直齿圆锥齿轮的时变弹流润滑分析

目的研究直齿圆锥齿轮传动过程中稳态和非稳态下的压力和膜厚,为降低直齿圆锥齿轮的表面磨损及齿轮设计提供理论指导。方法将一对直齿圆锥齿轮等效为一对圆锥滚子模型,运用无限长线接触理论,建立直齿圆锥齿轮啮合过程中的弹流润滑计算模型,先对直齿圆锥齿轮进行等温稳态弹流润滑分析,计算并分析了直齿圆锥齿轮大端和小端啮入、啮出点的油膜压力及油膜厚度,求解并分析了小端啮合区间五个特殊点的油膜压力和膜厚。考虑瞬态时变效应的影响,计算并分析了直齿圆锥齿轮在三个特殊瞬时点的油膜压力和油膜厚度。最后研究齿面在高斯分布粗糙度函数和余弦粗糙度函数作用下的弹流润滑数值解,在此基础上计算了不同幅值和波长下的油膜压力和油膜厚度。压力求解采用多重网格法,弹性变形采用多重网格积分法。结果稳态等温条件下,小端啮入点和啮出点的出口油膜厚度略小于大端,小端啮合区间的最小油膜厚度从啮入点到啮出点逐渐增大。在瞬态时变效应下,啮入点的油膜压力大于节点和啮出点的油膜压力,其油膜厚度较其他两个瞬时点的油膜厚度小。高斯分布粗糙度函数作用下的油膜压力在赫兹接触区有明显的局部压力峰,油膜厚度在赫兹接触区有局部波动;余弦粗糙度函数作用下的油膜压力和油膜厚度在赫兹接触区有波动,且粗糙度幅值和波长越大,波动程度越明显。结论采用高斯分布粗糙度函数时,油膜压力的变化相对比较缓和,采用余弦粗糙度函数的最大油膜压力小于采用高斯分布粗糙度函数的最大油膜压力,和高斯分布粗糙度函数相比,余弦粗糙度函数下的油膜厚度在赫兹接触区呈现周期性波动。

Analysis on Isothermal Time-varying Elastohydrodynamic Lubrication of Spur Bevel Gear

The work aims to reduce surface wear and provide theoretical guidance for gear design by studying pressure and film thickness in steady state and unsteady state during spur bevel gear transmission. A pair of spur bevel gears were equivalent to a pair of tapered roller models, calculation model of elastohydrodynamic lubrication during spur bevel gear meshing was established based upon infinite line contact theory. Isothermal elastohydrodynamic lubrication was analyzed first, oil film pressure and oil film thickness at point of engaging-in and point of engaging-out were calculated and analyzed on large end and small end of the gear. Oil film pressure and film thickness at five special points in small-end meshing interval were solved and analyzed. Allowing for the effects of transient time-varying effect, the oil film pressure and oil film thickness of spur bevel gear at three special instantaneous points were calculated and analyzed. Finally, numerical solution of the elastohydrodynamic lubrication under the effects of Gaussian rough asperity and cosine asperity was taken into account. On this basis, the oil film pressure and oil film thickness at different roughness peaks and wavelengths were calculated. The pressure was calculated in multi-grid method, and elastic deformation was calculated in multi-grid integration method. Under steady isothermal condition, the exit oil film thickness at point of engaging-in and point of engaging-out on the small end was slightly smaller than that on the large end. Minimum film thickness in small-end meshing interval gradually increased from the point of engaging-in to point of engaging-out. Under instantaneous transient effect, the oil film pressure at point of engaging-in was higher than that at point of engaging-out, and oil film thickness was lower than that at the other two instantaneous points. The oil film pressure under effect of Gaussian roughing asperity exhibited obvious partial pressure peak in Hertzian contact area, the oil film pressure showed partial depression in the Hertzian contact area. The oil film pressure and oil film thickness fluctuated in the Hertzian contact area under the effect of cosine roughness function, and fluctuation degree was more obvious as roughness amplitude and wavelength increased. Oil film pressure changes relatively mildly under the effect of Gaussian distribution roughness function, the maximum oil film pressure under the effect of cosine roughness function is lower than that under the effect of Gaussian distribution roughness function. Compared with oil film thickness under the effect of Gaussian distribution roughness function, the thickness under the effect of cosine roughness function shows periodic fluctuation in Hertzian contact zone.