船舶肋骨线型高精度拟合方法

High Precision Fitting Method for Ship Frame Line

船舶肋骨线型拟合的精度直接影响数控肋骨冷弯机弯制的精度,传统“用单条三次曲线拟合一整根肋骨线型”的方法具有无法严格经过所有给定点、误差分析无依据和未考虑曲率半径等缺陷。为避免这些缺陷,将整根肋骨看成多个分段,每个分段是一个独立的三次曲线,且参数数量正好等于已知数数量,使参数的解静定。针对由考虑曲率半径产生的非线性优化问题,将分段函数的处理从全局坐标系转换到局部坐标系,将分段的待求解参数从4个降维至2个,便于指定参数的初始解。利用坐标变换,将局部坐标系的结果转换回全局坐标系,拟合后的肋骨线型满足:严格经过所有给定点;曲率半径以高精度逼近给定值,误差的数量级为10^(-5)。

The fitting precision of ship frame line directly affects the bending precision of numerical control frame cold bending machine.The traditional method of“fitting the whole frame line with a single cubic curve”is of the defects of failing to strictly pass all the given points,having no basis for the error analysis,and not considering the curvature radius.In order to avoid the defects,the whole frame is regarded as multiple segments,each segment is an independent cubic curve,and the parameter quantity is exactly equal to the known number quantity,so that the parameter solution is statically determinate.In view of the nonlinear optimization problem caused by considering the curvature radius,the processing of segment function is transformed from the global coordinate system to the local coordinate system,and the dimension reduction from 4 to 2 of segment parameters to be solved are made,which is convenient to specify the initial solution of the parameters.By means of coordinate transformation,the results of the local coordinate system are converted back to the global coordinate system,and the fitted frame lines meet the following requirements:it strictly passes all the given points;the curvature radius approximates the given value with high precision,and the order of magnitude of error is 10^(-5).