【摘要】 基于控制离散步长来保证预测精度的思想,提出了一种改进的用于预测铣削稳定性叶瓣图的时域全离散法。一直以来,铣削工艺系统的动力学过程被看作带有单个延时反馈量的周期性线性系统,其数学模型是无限维时滞微分方程组。全离散法在一个周期内将时滞微分方程离散为有限个常微分方程,求解前后两步的状态转移矩阵,继而得到一个完整周期内的状态转移矩阵。在选定的转速范围内循环求解过程中,通过控制离散步长小于设定值来达到提高低转速条件下全离散法的收敛率的目的。通过仿真和切削实验,证明方法具有较高的预测精度和计算效率。更多还原

【Abstract】 A modified full-discretization method is proposed for milling stability prediction based on timestep control. The dynamic process of milling system is regarded as a linear periodic system with a single time delay and its mathematical model is formulated as delay-differential equations( DDEs). By dividing the delay period equally into a set of time steps,the state transition matrixes between the adjacent two steps could be deduced by the full-discretization method. Then the state transition matrix over one delay period is structured. By controlling the time steps not exceeding the set value when scanning the objective range of rotating speed,the full-discretization method converges faster than setting a constant time interval value. At last the modified method is verified by simulation and experiments.更多还原