基于正交试验的双圆弧齿轮约束模态模型研究

Research on Constraint Modal Model of Double Circular-Arc Gear Based on Orthogonal Experiment

齿轮模态分析主要依靠数值模态分析和试验模态分析法,存在求解过程繁琐且无法直接获取齿轮参数与模态频率振型之间耦合关系的问题。为进一步掌握齿轮主要参数对约束模态频率的影响,根据模态有限元计算理论,对双圆弧齿轮约束模态模型进行研究;分析前6阶模态振型图,采用正交试验方法,运用方差分析,计算各因素对模态频率的影响因子;定量分析双圆弧齿轮的齿数、模数、螺旋角、齿宽因素对约束模态的影响。结果表明:齿数是影响固有频率的主要因素,其次是模数、螺旋角和齿宽;对试验结果进行中心化一次非线性回归模型计算,建立双圆弧齿轮约束模态频率计算模型,实现双圆弧齿轮约束模态的快速计算,对比验证1阶频率计算值的准确性。研究结果为全面研究双圆弧齿轮的振动和噪声特性提供参考。

Modal analysis of gear mainly relies on numerical modal analysis and experimental modal analysis, it claims a tedious solving process and cannot acquire the coupling relationship of gear parameters with modal frequency and vibration mode directly.The constraint modal models of double circular-arc gear were constructed according to the numerical calculation theory of modal in order to further master influences of major gear parameters on natural frequency;the first 6-orders vibration modes were analyzed and influencing factors of various factors on modal frequency were calculated through orthogonal experiment and variance analysis;the influences of teeth number, modal number, helical angle and teeth width of double circular-arc gear on constraint modal of double circular-arc gear were analyzed quantitatively.The results show that teeth number is the primary influencing factor of natural frequency, followed by modal number, helical angle and teeth width successively;the centralized single nonlinear regression model was used to calculate the experimental results, a calculation model of constraint modal frequency of double circular-arc gear was established to realize the fast calculation of the constraint modal, and the calculation accuracies of 1 order frequencies were compared and verified.The research results provide reference for the study of vibration and noise characteristics of double circular-arc gear comprehensively.