The cutter runout effect has significant influence on the shape of cutter swept surface and the machining surface quality. Hence,it is necessary to integrate the cutter runout effect in cutter swept surface modeling,g...The cutter runout effect has significant influence on the shape of cutter swept surface and the machining surface quality. Hence,it is necessary to integrate the cutter runout effect in cutter swept surface modeling,geometric error prediction and tool path optimization for five-axis flank machining. In this paper,an envelope surface model considering cutter runout effect is first established,and geometric errors induced by runout effect are derived based on the relative motion analysis between the cutter and part in machining. In the model,the cutter runout is defined by four parameters,including inclination angle,location angle,offset value and the length of cutter axis. Then the runout parameters are integrated into the rotation surface of each cutting edge that is used to form the final cutter envelope surface for the five-axis machining process. Thus,the final resulting geometric errors of the machined surface induced by cutter runout can be obtained through computing the deviations from the nominal cutter swept surface. To reduce these errors,an iterative least square method is used to optimize the tool paths for five-axis flank machining. Finally,a validation example is given for a specific ruled surface. Results show the effectiveness and feasibility of the analytical model of geometric errors induced by cutter runout,and also show that the geometric errors can be reduced significantly using the proposed tool path planning method.展开更多
The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In...The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In motion optimization, the stiffness characteristics of the whole machining system, including machine tool and cutter, are not considered. The paper presents a new method to establish a general stiffness model of multi-axis machining system. An analytical stiffness model is established by Jacobi and point transformation matrix method. Based on the stiffness model, feed-direction stiffness index is calculated by the intersection of force ellipsoid and the cutting feed direction at the cutter tip. The stiffness index can help analyze the stiffness performance of the whole machining system in the available workspace. Based on the analysis of the stiffness performance, multi-axis motion optimization along tool paths is accomplished by mixed programming using Matlab and Visual C＋＋. The effectiveness of the motion optimization method is verified by the experimental research about the machining performance of a 7-axis 5-linkage machine tool. The proposed research showed that machining stability and production efficiency can be improved by multi-axis motion optimization based on the anisotropic force ellipsoid of the whole machining system.展开更多
In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeabili...In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.展开更多
为了提高机械臂工作效率,同时减少能量损耗及所受冲击,提出了一种基于自适应变换蝙蝠算法(Adaptive transformation bat algorithm,ATBA)的轨迹优化方法。利用5次多项式插值建立机械臂轨迹模型,通过在标准蝙蝠算法(Bat algorithm,BA)的...为了提高机械臂工作效率,同时减少能量损耗及所受冲击,提出了一种基于自适应变换蝙蝠算法(Adaptive transformation bat algorithm,ATBA)的轨迹优化方法。利用5次多项式插值建立机械臂轨迹模型,通过在标准蝙蝠算法(Bat algorithm,BA)的局部搜索中加入动态扰动系数,同时改进全局搜索与局部搜索的变换策略,得到了ATBA;将时间、能耗和冲击设为优化目标,对机械臂运动轨迹进行优化。对6自由度机械臂进行仿真分析,结果表明,该轨迹优化方法能有效地进行多目标寻优,得到理想的Pareto最优解集,通过实际工况构造归一化权重目标函数,选择期望解,较好地提高了轨迹、速度、加速度的平滑性及机械臂的运行效率。展开更多
In this paper, a new computation method and an optimization algorithm are presented for feedrate scheduling of five-axis machining in compliance with both machine drive limits and process limits. Five-axis machine too...In this paper, a new computation method and an optimization algorithm are presented for feedrate scheduling of five-axis machining in compliance with both machine drive limits and process limits. Five-axis machine tool with its ability of controlling tool orientation to follow the sculptured surface contour has been widely used in modern manufacturing industry. Feedrate scheduling serving as a kernel of CNC control system plays a critical role to ensure the required machining accuracy and reliability for five-axis machining. Due to the nonlinear coupling effects of all involved drive axes and the saturation limit of servo motors, the feedrate scheduling for multi-axis machining has long been recognized and remains as a critical challenge for achieving five-axis machine tools’ full capacity and advantage. To solve the nonlinearity nature of the five-axis feedrate scheduling problems, a relaxation mathematical process is presented for relaxing both the drive motors’ physical limitations and the kinematic constraints of five-axis tool motions. Based on the primary optimization variable of feedrate, the presented method analytically linearizes the machining-related constraints, in terms of the machines’ axis velocities, axis accelerations and axis jerks. The nonlinear multi-constrained feedrate scheduling problem is transformed into a manageable linear programming problem. An optimization algorithm is presented to find the optimal feedrate scheduling solution for the five-axis machining problems. Both computer implementation and laboratorial experiment testing by actual machine cutting were conducted and presented in this paper. The experiment results demonstrate that the proposed method can effectively generate efficient feedrate scheduling for five-axis machining with constraints of the machine tool physical constraints and limits. Compared with other existing numerical methods, the proposed method is able to find an accurate analytical solution for the nonlinear constrained five-axis feedrate scheduling prob展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 51075054)the National Basic Research Program of China ("973" Program) (Grant Nos. 2005CB726100 and 2011CB706800)the Fundamental Research Funds for the Central Universities (Grant No. DUT10ZD205)
文摘The cutter runout effect has significant influence on the shape of cutter swept surface and the machining surface quality. Hence,it is necessary to integrate the cutter runout effect in cutter swept surface modeling,geometric error prediction and tool path optimization for five-axis flank machining. In this paper,an envelope surface model considering cutter runout effect is first established,and geometric errors induced by runout effect are derived based on the relative motion analysis between the cutter and part in machining. In the model,the cutter runout is defined by four parameters,including inclination angle,location angle,offset value and the length of cutter axis. Then the runout parameters are integrated into the rotation surface of each cutting edge that is used to form the final cutter envelope surface for the five-axis machining process. Thus,the final resulting geometric errors of the machined surface induced by cutter runout can be obtained through computing the deviations from the nominal cutter swept surface. To reduce these errors,an iterative least square method is used to optimize the tool paths for five-axis flank machining. Finally,a validation example is given for a specific ruled surface. Results show the effectiveness and feasibility of the analytical model of geometric errors induced by cutter runout,and also show that the geometric errors can be reduced significantly using the proposed tool path planning method.
基金supported by National Natural Science Foundation of China (Grant No. 51075168)National Basic Research Program of China (973 Program, Grant No. 2011CB706803)National Hi-tech Research and Development Program of China (863 Program, Grant No. 2009AA04Z149)
文摘The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In motion optimization, the stiffness characteristics of the whole machining system, including machine tool and cutter, are not considered. The paper presents a new method to establish a general stiffness model of multi-axis machining system. An analytical stiffness model is established by Jacobi and point transformation matrix method. Based on the stiffness model, feed-direction stiffness index is calculated by the intersection of force ellipsoid and the cutting feed direction at the cutter tip. The stiffness index can help analyze the stiffness performance of the whole machining system in the available workspace. Based on the analysis of the stiffness performance, multi-axis motion optimization along tool paths is accomplished by mixed programming using Matlab and Visual C＋＋. The effectiveness of the motion optimization method is verified by the experimental research about the machining performance of a 7-axis 5-linkage machine tool. The proposed research showed that machining stability and production efficiency can be improved by multi-axis motion optimization based on the anisotropic force ellipsoid of the whole machining system.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 50775147 and 50835004)the National Basic Research Program of China ("973" Project) (Grant No. 2005CB724103)the Science & Technology Commission of Shanghai Municipality (Grant No. 07JC14028)
文摘In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.
文摘为了提高机械臂工作效率,同时减少能量损耗及所受冲击,提出了一种基于自适应变换蝙蝠算法(Adaptive transformation bat algorithm,ATBA)的轨迹优化方法。利用5次多项式插值建立机械臂轨迹模型,通过在标准蝙蝠算法(Bat algorithm,BA)的局部搜索中加入动态扰动系数,同时改进全局搜索与局部搜索的变换策略,得到了ATBA;将时间、能耗和冲击设为优化目标,对机械臂运动轨迹进行优化。对6自由度机械臂进行仿真分析,结果表明,该轨迹优化方法能有效地进行多目标寻优,得到理想的Pareto最优解集,通过实际工况构造归一化权重目标函数,选择期望解,较好地提高了轨迹、速度、加速度的平滑性及机械臂的运行效率。
基金supported by the National Natural Science Foundation of China (Grant No. 51525501)the Science Challenge Project (Grant No. TZ2016006-0102)+1 种基金the Dalian Science and Technology Project (Grant No. 2016RD08)Dr. Y.S. Lee was partially supported by the National Science Foundation (Grant No. CMMI-1547105) to North Carolina State University
文摘In this paper, a new computation method and an optimization algorithm are presented for feedrate scheduling of five-axis machining in compliance with both machine drive limits and process limits. Five-axis machine tool with its ability of controlling tool orientation to follow the sculptured surface contour has been widely used in modern manufacturing industry. Feedrate scheduling serving as a kernel of CNC control system plays a critical role to ensure the required machining accuracy and reliability for five-axis machining. Due to the nonlinear coupling effects of all involved drive axes and the saturation limit of servo motors, the feedrate scheduling for multi-axis machining has long been recognized and remains as a critical challenge for achieving five-axis machine tools’ full capacity and advantage. To solve the nonlinearity nature of the five-axis feedrate scheduling problems, a relaxation mathematical process is presented for relaxing both the drive motors’ physical limitations and the kinematic constraints of five-axis tool motions. Based on the primary optimization variable of feedrate, the presented method analytically linearizes the machining-related constraints, in terms of the machines’ axis velocities, axis accelerations and axis jerks. The nonlinear multi-constrained feedrate scheduling problem is transformed into a manageable linear programming problem. An optimization algorithm is presented to find the optimal feedrate scheduling solution for the five-axis machining problems. Both computer implementation and laboratorial experiment testing by actual machine cutting were conducted and presented in this paper. The experiment results demonstrate that the proposed method can effectively generate efficient feedrate scheduling for five-axis machining with constraints of the machine tool physical constraints and limits. Compared with other existing numerical methods, the proposed method is able to find an accurate analytical solution for the nonlinear constrained five-axis feedrate scheduling prob
