基于坐标映射的复杂曲面五轴加工关键技术研究
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摘要
随着以裁剪曲面、组合曲面及流形网格为代表的复杂曲面,被广泛用于表达零件几何外形,围绕其数控加工的一些深层次问题正逐渐显现出来。曲面造型中,因经常涉及布尔运算或其本身非显式的函数表达,传统路径规划模式往往无法充分满足这些复杂曲面零件数控加工的要求,如参数曲面通常采用等参数型路径,流形网格、组合曲面及裁剪曲面加工通常采用截平面路径等。截平面、等残留及等参数线型轨迹存在形状变化过快,大量的路径连接以及缺乏边界一致性等不足。在实际生产中,曲面五轴加工的刀轴矢量定制更多地依赖软件人为的反复校验和调整,保守加工参数的选择在延长生产周期的同时也抑制了机床加工能力的发挥。为此,针对复杂曲面零件,对基于坐标映射的五轴刀位轨迹规划策略和方法,和在此基础上进行的铣削力预测以及进给速度优化进行了深入研究,以期在保证加工精度的同时最大限度地提高加工效率。
提出基于定域映射的复杂曲面五轴加工刀位轨迹规划策略。根据定域映射建立曲面路径规划引导模型与映射域的参数化关系,构造映射域路径,通过逆向映射得到曲面加工的刀触点轨迹,结合满足机床运动学约束且整体光顺的刀具姿态生成五轴加工刀位轨迹。采用提出的弹簧长度能量函数与协调映射函数线性组合构造定域映射模型,在同时约束角度、长度变形的基础上,建立引导模型与映射域的参数化关系。通过推导圆环刀五轴加工条件下行距精确计算公式,提出初始刀轴矢量定制准则。借鉴等参数线法建立映射域路径规划模型,给出基于面积坐标和参数线性插值的刀触点轨迹生成方法,其中详细讨论了基于圆形映射域的螺旋型路径规划。针对各刀触点处初始刀轴矢量,提出基于机床运动学约束的关键点提取,以及通过关键点刀具位姿方向样条插值的整体光顺算法。计算机仿真和复杂曲面加工实验验证了路径规划策略的可行性。
针对复杂边界裁剪曲面加工,提出基于自由边界映射的环切型五轴刀位轨迹规划策略。通过引入自由边界映射,将裁剪曲面引导模型自然展开在映射域内。针对面积变形约束要求较高的情况,通过弹簧—质点模型对映射域进行迭代松弛。以自然展开映射域边界为起始,采用基于行距的偏置策略生成映射域等距路径,包括无局部干涉的初始边界修正偏置,单调链结合单元划分的全局干涉判断,以及有效环的提取和连接。基于面积坐标和参数线性插值生成环切型刀具轨迹。提出修正的机床运动学约束模型,将进给方向变化纳入刀具姿态优化,采用方向样条插值得到整体光顺的刀轴矢量。最后给出算例验证提出的模型。
基于刀具—工件相对运动分析,提出刀具沿任意曲线五轴加工自由曲面的铣削力精确预测模型。针对传统未变形切屑厚度计算公式以圆弧近似表达刀刃运动轨迹,存在逼近误差,且主要用于三轴加工铣削力预测的问题,通过研究铣削加工中切屑形成过程,结合刀具刀刃几何形状、机床运动结构、刀具轨迹以及工艺参数,推导了刀刃运动扫掠面方程,并在此基础上建立五轴加工未变形切屑厚度精确计算模型。通过固定刀轴矢量,提出的模型可用于三轴加工未变形切屑厚度的精确计算。根据仿真分析及槽切对比实验,提出的未变形切削厚度模型计算精度高于传统未变形切屑厚度模型。建立铣削力系数解析计算模型,并分别给出铝合金2024和7075-T6的铣削力系数曲线。针对传统Z-map模型在判断参与切削刀刃区域需要反复比较高度,提出基于投影和位置比较的参与切削刀刃判定准则。为了验证提出的铣削力模型,对球头刀三轴和五轴加工进行了多次实验,从铣削力的幅值和波形来看,仿真模型能够很好地预测铣削力的变化。
提出加工过程多约束进给速度自适应定制方法。首先,通过建立表面形貌仿真模型并结合国际标准ISO 12085:1996中定义的形貌参数,分析进给速度对零件表面形貌和使用性能的影响。然后,从保证加工精度和加工过程安全的角度,提出一种基于铣削力精确预测模型的多约束进给速度定制方法。研究了包含刀杆变形、刀具内应力和机床主轴扭矩在内的影响铣削加工过程的关键因素的计算。根据加工过程的一阶传递函数描述和比例积分控制优化进给速度。加工实验表明进给速度优化算法能够在满足给定加工精度的条件下提高加工效率。
最后,以典型的船用螺旋桨叶片比例模型加工为例,对提出的五轴刀位轨迹以及进给速度自适应定制模型进行验证。根据实验结果,在给定加工精度的条件下,提出的螺旋型、环切型五轴加工路径在轨迹长度、加工时间以及表面完成质量上要优于两种典型的三轴轨迹；采用优化进给速度的螺旋路径加工,叶片零件在精度满足要求的同时加工效率得到显著提升。
Geometrically complicated workpieces are often modeled by compound surface, meshed surface and trimmed surface. In the machining of these parts, the pathopography generated by traditional toolpath planning model can not conform to the surface geometry. Due to the implicit expression of surface, the iso-planar method is still commonly adopted to machine mesh model. Thanks to the predefined parameterization being sacrificed by Boolean operation in CAD stage, the toolpaths generated by iso-planar, iso-parameteric and iso-scallop model, are no longer boundary conformed in trimmed surface and compound surface machining. In these cases, it is hard to guarantee the machining efficiency and quality with respect to discontinuous cutting process and many "go-stop" motions of machine. In practical production, performance of machine is restrained and machining period is delayed in terms of manual scheduling and verification of tool posture and selection of conservative process parameters. So, in this dissertation, the NC machining of complicated surface is studied. The models of toolpath planning, cutting force prediction and feedrate optimization are proposed to improve the efficiency under given precision.
Designated mapping based toolpath planning method is proposed. Based on the designated mapping, the parametric relationship between surface guided model and mapped region is built. Cutter contact toolpath is constructed by reversely mapping the path interval based locus in mapped region with area coordinate. Then cutter location path is generated with machine kinematics-constrained and whole faired tool posture. The designated mapping is constructed by linearly combined spring length energy function and conformal mapping function. The principle of original tool axis determination is proposed which is derived from the precious calculation of path interval for the filleted-end milling cutter. The cutter contect point path is constructed with the aid of the area coordinate algorithm, path interval and parameter increment calculation. The special case of spiral type toolpath is discussed in detail. With respect to the original tool axis vector, whole faired tool axis vector is obtained by orientation spline interpolation of tool axis vector of "key point" selected by kinematical constraints of machine. The computer simulation and cutting experiment is operated for verification of the proposed model.
Natural boundary mapping based contour offset five-axis toolpath planning model is presented for complex trimmed surface with islands. The natural boundary mapping is defined on the basis of area gradient equation and area of mesh model which can represent the Dirichlet function. With the proposed mapping, natural boundary parameter region can be determined by constraining arbitrary two adjacent boundary points. Starting from boundary of mapped parameter region, the contour-parallel path is construed with offset-modification method based non-local interference regional offsetting, monotone chains and division based globe interference eliminating and tree-like data structure based offset loop connecting. For the contour offset cutting contact path mapped with area coordinate algorithm, a modified machine kinematical constraints criterion is presented with consideration of the influence of sharp change of feed direction. The computer simulation of trimmed surface with multi-irregular islands machining verified our method.
Based on the tool-workpiece relative motion, a precious cutting force prediction model is proposed for general milling tool cutting with curve path in five-axis machining condition. According to differential geometry, geometrical model of revolution surface and spiral flute of cutter is constructed and swept surface of flute during cutter moving is modeled with consideration of kinematic structure of multi-axis machine, toolpath and cutting parameters. With swept surface of flute, undeformed chip thickness is calculated which is more accurate than traditional model proved by slot cutting experiment. The detailed calculation of undeformed chip thickness for three-axis and five-axis ball-end cutting case is also derived. For cutting coefficients calibration, a single-cutting experiment based analytical model is proposed and used for aluminum 2024 and 7075-T6. The in-cutting tool region is automatically determined by a modified Z-map model. Validation tests are conducted under different cutting conditions for three-axis and five-axis machining. The comparison between predicted and measured values demonstrates the applicability of the proposed prediction model of cutting forces.
An adaptive feedrate schedule strategy is proposed for complex curved surface machining using process constraints and a tool motion analysis based precision cutting force prediction model. The influence of feedrate on surface topography and workpiece performance is first analyzed by surface topography simulation model and parameter defined in ISO 12085:1996. The adaptive feedrate schedule strategy is then proposed. In terms of the cantilever beam model, tool stress model and cutting torque model, key process constraints are calculated with the proposed precision cutting force model. With defining the material removal rate as objective function, the feedrate is scheduled by solving a constrained optimization problem. The machine experiment illustrates that the proposed feedrate schedule strategy is very useful in high precision and efficiency machining of complex curved surface.
Finally, the typical marine propeller is machined with the proposed five-axis toolpath planning model and the adaptive feedrate schedule strategy. The experiment results illustrated that presented spiral and contour offset five-axis toolpath are better than two traditional toolpath model in terms of tool path length, machining time, as well as machined surface quality with given machining precision. With the optimized feedrate, the efficiency is significantly improved in machining with spiral toolpath.
提出基于定域映射的复杂曲面五轴加工刀位轨迹规划策略。根据定域映射建立曲面路径规划引导模型与映射域的参数化关系,构造映射域路径,通过逆向映射得到曲面加工的刀触点轨迹,结合满足机床运动学约束且整体光顺的刀具姿态生成五轴加工刀位轨迹。采用提出的弹簧长度能量函数与协调映射函数线性组合构造定域映射模型,在同时约束角度、长度变形的基础上,建立引导模型与映射域的参数化关系。通过推导圆环刀五轴加工条件下行距精确计算公式,提出初始刀轴矢量定制准则。借鉴等参数线法建立映射域路径规划模型,给出基于面积坐标和参数线性插值的刀触点轨迹生成方法,其中详细讨论了基于圆形映射域的螺旋型路径规划。针对各刀触点处初始刀轴矢量,提出基于机床运动学约束的关键点提取,以及通过关键点刀具位姿方向样条插值的整体光顺算法。计算机仿真和复杂曲面加工实验验证了路径规划策略的可行性。
针对复杂边界裁剪曲面加工,提出基于自由边界映射的环切型五轴刀位轨迹规划策略。通过引入自由边界映射,将裁剪曲面引导模型自然展开在映射域内。针对面积变形约束要求较高的情况,通过弹簧—质点模型对映射域进行迭代松弛。以自然展开映射域边界为起始,采用基于行距的偏置策略生成映射域等距路径,包括无局部干涉的初始边界修正偏置,单调链结合单元划分的全局干涉判断,以及有效环的提取和连接。基于面积坐标和参数线性插值生成环切型刀具轨迹。提出修正的机床运动学约束模型,将进给方向变化纳入刀具姿态优化,采用方向样条插值得到整体光顺的刀轴矢量。最后给出算例验证提出的模型。
基于刀具—工件相对运动分析,提出刀具沿任意曲线五轴加工自由曲面的铣削力精确预测模型。针对传统未变形切屑厚度计算公式以圆弧近似表达刀刃运动轨迹,存在逼近误差,且主要用于三轴加工铣削力预测的问题,通过研究铣削加工中切屑形成过程,结合刀具刀刃几何形状、机床运动结构、刀具轨迹以及工艺参数,推导了刀刃运动扫掠面方程,并在此基础上建立五轴加工未变形切屑厚度精确计算模型。通过固定刀轴矢量,提出的模型可用于三轴加工未变形切屑厚度的精确计算。根据仿真分析及槽切对比实验,提出的未变形切削厚度模型计算精度高于传统未变形切屑厚度模型。建立铣削力系数解析计算模型,并分别给出铝合金2024和7075-T6的铣削力系数曲线。针对传统Z-map模型在判断参与切削刀刃区域需要反复比较高度,提出基于投影和位置比较的参与切削刀刃判定准则。为了验证提出的铣削力模型,对球头刀三轴和五轴加工进行了多次实验,从铣削力的幅值和波形来看,仿真模型能够很好地预测铣削力的变化。
提出加工过程多约束进给速度自适应定制方法。首先,通过建立表面形貌仿真模型并结合国际标准ISO 12085:1996中定义的形貌参数,分析进给速度对零件表面形貌和使用性能的影响。然后,从保证加工精度和加工过程安全的角度,提出一种基于铣削力精确预测模型的多约束进给速度定制方法。研究了包含刀杆变形、刀具内应力和机床主轴扭矩在内的影响铣削加工过程的关键因素的计算。根据加工过程的一阶传递函数描述和比例积分控制优化进给速度。加工实验表明进给速度优化算法能够在满足给定加工精度的条件下提高加工效率。
最后,以典型的船用螺旋桨叶片比例模型加工为例,对提出的五轴刀位轨迹以及进给速度自适应定制模型进行验证。根据实验结果,在给定加工精度的条件下,提出的螺旋型、环切型五轴加工路径在轨迹长度、加工时间以及表面完成质量上要优于两种典型的三轴轨迹；采用优化进给速度的螺旋路径加工,叶片零件在精度满足要求的同时加工效率得到显著提升。
Geometrically complicated workpieces are often modeled by compound surface, meshed surface and trimmed surface. In the machining of these parts, the pathopography generated by traditional toolpath planning model can not conform to the surface geometry. Due to the implicit expression of surface, the iso-planar method is still commonly adopted to machine mesh model. Thanks to the predefined parameterization being sacrificed by Boolean operation in CAD stage, the toolpaths generated by iso-planar, iso-parameteric and iso-scallop model, are no longer boundary conformed in trimmed surface and compound surface machining. In these cases, it is hard to guarantee the machining efficiency and quality with respect to discontinuous cutting process and many "go-stop" motions of machine. In practical production, performance of machine is restrained and machining period is delayed in terms of manual scheduling and verification of tool posture and selection of conservative process parameters. So, in this dissertation, the NC machining of complicated surface is studied. The models of toolpath planning, cutting force prediction and feedrate optimization are proposed to improve the efficiency under given precision.
Designated mapping based toolpath planning method is proposed. Based on the designated mapping, the parametric relationship between surface guided model and mapped region is built. Cutter contact toolpath is constructed by reversely mapping the path interval based locus in mapped region with area coordinate. Then cutter location path is generated with machine kinematics-constrained and whole faired tool posture. The designated mapping is constructed by linearly combined spring length energy function and conformal mapping function. The principle of original tool axis determination is proposed which is derived from the precious calculation of path interval for the filleted-end milling cutter. The cutter contect point path is constructed with the aid of the area coordinate algorithm, path interval and parameter increment calculation. The special case of spiral type toolpath is discussed in detail. With respect to the original tool axis vector, whole faired tool axis vector is obtained by orientation spline interpolation of tool axis vector of "key point" selected by kinematical constraints of machine. The computer simulation and cutting experiment is operated for verification of the proposed model.
Natural boundary mapping based contour offset five-axis toolpath planning model is presented for complex trimmed surface with islands. The natural boundary mapping is defined on the basis of area gradient equation and area of mesh model which can represent the Dirichlet function. With the proposed mapping, natural boundary parameter region can be determined by constraining arbitrary two adjacent boundary points. Starting from boundary of mapped parameter region, the contour-parallel path is construed with offset-modification method based non-local interference regional offsetting, monotone chains and division based globe interference eliminating and tree-like data structure based offset loop connecting. For the contour offset cutting contact path mapped with area coordinate algorithm, a modified machine kinematical constraints criterion is presented with consideration of the influence of sharp change of feed direction. The computer simulation of trimmed surface with multi-irregular islands machining verified our method.
Based on the tool-workpiece relative motion, a precious cutting force prediction model is proposed for general milling tool cutting with curve path in five-axis machining condition. According to differential geometry, geometrical model of revolution surface and spiral flute of cutter is constructed and swept surface of flute during cutter moving is modeled with consideration of kinematic structure of multi-axis machine, toolpath and cutting parameters. With swept surface of flute, undeformed chip thickness is calculated which is more accurate than traditional model proved by slot cutting experiment. The detailed calculation of undeformed chip thickness for three-axis and five-axis ball-end cutting case is also derived. For cutting coefficients calibration, a single-cutting experiment based analytical model is proposed and used for aluminum 2024 and 7075-T6. The in-cutting tool region is automatically determined by a modified Z-map model. Validation tests are conducted under different cutting conditions for three-axis and five-axis machining. The comparison between predicted and measured values demonstrates the applicability of the proposed prediction model of cutting forces.
An adaptive feedrate schedule strategy is proposed for complex curved surface machining using process constraints and a tool motion analysis based precision cutting force prediction model. The influence of feedrate on surface topography and workpiece performance is first analyzed by surface topography simulation model and parameter defined in ISO 12085:1996. The adaptive feedrate schedule strategy is then proposed. In terms of the cantilever beam model, tool stress model and cutting torque model, key process constraints are calculated with the proposed precision cutting force model. With defining the material removal rate as objective function, the feedrate is scheduled by solving a constrained optimization problem. The machine experiment illustrates that the proposed feedrate schedule strategy is very useful in high precision and efficiency machining of complex curved surface.
Finally, the typical marine propeller is machined with the proposed five-axis toolpath planning model and the adaptive feedrate schedule strategy. The experiment results illustrated that presented spiral and contour offset five-axis toolpath are better than two traditional toolpath model in terms of tool path length, machining time, as well as machined surface quality with given machining precision. With the optimized feedrate, the efficiency is significantly improved in machining with spiral toolpath.
引文
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