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标 题： A model of spur gears supported by ball bearings
由滚珠轴承支撑的直齿齿轮模型
作 者： F. Viadero
A. Fernandez del Rincon
R. Sancibrian
P. Garcia Fernandez
A. de Juan
关键词： Gear  [齿轮]
Transmission error  [ 传输错误]
Bearings  [ 轴承]
Tooth contact  [ 牙齿接触]
Load ratio  [ 负载比]
出版年： 2007
文集名： Computational Methods and Experimental Measruements XIII
计算方法与实验测量 XIII
会议名： 13th International Conference on Computational Methods and Experimental Measurements (CMEM XIII)
第十三届计算方法与实验测量国际会议（CMEM XIII）
届 次： 13th
摘 要： In this work a model of a 2D spur gear transmission is described for analysis of tooth contact forces and deformations. Assuming the position of each wheel is known, the contact points between gears are obtained taking into account the geometric description of the tooth profiles including profile errors and relief modifications. Then the deformation in each contact point is separated into a global and a local term combining a finite element model and an analytical formulation originating from Hertzian contact theory. The proposed procedure does not need new element meshing for each angular position thus obtaining an important computational advantage. Afterwards, a non-linear system of equations is obtained and solved for each gear position in order to calculate the meshing contact forces. The model can include the possibility of bidirectional single-flank or double-flank action as well as friction forces in the out-of-action line. Once the contact forces are known, it is possible to use the procedure in the calculation of loaded transmission error and meshing stiffness. Furthermore, each gear is supported by ball bearings that are included in the model taking into account their clearance and their variable stiffness due to the change in the number of balls supporting the load. This variable bearing compliance modifies the gear centre distance and as a consequence the transmission error during a turn. Using this methodology a numerical example is presented where the static behaviour of a spur gear transmission is described and analysed. Special attention is focused on the influence of load level on the final loaded transmission error.

本文描述了一种二维直齿齿轮传动模型，用于分析齿面接触力和变形。假设每个齿轮的位置已知，通过考虑齿形的几何特征（包括齿形误差和齿槽修正），可求得齿轮之间的接触点。随后，将每个接触点的变形分解为全局项和局部项，该方法结合了有限元模型与源自赫兹接触理论的解析公式。所提出的计算方法无需为每个齿侧位置重新划分网格，从而具有显著的计算优势。接着，针对每种齿轮位置建立非线性方程组并求解，以计算啮合接触力。该模型可包含双向单侧或双侧啮合以及非啮合线方向上的摩擦力。一旦接触力确定，便可利用该方法计算载荷下的传动误差和啮合刚度。此外，每个齿轮均采用球轴承支撑，该模型考虑了轴承的间隙以及因承载负荷的滚珠数量变化而产生的弹性刚度变化。这种可变的轴承刚度会改变齿轮中心距，从而影响传动过程中转速误差。本文通过数值实例展示了直齿齿轮传动系统的静力行为，并进行了分析，特别关注了载荷水平对最终传动误差的影响。
中文内容为网络AI翻译，专业术语未必准确，仅供参考。

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