三级直齿圆柱齿轮减速器的非线性数学模型

非线性数学模型是开展非线性系统研究工作不可缺少的基础之一文章在对级间耦合简化的基础上建立了三级直齿圆柱齿轮减速器的多自由度非线性数学模型该数学模型首先用非线性微分方程组来表达，然后将其化为状态变量空间表达形式它可直接用于非线性微分方程的求解，也可作适当的简化以满足不同场合的需要该模型在计算中应用了解刚性方程的方法，在大多数直齿圆柱齿轮传动的应用场合，都可以给出相当精确的结果此模型给出的解答与某火炮伺服系统用减速器的现场试验结果是一致

A NONLINEAR MATHEMATICAL MODEL OF THREE STEP SPUR REDUCTION GEAR

Nonlinear mathematical omdel is one of the indispensable basis when the research work of nonlinear system is carried out.In this paper,the multi degree of freedom nonlinear mathematical model of three step spur reduction gear based on simplifying intravitions between step and step is established.First,the mathematical model is formulated by use of nonlinear differential equations.Then,it is transformed into state variation space formulation mode.It is not only directly solved by use of the nonlinear differential equations,but also solved by use of simplified model in various cases,then the requirement is satisfied.The special calculating method for solving stiff differetial equations is adopted.The model can give a quite accurate solrtion and can be applied to most situation of spur gears.A calculating result of the model conform to reduction gear testing practice of a kind of gun servo mechanism.