星形人字齿轮传动系统振动模式的理论研究

采用集中质量法建立了含N个星轮的星形人字齿轮传动系统的弯-扭-轴耦合动力学模型和动力学方程。模型中将人字齿轮看作由两斜齿轮通过无质量弹簧连接而成。求解了系统的固有圆频率和固有振型，根据振动模式将星形人字齿轮传动系统的固有振动模式进行分类，并对其重根数和固有频数个数进行了理论研究。结果表明：星形人字齿轮传动系统含有4种典型振动模式，即：中心构件轴向-扭转耦合模态(重根数 r=1)，星轮模态(重根数 r=N-3，N>3)，中心构件平动模态(重根数 r=2)，星轮与中心轮耦合模态(重根数 r=2)。

Theoretical Research of Vibration Modes for Double-helical Star Gear Transmission Systems

Dynamics model and dynamics equations with coupled bent-torsional-axial of a double-helical star gear transmission system was established based on the lumped mass method. The double-helical gears were treated as two helical gears with opposite spiral angle connected by massless spring which had the bending, torsion and axial stiffnesses. The natural cyclic frequencies and vibration modes of the system were calculated. The structure of the vibration modes were well-defined, where the special structure resulted from the cyclic symmetry of the star herringbone gears. Vibration modes were classified into four categories and the multiplicities and numbers of the eigenvalue were analyzed. The results show that the double-helical star gear transmission system has four typical vibration modes: axial-rotational coupled vibration mode (multiplicity r=1), star gear mode (multiplicity r=N-3, N>3), center component translational vibration mode (multiplicity r=2), star gear and center gear coupled mode (multiplicity r=2).