Load distribution model along the line of contact for involute external gears
Load distribution model along the line of contact for involute external gears
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DOI：
10.1016/j.mechmachtheory.2009.12.009
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发表时间：
2010-05
影响因子：
5.2
通讯作者：
J. I. Pedrero;M. Pleguezuelos;M. Artés;Juan A. Antona
中科院分区：
文献类型：
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作者：
J. I. Pedrero;M. Pleguezuelos;M. Artés;Juan A. Antona
技术文献中提供的用于初步设计或标准化目的的直齿轮和斜齿轮的计算方法使用线性弹性理论(纳维尔方程)和赫兹接触模型给出的简单方程来计算弯曲和接触应力，假设载荷沿接触线均匀分布。然而，这些模型与实验结果并不能很好地吻合，因为沿作用线改变的齿对啮合刚度产生了不均匀的载荷分布，导致需要一些载荷分布系数来计算弯曲应力和接触应力。本文从最小弹性势能准则出发，建立了接触线上载荷分布不均匀的模型。该模型与Navier和Hertz方程相结合，得到了更接近实际的弯曲应力和接触应力。文中还给出了单位长度载荷在接触线上任意一点和啮合周期任意位置的近似精确的逆么正势方程。对系数稍作修改后，同样的公式也适用于底切牙齿。通过与有限元计算结果的比较，验证了计算结果的正确性。
Calculation methods of spur and helical gears for preliminary designs or standardization purposes available in technical literature use simple equations given by the linear theory of elasticity (Navier’s equation) and the Hertzian contact model to evaluate the bending and contact stresses, assuming the load to be uniformly distributed along the line of contact. However, these models are not in good agreement with experimental results because the changing meshing stiffness of the pair of teeth along the line of action produces a non-uniform load distribution, causing some load distribution factors to be required to compute bending and contact stresses. In this paper, a model of non-uniform load distribution along the line of contact, obtained from the minimum elastic potential energy criterion, is presented. This model combined with the equations of Navier and Hertz yields more realistic values of the bending and contact stresses. An approximate, accurate equation for the inverse unitary potential, allowing analytic calculations of the load per unit of length at any point of the line of contact and any position of the cycle of meshing, is also presented. The same equation, with a slight modification of the coefficients, is also valid for undercut teeth. Results have been validated by comparison with some studies carried out by the Finite Element Method.