面向五轴高效铣削加工的刀具可行空间GPU计算与刀具方向整体优化
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摘要
五轴数控加工的优势主要通过控制刀具方向实现,体现在:(1)改变刀具方向可以提高刀具可达性,实现叶轮、叶片和螺旋桨等复杂曲面加工;(2)加工叶轮根部等曲率大的区域时,只能用刚度较低的小半径刀具,通过选择合理刀具方向,可以缩短刀具悬伸量,提高铣削系统的整体刚度;(3)通过规划刀具方向能够更好的匹配刀具几何与工件曲面,可以使用侧铣加工等高效加工方式;(4)控制刀具方向可以控制刀具参与切削的区域,降低切削力和刀具磨损,提高加工表面质量。因此,合理规划刀具方向是规划五轴高效加工刀具路径的关键,理论上,五轴数控机床可以控制刀具方向到高斯球面上的任意一点,但由于干涉避免和机床工作空间等几何约束,刀具方向被限制在高斯球面上的一片可行域中,为了提高加工质量和加工效率,需要为每一个刀位在可行域中优化选择刀具方向。
本学位论文以复杂曲面五轴铣削加工为应用背景,研究基于可行空间的高效铣削加工刀具方向整体优化方法。五轴高效铣削加工刀具方向规划的难点是除满足几何约束外,还需要考虑速度平滑、刀具变形和加工稳定性等动态特性,以及切削过程中切削力等物理因素对加工质量的影响。目前的商用CAM软件主要考虑几何约束,本文从刀具可行空间出发整体优化刀具方向,除几何约束外,考虑到五轴数控加工中的动态特性和物理因素,重点在刀具方向光顺性整体优化、安全最短刀具长度规划和等距双NURBS刀具路径规划这三个方面开展研究,主要研究工作及创新性成果如下:
一.针对刀具可行空间计算速度慢的问题,提出了基于显卡硬件的刀具全局可达方向锥快速计算方法,及运用空间剖分法的加速处理机制。仿真计算表明该算法具有线性时间复杂度,且计算速度远快于现有文献中的C空间法(Chell A. Roberts, 2007)和可视锥法(S. Sarma, 2000)。在障碍物模型包含的三角形个数是文献(Gershon Elber, 2005)中的10倍时,用该算法检测一个刀位可达性的平均时间从1.23×10-3秒减少到4.63×10-5秒。
二.研究了在刀具可行空间中,通过优化刀具方向的光顺性来满足加工过程中机床动态特性需求的方法。根据连续刀具路径干涉避免、机床工作空间和加工工艺约束计算出了刀具可行方向锥,建立了在相邻刀触点之间刀具方向变化约束下的刀具方向最短路径模型,提出了整体优化刀具方向光顺性的算法。该算法在复杂曲面的五轴加工中,可以显著减少加工时间,七叶大弯角螺旋桨模的加工实验中,整体光顺刀具方向后,加工时间从51分钟减少到34分钟。
三.为改善刀具方向变动对切削力平稳性的影响和提高计算效率,提出了在刀触点网格基础上规划刀具方向的算法,求取同时保证进给和相邻行两个方向总体光顺的刀具方向,并通过插值得到所有刀触点处的刀具方向。仿真表明光顺刀具方向可以提高机床进给运动的平稳性和加工效率,应用于汽轮机叶片叶根部分的五轴数控加工中,规划13945个刀位点的刀具方向时,只需计算900个网格点处的可达方向锥,提高了计算效率,加工实验证明了算法的有效性和工程实用性。
四.刀具悬伸过长会降低铣削系统刚度,易造成振动和变形,进而影响加工的表面质量,论文提出了可用安全最短刀具的刀具方向规划算法。通过求解在刀具无干涉约束和相邻刀触点之间刀具方向变化约束下的刀具方向动态规划模型,规划出沿整个刀具路径的安全刀具长度。与现有文献(Y.R. Hwang, 2003)中规划光滑无干涉刀具路径的算法相比,该算法可以明显缩短刀具悬伸量。应用于复杂螺旋桨模的数控加工中,使刀具长度从55mm缩短到40mm,提高了加工表面质量。
五.研究了基于等距双NURBS曲线的五轴高效加工刀具路径规划方法。研究了采用有理对偶四元数曲线插值光顺刀具路径,把刀具有理运动转化为等距双NURBS刀具路径的方法;给出了圆锥铣刀沿有理对偶四元数曲线运动时包络面的解析解,描述了一般回转刀具沿有理对偶四元数曲线运动时获取特征点封闭解的方法,分析了特征点奇异的情况,给出了圆锥铣刀侧铣加工的NURBS刀具路径规划方法。在等距双NURBS刀具路径插补和小线段插补的对比实验中,等距双NURBS刀具路径可以使加工时间从15.384秒减少到3.38秒,且具有更平滑的进给速度和加工速度。
六.研制了基于可行空间的刀具方向规划软件(SurfMilling V1.0),该软件提供了刀具可行空间计算、安全最短刀具长度优化、刀具方向整体光顺、等距双NURBS刀具路径插值和后置处理功能。通用CAM软件一般由用户提供刀具方向规划策略,而论文开发的软件可以根据输入的障碍物模型、刀具模型和刀触点(或刀位点)序列自动规划出优化的数控程序,以汽轮机中压11级动叶片叶根连接处精加工为例介绍了软件的使用方法,用加工实验验证了输出的数控程序,加工误差达到了上海汽轮机厂的技术要求。
The advantages of 5-axis NC machining depend on the control of tool orientations: (1) The accessibility can be improved by changing tool orientations. Then the complicated shapes such as aerospace impeller, turbo blade and marine propeller can be machined. (2) Only the small-diameter cutters can be used when the surface is machined in a confined space. The use of short tool overhang length will be allowed if the tool orientation is optimized. The rigidity of the whole milling system will then be increased. (3) Simple and efficient tools can be used to machine complicated surface if tool orientations are reasonably generated. The highly efficient flank milling is allowed to machine aerospace impeller by using 5-axis machine tool. (4) The cutting area in a cutter will also be controlled by controlling tool orientations. The cutting force can be decreased, the surface quality can be improved and the cutter wear can be reduced. Theoretically, the tool orientations can be any point of the Gauss Sphere in 5-axis NC machining. In fact, the feasible tool orientations are only a limit area in the Gauss Sphere because of the constraints about collision avoidance and work space. For improving machining efficiency and quality, the tool orientation of each CL (Cutter Location) data should be optimized based on the feasibility area.
The access-based whole tool orientation optimization method is studied for 5-axis high efficiency NC machining of complicated shapes in this dissertation. It is necessary to consider some important factors in a practical cutting process when tool paths are generated. The factors consist of geometrical constraints (collision avoidance, machining precision, work space and fixture), kinematic constraints (singularity, velocity, acceleration and jerk), dynamic characters (rigidity and stability) and physical factors (cutting force) in the cutting process. How to optimally consider the four factors in the process of tool path generation is the key problem to improve manufacturing efficiency and quality of 5-axis NC machining. It is also the most challenging aspect in the research of tool path generation. Existing commercial general CAM software mainly focus on the method to satisfy the geometric constraints. We investigate the algorithms to wholly optimize tool orientations for 5-axis NC machining based on the feasibility space. The most obvious advantages of the method are that the dynamic characters and cutting force are also considered besides the geometric constraints. The three factors are considered by wholly smoothing tool orientations, generating the safe and shortest tool length and interpolating dual-NURBS tool path. The main research work and the novel contributions are listed as follows:
Firstly,a novel algorithm is proposed to efficiently calculate the cutter accessibility cone by using graphics hardware. Based on the definition of cutter location point, the problem to determine the global accessibility cone is changed into the problem to check the complete visibility of the disk and the cone surface. Then the GPU-based algorithm is proposed to check the cutter global accessibility. The methods to improve the computational efficiency are also discussed. The computational examples show that the time complexity of this algorithm is almost linear. Comparing with the exsiting algorithms such as C-configuration (Chell A. Roberts, 2007) and visibility cone (S. Sarma, 2000), the proposed algorithm is much more efficient. Though the triangle number in the obstacle model of this method is about 10 times as of the simulation algorithm (Gershon Elber, 2005), the average computational time to check the accessibility of one cutter location is only the 3.76% of the simulation algorithm.
Secondly, collision-free and orientation-smooth tool path are generated in the feasible space. The machining efficiency is improved by globally smoothing tool orientations. The feasibility cone is first selected from accessibility cone by considering the geometric constraints. Considering the constraints of tool orientation transition between two neighbor cutter contact points, the tool orientations are finally determined by globally smoothing tool orientations along the CC points. The cutting experiment of a complicated marine propeller shows that the cutting efficiency can be improved obviously by smoothing tool orientations. The cutting time is decreased from 51 minutes to 34 minutes. Only 66.67% of origin cutting time is used.
Thirdly, considering the computation speed and the relationship between cutting force and tool orientation, a novel mesh-based algorithm is proposed to optimize tool orientations. Based on the feasibility cone at each mesh point, the tool orientations at mesh points are first generated by globally smoothing tool orientations. The tool orientations at other CC points are finally determined by interpolation. The obtained tool orientations are smooth not only along the feed direction but also along the pick-feed direction. The algorithm is applied to machine a turbo blade. Only the accessibility cone of 900 cutter location points are necessary to computed for a tool path consisting of 13845 cutter location points. The computational efficiency is improved. The validity of the generated tool path is finally proved by a cutting experiment.
Fourthly, the use of shorter cutters without collision is a key advantage of 5-axis machining because the rigidity is greatly affected by the slenderness ratio of the cutter. An algorithm is proposed to optimize the safe and shortest tool length for 5-axis NC machining based on the safe and shortest tool length along an accessible tool orientation. The collision avoidance and tool orientation smoothness of the tool path are imposed as the constraints on the optimization model. Comparing with the existing algorithm (Y.R. Hwang, 2003), the obtained tool length can be obviously decreased by the proposed algorithm. The algorithm is applied to generate the tool length for the machining of the complicated marine propeller. The tool length is reduced from 55mm to 40mm. The cutting experiment shows that the machined surface quality is improved by using the shorter cutter.
Fifthly, the method to generate dual-NURBS tool path is investigated for 5-axis NC machining because of the obvious advantages of NURBS interpolation in dynamic characteristics. The smooth dual-NURBS tool paths are interpolated by a rational motion described by a dual quaternion curve. The analytical envelope surface of a conical cutter under the rational motion is studied. The close solution of the characteristic point of a general cutter under the rational motion is also discussed. Furthermore, the singularity of the characteristic point is also considered. An algorithm is proposed to generate tool path for the flank milling of a conical cutter. The experiment is adopted to compare the dual-NURBS tool path and linear tool path. The result shows that cutting time is reduced from 15.384 seconds to 3.38 seconds. Furthermore, the better efficiency and dynamic characteristic are both achieved when dual-NURBS tool path are used.
Sixthly, the software (SurfMilling V1.0) has been developed to implement the access-based whole tool orientation optimization algorithms. The functions of this software include accessibility cone computation, safe and shortest tool length generation, tool orientation optimization, dual-NURBS tool path interpolation and post-process. The tool path can be automatically generated based on the input obstacles, cutter geometry and CC points (or CL points). The software is introduced by using an example about the finishing machining of a turbo blade and the tool path is confirmed by a cutting experiment. The obtained turbo blade satisfies the technical requirements of Shanghai Turbine Co. Ltd.
本学位论文以复杂曲面五轴铣削加工为应用背景,研究基于可行空间的高效铣削加工刀具方向整体优化方法。五轴高效铣削加工刀具方向规划的难点是除满足几何约束外,还需要考虑速度平滑、刀具变形和加工稳定性等动态特性,以及切削过程中切削力等物理因素对加工质量的影响。目前的商用CAM软件主要考虑几何约束,本文从刀具可行空间出发整体优化刀具方向,除几何约束外,考虑到五轴数控加工中的动态特性和物理因素,重点在刀具方向光顺性整体优化、安全最短刀具长度规划和等距双NURBS刀具路径规划这三个方面开展研究,主要研究工作及创新性成果如下:
一.针对刀具可行空间计算速度慢的问题,提出了基于显卡硬件的刀具全局可达方向锥快速计算方法,及运用空间剖分法的加速处理机制。仿真计算表明该算法具有线性时间复杂度,且计算速度远快于现有文献中的C空间法(Chell A. Roberts, 2007)和可视锥法(S. Sarma, 2000)。在障碍物模型包含的三角形个数是文献(Gershon Elber, 2005)中的10倍时,用该算法检测一个刀位可达性的平均时间从1.23×10-3秒减少到4.63×10-5秒。
二.研究了在刀具可行空间中,通过优化刀具方向的光顺性来满足加工过程中机床动态特性需求的方法。根据连续刀具路径干涉避免、机床工作空间和加工工艺约束计算出了刀具可行方向锥,建立了在相邻刀触点之间刀具方向变化约束下的刀具方向最短路径模型,提出了整体优化刀具方向光顺性的算法。该算法在复杂曲面的五轴加工中,可以显著减少加工时间,七叶大弯角螺旋桨模的加工实验中,整体光顺刀具方向后,加工时间从51分钟减少到34分钟。
三.为改善刀具方向变动对切削力平稳性的影响和提高计算效率,提出了在刀触点网格基础上规划刀具方向的算法,求取同时保证进给和相邻行两个方向总体光顺的刀具方向,并通过插值得到所有刀触点处的刀具方向。仿真表明光顺刀具方向可以提高机床进给运动的平稳性和加工效率,应用于汽轮机叶片叶根部分的五轴数控加工中,规划13945个刀位点的刀具方向时,只需计算900个网格点处的可达方向锥,提高了计算效率,加工实验证明了算法的有效性和工程实用性。
四.刀具悬伸过长会降低铣削系统刚度,易造成振动和变形,进而影响加工的表面质量,论文提出了可用安全最短刀具的刀具方向规划算法。通过求解在刀具无干涉约束和相邻刀触点之间刀具方向变化约束下的刀具方向动态规划模型,规划出沿整个刀具路径的安全刀具长度。与现有文献(Y.R. Hwang, 2003)中规划光滑无干涉刀具路径的算法相比,该算法可以明显缩短刀具悬伸量。应用于复杂螺旋桨模的数控加工中,使刀具长度从55mm缩短到40mm,提高了加工表面质量。
五.研究了基于等距双NURBS曲线的五轴高效加工刀具路径规划方法。研究了采用有理对偶四元数曲线插值光顺刀具路径,把刀具有理运动转化为等距双NURBS刀具路径的方法;给出了圆锥铣刀沿有理对偶四元数曲线运动时包络面的解析解,描述了一般回转刀具沿有理对偶四元数曲线运动时获取特征点封闭解的方法,分析了特征点奇异的情况,给出了圆锥铣刀侧铣加工的NURBS刀具路径规划方法。在等距双NURBS刀具路径插补和小线段插补的对比实验中,等距双NURBS刀具路径可以使加工时间从15.384秒减少到3.38秒,且具有更平滑的进给速度和加工速度。
六.研制了基于可行空间的刀具方向规划软件(SurfMilling V1.0),该软件提供了刀具可行空间计算、安全最短刀具长度优化、刀具方向整体光顺、等距双NURBS刀具路径插值和后置处理功能。通用CAM软件一般由用户提供刀具方向规划策略,而论文开发的软件可以根据输入的障碍物模型、刀具模型和刀触点(或刀位点)序列自动规划出优化的数控程序,以汽轮机中压11级动叶片叶根连接处精加工为例介绍了软件的使用方法,用加工实验验证了输出的数控程序,加工误差达到了上海汽轮机厂的技术要求。
The advantages of 5-axis NC machining depend on the control of tool orientations: (1) The accessibility can be improved by changing tool orientations. Then the complicated shapes such as aerospace impeller, turbo blade and marine propeller can be machined. (2) Only the small-diameter cutters can be used when the surface is machined in a confined space. The use of short tool overhang length will be allowed if the tool orientation is optimized. The rigidity of the whole milling system will then be increased. (3) Simple and efficient tools can be used to machine complicated surface if tool orientations are reasonably generated. The highly efficient flank milling is allowed to machine aerospace impeller by using 5-axis machine tool. (4) The cutting area in a cutter will also be controlled by controlling tool orientations. The cutting force can be decreased, the surface quality can be improved and the cutter wear can be reduced. Theoretically, the tool orientations can be any point of the Gauss Sphere in 5-axis NC machining. In fact, the feasible tool orientations are only a limit area in the Gauss Sphere because of the constraints about collision avoidance and work space. For improving machining efficiency and quality, the tool orientation of each CL (Cutter Location) data should be optimized based on the feasibility area.
The access-based whole tool orientation optimization method is studied for 5-axis high efficiency NC machining of complicated shapes in this dissertation. It is necessary to consider some important factors in a practical cutting process when tool paths are generated. The factors consist of geometrical constraints (collision avoidance, machining precision, work space and fixture), kinematic constraints (singularity, velocity, acceleration and jerk), dynamic characters (rigidity and stability) and physical factors (cutting force) in the cutting process. How to optimally consider the four factors in the process of tool path generation is the key problem to improve manufacturing efficiency and quality of 5-axis NC machining. It is also the most challenging aspect in the research of tool path generation. Existing commercial general CAM software mainly focus on the method to satisfy the geometric constraints. We investigate the algorithms to wholly optimize tool orientations for 5-axis NC machining based on the feasibility space. The most obvious advantages of the method are that the dynamic characters and cutting force are also considered besides the geometric constraints. The three factors are considered by wholly smoothing tool orientations, generating the safe and shortest tool length and interpolating dual-NURBS tool path. The main research work and the novel contributions are listed as follows:
Firstly,a novel algorithm is proposed to efficiently calculate the cutter accessibility cone by using graphics hardware. Based on the definition of cutter location point, the problem to determine the global accessibility cone is changed into the problem to check the complete visibility of the disk and the cone surface. Then the GPU-based algorithm is proposed to check the cutter global accessibility. The methods to improve the computational efficiency are also discussed. The computational examples show that the time complexity of this algorithm is almost linear. Comparing with the exsiting algorithms such as C-configuration (Chell A. Roberts, 2007) and visibility cone (S. Sarma, 2000), the proposed algorithm is much more efficient. Though the triangle number in the obstacle model of this method is about 10 times as of the simulation algorithm (Gershon Elber, 2005), the average computational time to check the accessibility of one cutter location is only the 3.76% of the simulation algorithm.
Secondly, collision-free and orientation-smooth tool path are generated in the feasible space. The machining efficiency is improved by globally smoothing tool orientations. The feasibility cone is first selected from accessibility cone by considering the geometric constraints. Considering the constraints of tool orientation transition between two neighbor cutter contact points, the tool orientations are finally determined by globally smoothing tool orientations along the CC points. The cutting experiment of a complicated marine propeller shows that the cutting efficiency can be improved obviously by smoothing tool orientations. The cutting time is decreased from 51 minutes to 34 minutes. Only 66.67% of origin cutting time is used.
Thirdly, considering the computation speed and the relationship between cutting force and tool orientation, a novel mesh-based algorithm is proposed to optimize tool orientations. Based on the feasibility cone at each mesh point, the tool orientations at mesh points are first generated by globally smoothing tool orientations. The tool orientations at other CC points are finally determined by interpolation. The obtained tool orientations are smooth not only along the feed direction but also along the pick-feed direction. The algorithm is applied to machine a turbo blade. Only the accessibility cone of 900 cutter location points are necessary to computed for a tool path consisting of 13845 cutter location points. The computational efficiency is improved. The validity of the generated tool path is finally proved by a cutting experiment.
Fourthly, the use of shorter cutters without collision is a key advantage of 5-axis machining because the rigidity is greatly affected by the slenderness ratio of the cutter. An algorithm is proposed to optimize the safe and shortest tool length for 5-axis NC machining based on the safe and shortest tool length along an accessible tool orientation. The collision avoidance and tool orientation smoothness of the tool path are imposed as the constraints on the optimization model. Comparing with the existing algorithm (Y.R. Hwang, 2003), the obtained tool length can be obviously decreased by the proposed algorithm. The algorithm is applied to generate the tool length for the machining of the complicated marine propeller. The tool length is reduced from 55mm to 40mm. The cutting experiment shows that the machined surface quality is improved by using the shorter cutter.
Fifthly, the method to generate dual-NURBS tool path is investigated for 5-axis NC machining because of the obvious advantages of NURBS interpolation in dynamic characteristics. The smooth dual-NURBS tool paths are interpolated by a rational motion described by a dual quaternion curve. The analytical envelope surface of a conical cutter under the rational motion is studied. The close solution of the characteristic point of a general cutter under the rational motion is also discussed. Furthermore, the singularity of the characteristic point is also considered. An algorithm is proposed to generate tool path for the flank milling of a conical cutter. The experiment is adopted to compare the dual-NURBS tool path and linear tool path. The result shows that cutting time is reduced from 15.384 seconds to 3.38 seconds. Furthermore, the better efficiency and dynamic characteristic are both achieved when dual-NURBS tool path are used.
Sixthly, the software (SurfMilling V1.0) has been developed to implement the access-based whole tool orientation optimization algorithms. The functions of this software include accessibility cone computation, safe and shortest tool length generation, tool orientation optimization, dual-NURBS tool path interpolation and post-process. The tool path can be automatically generated based on the input obstacles, cutter geometry and CC points (or CL points). The software is introduced by using an example about the finishing machining of a turbo blade and the tool path is confirmed by a cutting experiment. The obtained turbo blade satisfies the technical requirements of Shanghai Turbine Co. Ltd.
引文
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