基于指数窗截取递推最小二乘法的齿轮啮合刚度辨识算法研究

齿轮在机械传动系统中有着广泛应用,由于齿轮啮合过程中参与啮合的轮齿对数周期变化,因此,齿轮啮合刚度为时变参数,在啮合时会产生啮合振动。当齿轮副出现齿根裂纹时,啮合刚度会减小,齿轮啮合产生的系统振动响应也发生改变,通过振动响应辨识齿轮啮合刚度能够监测齿轮副的健康状态。针对齿轮啮合刚度的时变特征,提出了基于指数窗截取递推最小二乘(Exponential window recursive least square,EWRLS)算法和振动信号瞬时频率的齿轮啮合刚度辨识方法。进行啮合刚度辨识时,EWRLS算法将输入、输出齿轮的转速曲线分别作为辨识输入信号和观测信号,使用指数窗函数进行数据截断,使用递推最小二乘算法估计系统参数。为了计算输入、输出齿轮的转速曲线,使用经验模态分解(Empirical mode decomposition,EMD)方法将振动信号分解为具有不同变化频率的本征模态函数(Intrinsic mode function,IMF),并根据IMF的平均频率重构输入、输出齿轮的特征信号。通过Hilbert变换计算特征信号的瞬时频率曲线,从而获得各齿轮的转速曲线。使用仿真和实测信号对算法进行验证,结果表明,EWRLS算法能够辨识齿轮副的时变啮合刚度。

Research of Gear Meshing Stiffness Identification Algorithm based on Exponential Window Interception Recursive Least Square Method

Gear is widely applied in mechanical transmission systems.Gear meshing stiffness is a time varying parameter because of the periodical changing of the numbers of teeth involved in meshing process,the meshing vibration is generated during gear meshing.When the cracks are existed in roots of gear teeth,the mesh?ing stiffness decreased,vibration response of the system due to gear meshing changed as well.Thus,identifying gear meshing stiffness through vibration response is a method monitoring healthy state of gear pairs.For the time-varying character of meshing stiffness,a gear meshing stiffness identification algorithm is proposed based on exponential window recursive least square method(EWRLS)interception and instantaneous frequency of the vibration signal.During the identification of meshing stiffness,EWRLS algorithm takes the speed curves of the input and output gears as the identification input signal and observation signal,respectively.In the algorithm,the exponential window is applied to intercept data,and the recursive least square algorithm is applied to esti?mate parameters of the system.To calculate speed curve of the input and output gears,the empirical mode de?composition(EMD)method is used to decompose vibration signal into intrinsic mode function(IMF)of differ?ent frequency,the IMFs are used to reconstruct character signals of input and output gears basing on the mean frequency of IMFs.The Hilbert transform is applied to calculate the instantaneous frequency curve of the charac?ter signals to obtain the speed curves of gears.The simulated signal and measured signal are used to validate the algorithm,results show that the EWRLS algorithm can identify time-varying meshing stiffness of gear pair.