塑料斜齿轮黏弹性数值模拟研究

Study on Numerical Simulation of Viscoelasticity of Plastic Helical Gear

以聚甲醛塑料材料为例,选择了广义Kelvin模型作为塑料齿轮研究的黏弹性模型,分析得出钢制齿轮与塑料齿轮啮合的黏弹性变形方程,无量纲化弹流润滑方程并离散化建立非线性方程组,推演该方程组的雅克比矩阵并利用Newton-Raphson迭代方法求解该方程组后得到油膜形状及压力分布。在黏弹性基础上分析油膜形状和油膜厚度,考虑速度和载荷对压力分布及油膜分布的影响。结果表明:塑料齿轮相对较软,在啮合过程中在接触区内与金属斜齿轮啮合在润滑状态下的油膜形状也相对缓和;考虑塑料齿轮的黏弹特性,油膜在主要承载区域油膜厚度增加;当速度增加时,油膜厚度变厚,压力峰值向入口移动;当载荷增加时,油膜厚度变薄,压力峰值向出口移动。

Taking POM plastic materials as an example,selecting generalized Kelvin Model as vis- co--elasticity model for study plastic gear, the visco--elasticity deformation equation of plastic gear meshing with steel gear is obtained. Elastohydrodynamic lubrication equations are established with di- mensionless method and following nonlinear equations are solved with discretization method to get the oil film shape and the pressure distribution with Newton--Raphson Iteration Method. The shape and thickness of oil film are both analyzed based on the plastic characteristics of visco--elasticity with the consideration of velocity and load. Results show that, the soft plastic gear being meshed with steel one is gradual film shape in the contact area being lubricated. Considering the visco--elasticity of plastics, the film shape becomes thicker in the main loading zone, the film gets thicker and the pressure peak moves towards entrance with increasing velocity. The film gets thinner and the pressure peak moves towards exit with the increasing load.