Accurate analysis of the air gap magnetic field is the focus of research in the field of precision permanent magnet linear synchronous motors. In this paper, the two-dimensional air gap magnetic field of a secondary trapezoidal Halbach permanent magnet array coreless permanent magnet linear synchronous motor (PMLSM) was taken as our research object. On the basis of the equivalent surface current method, we proposed an improved equivalent analytical algorithm with a trapezoidal side length unit. The equivalent analytical model of the magnetic induction vector of the two-dimensional air gap was established, and the air gap magnetic field of the trapezoidal Halbach array coreless PMLSM was calculated. At the same time, we analyzed the influence of the bottom angle α of a trapezoidal permanent magnet equivalent width coefficient α_w, pole height coefficient α_h, and air gap height coefficient α_g on the amplitude (B_peak) and total harmonic distortion (THD_B) of the central magnetic field in the air gap. The results show that α and α_w have a significant influence on the B_peak and THD_B of the central magnetic field air gap. With the synergy of α and α_w, we identified the “flux convergence” effect, which makes the maximum range of B_peak α > 90° and α_w < 0.5. We also found the “equilateral” effect, which causes the minimum region of THD_B to change linearly. The calculation results of the improved equivalent surface current analytical model established in this paper agree with those verified by the finite element method. The calculation is convenient, and the accuracy of the result is high. This research provides a new method for analyzing the air gap magnetic field of a permanent magnet with a nonrectangular cross-section and lays a theoretical foundation for optimizing the PMLSM pole model.

The design of heat transfer performance of regenerator is the key technology of Stirling machine and is of great significance to ensure the operation efficiency of equipment. In this study the temperature difference between the two ends of regenerator at room temperature is less than 50K. This paper attempts to study the heat transfer performance of the straight channel grid regenerator at room temperature and verify its accuracy. At first, a straight-channel grid regenerator was designed in this study by analyzing the influence of structural parameters on the regenerator in order to reduce the flow resistance loss. The Pore Scale method and Representative Elementary Volume methods were combined to analyze the heat transfer characteristics of the grid regenerator. Compared with the wire mesh regenerator under the same condition, the straight-channel grid regenerator’s flow resistance could reduce by 96.2%. When the length-diameter ratio is 2:1 and the porosity is between 0.4 and 0.5, the heat transfer performance of the grid regenerator is satisfactory when it is applied in Stirling heat pump at room temperature. Then, A segmented variable porosity grid regenerator was designed based on the grid regenerator, and its performance was proved to be better than that of the grid regenerator. Finally, the two regenerators were developed based on additive manufacturing technology, and a single blow experiment platform was built. The experimental results fit well with the simulation results, with the maximum error being less than 1.5%. The experimental results prove the correctness of the model, which lays a foundation for the subsequent analysis of the periodic heat transfer characteristics of the straight-channel grid regenerator.

The regenerator plays an extremely important role in the Stirling circulation. A grid regenerator can be used for inverse Stirling machines at room temperature due to its low flow resistance. This paper proposes a hexagonal grid regenerator to theoretically explore heat transfer properties in the inverse Stirling cycle and establishes an approximate analytical model to analyze the effect mechanism of working frequency, thermal diffusivity and wall thickness on the oscillation flow. The results show that the wall thickness is one of the key factors affecting the equivalent heat transfer coefficient. Specifically, too small or too large wall thickness increases the instability of the heat transfer process. The ultimate wall thickness is determined by the equivalent heat transfer coefficient and thermal penetration depth, whose optimal value ensures not only sufficient heat exchange but also the full utilization of materials. With the increase in frequency, heat exchange performance is improved monotonously. Therefore, high–frequency operation can improve the heat exchange performance of the regenerator. In addition, an optimization criterion for the size of regenerator with the specific capacity of heat transfer as the objective parameter is proposed based on the equivalent heat transfer coefficient. The optimal parameters were obtained when relative thickness was set as 0.8 mm and the equivalent heat transfer coefficient was up to 10⁴–10⁵ W/m²·K indicating that the grid regenerator has broad application prospects in the inverse Stirling cycle.

This study seeks to improve the performance of a low-temperature differential free-piston Stirling air conditioner (FPSAC). To achieve this, a novel approach is proposed, which replaces the conventional simple harmonic drive with a multi-harmonic drive. This modification aims to optimize the motion of the driving piston, bringing it closer to the ideal movement pattern. The research involves both thermodynamic and dynamic coupling simulations of the FPSAC, complemented by experimental verification of its key performance parameters. A thermodynamic model for the gas medium, employing a quasi-one-dimensional dynamic approach for compressible fluids, and a nonlinear two-dimensional vibration dynamic model for the solid piston are developed, focusing on the low-temperature differential FPSAC physical model. The finite difference method is employed to numerically simulate the entire system, including the electromagnetic thrust of the multi-harmonic-driven linear oscillating motor, fluid transport equations, and the nonlinear dynamic equations of the power and gas control pistons. Variations in displacement, velocity, and pressure for each control volume at any given time are obtained, along with the indicator and temperature–entropy diagrams after the system stabilizes. The simulation results show that, in cooling mode, assuming no heat loss or mechanical friction, the Stirling cooler operates at a frequency of 80 Hz. Using the COP_sin value for the simple harmonic drive as a baseline, performance is improved by altering the driving method. Under the multi-harmonic drive, the COP_c5 increased by 10.03% and COP_c7 by 14.23%. In heating mode, the COP under the multi-harmonic drive improved by 0.51% for COP_h5 and 2.61% for COP_h7. Performance experiments were conducted on the low-temperature differential FPSAC, and the key parameter test results showed good agreement with the simulation outcomes. The maximum deviation at the trough was found to be less than 2.45%, while at the peak, the maximum error did not exceed 3.61%. When compared to the simple harmonic drive, the application of the multi-harmonic drive significantly enhances the overall efficiency of the FPSAC, demonstrating its superior performance. The simulation analysis and experimental results indicate a significant improvement in the coefficient of performance of the Stirling cooler under the multi-harmonic drive at the same power level, demonstrating that the multi-harmonic drive is an effective approach for enhancing FPSAC performance. Furthermore, it should be noted that the method proposed in this study is applicable to other types of low-temperature differential free-piston Stirling air conditioners.

The main purpose of this paper is to analyze the heat transfer mechanism of a new type of regenerator with a low temperature difference and low current resistance under oscillatory flow at room temperature. Taking the single tube of the regenerator as the research object, the exact analytical solution of the radial heat transfer characteristics of the regenerator is obtained by studying its analytical model. The factors affecting the heat transfer characteristics are analyzed, and then the regenerator is optimized to improve the performance and efficiency of the regenerator system. In this study, we systematically analyzed the radial heat transfer characteristics of a regenerator under isochoric process conditions. A closed-system physical model of the incompressible isochoric process under oscillating flow was established. Then, the radial analytical solutions of pressure fluctuation, fluid velocity, fluid-solid temperature, and heat were derived in the complex number field. Furthermore, the fluid velocity, fluid-solid coupling wall temperature, heat, and equivalent heat transfer coefficient were assessed. Furthermore, the influences of frequency, inner diameter R1 of the regenerator, and different working medium and materials on the above parameters were discussed. It was found that the analysis and evaluation of fluid velocity, fluid-structure coupling wall temperature, heat, and equivalent heat transfer coefficient are helpful in understanding the dynamic characteristics of radial heat transfer in a regenerator system. Through the study of radial heat transfer under oscillating flow, it was found that the working medium, frequency, inner diameter of the regenerator, and material quality of the regenerator are helpful for the design optimization of the regenerator. Furthermore, our investigations established that the variation law of wall fluid-solid coupling temperature amplitude could be divided into three parts: the unidirectional flow part; the low-frequency part, where the temperature amplitude falls rapidly with increasing frequency; and the high-frequency part, where the temperature amplitude increases with the frequency. In addition, the variation of radial heat transfer of the fluid-solid coupling surface is similar to the changes in the temperature amplitude. We also discovered that the equivalent heat transfer coefficient of the fluid-solid surface is related to thermal conductivity of the material. Specifically, larger thermal conductivity values result in greater equivalent heat transfer coefficients. Based on the research into the radial heat transfer characteristics, the new regenerator has great application potential in the Stirling air conditioning system at room temperature.

Unlike traditional free-piston Stirling heat engines or heat pumps, the free piston Stirling air conditioning (FPSAC) is specifically designed for electric vehicle air conditioning under ambient room temperature conditions. In the FPSAC system, the displacer and the power piston are coupled through gas forces, emphasizing the importance of investing the thermodynamic–kinetic coupling characteristics. This study analyzed the damping terms within the dynamic equations of the FPSAC model and solved these equations to reveal system dynamics. By linearizing the working chamber’s pressure, the study examined the machine’s dynamic behavior, presenting solutions for amplitude and phase angle. Derived expressions for the displacement and acceleration of both the power piston and the displacer further support this analysis. The research evaluates the influence of driving force on amplitude and phase angle, alongside the impact of damping coefficients, thereby isolating thermodynamic–dynamic coupling characteristics. Control equations integrating dynamics and thermodynamics were developed, and a comprehensive system model was constructed using MATLAB(2020a)/Simulink to simulate acceleration and displacement variation in the pistons. Key findings include: (1) a positive correlation between driving force and displacer, where increased force leads to higher amplitudes; (2) a frequency of 65 Hz reveals a singularity occurs in displacer amplitude, resulting in system instability; (3) phase angle between pistons reduces to below 10° when the driving force exceeds 150 N; and (4) the power piston’s amplitude decreases with an increase in damping C_1, while changes in damping C₂ primarily affect the displacer’s singularity position around 65 Hz, with higher C₂ values shifting the singularity to lower frequencies.