Development of enhanced force models to analyze the nonlinear hysteresis response of miniaturized pneumatic artificial muscles

Miniaturized pneumatic artificial muscles (MPAMs), designed to replicate natural muscle actuation, offer unique attributes such as a high power-to-weight ratio, flexibility, easy integration, and compactness, making them favourable for many applications. The present paper aims at the development of an accurate semi-analytical force model considering the effect of the bladder material and friction terms to predict the nonlinear force-deformation response of MPAMs during contraction and expansion cycles. Existing force models for MPAMs exhibit limitations to accurately capturing the force-deformation behaviours due to several simplification factors. This study enhances these models by integrating correction terms to accurately address the nonlinearity and frictional effects exhibited by MPAMs. An analysis of the hysteresis loops resulting from the cyclic loading and unloading of MPAMs under specific pressures is undertaken to compare different methodologies in order to determine the most accurate correction terms. To investigate the nonlinear behaviour of MPAMs, the stress-strain relationship of the bladder material and results from force-deformation experimental tests on the entire actuator are considered and for the effect of friction term, theoretical and empirical approaches are investigated. Results suggest that the theoretical force model based on analytical and empirical friction forces, respectively, slightly overestimates and underestimates the force experienced by MPAMs during contraction while slightly underestimate and overestimates during expansion, respectively. A comparative analysis between MPAMs featuring Ecoflex-50 silicone and Ecoflex30 + PDMS mixture as bladder materials has also been conducted to further investigate the effect of bladder materials on their force and contraction outputs under inlet pressures ranging from 0 kPa to 300 kPa. It is shown that the MPAM feauting Ecoflex-50 bladder, exhibits lower dead-band pressure and an overall reduced blocked force in comparison to MPAM with bladder made of Ecoflex30 + PDMS while exhibiting a substantially enhanced free contraction capacity.