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 Nonlinear mathematical model is one of the indispensable foundations for nonlinear system research. Based on the simplified coupling between stages, a nonlinear mathematical model of three degree spur gear reducer with multiple degrees of freedom is established. The mathematical model Firstly, it is expressed by nonlinear differential equations and then transformed into a spatial representation of state variables. It can be directly used to solve nonlinear differential equations, and can be appropriately simplified to meet the needs of different occasions. In the application of most spur gear drive applications can give quite accurate results  The solution given by this model is consistent with the field test results of reducer for a gun servo system