﻿ 修形斜齿轮啮合线振动加速度数值分析和试验验证
 舰船科学技术  2016, Vol. 38 Issue (12): 79-82 PDF

Numerical and experimental study on vibration acceleration in line of action of helical gears with flank modification
SU Bao-long
Navy Equipment Representative Office of Harbin Turbine Company Limited, Harbin 150046, China
Abstract: In the present work, a coupled bending-torsion-axial vibration model of helical gear was developed considering flank modification. Helical gears vibration acceleration in line of action was numerically determined using this model. Furthermore, helical gears with flank modification were manufactured and a power circulatory type gear test rig for vibration measurement was established. The vibration acceleration in line of action was measured using a pair of grating sensors. It is shown that the vibration acceleration in line of action predicted by the present model is in the similar trend with the experimental results, and the root mean square values of vibration acceleration are reduced to 55.3% of that of the gears without flank modification. Vibration level of helical gear is dramatically decreased through flank modification.
Key words: helical gears     flank modification     vibration acceleration in line of action     experiment
0 引 言

1 斜齿轮振动分析模型

 $z = y\tan \beta\text{。}$ (1)
 图 1 斜齿轮弯曲-扭转-轴向耦合振动模型 Fig. 1 Bending-torsion-axial vibration model of helical gears

 $\left\{ \begin{array}{l} {m_p}{{\ddot y}_p} + {c_{py}}{{\dot y}_p} + {k_{py}}{y_p} =-{F_y}\text{，}\\ {m_p}{{\ddot z}_p} + {c_{pz}}{{\dot z}_p} + {k_{pz}}{z_p} =-{F_z}\text{，}\\ {I_p}{{\ddot \theta }_p} =-{F_y} \cdot {R_p} + {T_p}\text{。} \end{array} \right.$ (2)
 $\left\{ \begin{array}{l} {m_g}{{\ddot y}_g} + {c_{gy}}{{\dot y}_g} + {k_{gy}}{y_g} = {F_y}\text{，}\\ {m_g}{{\ddot z}_g} + {c_{gz}}{{\dot z}_g} + {k_{gz}}{z_g} = {F_z}\text{，}\\ {I_g}{{\ddot \theta }_g} = {F_y} \cdot {R_g}-{T_g}\text{。} \end{array} \right.$ (3)

 $q = {R_p}{\vartheta _p}-{R_g}{\vartheta _g}\text{，}$ (4)

 \left\{ \begin{aligned} & {m_p}{{\ddot y}_p} + {c_{py}}{{\dot y}_p} + {k_{py}}{y_p} + \cos \beta {c_m}({{\dot y}_p}-{{\dot y}_g} + \dot q) +\\ & \quad \quad \cos \beta {k_m}({y_p}-{y_g} + q) = {F_s} + {F_u}\text{，}\\ & {m_p}{{\ddot z}_p} + {c_{pz}}{{\dot z}_p} + {k_{pz}}{z_p} + \sin \beta {c_m}\tan \beta ({{\dot y}_p}-{{\dot y}_g} + \dot q) +\\ & \quad \quad \sin \beta {c_m}({{\dot z}_p}-{{\dot z}_g}) + \sin \beta {k_m}\tan \beta ({y_p}-{y_g} + q) +\\ & \quad \quad \sin \beta {k_m}({z_p}-{z_g}) = \tan \beta ({F_s} + {F_u})\text{，}\\ & {m_g}{{\ddot y}_g} + {c_{gy}}{{\dot y}_g} + {k_{gy}}{y_g} + \cos \beta {c_m}({{\dot y}_g}-{{\dot y}_p}-\dot q)+\\ & \quad \quad \cos \beta {k_m}({y_g}-{y_p}-q) =-{F_s}-{F_u}\text{，}\\ & {m_g}{{\ddot z}_g} + {c_{gz}}{{\dot z}_g} + {k_{gz}}{z_g}-\sin \beta {c_m}\tan \beta ({{\dot y}_p}-{{\dot y}_g} + \dot q) +\\ & \quad \quad \sin \beta {c_m}({{\dot z}_g}-{{\dot z}_p})-\sin \beta {k_m}\tan \beta ({y_p}-{y_g} + q) +\\ & \quad \quad \sin \beta {k_m}({z_g}-{z_p}) =-\tan \beta ({F_s} + {F_u})\text{，}\\ & ({m_t}\ddot q + {c_m}\cos \beta \dot q + {k_m}\cos \beta q + {c_m}\cos \beta ({{\dot y}_p}-{{\dot y}_g}) +\\ & \quad \quad {k_m}\cos \beta ({y_p}-{y_g}) = {T_p}/{R_p} + ({F_s} + {F_u})\text{。} \end{aligned} \right. (5)

2 振动模型计算算例

 图 2 齿廓修形和齿向修形示意图 Fig. 2 Schematic of profile modification and lead correction

 图 3 修形前后斜齿轮仿真振动加速度 Fig. 3 Simulated vibration acceleration of helical gears before and after flank modification
3 试验验证

 图 4 啮合线振动加速度测试试验台布置 Fig. 4 Vibration acceleration in line of action test rig arrangement

 $\Delta \ddot x = {\ddot x_p}-{\ddot x_g} = {\ddot \varphi _p}{R_{{{bp}}}}-{\ddot \varphi _g}{R_{{{bg}}}}\text{。}$ (6)

 图 5 修形前后试验斜齿轮接触印痕 Fig. 5 Contact pattern of helical gears before and after flank modification

 图 6 修形前后试验斜齿轮啮合线振动加速度 Fig. 6 Tested vibration acceleration in line of action of helical gears before and after modification

4 结 语

1）通过斜齿轮弯曲-扭转-轴向耦合振动分析模型进行计算，发现斜齿轮修形后，其啮合线振动加速度波动明显降低。

2）通过齿轮接触印痕试验证明了该试验件安装对中状态良好。

3）通过实验测试高速下修形斜齿轮啮合线振动加速度均方根，和仿真模型计算结果对比，发现两者修形后振动加速度均方根降低幅度基本一致，仿真结果降低了 53.2%，试验测试结果降低了 55.3%，证明了仿真模型的有效性。

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