The double-row self-aligning ball bearing commonly runs with angular misalignment between the inner and outer rings, and the angular misalignment significantly affects the bearing performance. However, the effect of angular misalignment on the dynamic characteristics of the double-row self-aligning ball bearing has not been studied thoroughly. This paper investigates the effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing. The quasi-static model for the double-row self-aligning ball bearing is established with five degrees of freedom, namely, three translational displacements along x, y, and z directions and two tilting angles around x-axis and y-axis. The internal clearance between balls and raceways is included in the presented model. The formulation of the three-dimensional stiffness matrix for the double-row self-aligning ball bearing is analytically derived, and is verified by comparing with the available dada in published literature. Finally, the stiffness of the double-row self-aligning ball bearing under various angular misalignment conditions is analyzed systematically. The results show that the tilting angles vary the contact angles and contact forces of the compressed balls in the double-row self-aligning ball bearing, thus affect the bearing stiffness; the bearing stiffness decreases with the internal clearance; the angular misalignment significantly impacts the stiffness of the bearing running at a low speed.

中文翻译：

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角度不对中对双列调心球轴承刚度的影响

双列调心球轴承通常在内圈和外圈之间存在角度不对中，角度不对中会显着影响轴承性能。然而，角度不对中对双列调心球轴承动态特性的影响尚未得到深入研究。本文研究了角度不对中对双列调心球轴承刚度的影响。双列调心球轴承的准静态模型建立了五个自由度，即沿x、y、z方向的三个平移位移和绕x轴和y轴的两个倾斜角。滚珠和滚道之间的内部间隙包含在所呈现的模型中。双列调心球轴承三维刚度矩阵的公式是通过分析推导出来的，并通过与已发表文献中的可用数据进行比较来验证。最后，系统地分析了双列调心球轴承在各种角度不对中条件下的刚度。结果表明，倾角会改变双列调心球轴承中压缩球的接触角和接触力，从而影响轴承刚度；轴承刚度随着内部游隙的增加而降低；角度不对中会显着影响低速运行的轴承的刚度。系统分析了双列调心球轴承在各种角度不对中条件下的刚度。结果表明，倾角会改变双列调心球轴承中压缩球的接触角和接触力，从而影响轴承刚度；轴承刚度随着内部游隙的增加而降低；角度不对中会显着影响低速运行的轴承的刚度。系统分析了双列调心球轴承在各种角度不对中条件下的刚度。结果表明，倾角会改变双列调心球轴承中压缩球的接触角和接触力，从而影响轴承刚度；轴承刚度随着内部游隙的增加而降低；角度不对中会显着影响低速运行的轴承的刚度。