高速高精度电子齿轮箱自抗扰控制研究

针对展成法加工齿轮切削力呈周期性变化引起刀具与工件的相对位姿偏差, 导致工件齿轮加工误差的问题, 文章提出一种基于自抗扰控制(active disturbance rejection control, ADRC) 的主从式电子齿轮箱(electronic gearbox, EGB) 控制方法。首先, 分析滚齿加工过程中机床各运动轴之间的联动关系, 建立斜齿轮加工运动控制数学模型, 确立主从式 EGB 结构模型; 其次, 建立 EGB 中各轴跟踪误差与工件齿轮齿廓偏差、齿距偏差和螺旋线偏差之间的数学关系, 采用交叉耦合控制(cross-coupling control, CCC) 补偿方式求解出各运动轴的补偿量, 对从动轴进行补偿; 然后, 构建基于传统比例积分微分(proportional integral derivative, PID) 控制和扩张状态观测器(extended state observer, ESO) 的 ADRC-EGB, 评估 EGB 从动轴所受的干扰并进行补偿, 提高其同步精度和鲁棒性。最后, 在开放式实时半实物仿真平台开展滚齿加工运动模拟实验。结果表明该 EGB 控制结构相较于传统 EGB 具有更高的同步控制精度和抗干扰能力。

To reduce machining errors caused by the relative pose deviation between the tool and the gear due to the time-varying cutting force in gear generating machining, this paper proposes a master-slave electronic gearbox(EGB) control method based on active disturbance rejection control(ADRC). Firstly, the mathematical model of helical gear machining motion control was established based on the motion relationship of the gear hobbing machine axes, and thus the master-slave EGB structure was determined. Then, the mathematical relationship between the tracking deviation of motion axes and the gear profile deviation, pitch deviation and helix deviation in EGB was established, and the compensation amount of each motion axis was solved. The compensation was performed on the slave axis by using the cross-coupling control(CCC) method. Secondly, ADRC-EGB based on proportional integral derivative(PID) control and extended state observer(ESO) was constructed. The disturbance on the slave axis of EGB was predicted and compensated to improve its synchronization accuracy and robustness. Finally, a simulation experiment of gear hobbing motion was carried out on a real-time hardware-in-loop platform. The experimental results showed that compared with the traditional EGB control methods, the proposed EGB control method had higher synchronization control accuracy and anti-disturbance ability.