Development of a Directional Vibrator Using Shape-Memory Alloy Wires

Abstract

Haptic feedback has attracted significant attention in virtual reality (VR), augmented reality (AR), and teleoperation because it can provide rich tactile information of an object through skin without increasing visual load. Among the many tactile presentation methods, vibration is the most widely used, and numerous vibration actuators have been incorporated into tactile displays. For directional control, attempts have been made to generate directional acceleration within a two-dimensional plane using a single device, but the reported device produces a single-shot impact rather than continuous vibration and offers limited control of the acceleration magnitude. To address this, we focus on a shape-memory alloy (SMA) wire. The wire contracts when heated by an applied current and returns to its original length when the current is stopped. Such repeated contraction and recovery generate vibration in synchronization with a pulse current. This paper proposes a vibrator that suspends a moving part with four SMA wires to generate two-dimensional directional acceleration with a single compact device. Through driving experiments, we show that the device generates acceleration aligned with the axis of each of eight target directions spaced at 45° intervals, and that the magnitude of the acceleration can be adjusted through the duty ratio at a fixed driving frequency. The perceptual evaluation of the presented direction is left for future work.

1. Introduction

In recent virtual/augmented reality (VR/AR) interfaces and teleoperation environments, haptic feedback has attracted significant attention because it can provide rich tactile information through skin contact without increasing the visual load on the user. The presentation of directional information, typified by navigation and operation guidance, is particularly effective in situations where visual information tends to become overloaded. During vehicle driving or AR content use, for example, interfaces are required that can direct the user’s attention without demanding additional eye movements. The importance of information presentation through non-visual modalities is therefore growing. Such applications demand an actuator that is compact while being capable of presenting multidirectional tactile cues.

Among the many tactile presentation methods, including those based on pressure and friction, vibration-based tactile displays are the most widely used. A variety of vibrawoo tors have been developed for this purpose, differing mainly in how they convert input signals into motion, and they have been incorporated into interfaces ranging from handheld devices whose whole body oscillates to wearable systems with many small elements across the skin [1]. Representative examples include eccentric rotating mass (ERM) vibrators, linear resonant actuators (LRAs), and piezoelectric actuators (PZAs). Each of these, however, has its own strengths and limitations in terms of compactness, response speed, and controllability. ERM vibrators are low in cost but respond slowly and couple frequency and amplitude to the applied voltage, limiting the range of presentable patterns [2,3]. LRAs respond faster but, being driven at resonance, lose output away from the resonant frequency and exhibit residual vibration [2,3]. PZAs offer fast, wideband vibration but require a high driving voltage and a dedicated driving circuit [2,3].

Shape-memory alloys (SMAs) have been used as a compact and lightweight actuation source in a wide range of fields, from aerospace mechanisms, such as a passive lock-and-release actuator driven by solar radiation [4], to medical and wearable devices, and they have also been increasingly applied to haptic interfaces [5]. SMA wires have been investigated as an actuation source [6,7,8,9,10]. Because an SMA wire is actuated by Joule-heating-induced phase transformation, it requires neither an electromagnetic motor nor a resonance mechanism, offering the potential to control vibration frequency and amplitude with a simple driving configuration. Several implementations have been reported, including directly transmitting the micro-vibration of an SMA wire to the skin [7], delivering stimuli through a pin mechanism driven by an SMA wire [6,8,9], and arranging multiple vibration units on eyeglasses or a headband to present tactile sensations around the face [10]. We have also developed a vibrator that delivers vibration through a moving element driven by an SMA wire, demonstrating that an SMA wire can serve as a practical actuation source [11].

Using these actuators, two main approaches have been studied for presenting direction with vibrators: waveform-based approaches, which drive a single vibrator with asymmetric vibration waveforms to indicate a direction [12,13,14,15,16], and spatial-arrangement approaches, which arrange multiple vibrators at different locations [17,18,19,20,21]. In waveform-based approaches, a vibrator is driven by an asymmetric acceleration waveform, which is perceived as a continuous pull in a specific direction owing to the nonlinear characteristics of human tactile perception. Amemiya et al. established this principle using a single ungrounded vibrator [12,13], and subsequent studies reproduced the same effect with compact voice-coil vibrators and examined its dependence on driving conditions such as frequency [14,15,16]. While a single vibrator can indicate a direction in this way, it conveys only one axis, such as left–right motion; presenting additional directions requires multiple vibrators, which increases the volume, mass, and complexity of the device and makes planar directional presentation difficult.

In spatial-arrangement approaches, multiple vibrators are placed at different locations and driven sequentially so that the perceived position of vibration shifts across the body to indicate a direction. This principle has been applied to various body sites and form factors, including a glove that guides the hand in three-dimensional space [17], a layout that presents rotational patterns around the hand [19], and a head-mounted device for navigation cues [21]. The number of directions that such layouts can present is fundamentally limited by how closely vibrators can be placed while remaining distinguishable, which depends on factors such as vibrator type and vibration intensity [18,20]. Consequently, presenting more directions requires more vibrators and a larger device, while keeping the device compact entails a more complex internal structure and control system. As a result, presenting two-dimensional directional vibration with a single compact vibrator remains challenging.

To overcome these limitations, a different approach has recently been explored, in which directional acceleration is generated within a two-dimensional plane using a single device [22]. However, this device produces a single-shot impact rather than continuous vibration, and thus does not function as a vibrator. Moreover, controlling the magnitude of the generated acceleration remains difficult. The significance of generating directional acceleration is supported by the close relationship between acceleration and vibrotactile perception: the perceived intensity of vibrotactile stimuli has been shown to increase monotonically with the acceleration amplitude of the vibration [23]. Therefore, generating directional acceleration in a controlled manner is itself meaningful for vibrotactile presentation.

We previously developed a compact vibrator that drives a moving element with an SMA wire and a tension spring, and measured the acceleration it generated [11]. However, extending this device to two-dimensional directional control posed a problem: the tension spring, which was required to restore the wire, biased the generated acceleration toward a single direction and broke the structural symmetry of the device, making two-dimensional directional presentation difficult.

To address this problem, this paper proposes a directional vibrator using SMA wires. In the proposed structure, a weight is suspended by four SMA wires arranged along the diagonals of a square and driven by pulse-width-modulated (PWM) current signals. This symmetric, spring-free configuration enables the generation of two-dimensional directional acceleration with a single compact device. A prototype was fabricated, and driving experiments were conducted under three different driving frequencies. The results demonstrate that the device generates directional acceleration and that its magnitude can be adjusted by changing the driving conditions. The perceptual evaluation of the presented direction is left for future work using user experiments.

2. Materials and Methods

2.1. Phase Transformation of Shape-Memory Alloys

Shape-memory alloys differ from ordinary metals in how much strain they can recover. In ordinary metals, recoverable deformation is restricted to the elastic range, and any deformation beyond it remains as permanent plastic strain. By contrast, shape-memory alloys recover comparatively large strains through a reversible transformation between two solid phases. Which of two behaviors appears depends on the temperature and stress conditions under which the alloy is deformed. When a deformation is imposed in the low-temperature phase, it is recovered by subsequent heating, and this behavior is the shape-memory effect. When a deformation is imposed in the high-temperature phase, it is recovered upon unloading alone, and this behavior is the superelastic effect.

The phase transformation underlying these behaviors is illustrated in Figure 1. The high-temperature phase is austenite, and the low-temperature phase is martensite. When the alloy is cooled in the absence of load, austenite transforms into twinned martensite; this transformation begins at the martensite-start temperature (M_s) and is completed at the martensite-finish temperature (M_f). If the twinned martensite is then loaded, it deforms first elastically and subsequently by reorientation of its twin variants, accumulating a large apparent strain. Removing the load recovers only the elastic portion, so the alloy is left in a detwinned state that retains the imposed shape. Heating this detwinned martensite drives the reverse transformation to austenite, which proceeds from the austenite-start temperature (A_s) to the austenite-finish temperature (A_f) and restores the original shape. This thermally completed recovery is the shape-memory effect.

When the alloy is instead loaded while in the austenite phase, it first deforms elastically and then transforms into martensite under the applied stress, again producing a large strain. Because austenite is the stable phase at this temperature, unloading reverses the stress-induced transformation and the strain is recovered without any thermal operations. This stress-driven recovery is termed superelastic effect.

2.2. Driving the SMA Wire with Pulse Current

In this study, the SMA wire is driven by its shape-memory effect. The wire is driven by a pulse current, whose waveform is shown in Figure 2. While the wire is energized, it is heated by Joule heating and transforms to the austenite phase. As a result, the wire contracts. Once it is de-energized, the wire radiates heat during the non-energized interval and transforms back to the martensite phase. The wire then returns to its original length. Because the wire is thin and has a large surface area relative to its volume, this heat radiation proceeds quickly, so the wire can recover within a short non-energized interval. The wire vibrates as it repeats this contraction and recovery in step with the pulse current.

The current is specified by two parameters: the frequency and the duty ratio. The duty ratio d is defined as the ratio of the pulse width W, during which the current is supplied, to the period T of one cycle, so that the duty ratio represents the fraction of each period for which the wire is energized:

$$\mathrm{D}\mathrm{u}\mathrm{t}\mathrm{y} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o} d \left(\%\right)={\displaystyle \frac{W}{T}}$$

(1)

The period T is the reciprocal of the driving frequency f:

$$\mathrm{F}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y} f \left(Hz\right)= {\displaystyle \frac{1}{T}}$$

(2)

The frequency controls the timing at which heat is supplied to the wire, while the duty ratio controls the amount of heat supplied by each pulse. The motion of the wire is governed by the heat input determined by these two parameters.

2.3. Device Configuration

Figure 3 shows a schematic diagram of the device structure. The device consists of a fixed part consisting of posts and a base, a moving part that has mass, and four SMA wires suspending the moving part. The xy-coordinate system is defined as shown in Figure 3b. Hereafter, the SMA wire at 45° to the positive x-axis is referred to as SMA1, and the remaining wires are designated SMA2, SMA3, and SMA4 in the counterclockwise direction. Because the SMA wire’s poor wettability with solder makes soldering difficult, the wires are fastened with nuts. One end of each of the four SMA wires is fastened to the moving part, while the other end is fastened to a post of the fixed part. The wires are fixed so that the moving part is suspended by the tension of the SMA wires. A photograph of the actual device is shown in Figure 4.

The wire used to drive the device is a commercially available SMA wire, BioMetal Fiber 100, supplied by Toki Corporation (Tokyo, Japan) [24]. It is a NiTiCu alloy drawn to a diameter of 0.1 mm, and a 2.5 cm length was used for each wire in this study. Its physical properties are listed in

Table 1. Physical properties of the SMA wire.

Physical Property	Value
Standard diameter (μm)	100
Practical force produced (load) (gf)	70
Practical kinetic strain (%)	4.0
Standard power (W/m)	5.40
Standard resistance (Ω/m)	135
Tensile strength (Kgf)	0.8
Weight (mg/m)	50

. The transformation from martensite to austenite begins at approximately 70 °C (A_s), and the transformation from austenite to martensite begins at approximately 65 °C (M_s). The base of the fixed part was a 45 mm × 45 mm universal board (ICB90GH). Conductive brass spacers were used for the posts. The moving part was a 3 g weight (TAMIYA, 15343, Shizuoka, Japan). A 5 V–3 A AC adapter (Linkman, ATS018T-W050U, Tokyo, Japan) was used as the DC power supply, and four 2SD880s (Unisonic Technologies, New Taipei City, Taiwan) were used as the NPN transistors.

2.4. Vibration Generation Mechanism

Figure 5 shows a schematic diagram of the vibration generation mechanism. When the SMA wire on the left is energized, it contracts in that direction, pulling the moving part to the left. By the reaction force, the entire device moves to the right.

2.5. Directional Control of Moving Part

By selecting SMA wires to be energized, the moving part can be moved two-dimensionally in the eight directions shown in Figure 6a, at intervals of 45° measured from the positive x-axis. In this paper, the direction in which the moving part moves is referred to as the “target direction.” When a single SMA wire is energized, the moving part moves at 45° to the x- and y-axes; when two adjacent SMA wires are energized simultaneously, the moving part moves along the x- or y-axes.

For example, when the SMA wire at 135° from the positive x-axis (SMA2) is energized, as in Figure 6b, the moving part moves in the same 135° direction. When the two SMA wires at 45° (SMA1) and 135° (SMA2) are energized simultaneously, as in Figure 6c, the moving part moves in the 90° direction, between the positions of the SMA wires. In this way, the target direction is controlled by selecting which SMA wires to energize.

Note that, as described in Section 2.4, the moving part and the fixed part receive forces in opposite directions. When the moving part is driven toward the target direction, the fixed part receives a reaction force in the direction opposite to the target direction.

2.6. Pulse Current Signal and the Resulting Motion of the Moving Part

Figure 7 shows the pulse current applied to the SMA wire and the resulting motion of the moving part when a pulse voltage is applied to the upper-left SMA wire (SMA2), viewed from the top. In the initial state, the moving part is located at the center. When the SMA wire is energized, the moving part moves toward the energized SMA wire, that is, in the target direction. When energization stops, the contracted SMA wire relaxes, and the moving part begins to move in the direction opposite to the target direction. The vibration then gradually attenuates, and the moving part finally settles at its initial position, at which point the vibration ceases.

2.7. PWM Control Circuit

Figure 8 shows the circuit diagram of the SMA wire driving circuit. The collector of every transistor is connected to the DC power supply, each base is connected to a voltage signal source such as a microcomputer, and each emitter is connected to an SMA wire. The power supply and all SMA wires are connected to a common ground (GND). By driving each base with a PWM signal, the driving frequency and duty ratio of the energization applied to each SMA wire can be controlled individually.

The voltage of the PWM signal applied to the base of each transistor (2SD880) is 5 V. Because the transistors operate as emitter followers with a base–emitter voltage of 1 V, the voltage across each SMA wire is 4 V. With a wire resistance of approximately 3.4 Ω, this corresponds to an estimated peak pulse current of about 1.2 A, and a peak instantaneous power per wire of approximately 4.7 W. Because the energization is pulsed at a small duty ratio, the average power is much lower; for example, at a duty ratio of approximately 1%, the average power per wire is 47 mW. The driving conditions of the circuit are summarized in

Table 2. Electrical driving conditions of the circuit.

Physical Property	Value
PWM signal voltage (transistor base) (V)	5
Base-emitter voltage (V)	1
Voltage across SMA wire (V)	4
Wire resistance (Ω)	3.4
Peak pulse current (A)	1.2
Peak instantaneous power per wire (W)	4.7

.

3. Measurement System and Experimental Setup

This section describes the system that inputs signals to the fabricated device and measures the acceleration of the fixed part.

3.1. Measurement Device

Figure 9 shows the arrangement of four acceleration sensors and an overview photograph of the device with the acceleration sensors mounted. An MDK022 (Marutsu Elec, Tokyo, Japan) was used as the three-axis acceleration sensor. Its measurement range is ±2 G, and its sensitivity is 660 mV/G. As shown in Figure 9a, the sensors were soldered to a universal board. This universal board was fixed as the top base of the device shown in Figure 9b. The mass of the device with the acceleration sensors mounted was 40.3 g.

As described in Section 2.4, the moving part and the fixed part experience forces in opposite directions; therefore, the measured acceleration of the fixed part is ideally opposite to the acceleration of the moving part.

3.2. Experimental System

Figure 10 shows a schematic diagram of the experimental system. The experimental system consists of five elements: a PC, an Arduino Mega 2560 (Arduino, Monza, Italy), an Arduino Due, an accelerometer, and the SMA actuator. The PC supplies power to the Arduinos and transmits settings, receives data from the Arduinos, and processes the data. The Arduino Mega generates the pulse signal according to the settings received from the PC, and this signal drives the SMA wires through the PWM control circuit described in Figure 8. The Arduino Due digitizes and records the acceleration sensor’s output voltage at 12-bit resolution. A Hampel filter was then applied to remove outliers. The Arduino Due’s input voltage range is 0–3.3 V, and its voltage resolution is 0.805 mV. Therefore, the acceleration resolution of the MDK022 is 0.0012 G.

3.3. Analysis Method

To evaluate the in-plane directionality and the magnitude of the generated acceleration, feature quantities are introduced. From the acceleration values $a_x\left(t\right)$ and $a_y\left(t\right)$ measured at each sampling time t, the magnitude of the in-plane acceleration $\sqrt{a_x{\left(t\right)}^2+ a_y{\left(t\right)}^2}$ and the angle $\theta \left(t\right)=\mathit{arctan}\left( a_y\left(t\right)/a_x\left(t\right)\right)$ are calculated. One period of the driving pulse contains an energized interval, in which the pulse is ON, and a non-energized interval, in which it is OFF. The peak of acceleration generated by the vibration is categorized into one of these two intervals.

A schematic diagram of these feature quantities is shown in Figure 11. The measurement record is divided at the instants at which the energization state switches, and these two intervals are treated separately throughout the analysis. In the i-th interval, the first peak value of the in-plane acceleration is denoted by $a_{1_{\mathrm{s}\mathrm{t}},i}$, and the maximum value by $a_{max,i}$. To suppress the influence of small spurious peaks caused by noise, peaks were detected on the basis of their prominence: the smaller of the two drops from the peak to the adjacent valleys on its left and right. In the i-th interval, peaks with a prominence below a threshold $0.2a_{\mathrm{m}\mathrm{a}\mathrm{x},i}$ were discarded, peaks with a prominence of at least $0.2a_{\mathrm{m}\mathrm{a}\mathrm{x},i}$ were retained, and the first such peak in the interval was taken as $a_{1_{\mathrm{s}\mathrm{t}},i}$.

4. Results

This section presents the experimental results obtained using the measurement system described in Section 3.

To characterize the device’s dynamic response, the acceleration waveform from a single driving pulse and the frequency response obtained by FFT analysis are first examined.

The directional characteristics of the generated acceleration are then evaluated by measuring the in-plane acceleration under single-pulse driving at 1 Hz and continuous driving at 20 Hz and 50 Hz, and projecting the acceleration vector onto the phase plane.

Finally, the relationship between the duty ratio and the peak acceleration magnitude is investigated.

4.1. Time-Domain Response and Frequency Characteristics Under Single-Pulse Driving

The SMA wires were driven by a single pulse at 1 Hz with a 1.0% duty ratio, and the acceleration was measured at a 30 μs sampling interval. Data were obtained for all eight target directions of 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°. Figure 12a,b show the time-series acceleration for two representative driving directions, with shaded regions indicating the ON interval of the pulse signal.

As seen in Figure 12, the first rise occurs within 2 ms, and the maximum acceleration is reached approximately 14 ms after the start of energization. However, there is an approximately 1 ms interval before the rise during which the acceleration changes little. In addition, the device vibrates both during and after energization rather than simply contracting and relaxing.

To characterize the frequency response of the device structure itself, the power spectra of the accelerations $a_x$ and $a_y$ in the x- and y-axes directions for each driving direction condition are shown in Figure 13. These results show that the structure has peaks near 343 Hz and near 450 Hz. This indicates that the device does not behave as a simple first-order system.

4.2. Directional Characteristics of Generated Acceleration

The acceleration was measured under three driving frequencies: 1 Hz with a single pulse, and 20 Hz and 50 Hz with repeated pulses. The duty ratio ranges were 0.3–1.5% in increments of 0.1% for 1 Hz, 0.5–1.5% for 20 Hz, and 0.5–1.8% for 50 Hz, with the same increment applied throughout. The sampling interval was 30 μs for all conditions. For each driving frequency, a representative duty ratio is selected to evaluate the directional characteristics of the generated acceleration across all target directions.

The acceleration is obtained as time-domain waveforms of the orthogonal components x and y. While the time-domain waveform under the 1 Hz condition was shown in Figure 12, Figure 14 shows examples of the time-domain waveforms under the 20 Hz and 50 Hz driving conditions, where the shaded regions indicate the energized intervals. Each energized interval is followed by a rise in acceleration and a subsequent decaying oscillation, and this response is repeated in synchronization with the pulses.

To examine the direction of the generated acceleration, these time-domain data are converted into points on the x–y plane following the procedure described in Section 3.3. Figure 15 shows the results for the 1 Hz driving condition at a duty ratio of 1.0%, with the plotted accelerations color-coded by energized and non-energized states using a color map. As shown in Figure 15a, we clearly distinguish “the target direction”, which denotes the specific orientation toward which the moving part is intended to be driven, from “the axis of the target direction”, the straight line passing through this direction and its opposite.

The acceleration during energization is distributed along this axis in Figure 15. However, Figure 15c,e,g show that the vibration of the non-energized state deviates from the axis.

Figure 16 shows the results for the 20 Hz driving condition at a duty ratio of 1.5%, with the plotted accelerations using a color map. In every case, acceleration is generated along the axis of the target direction. In Figure 16c,g, acceleration that is not aligned with this axis is also generated. In addition, in Figure 16b,f,h, the acceleration is slightly inclined from the axis of the target direction.

Figure 17 shows the results for the 50 Hz driving condition at a duty ratio of 1.8%, with the plotted accelerations using a color map. In every case, acceleration is generated along the axis of the target direction with little off-axis component.

Figure 18, Figure 19 and Figure 20 show histograms of the angular error with respect to the target direction, aggregated over all eight target directions, measured when the in-plane acceleration magnitude reaches its first peak value and when it reaches its maximum value, under driving conditions of 1 Hz at a duty ratio of 1.0%, 20 Hz at 1.5%, and 50 Hz at 1.8%, respectively. The histograms use a bin width of 45°, spanning 0° to 315°. In each figure, the energized and non-energized intervals are shown separately, each at the first peak and at the maximum value. It should be noted that because the fixed part is accelerated by the reaction force of the moving part, its acceleration is ideally oriented in the direction opposite to that of the moving part.

In Figure 18a, the first peak during energization is oriented opposite to the target direction, indicating that the moving part is accelerated in the target direction. Figure 18b,c show that the measured fixed-part acceleration is concentrated at 0° and 180° relative to the target direction, distributed across both sides rather than biased toward one side. This indicates that although the acceleration is aligned with the axis of the target direction, its orientation is not distinguished. In Figure 19a,c and Figure 20a,c, there is no angular directionality. On the other hand, the first peak in the non-energized interval, as shown in Figure 19b and Figure 20b, is oriented opposite to the target direction, indicating that the moving part is accelerated in the target direction.

4.3. Control of Acceleration Magnitude via Duty Ratio and Driving Frequency

This section examines how the duty ratio d and the driving frequency f affect the magnitude of the generated acceleration. To this end, the peak acceleration magnitude is measured as a function of the duty ratio at three driving frequencies, 1 Hz, 20 Hz, and 50 Hz.

The acceleration was measured under three driving frequencies: 1 Hz with a single pulse, and 20 Hz and 50 Hz with repeated pulses. The duty ratio ranges were 0.3–1.5% at 1 Hz, 0.5–1.5% at 20 Hz, and 0.5–1.8% at 50 Hz, in increments of 0.1%. The sampling interval was 30 μs for all conditions. For each driving frequency and duty ratio condition, acceleration data were collected for all eight target directions. Figure 21 shows the relationship between the duty ratio and the peak acceleration magnitude for each driving frequency, separately for the energized (SMA ON) and non-energized (SMA OFF) intervals, with the mean across all eight target directions plotted as the marker and the standard deviation as the error bar.

Figure 21a shows that, at 1 Hz, the maximum acceleration during energization increases with duty ratio from 0.3% to 0.7%, then becomes constant regardless of duty ratio. At 20 Hz and 50 Hz, the maximum acceleration during energization does not change with duty ratio.

Figure 21b shows that the maximum acceleration increases with the duty ratio for all three frequencies, and that a lower driving frequency yields a higher maximum acceleration under the same duty ratio.

These results show that, at a fixed driving frequency, the magnitude of the generated acceleration can be adjusted by varying the pulse current duty ratio in the non-energized interval.

5. Discussion

In this study, we proposed a directional vibrator in which a weight is suspended by four SMA wires arranged along the diagonals of a square and driven by PWM current signals.

Here we discuss the dynamic behavior of the device observed under single-pulse driving. The time-domain response showed that the device continued to vibrate not only during energization but also after the pulse ended, rather than simply contracting and relaxing once. This behavior cannot be explained by the contraction of the SMA wire alone, which would produce a single rise and decay following the pulse. Instead, it indicates that the suspended weight and the SMA wires together form an oscillatory system that behaves like a second-order system. This interpretation can be supported by the frequency spectra, which exhibited clear peaks near 343 Hz and 450 Hz; these peaks correspond to the natural frequencies of the structure, confirming that the device possesses inherent oscillatory modes rather than responding as a simple first-order element.

In addition, the acceleration showed almost no change during approximately the first 1 ms after the onset of energization, before the clear rise began. This initial delay is attributed to the time required for the SMA wire to take up its slack and reach its transformation temperature before generating a clear reaction force. Until the wire begins to contract and transmit force to the weight, no appreciable acceleration is produced, which accounts for the short interval observed before the response.

We next discuss the directional characteristics of the generated acceleration. The behavior differed between the energized and non-energized states. The energized-state acceleration was distributed along the axis of the target direction, whereas the non-energized state sometimes deviated from it, as observed under the 1 Hz and 20 Hz conditions. This difference arises because the SMA wire actively generates force through contraction during energization, while in the non-energized state it relaxes and returns passively toward its structural equilibrium; the latter motion is therefore governed by the structure rather than by the intended driving direction.

In addition, under the 20 Hz condition, the acceleration was slightly inclined from the axis of the target direction in Figure 16b,f,h. This inclination is considered to originate from structural imperfections, such as asymmetry in the weight geometry or imbalance in the wire tension.

Under the 50 Hz condition, in contrast, the acceleration was aligned with the axis of the target direction in all eight directions with a minor off-axis component. This frequency dependence is explained by the length of the non-energized interval relative to the decay time of the structural vibration. As the driving frequency increases, the non-energized interval becomes shorter, and under the 50 Hz condition the wire begins to contract under the next pulse before the vibration excited by the previous pulse has attenuated. As a result, the passive structural vibration that causes off-axis acceleration has less influence, and the acceleration remains aligned with the axis of the target direction.

We further discuss the orientation of the generated acceleration evaluated from the angular histograms. The orientation of the acceleration showed a clear frequency dependence. At the low driving frequency of 1 Hz, the acceleration was aligned with the axis of the target direction at both the first peak and the maximum value, in both the energized and non-energized intervals. At the higher driving frequencies of 20 Hz and 50 Hz, however, the acceleration in the energized interval showed no clear angular directionality, whereas that in the non-energized interval remained aligned with the axis of the target direction.

The absence of angular directionality in the energized interval at higher frequencies is considered to be because the energized interval is too short for the device to begin effective motion; during this interval the acceleration changes little, so no clear orientation appears. In the non-energized interval, by contrast, the moving part is released and accelerated toward the axis of the target direction.

Finally, we discuss how peak acceleration depends on the duty ratio at a fixed driving frequency. We examine the energized interval shown in Figure 21a and the non-energized interval shown in Figure 21b in turn.

In the energized interval, the maximum acceleration did not increase with the duty ratio, but the underlying mechanism differed between the low- and high-frequency conditions. At 1 Hz, the acceleration first increased with the duty ratio and then saturated. This saturation can be attributed to the onset of stress-induced martensitic transformation in the SMA wire. Because the wire is subjected to a constant tensile bias load, a temperature rise promotes not only thermally driven but also stress-induced martensitic transformation beyond a certain duty ratio. Once this occurs, the apparent tangent modulus of the wire decreases under tensile stress, as reported by Šittner et al. [25], which limits any further increase in the contraction force of the wire. Meanwhile, the opposing bias tension continues to rise as the wire contracts, so the two forces approach a balance beyond which the acceleration no longer increases. At 20 Hz and 50 Hz, by contrast, the acceleration did not increase with the duty ratio at all, because the energization duration, approximately 0.75 ms at 20 Hz and 0.36 ms at 50 Hz, is shorter than the roughly 1 ms delay observed before the onset of wire contraction in Figure 12. Within such a short energized interval, the wire has not yet begun to contract, so no effective motion is generated regardless of the duty ratio. Controlling the acceleration during the energized interval would therefore require a control method that also accounts for the stress-induced transformation.

In the non-energized interval, the maximum acceleration increased with the duty ratio at all three frequencies, and a lower driving frequency yielded a higher acceleration under the same duty ratio. Both trends can be understood in terms of the heat supplied to the wire by a single pulse. From Equations (1) and (2), at a fixed frequency f, a larger duty ratio d corresponds to a longer pulse width W. Also, when the duty ratio is fixed, decreasing the frequency lengthens the pulse width W. A longer pulse width means greater Joule heating per pulse, which leads to a greater degree of thermally induced transformation toward the austenite phase during energization. Upon de-energization, the austenite reverts to martensite and releases the accumulated transformation strain. Because a greater proportion of austenite is presumed to have formed under a longer pulse width, the released strain becomes larger, and the resulting displacement of the vibrator increases, producing a higher acceleration.

These results indicate that, in the non-energized interval, the acceleration magnitude can be adjusted through the duty ratio at a fixed driving frequency, and is also affected by the driving frequency at a fixed duty ratio. Because both parameters act on the wire through the supplied Joule heat, they are thermally coupled rather than independent. A quantitative characterization of this thermal control by the two parameters in the present device is left for future work.

Finally, we note several aspects that were not investigated experimentally in this study. Power consumption was estimated only for the instantaneous and average values, and the precise power consumption under continuous operation was not quantified. Because the wire resistance varies with temperature and the average power depends on the driving conditions, an accurate measurement under continuous operation remains to be carried out. In addition, the long-term durability and the repeatability of the SMA wires under repeated driving were not evaluated, so the fatigue behavior and the stability of the generated acceleration over extended operation remain to be confirmed. These aspects are left for future work, in which thermal behavior, power consumption during continuous operation, and durability under repeated driving will be examined to provide data for practical design.

6. Conclusions

This study presents a directional vibrator driven by SMA wires in which four wires arranged diagonally across a square frame drive a suspended moving part. A prototype was fabricated, and its dynamic response, the directionality of the generated acceleration, and the relationship between the pulse-current parameters and the acceleration magnitude were evaluated experimentally. The main findings of this study are summarized below:

(i)

Time-domain observation of the single-pulse response and FFT analysis revealed the natural frequencies of the device and indicated that the structure does not behave as a simple first-order system.

(ii)

When the vibrator was driven in eight target directions, the generated acceleration was aligned with the axis of each target direction.

(iii)

The magnitude of the generated acceleration could be adjusted through the duty ratio of the pulse current at a fixed driving frequency in the non-energized interval.

Future work will proceed in five directions. First, user experiments will be conducted to clarify whether users perceive the generated acceleration as a tactile cue in the intended direction and whether its orientation and magnitude can be discriminated. Second, the response characteristics, including the response time, will be evaluated quantitatively and compared with those of other vibrators. Third, the control of the acceleration magnitude by the duty ratio and the driving frequency will be characterized quantitatively, taking into account that the two parameters are thermally coupled through the Joule heating of the wire. Fourth, the power consumption during continuous driving will be quantitatively evaluated, including its dependence on driving conditions and the effect of temperature-dependent changes in wire resistance, to provide reliable data for practical design. Fifth, the long-term durability and repeatability of the SMA wires under repeated driving will be evaluated, including the fatigue behavior and the stability of the generated acceleration over extended operation.