基于铣削力建模的复杂曲面加工误差补偿研究
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摘要
复杂曲面由于具有优良的功能特性和表面的美观,被广泛应用于航空航天、汽车零部件、模具的表面设计中。该类表面均要求具有高的尺寸精度和表面质量,一般在多轴CNC机床上进行加工,其半精铣和精铣的过程一般采用球头铣刀进行。表面质量通常用表面精度、表面粗糙度、表面残余应力的性质及其大小和表面加工硬化程度等指标来表征。目前针对复杂曲面精度的研究较少,尤其是涉及到复杂曲面几何特征的由刀具系统的受力变形产生的误差的研究较少。本文通过对复杂曲面几何特征和多轴铣削加工过程运动学的综合分析,深入分析表面精度与曲面曲率、刀具位姿及其它铣削参数(切削速度、轴向切深、径向切深和每齿进给量等)的关系,提出提高表面精度的曲面加工误差补偿方法及高精度走刀路径的选择方式,为复杂曲面多轴加工的精度控制提供科学的依据和可行的方法。
在分类讨论了复杂曲面法曲率半径的求解方法的基础上,考虑曲率半径和刀具前倾角,对复杂曲面多轴球头铣削过程的铣削力进行了理论建模与仿真。针对多轴球头铣削特点,采用Lee和Altintas的瞬时刚性力模型,建立了刀具-工件接触区域内任意一点的微元铣削力公式；采用解析几何的方法建立了基于曲率半径和前倾角的切入、切出角以及轴向极限位置角的模型,进一步建立了刀具-工件接触区域模型；针对立式5轴加工中心DMU-70V,建立了各相关坐标系之间的转化关系模型,提出了三维整体铣削力模型并采用Matlab实现了仿真,通过仿真结果分析了曲率半径和刀具前倾角对三向铣削力的影响规律,为后续的精度预测与控制提供了可靠的理论依据。
刀具系统的变形和偏心对铣削力和加工误差有着重要的影响。为求解刀具系统的受力变形,铣削力被简化成为作用在刀具-工件接触区域一点上的集中作用力,X、Y方向上的集中力作用点处的挠度即为刀具受力变形量,区别于传统的两段式悬臂梁刀具受力变形模型,针对球头铣刀的三段式(刀杆、刀具刀刃部分-非球头和球头部分)结构,利用材料力学,建立了球头铣刀三段式悬臂梁刀具受力变形模型；通过比较新的三段式模型、传统两段式模型和使用ANSYS 12.0 Workbench有限元分析软件仿真得到的刀具变形结果,证明新的刀具受力模型与有限元结果较为相近；进行了刀具偏心对铣削力影响的扩展研究,发现刀具偏心不只影响每齿进给量,而且还对刀具有效切削半径和刀具旋转角度有一定的影响；基于三段式悬臂梁球头铣刀变形模型和刀具偏心扩展研究,提出复杂曲面铣削力的扩展模型。
根据机床坐标系下X、Y方向上集中力作用点处的刀具系统变形量,建立了复杂曲面加工路径上任意一点处工件局部坐标系下法向量方向曲面误差模型；对每一CL数据点,基于复杂曲面多轴加工特点,计算曲面误差,并通过迭代运算,对曲面误差进行补偿,使其满足加工要求。选用典型的正弦曲面进行刀具变形误差建模,并对其刀轨文件进行了离线误差补偿,证实了经过误差补偿后的走刀路径比未补偿的路径与理想路径相近。
对多轴铣削,除了可以通过基于分析不同走刀路径上的曲面曲率选择最佳的走刀路径方向来减小刀具变形,提高加工精度外,还可以通过对刀具倾角的分析进行选择最佳的刀具位姿来提高加工精度。本文分三种(平面、凸面和凹面)曲面分别讨论了步长和行距与曲率半径之间的关系,以高精度为目标,研究了三种典型走刀路径生成方式(参数线法、截平面法和等残留高度法)的走刀路径方向的选择问题；通过分析刀具前倾角与进给(X)、垂直进给(Y)方向刀具系统变形量和曲面法向误差之间的关系,发现进给(X)方向和垂直进给(Y)方向刀具系统变形量均随着刀具前倾角的增大而先增大后减小,曲面法向误差随着刀具前倾角的增大而增大,因此在满足其它要求的情况下,尽量取小的刀具前倾角值是最优的选择；选取典型复杂曲面进行了新的等残留高度法走刀路径方向的选择实例验证,结果表明本文提出的等残留高度法可以显著减少加工时间,提高加工效率,而且通过优选初始路径,得到最小的曲面误差的加工方向。
Complex surfaces have been widely used in aerospace, automotive and die/mold industries, because of their excellent functional properties and appearence. These kinds of surfaces are required to have high requirements on dimensional precision and surface quality. Multi-axis CNC machine tools are usually used for complex surfaces machining, and ball-end mills are usually used in semi-finish and finish milling processes. The surface quality includes surface precision, surface roughness, surface residual stress and surface work hardening etc. Complex surfaces and especially the surfaces with non-single curvature are seldom investigated. Among them, little overall and systematic research, especially the research on surface error due to cutting force-induced tool deflections has been made, and these surface errors are closely related with the geometric features of complex surfaces. In this dissertation, by analysising the geometric features of complex surfaces and the kinematics of multi-axis ball-end milling process synthetically, the relationships among surface precision, curvature radius, cutter orientation and cutting parameters have been thoroughly analyzed. The error compensation method and tool path direction selection method for high surface precision have been proposed. It is an important foundation subject for precision control in multi-axis ball-end milling.
The solving methods for curvature radius of complex surfaces are discussed separately. Considering the curvature radius and tool inclination angle, the theoretical-model and simulation of cutting forces on multi-axis ball-end milling of complex surfaces are carried. According to the characteristic of multi-axis ball-end milling, equations to estimate the cutting forces at a differential element on the cutting edge are established based on the instantaneous cutting force model proposed by Lee and Altintas. Start/exit radial immersion angles and limit axial position angles are solved using analytical geometry method taking into account the curvature radius and tool inclination angle, and then contact areas between cutter and workpiece are obtained. The mappings among all related coordinate of DMU-70V vertical machining center are modeled,3-dimensional cutting forces were modeled and simulated using Matlab software. The simulation results show the influence of curvature radius and tool inclination angle on the cutting forces in the X, Y, Z directions. It provides the reliable theoretical basis for the subsequent prediction and control of surface precision.
The cutting forces are simplified to concentrated forces which act on a point of cutter-workpiece contact area. The deflections of action points of concentrated forces in the X, Y directions are cutting force-induced tool deflections. Different from the traditional two segments cantilever beam tool deflection model, addressing the three parts (shank, flute-non ball-end and ball-end parts) of ball-end mill, three segments cantilever beam tool deflection model was built using materials mechanics method for ball-end mill. The comparison results show that, the tool deflection magnitude calculated by the new three segments method match better with the results of ANSYS 12.0 Workbench method than the results of the traditional two segments. Cutter eccentricity has an important impact on cutting forces through acting on feed per tooth, effective cutting radius and tool rotation angle. Then the extended researches on the cutting force model of complex surfaces were explored based on the three segments cantilever beam tool deflection model and the extended research on cutter eccentricity.
Based on tool deflection values of the acting point of force in the X, Y directions, for arbitrary point of tool path in the workpiece local coordinate system, the complex surfaces error model in the normal direction was established. After the error modeling, the error compensation was finished using iterative algorithm on every CL point based on the features analysis of multi-axis ball-end milling of complex surfaces. A typical sinusoidal surface was chosen for tool deflection error modeling, and off-line error compensation of the tool path file was finished. The results show that the tool paths after error compensation match better with the designed ones than those without error compensation.
Different from the case of 3-axis milling, the tool deflection in multi-axis milling could decrease by choosing not only the best tool path direction based on the analysis of curvature radius of different tool path direction, but also the best tool inclination angle. In this dissertation, the relationship between step length and path internal with the curvature radius was discussed separately for three surface types (plane, convex and concave surface). For getting high precision, the selection of tool path direction was discussed for three typical tool path generation methods (iso-parametric, iso-planar and iso-scallop method). Through analyzing the relationship between tool deflections in the X, Y directions and surface normal error with the tool inclination angle, selecting the tool inclination angle as small as possible is best for high suface precision. An example was presented to verify the newly proposed iso-scallop method for tool path generation, the results show that the cutting time could decrease with the new method. For different initial tool paths, the different average curvature radii in the direction perpendicular to the tool path could result in different surface normal errors.
在分类讨论了复杂曲面法曲率半径的求解方法的基础上,考虑曲率半径和刀具前倾角,对复杂曲面多轴球头铣削过程的铣削力进行了理论建模与仿真。针对多轴球头铣削特点,采用Lee和Altintas的瞬时刚性力模型,建立了刀具-工件接触区域内任意一点的微元铣削力公式；采用解析几何的方法建立了基于曲率半径和前倾角的切入、切出角以及轴向极限位置角的模型,进一步建立了刀具-工件接触区域模型；针对立式5轴加工中心DMU-70V,建立了各相关坐标系之间的转化关系模型,提出了三维整体铣削力模型并采用Matlab实现了仿真,通过仿真结果分析了曲率半径和刀具前倾角对三向铣削力的影响规律,为后续的精度预测与控制提供了可靠的理论依据。
刀具系统的变形和偏心对铣削力和加工误差有着重要的影响。为求解刀具系统的受力变形,铣削力被简化成为作用在刀具-工件接触区域一点上的集中作用力,X、Y方向上的集中力作用点处的挠度即为刀具受力变形量,区别于传统的两段式悬臂梁刀具受力变形模型,针对球头铣刀的三段式(刀杆、刀具刀刃部分-非球头和球头部分)结构,利用材料力学,建立了球头铣刀三段式悬臂梁刀具受力变形模型；通过比较新的三段式模型、传统两段式模型和使用ANSYS 12.0 Workbench有限元分析软件仿真得到的刀具变形结果,证明新的刀具受力模型与有限元结果较为相近；进行了刀具偏心对铣削力影响的扩展研究,发现刀具偏心不只影响每齿进给量,而且还对刀具有效切削半径和刀具旋转角度有一定的影响；基于三段式悬臂梁球头铣刀变形模型和刀具偏心扩展研究,提出复杂曲面铣削力的扩展模型。
根据机床坐标系下X、Y方向上集中力作用点处的刀具系统变形量,建立了复杂曲面加工路径上任意一点处工件局部坐标系下法向量方向曲面误差模型；对每一CL数据点,基于复杂曲面多轴加工特点,计算曲面误差,并通过迭代运算,对曲面误差进行补偿,使其满足加工要求。选用典型的正弦曲面进行刀具变形误差建模,并对其刀轨文件进行了离线误差补偿,证实了经过误差补偿后的走刀路径比未补偿的路径与理想路径相近。
对多轴铣削,除了可以通过基于分析不同走刀路径上的曲面曲率选择最佳的走刀路径方向来减小刀具变形,提高加工精度外,还可以通过对刀具倾角的分析进行选择最佳的刀具位姿来提高加工精度。本文分三种(平面、凸面和凹面)曲面分别讨论了步长和行距与曲率半径之间的关系,以高精度为目标,研究了三种典型走刀路径生成方式(参数线法、截平面法和等残留高度法)的走刀路径方向的选择问题；通过分析刀具前倾角与进给(X)、垂直进给(Y)方向刀具系统变形量和曲面法向误差之间的关系,发现进给(X)方向和垂直进给(Y)方向刀具系统变形量均随着刀具前倾角的增大而先增大后减小,曲面法向误差随着刀具前倾角的增大而增大,因此在满足其它要求的情况下,尽量取小的刀具前倾角值是最优的选择；选取典型复杂曲面进行了新的等残留高度法走刀路径方向的选择实例验证,结果表明本文提出的等残留高度法可以显著减少加工时间,提高加工效率,而且通过优选初始路径,得到最小的曲面误差的加工方向。
Complex surfaces have been widely used in aerospace, automotive and die/mold industries, because of their excellent functional properties and appearence. These kinds of surfaces are required to have high requirements on dimensional precision and surface quality. Multi-axis CNC machine tools are usually used for complex surfaces machining, and ball-end mills are usually used in semi-finish and finish milling processes. The surface quality includes surface precision, surface roughness, surface residual stress and surface work hardening etc. Complex surfaces and especially the surfaces with non-single curvature are seldom investigated. Among them, little overall and systematic research, especially the research on surface error due to cutting force-induced tool deflections has been made, and these surface errors are closely related with the geometric features of complex surfaces. In this dissertation, by analysising the geometric features of complex surfaces and the kinematics of multi-axis ball-end milling process synthetically, the relationships among surface precision, curvature radius, cutter orientation and cutting parameters have been thoroughly analyzed. The error compensation method and tool path direction selection method for high surface precision have been proposed. It is an important foundation subject for precision control in multi-axis ball-end milling.
The solving methods for curvature radius of complex surfaces are discussed separately. Considering the curvature radius and tool inclination angle, the theoretical-model and simulation of cutting forces on multi-axis ball-end milling of complex surfaces are carried. According to the characteristic of multi-axis ball-end milling, equations to estimate the cutting forces at a differential element on the cutting edge are established based on the instantaneous cutting force model proposed by Lee and Altintas. Start/exit radial immersion angles and limit axial position angles are solved using analytical geometry method taking into account the curvature radius and tool inclination angle, and then contact areas between cutter and workpiece are obtained. The mappings among all related coordinate of DMU-70V vertical machining center are modeled,3-dimensional cutting forces were modeled and simulated using Matlab software. The simulation results show the influence of curvature radius and tool inclination angle on the cutting forces in the X, Y, Z directions. It provides the reliable theoretical basis for the subsequent prediction and control of surface precision.
The cutting forces are simplified to concentrated forces which act on a point of cutter-workpiece contact area. The deflections of action points of concentrated forces in the X, Y directions are cutting force-induced tool deflections. Different from the traditional two segments cantilever beam tool deflection model, addressing the three parts (shank, flute-non ball-end and ball-end parts) of ball-end mill, three segments cantilever beam tool deflection model was built using materials mechanics method for ball-end mill. The comparison results show that, the tool deflection magnitude calculated by the new three segments method match better with the results of ANSYS 12.0 Workbench method than the results of the traditional two segments. Cutter eccentricity has an important impact on cutting forces through acting on feed per tooth, effective cutting radius and tool rotation angle. Then the extended researches on the cutting force model of complex surfaces were explored based on the three segments cantilever beam tool deflection model and the extended research on cutter eccentricity.
Based on tool deflection values of the acting point of force in the X, Y directions, for arbitrary point of tool path in the workpiece local coordinate system, the complex surfaces error model in the normal direction was established. After the error modeling, the error compensation was finished using iterative algorithm on every CL point based on the features analysis of multi-axis ball-end milling of complex surfaces. A typical sinusoidal surface was chosen for tool deflection error modeling, and off-line error compensation of the tool path file was finished. The results show that the tool paths after error compensation match better with the designed ones than those without error compensation.
Different from the case of 3-axis milling, the tool deflection in multi-axis milling could decrease by choosing not only the best tool path direction based on the analysis of curvature radius of different tool path direction, but also the best tool inclination angle. In this dissertation, the relationship between step length and path internal with the curvature radius was discussed separately for three surface types (plane, convex and concave surface). For getting high precision, the selection of tool path direction was discussed for three typical tool path generation methods (iso-parametric, iso-planar and iso-scallop method). Through analyzing the relationship between tool deflections in the X, Y directions and surface normal error with the tool inclination angle, selecting the tool inclination angle as small as possible is best for high suface precision. An example was presented to verify the newly proposed iso-scallop method for tool path generation, the results show that the cutting time could decrease with the new method. For different initial tool paths, the different average curvature radii in the direction perpendicular to the tool path could result in different surface normal errors.
引文
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