基于四次贝塞尔曲线的起重机转弯非圆曲线轨道优化设计

为解决有轨起重机在转弯时出现的啃轨、卡轨问题,提出了基于贝塞尔曲线的起重机非圆曲线轨道方案。方案选用四次贝塞尔曲线作为转弯内轨曲线,针对起重机单轮和多轮情况,通过起重机大车行走机构的几何关系计算出外侧前后点的轨迹。以外侧前后点最小偏差量为优化目标函数,利用多始点启发式全局优化算法搜寻最优的贝塞尔曲线参数,并通过Hermite插值法拟合出外轨轨迹。计算结果表明,与传统圆弧转弯轨道相比,以非圆贝塞尔曲线作转弯轨道时在起重机转弯过程中出现的外侧前后点最大偏差量大幅减小。此外还分析得出,偏差量会随着基距和轨距的增大而增大,随着圆弧内轨半径和直轨道夹角的增大而减小。另外,通过计算比较非圆四次贝塞尔曲线轨道曲率半径与圆弧轨道情况下单轮和2轮台车卡轨时极限曲率半径,验证了起重机大车转弯的实际通过性,最后利用ADAMS进行动态仿真实验论证。

Optimization Design of Non-circular Curve Track of Crane Turning Based on Four Times Bezier Curve

In order to solve the problems of rail gnawing and jamming in the turning of rail crane, a non-circular curve scheme of the crane based on Bezier curve is proposed. In the scheme, the fourth Bezier curve is chosen as the turning curve of the inner rail. According to the single wheel and multi-wheel situation of the crane, the tracks of the front and rear points on the outer side are calculated through the geometric relationship of the traveling mechanism of the crane cart. Taking the minimum deviation of the front and back points as the objective function of optimization, and the optimal parameters of Bezier curve are searched by the multi-start point heuristic global optimization algorithm, and the outer orbit trajectory is fitted by Hermite interpolation. The calculation results show that the maximum deviation of the front and rear points on the outside of the crane during the turning process decreases significantly when the non-circular Bezier curve is used as the turning track compared with the traditional circular turning track. In addition, it is also analyzed that the deviation will increase with the increase of the base distance and the gauge distance, and decrease with the increase of the radius of the arc inner rail and the angle between the straight track. In addition, the curvature radius of non-circular quadruple Bezier curve track is calculated and compared with the curvature radius of single-wheeled and two-wheeled trolleys when they are stuck on circular track, which verifies the actual passability of the crane's turning. Finally, ADAMS is used to carry out dynamic simulation experiment and demonstrate the calculation.