Engineering design and analysis of EHL for involute cylindrical spur gear transmission
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摘要: 通过分析齿轮润滑机理，揭示了齿轮副啮合线上相对滑动速度的变化规律。根据道森·希金森最小油膜经验公式，对影响齿轮润滑性能的关键因素—当量曲率半径和卷吸速度随传动比和变位系数变化的规律进行分析，基于精确齿廓计算出齿面载荷沿啮合线分布情况。通过编程计算相应的关系曲线图，分析了传动比、变位系数、压力角及中心距等齿轮设计参数对齿轮副最小油膜厚度的影响，结果表明：传动比会使最小油膜厚度曲线倾斜和旋转，变位系数决定了膜厚曲线沿啮合线的起始点和终止点，并引起齿轮副中心距变化间接影响最小油膜厚度，中心距、压力角与最小膜厚的关系是正相关关系。最后，根据膜厚比关系判断齿轮润滑状态，通过实例计算曲线可见，该齿轮副最小油膜厚度点并未发生在小齿轮齿根与大齿轮齿顶啮合点处，因此采用啮合节点油膜厚比来判定齿轮润滑状态。以上所得结论对于齿轮传动弹流润滑设计提供了一定的参考依据。Abstract: Through the analysis of gear lubrication mechanism, the change law of relative sliding speed on the meshing line of gear pair is revealed. According to Dowson-Higginson's empirical formula of minimum oil film, the laws of equivalent curvature radius and entrainment speed changing with transmission ratio and modification coefficient, which are key factors affecting gear lubrication performance, are analyzed. Based on accurate tooth profile, the distribution of tooth surface load along the meshing line is calculated. The influence of gear design parameters such as transmission ratio, modification coefficient, pressure angle and center distance on the minimum oil film thickness of gear pair is analyzed by programming and calculating the corresponding relationship curves. The results show that the transmission ratio makes the minimum oil film thickness curve incline and rotate, the modification coefficient determines the starting and ending points of the film thickness curve along the meshing line, and causes the change of the center distance of the gear pair to indirectly affect the minimum film thickness. The relationship between the center distance, pressure angle and the minimum film thickness is positive correlation. Finally, the gear lubrication state is judged according to the film thickness ratio relationship. It can be seen from the calculation curve of an example that the minimum oil film thickness point of the gear pair does not occur at the meshing point of the pinion tooth root and the big gear tooth top, so the oil film thickness ratio of the meshing node is used to determine the gear lubrication state. The above conclusion provides a reference for the design of elastohydrodynamic lubrication of gear transmission.
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表 1 齿轮参数表
参数名称 数值 参数名称 数值 齿顶高系数ha* 0.95 模数m 2 压力角α/（°） 25 顶隙系数c* 0.2 齿数z1 20 齿数z2 17 变位系数x1 0.23 变位系数x2 0.299 重合度εa 1.224 啮合角α'/（°） 28.06 主动轮输入转速/（r/min） 300 啮合中心距a'/mm 38 主动轮输入功率/W 1 000 齿宽b/mm 24 
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表 2 齿轮变位引起的啮合参数变化
变位情况 中心距a′/mm 啮合角α′/（°） 啮合线长L/mm 情况1 38 28.06 17.88 情况2 37 25 15.64 情况3 36.5 23.27 14.42
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