Data underlying the publication: Perceived Intensity of Pneumatic Vibrotactile Stimuli: Effects of Pressure, Frequency, and Stiffness

Vibrotactile actuators are used in many different haptic devices, e.g. game controllers and smartphones. These vibrotactile actuators are typically made of rigid materials. In this work, we use soft pneumatic actuators known as Pneumatic Unit Cell (PUC) to characterize the perceived intensity of vibrotactile stimuli when presented at the tip of the index finger. This study investigates how three parameters—stimulus pressure (4 to 30 kPa), inflation-deflation frequency (20 to 100 Hz), and actuator stiffness (determined by top layer thicknesses of 0.9 mm and 1.2 mm)—influence the perceptual intensity of the stimuli. Psychophysical experiments involving 16 participants were conducted using the AEPsych toolbox.<br>Statistical analysis was conducted to assess the influence of the three parameters on perceived vibrotactile intensity. A 3×3 repeated-measures ANOVA was performed at nine representative pressure-frequency combinations to evaluate the main effects of pressure and frequency for each actuator design. To examine interaction effects, two separate one-way repeated-measures ANOVA tests were conducted for each actuator design to compare the Just Noticeable Differences (JNDs) across three pressure slices (33 Hz, 63 Hz, and 93 Hz) and three frequency slices (10 kPa, 18 kPa, and 26 kPa). The mean of JNDs (mean of pressure slices JNDs and mean of frequency slices JNDs) were then used to compare the relative influence of pressure and frequency, using a paired t-test for the 0.9 mm PUC actuator and a Wilcoxon signed-rank test for the 1.2 mm PUC actuator. To analyze the effect of actuator stiffness, we evaluated the frequency adjustment required at 17 kPa and the pressure adjustment required at 60 Hz in the 1.2 mm PUC actuator to match the perceived intensity of a reference stimulus from the 0.9 mm PUC actuator. A paired t-test was performed in both cases to determine the influence of actuator stiffness.<br>These reveal that all the three parameters - pressure, frequency, and actuator stiffness significantly affect perceptual intensity. The findings indicate that both pressure and frequency exhibit a positive main effect and a positive interaction effect on perceived vibrotactile intensity. Additionally, the results show that, for a given frequency, pressure variations produce more perceptually distinct stimuli than frequency variations for a given pressure. Finally, presenting vibrotactile stimuli on a less stiff PUC actuator was perceived as being less intense than when the same stimulus was presented on a stiffer PUC actuator. Overall, this study provides key insights into the combined influence of pressure, frequency and actuator stiffness on the perceived vibrotactile intensity.

振动触觉驱动器（vibrotactile actuators）广泛应用于各类触觉设备中，例如游戏手柄与智能手机。传统振动触觉驱动器多采用刚性材料制备。本研究采用被称为气动单元胞（Pneumatic Unit Cell, PUC）的软体气动驱动器，在食指指尖处呈现振动触觉刺激，以表征其感知强度。本研究探究三类参数对刺激感知强度的影响：刺激压力（4~30 kPa）、充放气频率（20~100 Hz）以及驱动器刚度（由顶层厚度0.9 mm与1.2 mm两种规格确定）。本研究借助AEPsych工具箱开展了包含16名受试者的心理物理实验。

为评估三类参数对振动触觉刺激感知强度的影响，本研究开展了统计分析：针对每种驱动器设计，选取9组典型压力-频率组合开展3×3被试内方差分析（repeated-measures ANOVA），以检验压力与频率的主效应；为考察交互效应，针对每种驱动器设计分别开展两组单因素被试内方差分析，分别比较3个压力切片（33 Hz、63 Hz、93 Hz）与3个频率切片（10 kPa、18 kPa、26 kPa）下的差别阈限（Just Noticeable Differences, JNDs）。随后分别计算压力切片与频率切片的差别阈限均值，以此比较压力与频率的相对影响：针对0.9 mm厚度的PUC驱动器采用配对t检验，针对1.2 mm厚度的PUC驱动器则采用Wilcoxon符号秩检验。为分析驱动器刚度的影响，本研究在1.2 mm厚度的PUC驱动器中，分别测试了在17 kPa压力下匹配0.9 mm厚度PUC驱动器参考刺激感知强度所需的频率调整量，以及在60 Hz频率下所需的压力调整量；两种场景下均采用配对t检验以评估驱动器刚度的影响效应。

研究结果表明，压力、频率与驱动器刚度这三类参数均会对刺激感知强度产生显著影响：压力与频率均对振动触觉刺激的感知强度存在正向主效应与正向交互效应；此外，在固定频率下，压力变化带来的感知差异显著大于固定压力下频率变化带来的感知差异；最后，相较于刚度更高的PUC驱动器，在刚度更低的PUC驱动器上呈现的相同振动触觉刺激会被感知为强度更低。综上，本研究阐明了压力、频率与驱动器刚度三者的联合作用对振动触觉刺激感知强度的关键影响机制。