人字齿轮最佳齿向修形设计的Kriging响应面法

Kriging Response Surface Method for Optimal Axial Modification of Herringbone Gear

为了最大程度地降低人字齿轮时变啮合刚度引起的振动,改善齿面载荷分布不均,将人字齿轮两侧修形量单独考虑,提出一种以动载系数最小、结合Kriging响应面的人字齿轮最佳齿向修形设计方法。首先,根据两侧修形量与时变啮合刚度函数建立的BP神经预测网络来得到Kriging响应面所需的样本数据。然后,通过Kriging模型建立时变啮合刚度各参数响应面。其次,建立人字齿轮弯扭轴耦合动力学模型,并将Kriging预测的人字齿轮时变啮合刚度函数带入动力学微分方程中,求解动载系数并建立响应面,得到全局最优齿向修形参数。最后,通过算例证实人字齿两侧最佳鼓形量并不一致,能够较好地补偿人字齿轮实际传动中由于误差和变形导致的两侧不同的啮合歪斜度,所优化获得的修形人字齿轮动载系数相比未修形下的动载系数减少41.29%,且比常规修形方法(ISO)的减少了15.04%。

In order to minimize the vibration caused by the time-varying meshing stiffness of herring-bone gear and to improve uneven distribution of tooth surface loads,considering the amount of modification on both sides of a herringbone gear separately,a method for optimization of herringbone gear axial modification was proposed based on minimize of dynamic load factor combined with Kriging response surface.Firstly,The BP neural network was established based on the two sides of the longitudinal correction and time-varying meshing stiffness function to obtain the sample data needed for the Kriging response surface.Then,the time-varying meshing stiffness parameter response surface was established by Kriging model.Secondly,the dynamics model coupled with lateral,torsional and shaft for herringbone gear pair was established,and the time-varying meshing stiffness function which was predicted by Kriging,applied to dynamical differential equation,and then the dynamic load factor response surface was established,so optimal parameters of globel gear axial modification was obtained.Finally,example shows that the best value of crowning on both sides of the herringbone tooth is not uniform,it can better compensate for the different meshing skewness caused by the error and deformation in the actual transmission of the herringbone gear.The dynamic load factor of the herringbone gear obtained in this paper is reduced by 41.29%compared to the unmodified form,and is reduced by 15.04%compared with the conventional modification method(ISO).