Study on a Nonlinear Dynamic Model and Its Parameters Determination Method for Half-Sine Programmer

半正弦波形发生器的非线性动力学模型及模型参数标定方法研究

¹ School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China
² Qingdao Research Institute, Northwestern Polytechnical University, Qingdao 266200, China
³ Beijing Institute of Electronic System Engineering, Beijing 100854, China
⁴ Shanghai Aerospace System Engineering, Shanghai 201109, China

Received: 10 November 2018

Abstract

A nonlinear dynamic model for describing shock response of half-sine programmer in shock test is constructed, in which many important factors in half-sine programmer such as size, hard nonlinearity, damping and initial impact velocity are considered, based on the damped Duffing equation, and the empirical static stiffness and shock stiffness calculation formulas of cylindrical rubber isolator. The shock pulse of half-sine programmer is measured and calculated by using shock test machine and Runge-Kutta method. Taking the minimum determination coefficient between the calculated and the measured shock pulse as the optimization objective, the parameters in the present model are determined by using quantum genetic algorithm (QGA), and meanwhile the extreme capacity in the present model for describing the dynamic behavior of half-sine programmer under shock excitations can also be verified. Experiments were implemented with drop shock test machine. The experimental results show that the present model is precise and efficient, and the prediction errors of pulse peaks and pulse widths were all below 5%, the waveform fitting errors between the calculated and the measured pulses are all less than 15%. The present results are helpful for designing the half-sine programmer.

摘要

借鉴有阻尼达芬方程、圆柱形橡胶隔振器的静刚度和冲击刚度经验公式，建立了预测半正弦波形发生器冲击波形的非线性动力学模型。该模型综合考虑了半正弦波形发生器的尺寸、硬非线性、阻尼、冲击初速度等复杂因素。结合冲击试验机和龙格库塔方法，给出了半正弦波形发生器冲击波形的测量和计算方法。以预测波形和实测波形的确定系数最小为优化目标，采用量子遗传算法对模型中的相关参数进行反辨识，同时也验证了该非线性模型针对半正弦波形发生器在冲击激励下的动力学行为的极限描述能力。结果表明，所建立的模型精度较高，其中峰值和脉宽误差均在5%以下，波形拟合误差小于15%。该模型及参数反辨识方法有助于精确地设计半正弦波形发生器。