(n_5\) refers to the number of auxiliary legs (one connected to the main leg).
Various methods have been proposed by many researchers to model the behavior of SMAs with shape memory, which depend on the thermomechanical properties accompanying the macroscopic changes in the crystal structure associated with the phase transition. The formulation of constitutive methods is inherently complex. The most commonly used phenomenological model is proposed by Tanaka28 and is widely used in engineering applications. The phenomenological model proposed by Tanaka [28] assumes that the volume fraction of martensite is an exponential function of temperature and stress. Later, Liang and Rogers29 and Brinson30 proposed a model in which the phase transition dynamics was assumed to be a cosine function of voltage and temperature, with slight modifications to the model. Becker and Brinson proposed a phase diagram based kinetic model to model the behavior of SMA materials under arbitrary loading conditions as well as partial transitions. Banerjee32 uses the Bekker and Brinson31 phase diagram dynamics method to simulate a single degree of freedom manipulator developed by Elahinia and Ahmadian33. Kinetic methods based on phase diagrams, which take into account the nonmonotonic change in voltage with temperature, are difficult to implement in engineering applications. Elakhinia and Ahmadian draw attention to these shortcomings of existing phenomenological models and propose an extended phenomenological model to analyze and define shape memory behavior under any complex loading conditions.
The structural model of SMA wire gives stress (\(\sigma\)), strain (\(\epsilon\)), temperature (T), and martensite volume fraction (\(\xi\)) of SMA wire. The phenomenological constitutive model was first proposed by Tanaka28 and later adopted by Liang29 and Brinson30. The derivative of the equation has the form:
where E is the phase dependent SMA Young’s modulus obtained using \(\displaystyle E=\xi E_M + (1-\xi )E_A\) and \(E_A\) and \(E_M\) representing Young’s modulus are austenitic and martensitic phases, respectively, and the coefficient of thermal expansion is represented by \(\theta _T\). The phase transition contribution factor is \(\Omega = -E \epsilon _L\) and \(\epsilon _L\) is the maximum recoverable strain in the SMA wire.
The phase dynamics equation coincides with the cosine function developed by Liang29 and later adopted by Brinson30 instead of the exponential function proposed by Tanaka28. The phase transition model is an extension of the model proposed by Elakhinia and Ahmadian34 and modified based on the phase transition conditions given by Liang29 and Brinson30. The conditions used for this phase transition model are valid under complex thermomechanical loads. At each moment of time, the value of the volume fraction of martensite is calculated when modeling the constitutive equation.
The governing retransformation equation, expressed by the transformation of martensite to austenite under heating conditions, is as follows:
where \(\xi\) is the volume fraction of martensite, \(\xi _M\) is the volume fraction of martensite obtained before heating, \(\displaystyle a_A = \pi /(A_f – A_s)\), \ ( \displaystyle b_A = -a_A/C_A\) and \(C_A\) – curve approximation parameters, T – SMA wire temperature, \(A_s\) and \(A_f\) – beginning and end of the austenite phase, respectively, temperature.
The direct transformation control equation, represented by the phase transformation of austenite to martensite under cooling conditions, is:
where \(\xi _A\) is the volume fraction of martensite obtained before cooling, \(\displaystyle a_M = \pi /(M_s – M_f)\), \(\displaystyle b_M = -a_M/C_M\) and \ ( C_M \) – curve fitting parameters, T – SMA wire temperature, \(M_s\) and \(M_f\) – initial and final martensite temperatures, respectively.
After equations (3) and (4) are differentiated, the inverse and direct transformation equations are simplified to the following form:
During forward and backward transformation \(\eta _{\sigma}\) and \(\eta _{T}\) take different values. The basic equations associated with \(\eta _{\sigma}\) and \(\eta _{T}\) have been derived and discussed in detail in an additional section.
The thermal energy required to raise the temperature of the SMA wire comes from the Joule heating effect. The thermal energy absorbed or released by the SMA wire is represented by the latent heat of transformation. The heat loss in the SMA wire is due to forced convection, and given the negligible effect of radiation, the heat energy balance equation is as follows:
Where \(m_{wire}\) is the total mass of the SMA wire, \(c_{p}\) is the specific heat capacity of the SMA, \(V_{in}\) is the voltage applied to the wire, \(R_{ohm} \ ) – phase-dependent resistance SMA, defined as; \(R_{ohm} = (l/A_{cross})[\xi r_M + (1-\xi )r_A]\ ) where \(r_M\ ) and \(r_A\) are the SMA phase resistivity in martensite and austenite, respectively, \(A_{c}\) is the surface area of ​​the SMA wire, \(\Delta H \) is a shape memory alloy. The latent heat of transition of the wire, T and \(T_{\infty}\) are the temperatures of the SMA wire and the environment, respectively.
When a shape memory alloy wire is actuated, the wire compresses, creating a force in each branch of the bimodal design called fiber force. The forces of the fibers in each strand of the SMA wire together create the muscle force to actuate, as shown in Fig. 9e. Due to the presence of a biasing spring, the total muscle force of the Nth multilayer actuator is:
Substituting \(N = 1\) into equation (7), the muscle strength of the first stage bimodal drive prototype can be obtained as follows:
where n is the number of unimodal legs, \(F_m\) is the muscle force generated by the drive, \​​(F_f\) is the fiber strength in the SMA wire, \(K_x\) is the bias stiffness. spring, \(\alpha\) is the angle of the triangle, \(x_0\) is the initial offset of the bias spring to hold the SMA cable in the pre-tensioned position, and \(\Delta x\) is the actuator travel.
The total displacement or movement of the drive (\(\Delta x\)) depending on the voltage (\(\sigma\)) and strain (\(\epsilon\)) on the SMA wire of the Nth stage, the drive is set to (see Fig. additional part of the output):
The kinematic equations give the relationship between drive deformation (\(\epsilon\)) and displacement or displacement (\(\Delta x\)). The deformation of the Arb wire as a function of the initial Arb wire length (\(l_0\)) and the wire length (l) at any time t in one unimodal branch is as follows:
where \(l = \sqrt{l_0^2 +(\Delta x_1)^2 – 2 l_0 (\Delta x_1) \cos \alpha _1}\) is obtained by applying the cosine formula in \(\Delta\)ABB ‘, as shown in Figure 8. For the first stage drive (\(N = 1\)), \(\Delta x_1\) is \(\Delta x\), and \(\alpha _1\) is \(\alpha \) as shown in As shown in Figure 8, by differentiating the time from Equation (11) and substituting the value of l, the strain rate can be written as:
where \(l_0\) is the initial length of the SMA wire, l is the length of the wire at any time t in one unimodal branch, \(\epsilon\) is the deformation developed in the SMA wire, and \(\alpha \) is the angle of the triangle , \(\Delta x\) is the drive offset (as shown in Figure 8).
All n single-peak structures (\(n=6\) in this figure) are connected in series with \(V_{in}\) as the input voltage. Stage I: Schematic diagram of the SMA wire in a bimodal configuration under zero voltage conditions Stage II: A controlled structure is shown where the SMA wire is compressed due to inverse conversion, as shown by the red line.
As a proof of concept, an SMA-based bimodal drive was developed to test the simulated derivation of the underlying equations with experimental results. The CAD model of the bimodal linear actuator is shown in fig. 9a. On the other hand, in fig. 9c shows a new design proposed for a rotational prismatic connection using a two-plane SMA-based actuator with a bimodal structure. The drive components were fabricated using additive manufacturing on an Ultimaker 3 Extended 3D printer. The material used for 3D printing of components is polycarbonate which is suitable for heat resistant materials as it is strong, durable and has a high glass transition temperature (110-113 \(^{\circ }\) C). In addition, Dynalloy, Inc. Flexinol shape memory alloy wire was used in the experiments, and the material properties corresponding to the Flexinol wire were used in the simulations. Multiple SMA wires are arranged as fibers present in a bimodal arrangement of muscles to obtain the high forces produced by multilayer actuators, as shown in Fig. 9b, d.
As shown in Figure 9a, the acute angle formed by the movable arm SMA wire is called the angle (\(\alpha\)). With terminal clamps attached to the left and right clamps, the SMA wire is held at the desired bimodal angle. The bias spring device held on the spring connector is designed to adjust the different bias spring extension groups according to the number (n) of SMA fibers. In addition, the location of the moving parts is designed so that the SMA wire is exposed to the external environment for forced convection cooling. The top and bottom plates of the detachable assembly help keep the SMA wire cool with extruded cutouts designed to reduce weight. In addition, both ends of the CMA wire are fixed to the left and right terminals, respectively, by means of a crimp. A plunger is attached to one end of the movable assembly to maintain clearance between the top and bottom plates. The plunger is also used to apply a blocking force to the sensor via a contact to measure the blocking force when the SMA wire is actuated.
The bimodal muscle structure SMA is electrically connected in series and powered by an input pulse voltage. During the voltage pulse cycle, when voltage is applied and the SMA wire is heated above the initial temperature of the austenite, the length of the wire in each strand is shortened. This retraction activates the movable arm subassembly. When the voltage was zeroed in the same cycle, the heated SMA wire was cooled below the temperature of the martensite surface, thereby returning to its original position. Under zero stress conditions, the SMA wire is first passively stretched by a bias spring to reach the detwinned martensitic state. The screw, through which the SMA wire passes, moves due to the compression created by applying a voltage pulse to the SMA wire (SPA reaches the austenite phase), which leads to the actuation of the movable lever. When the SMA wire is retracted, the bias spring creates an opposing force by further stretching the spring. When the stress in the impulse voltage becomes zero, the SMA wire elongates and changes its shape due to forced convection cooling, reaching a double martensitic phase.
The proposed SMA-based linear actuator system has a bimodal configuration in which the SMA wires are angled. (a) depicts a CAD model of the prototype, which mentions some of the components and their meanings for the prototype, (b, d) represent the developed experimental prototype35. While (b) shows a top view of the prototype with electrical connections and bias springs and strain gauges used, (d) shows a perspective view of the setup. (e) Diagram of a linear actuation system with SMA wires placed bimodally at any time t, showing the direction and course of the fiber and muscle strength. (c) A 2-DOF rotational prismatic connection has been proposed for deploying a two-plane SMA-based actuator. As shown, the link transmits linear motion from the bottom drive to the top arm, creating a rotational connection. On the other hand, the movement of the pair of prisms is the same as the movement of the multilayer first stage drive.
An experimental study was carried out on the prototype shown in Fig. 9b to evaluate the performance of a bimodal drive based on SMA. As shown in Figure 10a, the experimental setup consisted of a programmable DC power supply to supply input voltage to the SMA wires. As shown in fig. 10b, a piezoelectric strain gauge (PACEline CFT/5kN) was used to measure the blocking force using a Graphtec GL-2000 data logger. The data is recorded by the host for further study. Strain gauges and charge amplifiers require a constant power supply to produce a voltage signal. The corresponding signals are converted into power outputs according to the sensitivity of the piezoelectric force sensor and other parameters as described in Table 2. When a voltage pulse is applied, the temperature of the SMA wire increases, causing the SMA wire to compress, which causes the actuator to generate force. The experimental results of the output of muscle strength by an input voltage pulse of 7 V are shown in fig. 2a.
(a) An SMA-based linear actuator system was set up in the experiment to measure the force generated by the actuator. The load cell measures the blocking force and is powered by a 24 V DC power supply. A 7 V voltage drop was applied along the entire length of the cable using a GW Instek programmable DC power supply. The SMA wire shrinks due to heat, and the movable arm contacts the load cell and exerts a blocking force. The load cell is connected to the GL-2000 data logger and the data is stored on the host for further processing. (b) Diagram showing the chain of components of the experimental setup for measuring muscle strength.
Shape memory alloys are excited by thermal energy, so temperature becomes an important parameter for studying the shape memory phenomenon. Experimentally, as shown in Fig. 11a, thermal imaging and temperature measurements were performed on a prototype SMA-based divalerate actuator. A programmable DC source applied input voltage to the SMA wires in the experimental setup, as shown in Figure 11b. The temperature change of the SMA wire was measured in real time using a high resolution LWIR camera (FLIR A655sc). The host uses the ResearchIR software to record data for further post-processing. When a voltage pulse is applied, the temperature of the SMA wire increases, causing the SMA wire to shrink. On fig. Figure 2b shows the experimental results of the SMA wire temperature versus time for a 7V input voltage pulse.