齿轮副的静、动态数值计算与动态光弹性实验研究
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摘要
本文以标准渐开线直齿圆柱齿轮作为研究对象。利用共轭曲面原理推导出齿根齿形曲线方程,并据此创建出精确的二维和三维全齿数齿轮模型。论证了齿轮加工刀具齿顶圆弧半径对齿根齿形曲线的曲率以及齿根弯曲强度的影响。针对四种加载方式进行静、动态有限元计算,并对简化的齿轮模型进行误差分析。
本文提出一种新的边界条件,同时约束两轮的径向和轴向位移,保留两轮的周向转动自由度,在主动轮上施加由于高速旋转引起的惯性转矩,在从动轮上施加因外部阻力引起的扭矩负载。利用创建的三维齿轮啮合模型结合新的边界条件进行有限元计算,通过对比可知,采用新边界条件得到的结果更接近真实值。
齿轮传动是最重要的传动形式之一,良好润滑是保证齿轮正常运转的关键因素,为了研究各种齿轮参数对润滑油膜的影响,引入多重网格法求解齿轮在重载下的弹流润滑问题,计算结果令人满意。多重网格法具有收敛速度快,数值稳定性好的优点,已经被证明是一种功能强大的数值计算方法。计算结果显示,通过增大齿轮的模数、传动比、分度圆压力角、齿轮转速和润滑油粘度等参数可以增加齿面间的润滑油膜的厚度,从而有效地减小磨损、胶合等失效形式发生的几率。
综合考虑轮齿在不同啮合点处的当量曲率半径、卷吸速度、轮齿所受载荷随时间的变化,以及压力对润滑油粘度和密度的影响,利用多重网格技术求得齿轮在非稳态弹流润滑条件下的完全数值解。分析了轮齿在整个啮合过程中受到的载荷以及冲击载荷对齿轮弹流润滑的影响,并将计算出的油膜压力作为加载参数进行考虑弹流润滑影响的齿轮强度有限元计算,这一工作是前人没有做过的探索性工作。
以光弹性法原理为基础,在一对由聚碳酸脂材料制成的齿轮啮合模型上施加不同脉宽的冲击载荷,通过“动态光力学实验的数字图像采集系统”记录模型受到冲击载荷作用后不同瞬时产生的等差线条纹图。对比实验数据与有限元计算结果可知,两者的吻合性非常好。
The standard involute cylinder gear is studied in this paper. The formula for the tooth shape curves of dedendum is deduced by means of the Theory of Conjugate Surfaces, and the two-dimension and three-dimension accurate models are established based on the formula. The effect to curvature and intensity of root caused by the variation of cutter tip curvature radius was analyzed. Static and dynamic FEM calculations were executed under four loading conditions and the error was analyzed for the simplified gear model.
A new boundary condition is proposed in present work that the radial and axial displacement is constrained and the rotation is allowed. The inner torsion caused by the high speed rotation is applied on the initiative wheel, and the distortion load arose from the outer resistance is acted on the driven wheel. The three-dimension gear contact model is created and then is used for finite element analysis. The results indicate that the calculation according to the new boundary condition is more approach to the true value than the old one.
The gear transmission is one of the most important mechanical transmissions. Well lubrication between of the gears is the key factor effecting the gear transmission. In order to analyze the influence of various parameters on film of gear lubrication, the multi-grid method is introduced by its application in the elastohydrodynamic lubrication (EHL) of involute spur gear. The results presented in this paper are satisfied and the multi-grid method has been proved as a powerful and robust algorithm for its good numerical stability and high convergence speed. The calculation and analysis indicate that the oil film thickness will be become thicker with the increase of gear modulus, transmission ratio, pressure angle, rotating velocity and oil viscosity. This would decrease the wearing and gluing of the gear.
A full transient elastohydrodynamic lubrication solution of an involute spur gear was obtained by utilizing the multigrid method, which takes into account the variation of equivalent curvature, entertainment velocity and load with time along the line ofaction, without the lubricant thermal and rheological effects. The influences of load spectrum, where the load is carried by one pair of teeth and two pairs of teeth repeatedly, and impact load when the teeth come into action on the elastohydrodynamic lubrication are analyzed as well. The dynamic results are compared with static ones.
The impact loadings with different pulse width are exerted on the model of polycarbonate gears in Photoelastic experiment. The dynamic photoelastic isochromatic fringe images at different moment were recorded by means of instantaneous image capturing system. The experimental results coincide well with the results calculated by FEM.
本文提出一种新的边界条件,同时约束两轮的径向和轴向位移,保留两轮的周向转动自由度,在主动轮上施加由于高速旋转引起的惯性转矩,在从动轮上施加因外部阻力引起的扭矩负载。利用创建的三维齿轮啮合模型结合新的边界条件进行有限元计算,通过对比可知,采用新边界条件得到的结果更接近真实值。
齿轮传动是最重要的传动形式之一,良好润滑是保证齿轮正常运转的关键因素,为了研究各种齿轮参数对润滑油膜的影响,引入多重网格法求解齿轮在重载下的弹流润滑问题,计算结果令人满意。多重网格法具有收敛速度快,数值稳定性好的优点,已经被证明是一种功能强大的数值计算方法。计算结果显示,通过增大齿轮的模数、传动比、分度圆压力角、齿轮转速和润滑油粘度等参数可以增加齿面间的润滑油膜的厚度,从而有效地减小磨损、胶合等失效形式发生的几率。
综合考虑轮齿在不同啮合点处的当量曲率半径、卷吸速度、轮齿所受载荷随时间的变化,以及压力对润滑油粘度和密度的影响,利用多重网格技术求得齿轮在非稳态弹流润滑条件下的完全数值解。分析了轮齿在整个啮合过程中受到的载荷以及冲击载荷对齿轮弹流润滑的影响,并将计算出的油膜压力作为加载参数进行考虑弹流润滑影响的齿轮强度有限元计算,这一工作是前人没有做过的探索性工作。
以光弹性法原理为基础,在一对由聚碳酸脂材料制成的齿轮啮合模型上施加不同脉宽的冲击载荷,通过“动态光力学实验的数字图像采集系统”记录模型受到冲击载荷作用后不同瞬时产生的等差线条纹图。对比实验数据与有限元计算结果可知,两者的吻合性非常好。
The standard involute cylinder gear is studied in this paper. The formula for the tooth shape curves of dedendum is deduced by means of the Theory of Conjugate Surfaces, and the two-dimension and three-dimension accurate models are established based on the formula. The effect to curvature and intensity of root caused by the variation of cutter tip curvature radius was analyzed. Static and dynamic FEM calculations were executed under four loading conditions and the error was analyzed for the simplified gear model.
A new boundary condition is proposed in present work that the radial and axial displacement is constrained and the rotation is allowed. The inner torsion caused by the high speed rotation is applied on the initiative wheel, and the distortion load arose from the outer resistance is acted on the driven wheel. The three-dimension gear contact model is created and then is used for finite element analysis. The results indicate that the calculation according to the new boundary condition is more approach to the true value than the old one.
The gear transmission is one of the most important mechanical transmissions. Well lubrication between of the gears is the key factor effecting the gear transmission. In order to analyze the influence of various parameters on film of gear lubrication, the multi-grid method is introduced by its application in the elastohydrodynamic lubrication (EHL) of involute spur gear. The results presented in this paper are satisfied and the multi-grid method has been proved as a powerful and robust algorithm for its good numerical stability and high convergence speed. The calculation and analysis indicate that the oil film thickness will be become thicker with the increase of gear modulus, transmission ratio, pressure angle, rotating velocity and oil viscosity. This would decrease the wearing and gluing of the gear.
A full transient elastohydrodynamic lubrication solution of an involute spur gear was obtained by utilizing the multigrid method, which takes into account the variation of equivalent curvature, entertainment velocity and load with time along the line ofaction, without the lubricant thermal and rheological effects. The influences of load spectrum, where the load is carried by one pair of teeth and two pairs of teeth repeatedly, and impact load when the teeth come into action on the elastohydrodynamic lubrication are analyzed as well. The dynamic results are compared with static ones.
The impact loadings with different pulse width are exerted on the model of polycarbonate gears in Photoelastic experiment. The dynamic photoelastic isochromatic fringe images at different moment were recorded by means of instantaneous image capturing system. The experimental results coincide well with the results calculated by FEM.
引文
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