Dynamic characteristic of aviation spiral bevel gear with ERSFD
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摘要:
将弹性环式挤压油膜阻尼器（ERSFD）引入弧齿锥齿轮传动（SBGD）系统中以改善其动态特性。基于广义雷诺方程建立内外油膜控制方程，并通过半解析方法得到弹性环的变形，获得ERSFD油膜力后基于径向基（RBF）神经网络建立其近似模型，建立带有ERSFD支撑的8自由度SBGD系统双向流固耦合动力学模型，借助分时迭代方法获得系统稳态响应。结果表明：内油膜压力沿圆周分段式分布，且沿偏移线为非对称分布；ERSFD的存在有效削弱了油膜力与偏心率之间的非线性关系；弹性环凸台厚度的增加，使系统振动响应的幅值整体下降，并抑制了5200～8200 r/min转速范围内系统的混沌行为，有效改善了SBGD系统动态特性。
Abstract:Elastic ring squeeze film damper (ERSFD) was introduced into the spiral bevel gear drive (SBGD) to improve its dynamic characteristics. Based on the generalized Reynolds equation, the internal and external oil film control equations were established. The deformation of the elastic ring was obtained by semi-analytical method. After obtaining the ERSFD oil film force, an approximate model was established based on the radial basis function （RBF） neural network. A bidirectional fluid-structure interaction dynamic model of an 8 degree of freedom spiral bevel gear transmission system with ERSFD support was established. The steady-state response of the system was obtained by the block interation method. The results showed that the inner oil film pressure was distributed in segments along the circumference and asymmetrically distributed along the offset line. The existence of ERSFD effectively weakened the nonlinear relationship between oil film force and eccentricity. The increasing thickness of the elastic ring boss reduced the amplitude of the vibration response of the system, suppressed the chaotic behavior of the system within the speed range of 5200−8200 r/min, and effectively improved the dynamic characteristics of the spiral bevel gear transmission system.
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图 3 内油膜上下表面速度示意图
Figure 3. Schematic diagram of the velocity of the upper and lower surfaces of the inner oil film
图 10 β = π/4时油膜分力及油膜压力随偏心率的变化曲线
Figure 10. Variation curves of oil film component force and oil film pressure with eccentricity for β = π/4
图 11 不同凸台厚度下，主动轮横向振动位移响应随转速变化分岔图
Figure 11. Bifurcation diagram of the lateral vibration displacement response of the pinion with the change of rotational speed under different boss thicknesses
图 12 主动轮转速为2200 r/min下，不同凸台厚度对应的系统振动响应
Figure 12. Vibration response of the system corresponding to different boss thicknesses when the pinion speed is 2200 r/min
图 13 主动轮转速5800 r/min下，不同凸台厚度对应的系统振动响应
Figure 13. Vibration response of the system corresponding to different boss thicknesses when the pinion speed is 5800 r/min
图 14 主动轮转速7600 r/min下，不同凸台厚度对应的系统振动响应
Figure 14. Vibration response of the system corresponding to different boss thicknesses when the pinion speed is 7600 r/min
表 2 ERSFD相关参数
Table 2. ERSFD related parameters
参数 数值 凸台数 8 凸台对应角度/（°） π/4 弹性环长度/mm 20 渗油孔数 8 流体黏度/（Pa·s） 0.01844 内油膜初始间隙/mm 0.2 外油膜初始间隙/mm 0.2 
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表 3 SBGD相关参数
Table 3. SBGD related parameters
参数 数值及说明 主动轮 从动轮 齿数 47 53 质量/kg 0.8 1.5 转动惯量/（kg·mm2） 1040 3120 旋向 左旋 右旋 偏心距/μm 0.5 压力角/（°） 20 中点螺旋角/（°） 20 轴交角/（°） 108 齿宽/mm 30 平均传动误差/mm 0.02 平均啮合刚度/108 （N/m） 3 啮合阻尼/（N·s/m） 1000 径向支承刚度/108 （N/m） 3 径向支撑阻尼/（N·s/m） 500 轴向支承刚度/108 （N/m） 5 轴向支撑阻尼/（N·s/m） 500
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