The smoothing function is used to solve the problem of low simulation efficiency of multi-stage stiffness Dual Mass Flywheel (DMF) model, and the influence of different smoothing functions and fitting factor β on the fitting effect is studied. Firstly, based on the analysis of the working principle of multi-stage stiffness DMF, a mathematical model of DMF considering multi-stage stiffness and damping nonlinearity is established, and the accuracy of the model is verified by bench test. Then, tanh function, arctangent function, and sigmoid function are used to smooth the segment points in the DMF model, which solves the problem of inefficiency and not easy to converge in simulation. Finally, a 3-DOF model of the transmission system with DMF is established to simulate and analyze the smooth effect of the smoothing function and the performance difference between different smoothing functions. The results show that the smoothing function can effectively improve the stability of the simulation model. By comparing the three smoothing functions, it can be seen that the sigmoid function has the most obvious effect, which can shorten the simulation time by 52%.

中文翻译：

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基于平滑函数拟合的多级非线性双质量飞轮扭转阻尼器建模

利用平滑函数解决多级刚度双质量飞轮(DMF)模型仿真效率低的问题，研究了不同平滑函数和拟合因子β对拟合效果的影响。首先，在分析多级刚度DMF工作原理的基础上，建立了考虑多级刚度和阻尼非线性的DMF数学模型，并通过台架试验验证了模型的准确性。然后利用tanh函数、反正切函数、sigmoid函数对DMF模型中的段点进行平滑处理，解决了仿真中效率低、不易收敛的问题。最后，建立含DMF的传动系统3-DOF模型，对平滑函数的平滑效果和不同平滑函数之间的性能差异进行仿真分析。结果表明，平滑函数可以有效提高仿真模型的稳定性。通过比较三种平滑函数，可以看出sigmoid函数效果最明显，可以将仿真时间缩短52%。