A simplified dynamic model for the prediction of displacer's free stroke in Hofbauer cycle machine.

• A simplified dynamic model is developed for prediction of displacer's free stroke. • Experiments on Hofbauer cycle machine is carried out. • A simplified method of determining the masses in chambers with leakage is proposed. • Relative error of predicted pressure is in the range of -0.26% ∼ 0.85% • Relative error of predicted free stroke is in the range of -2.45% ∼ +3.02%. Hofbauer cycle machine is one promising technology for heating. It has many advantages compared to conventional Vuilleumier machines due to its non-continuous motions. However, its non-continuous motions also bring challenges for control. In this work, a simplified dynamic model is proposed to predict the free stroke for control. Based on assumption of a mass-spring system for the displacers, a simplified solution is deduced. The simplified solution is based on constant position of pressure balance points and a linear change of gas mass in the working chamber. Experiments on a prototype machine were carried out to validate the model. Motions of displacers are analyzed and causes for abnormal motions are revealed. Then, the predicted free stroke is obtained based on the simplified model and compared with the measured results. The relative error is in the range of -2.45% ∼ +3.02%. Thus, the simplified model could provide a reference for quick control in Hofbauer cycle machines. [ABSTRACT FROM AUTHOR]