考虑摩擦的磨损和修形齿轮啮合刚度计算

研究齿面偏差对齿轮啮合刚度的影响，对准确获得齿轮系统动态特性具有重要意义。本文基于改进能量法，提出了一个求解考虑齿面摩擦的直齿轮啮合刚度的完整模型。该模型通过齿廓的参数方程，实现考虑齿轮加工刀具圆角半径和齿面偏差对齿轮单齿啮合刚度的影响；通过齿形误差带来的齿间间隙和轮齿加载变形量的关系，求解出双齿啮合区齿轮副总刚度。分析了磨损齿轮和修形齿轮的啮合刚度、齿间载荷分配系数和传递误差。结果表明：齿面非均匀磨损量会显著降低双齿啮合区刚度并降低重合度，轻载条件下尤为严重；修形齿轮载荷大于修形设计载荷值时，修形效果不明显，而载荷小于修形设计载荷值时，可能出现刚度不足、重合度减小和加载传动误差显著增大等问题。

Stiffness Calculation Considering Friction for a Spur Gear Pair with Tooth Wear and Profile Modification

In order to obtain more accurate dynamic characteristics of gear systems, it is important to investigate mesh stiffness of a gear pair with tooth deviations. A complete mesh stiffness model was proposed base on the energy method with consideration of friction. The presented model considers the influence of wear and profile modification on mesh stiffness by parameter equations of tooth flank and obtains the total mesh stiffness of two meshing gear pairs by the relationship of tooth clearances derived from tooth deviations and deformation under loading. The total mesh stiffness, load sharing between two tooth pairs in mesh and loaded static transmission errors of wear gears and profile modification gears were analysed. Numerical simulations show that especially under light load, nonuniform wear of tooth profile will induce remarkable mesh stiffness reduction and contact ratio decrement. When gear load is greater than the profile modification design load, the benefits of modification are not obvious. If the load is lighter than the profile modification design load, the following problems may arise, such as a lack of mesh stiffness, a decrease in contact ratio and a significant increment of loaded static transmission.