基于中点弦测法的中低速磁浮轨道不平顺误差研究

Research on Irregularity Error of Medium and Low Speed Maglev Track Based on Midpoint Chord Measurement Method

中低速磁浮轨道10 m弦测值作为评价轨道几何平顺性的标准时,由于弦测值在幅频范围内存在畸变并受基准线选取的影响而产生较大误差。本文推导了弦测法“以小推大”的传递函数,进一步定义了“以小推大”及其逆推算法的误差放大系数;分析了弦长、矩阵维度对误差积累特性的影响,结合传递函数分析不同波长对误差的敏感性差异,并通过数值模拟进行验证。结果表明:“以小推大”算法及其逆推算法在传递函数为0的波长范围内误差积累较严重,轨道不平顺功率谱密度出现阶跃信号;随着矩阵维度的增加,“以小推大”逆推算法的误差快速积累,推得的小弦长越小则误差积累越小。应用“以小推大”算法时应减小大小弦长比值;对于“以小推大”逆推算法,要减小采样步长、可换算最小弦长以及矩阵维度。

When the 10 meter chord measurement value of a medium and low speed maglev track was used as a standard to evaluate the geometric irregularity of the track,significant errors occur due to the distortion of the chord measurement value in the amplitude frequency range and the influence of the reference line selection.This paper derived the transfer function of“using small to push big”and further defined the error amplification coefficients of“using small to push big”and its inverse calculation methods.The influence of chord length and matrix dimension on error accumulation characteristics was analyzed,the sensitivity differences of different wavelengths to errors were analyzed by combining with transfer function,which was verified through numerical simulation.The results show that the error accumulation of“using small to push big”and its inverse calculation method is serious within the wavelength range of the transfer function of 0,and the spectral density of the track irregularity power has a step signal.As the dimension of the matrix increases,the error accumulation of the“using small to push big”inverse calculation method quickly accumulates.The smaller the derived small chord length,the smaller the error accumulation will be.When applying the algorithm of“using small to push big”,the ratio of size to chord length should be reduced.For the“using small to push big”inverse algorithm,it is necessary to reduce the sampling step size,the minimum chord length which can be converted and the matrix dimension..