一元三次方程在矿机速度平滑中的应用与实现

速度平滑问题是高速数控加工及煤矿提升机为提高加工精度与设备寿命而提出的,针对该速度平滑问题建立分段模型,基于加速度与速度的关系,推导了各段速度、行程和时间的解析解,推导了模型中关键一元三次方程的通用解,并将其运用到速度平滑分段求解问题中。本方法应用于煤矿提升机速度平滑问题中,显示出易于程序实现、计算量小、过渡曲线平滑的特点,能很好适应高速运动设备速度平滑的场景。目前该方法已推广至多个实际项目中。

Application and implementation of simple cubic equation in velocity smoothing of mine hoist

Velocity smoothing is one problem which is proposed in high speed machining and coal mine safety production,the aim of which is to improve machining accuracy and equipment life.Aiming at this problem,this paper proposes a stage wise model and deduces the closed-form expression solution for each stage based on the relationship of acceleration and velocity,and then deduces the general solutions of cubic equation in detail for the model.Finally,the solutions are applied to the velocity smoothing.The proposed schema shows the advantages of easy to program and smoothing in transition curve when being applied for velocity smoothing in coalmine.The result demonstrates that the proposed method adapts the high-speed scenarios well and has used in other several projects.