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.

霍夫鲍尔循环机是一种很有前途的加热技术。由于其非连续运动，与传统的 Vuilleumier 机器相比，它具有许多优点。然而，它的非连续运动也给控制带来了挑战。在这项工作中，提出了一个简化的动态模型来预测控制的自由行程。基于对置换器的质量弹簧系统的假设，推导出了一个简化的解决方案。简化的解决方案基于压力平衡点的恒定位置和工作室中气体质量的线性变化。在原型机上进行了实验以验证模型。分析置换器的运动并揭示异常运动的原因。然后，根据简化模型得到预测的自由行程，并与实测结果进行比较。相对误差在-2.45% ∼ +3.02% 范围内。因此，该简化模型可为霍夫鲍尔循环机的快速控制提供参考。