平面机构动力平衡最优化计算的一种数学模型

本文论述了机构震动力、震动力矩、平衡力矩与固定支承运动副反力之间的关系,得出了可用固定支承运动副反力极小化计算代替震动力和震动力矩的平衡计算的结论。文中提出了机构动力平衡约束最优化的一种数学模型;引用机构动态静力分析的矩阵法建立了运动副反力、平衡力矩与平衡质量参数间的关系式,简化了上述数学模型所需计算公式的推导过程。

A Mathematical Model for Optimum Calculation of Dynamic Balance of Planar Mechanisms

The relationships between shaking force, shaking moment, equilibrium moment and reaction of kinematic pair of fixed support are discussed. It is shown that the balancing calculation of shaking force and shaking moment can be replaced by the minimization calculation of the reaction of kinematic pair of fixed support. A mathematical model for dynamic balance of mechanism with constraint optimization is proposed. The unknown parameters of balancing mass fixed on the rotating link connected to the fixed link are taken as variables in the calculation. The objective function is the minimized reaction of kinematic pair of fixed support and the cons-traint conditions are the restriction on the fluctuation of equilibrium moment and the restriction on the reaction of kinematic pair unconnected to fixed link. The matrix method is used to establish the relations between the reaction of kinematic pair, the equilibrium moment and the parameters of balancing mass, thus simplifying the derivation of the calculating formulae.