Stiffness estimation of planar spiral spring based on Gaussian process regression

Abstract

Planar spiral spring is important for the dimensional miniaturisation of motor-based elastic actuators. However, when the stiffness calculation of the spring arm is based on simple beam bending theory, the results possess substantial errors compared with the stiffness obtained from finite-element analysis (FEA). It deems that the errors arise from the spiral length term in the calculation formula. Two Gaussian process regression models are trained to amend this term in the stiffness calculation of spring arm and complete spring. For the former, 216 spring arms’ data sets, including different spiral radiuses, pitches, wrap angles and the stiffness from FEA, are employed for training. The latter engages 180 double-arm springs’ data sets, including widths instead of wrap angles. The simulation of five spring arms and five planar spiral springs with arbitrary dimensional parameters verifies that the absolute values of errors between the predicted stiffness and the stiffness from FEA are reduced to be less than 0.5% and 2.8%, respectively. A planar spiral spring for a powered ankle–foot prosthesis is designed and manufactured to verify further, of which the predicted value possesses a 3.25% error compared with the measured stiffness. Therefore, the amendment based on the prediction of trained models is available.