模具高速铣削刀具轨迹规划与工艺参数优选技术的研究
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摘要
高速切削由于其高效高精可加工高硬材料的特点，能够满足自由曲面精加工的需求，上世纪90年代以来，逐渐走向实用，在复杂自由曲面制造领域得到了广泛应用，并正在成为当代先进制造技术的重要发展趋势。高速铣削应用于模具加工中，在改善表面质量的同时提高了加工效率，可以在一次装夹中完成粗精加工的所有工序甚至取消手工操作。模具等零件的高速铣削加工多为难加工材料且材料去除量大、消耗时间长、刀具寿命短，随着工件形状复杂程度的增加，提高自由曲面加工精度和加工效率变得越来越重要。
环形刀五轴数控加工自上世纪60年代以来开始得到应用，环形刀五轴数控加工在改善表面质量和提高加工效率方面显示出了更大的优势。数控编程是数控加工的基础，刀具运动轨迹规划是多坐标数控编程的基础和关键。因此，针对自由曲面五轴数控加工问题，通过刀具位姿、路径规划和工艺参数选择来实现在保证精度前提下，加工效率的提高成为急待解决的问题。
刀具轨迹规划需配合工艺参数选择最终生成数控加工程序，在以往编程过程中没有考虑进给速度的频繁变化导致铣削过程本身加工工艺环境的不断恶化。因此，本文将高速铣削自动编程和轨迹规划的研究从系统论的角度结合机床的动力学特性进行研究，建立位姿与轨迹优化控制理论和工艺参数优化模型，并对位姿与轨迹优化和工艺参数优化进行有效集成与融合，主要研究内容如下：
(1)高速高精数控编程系统需完成的任务和关键问题研究。在对高速铣削数控编程系统相关问题研究的基础上，建立了多轴数控加工刀具姿态的控制和优化、最大行距的计算、工艺参数优化选择等方面的完善的数控编程系统框架，对影响精度和效率的关键问题进行了分析。
(2)环形刀五轴数控加工刀具路径规划的研究。基于杜邦指标线，推导出了环形铣刀五轴铣削复杂曲面时的局部可铣性充要条件，在求得等残留高度算法最大加工带宽的同时确定了无局部曲率干涉的刀具姿态，生成了刀具轨迹并与传统算法进行了比较。
(3)等残留高度算法的首条路径优化。分析了带宽与曲面特性的关系，基于最大平坦度方向可以减少刀位点数量的原则优化了等残留高度算法中的首条路径，使其与曲面的曲率特性相关；应用前述自适应刀轴矢量算法中刀具姿态和带宽的确定方法生成刀具轨迹，并与前述方法进行比较可得首条路径优化后的刀具路径更能提高加工效率。
(4)速度和加速度动态特性研究。应用恒表面切削速率方法对上述方法生成的刀具轨迹，基于MATLAB方法进行速度和加速度分析，比较其速度和加速度特性，并指出带宽由曲面的曲率特性和倾角大小共同确定，当步长变化均匀时可以优化加速度曲线，初始路径的选择可以优化刀具轨迹。
(5)高速铣削中切削工艺参数的优化。基于a p，n，fz，ae四个主要切削参数，针对塑料模具钢P1.2738进行了四因素四水平正交切削试验；采用极差分析法分析了各因素对表面粗糙度Ra的影响规律并获得了最佳参数组合为A2B3C1D1；应用正交回归方法建立了表面粗糙度Ra预测模型，经检验回归方程和回归系数均程高度显著可以进行预测，根据预测方程所绘制各单因素对表面粗糙度Ra的影响规律与极差分析法一致；利用人工神经网络BP算法建立了4输入1输出、隐层结点数为12的三层表面粗糙度预测模型，将预测结果与BP算法进行比较得出BP预测效果优于正交回归分析方法；基于BP网络所建立的表面粗糙度Ra预测模型结合遗传算法以最小的表面粗糙度和最大的材料去除率为优化目标，求得了满足条件的最优参数组合。
(6)针对传统等残留高度算法，自适应刀轴矢量的等残留高度算法和首条路径优化后的自适应刀轴矢量等残留高度算法三种刀具路径方法生成的刀具轨迹，结合在铣削工艺参数优化中得到的最优参数组合，以塑料模具钢P1.2738为试验材料，应用DMU125P五轴数控机床对三种方法生成的刀具轨迹进行加工对比试验，验证了本文方法可以在保证精度的前提下明显提高加工效率。
High speed cutting, because of its high efficiency and high precision, can be used tocut high hardness materials. Since the1990s，it is gradually used in the complex freesurface manufacturing and is becoming an important development trend as advancedmanufacturing technology. High speed milling can improve surface quality and theprocessing efficiency in mold processing，simultaneously. It can finish all the roughand the finish machining process, even cancel the manual operation in one clamping.In general, molds and parts that processed by high speed milling are materials that aremore difficult to process and have large amount of material removal, so consumelonger time and shorten tool life. With the increase of the degree of complex shape ofwork-piece，improve machining precision and machining efficiency of the free surfaceis becoming more and more important.
NC machining began to get application since the1960s，five axis NC machiningwith torus cutter show more advantages because it can improve surface quality andimprove processing efficiency. The data show that，20%-30%of the numericalcontrol machine stop production, because it can't prepare NC program，so affects theutilization rate of the machine tool directly. Tool path is the basis and key factor inmulti-axis NC machining programming. Therefore, through the controlling ofinclinable angle, yaw angle of the tool and path planning in five axis machining toachieve accuracy in guarantee under the premise of processing to enhance theefficiency are the urgent problems.
Tool path planning cooperated with craft parameter selecting generate the NCprogram. We did not consider the frequent changes of feed speed and the worseningof environment from programming in milling process itself in the past. Therefore, thispaper will research tool path planning of high speed milling and combine it withmachine tool's dynamic characteristics from the point of system theory. Establish toolorientation and tool path optimization control theory, establish the model of parameteroptimization，and carry on effective integration and fusion. The main research contentis as follows：
(1)Research on the key problems of high speed and high precision NCprogramming system. Base on the study of NC programming system and relatedproblems of high speed milling，establish the system framework of multi-axis NC machining from the optimization of tool orientation and the calculation of maximumstep-width，cooperated with the selection of optimized parameter，pointed out the keyissues of influencing accuracy and efficiency.
(2)Research on tool path planning of five axis NC machining with torus cutter.Analysis the relative position relationship of the three frames in five axis NCmachining，calculated the global coordinates of the cutter location and the vector ofcutter. Based on the Dupont index line, this paper deduced the necessary andsufficient condition that can avoid gouging when milling complex surface in five axiswith torus cutter. We generated tool path by the method in this paper and compared itwith the traditional algorithm, the results indicate that the present constantscallop-height machining achieves the specified machining accuracy with fewer andshorter tool paths than the existing tool path generation approaches.
(3)Optimization of the master cutter path of constant scallop-height algorithm.Analysis the relationship between the strip width and the surface characteristics, themaster cutter path have been chosen from the maximum flatness direction that canreduce the number of cutter location point, make it be related with the curvature of thesurface characteristics. The tool paths are generated by the method of self-adaptivetool orientation.
(4) Research on the dynamic characteristic of velocity and acceleration. Based onconstant surface cutting rate method and MATLAB, we analysis and compare thecharacteristic of velocity and acceleration of tool path that generated by the abovethree kinds of method. Point out that strip widths are identified by both the curvaturecharacteristics of the surface and tool orientation, acceleration curve can be optimizedwhen step changes uniform, the choice of the master cutter tool path can optimize toolpath.
(5) Optimization of process parameters in high speed milling. Based on the fourmain cutting parameter:a p，n，fz，ae, the experiment was carried out on plasticdie-mold steel P1.2738on a high-speed5-axis machining center by using four factorsof the four levels orthogonal test. By using maximum difference method gains thefour experimental factors on the surface roughness of the different effect, draws thetrend curve of the milling parameters on the surface roughness, and analyzes causes oftheir impact, get the best parameter combination A2B3C1D1. Based on multipleregression, we presented the prediction model for the surface roughness. In this paper, we verified the regression factor coefficients and significances of the regressionequation, the trend curve of the milling parameters on the surface roughness iscoincident with the maximum difference method. Based on artificial neural network,we presented the prediction model of surface roughness. There are one input layer offour neurons, one output layer of one neuron and one hidden layer of12neurons, themain factors are included in the input layer of the network. The average relative errorof prediction results is2.6825%while that of the multiple orthogonal regression is7.8156%, which show that the BP model can basically draw the relationship betweeninput parameters and output parameters. Based on the ANN and the genetic algorithm,we optimized the milling parameters. The objective functions are the biggestmachining material removal and the minimum surface roughness. We built Themulti-objective optimal model and gave the optimization results.
(6) Based on tool path that generated by the following three method: traditionalconstant scallop algorithm, self-adaptive tool orientation method and self-adaptivetool orientation method of optimized master cutter path. Combined with the optimalparameter, we conducted the experiment on plastic die-mold steel P1.2738on ahigh-speed5-axis machining center DMU125P, the results show that the tool pathgenerated by self-adaptive tool orientation method of optimized master cutter path canimprove the processing efficiency obviously.
环形刀五轴数控加工自上世纪60年代以来开始得到应用，环形刀五轴数控加工在改善表面质量和提高加工效率方面显示出了更大的优势。数控编程是数控加工的基础，刀具运动轨迹规划是多坐标数控编程的基础和关键。因此，针对自由曲面五轴数控加工问题，通过刀具位姿、路径规划和工艺参数选择来实现在保证精度前提下，加工效率的提高成为急待解决的问题。
刀具轨迹规划需配合工艺参数选择最终生成数控加工程序，在以往编程过程中没有考虑进给速度的频繁变化导致铣削过程本身加工工艺环境的不断恶化。因此，本文将高速铣削自动编程和轨迹规划的研究从系统论的角度结合机床的动力学特性进行研究，建立位姿与轨迹优化控制理论和工艺参数优化模型，并对位姿与轨迹优化和工艺参数优化进行有效集成与融合，主要研究内容如下：
(1)高速高精数控编程系统需完成的任务和关键问题研究。在对高速铣削数控编程系统相关问题研究的基础上，建立了多轴数控加工刀具姿态的控制和优化、最大行距的计算、工艺参数优化选择等方面的完善的数控编程系统框架，对影响精度和效率的关键问题进行了分析。
(2)环形刀五轴数控加工刀具路径规划的研究。基于杜邦指标线，推导出了环形铣刀五轴铣削复杂曲面时的局部可铣性充要条件，在求得等残留高度算法最大加工带宽的同时确定了无局部曲率干涉的刀具姿态，生成了刀具轨迹并与传统算法进行了比较。
(3)等残留高度算法的首条路径优化。分析了带宽与曲面特性的关系，基于最大平坦度方向可以减少刀位点数量的原则优化了等残留高度算法中的首条路径，使其与曲面的曲率特性相关；应用前述自适应刀轴矢量算法中刀具姿态和带宽的确定方法生成刀具轨迹，并与前述方法进行比较可得首条路径优化后的刀具路径更能提高加工效率。
(4)速度和加速度动态特性研究。应用恒表面切削速率方法对上述方法生成的刀具轨迹，基于MATLAB方法进行速度和加速度分析，比较其速度和加速度特性，并指出带宽由曲面的曲率特性和倾角大小共同确定，当步长变化均匀时可以优化加速度曲线，初始路径的选择可以优化刀具轨迹。
(5)高速铣削中切削工艺参数的优化。基于a p，n，fz，ae四个主要切削参数，针对塑料模具钢P1.2738进行了四因素四水平正交切削试验；采用极差分析法分析了各因素对表面粗糙度Ra的影响规律并获得了最佳参数组合为A2B3C1D1；应用正交回归方法建立了表面粗糙度Ra预测模型，经检验回归方程和回归系数均程高度显著可以进行预测，根据预测方程所绘制各单因素对表面粗糙度Ra的影响规律与极差分析法一致；利用人工神经网络BP算法建立了4输入1输出、隐层结点数为12的三层表面粗糙度预测模型，将预测结果与BP算法进行比较得出BP预测效果优于正交回归分析方法；基于BP网络所建立的表面粗糙度Ra预测模型结合遗传算法以最小的表面粗糙度和最大的材料去除率为优化目标，求得了满足条件的最优参数组合。
(6)针对传统等残留高度算法，自适应刀轴矢量的等残留高度算法和首条路径优化后的自适应刀轴矢量等残留高度算法三种刀具路径方法生成的刀具轨迹，结合在铣削工艺参数优化中得到的最优参数组合，以塑料模具钢P1.2738为试验材料，应用DMU125P五轴数控机床对三种方法生成的刀具轨迹进行加工对比试验，验证了本文方法可以在保证精度的前提下明显提高加工效率。
High speed cutting, because of its high efficiency and high precision, can be used tocut high hardness materials. Since the1990s，it is gradually used in the complex freesurface manufacturing and is becoming an important development trend as advancedmanufacturing technology. High speed milling can improve surface quality and theprocessing efficiency in mold processing，simultaneously. It can finish all the roughand the finish machining process, even cancel the manual operation in one clamping.In general, molds and parts that processed by high speed milling are materials that aremore difficult to process and have large amount of material removal, so consumelonger time and shorten tool life. With the increase of the degree of complex shape ofwork-piece，improve machining precision and machining efficiency of the free surfaceis becoming more and more important.
NC machining began to get application since the1960s，five axis NC machiningwith torus cutter show more advantages because it can improve surface quality andimprove processing efficiency. The data show that，20%-30%of the numericalcontrol machine stop production, because it can't prepare NC program，so affects theutilization rate of the machine tool directly. Tool path is the basis and key factor inmulti-axis NC machining programming. Therefore, through the controlling ofinclinable angle, yaw angle of the tool and path planning in five axis machining toachieve accuracy in guarantee under the premise of processing to enhance theefficiency are the urgent problems.
Tool path planning cooperated with craft parameter selecting generate the NCprogram. We did not consider the frequent changes of feed speed and the worseningof environment from programming in milling process itself in the past. Therefore, thispaper will research tool path planning of high speed milling and combine it withmachine tool's dynamic characteristics from the point of system theory. Establish toolorientation and tool path optimization control theory, establish the model of parameteroptimization，and carry on effective integration and fusion. The main research contentis as follows：
(1)Research on the key problems of high speed and high precision NCprogramming system. Base on the study of NC programming system and relatedproblems of high speed milling，establish the system framework of multi-axis NC machining from the optimization of tool orientation and the calculation of maximumstep-width，cooperated with the selection of optimized parameter，pointed out the keyissues of influencing accuracy and efficiency.
(2)Research on tool path planning of five axis NC machining with torus cutter.Analysis the relative position relationship of the three frames in five axis NCmachining，calculated the global coordinates of the cutter location and the vector ofcutter. Based on the Dupont index line, this paper deduced the necessary andsufficient condition that can avoid gouging when milling complex surface in five axiswith torus cutter. We generated tool path by the method in this paper and compared itwith the traditional algorithm, the results indicate that the present constantscallop-height machining achieves the specified machining accuracy with fewer andshorter tool paths than the existing tool path generation approaches.
(3)Optimization of the master cutter path of constant scallop-height algorithm.Analysis the relationship between the strip width and the surface characteristics, themaster cutter path have been chosen from the maximum flatness direction that canreduce the number of cutter location point, make it be related with the curvature of thesurface characteristics. The tool paths are generated by the method of self-adaptivetool orientation.
(4) Research on the dynamic characteristic of velocity and acceleration. Based onconstant surface cutting rate method and MATLAB, we analysis and compare thecharacteristic of velocity and acceleration of tool path that generated by the abovethree kinds of method. Point out that strip widths are identified by both the curvaturecharacteristics of the surface and tool orientation, acceleration curve can be optimizedwhen step changes uniform, the choice of the master cutter tool path can optimize toolpath.
(5) Optimization of process parameters in high speed milling. Based on the fourmain cutting parameter:a p，n，fz，ae, the experiment was carried out on plasticdie-mold steel P1.2738on a high-speed5-axis machining center by using four factorsof the four levels orthogonal test. By using maximum difference method gains thefour experimental factors on the surface roughness of the different effect, draws thetrend curve of the milling parameters on the surface roughness, and analyzes causes oftheir impact, get the best parameter combination A2B3C1D1. Based on multipleregression, we presented the prediction model for the surface roughness. In this paper, we verified the regression factor coefficients and significances of the regressionequation, the trend curve of the milling parameters on the surface roughness iscoincident with the maximum difference method. Based on artificial neural network,we presented the prediction model of surface roughness. There are one input layer offour neurons, one output layer of one neuron and one hidden layer of12neurons, themain factors are included in the input layer of the network. The average relative errorof prediction results is2.6825%while that of the multiple orthogonal regression is7.8156%, which show that the BP model can basically draw the relationship betweeninput parameters and output parameters. Based on the ANN and the genetic algorithm,we optimized the milling parameters. The objective functions are the biggestmachining material removal and the minimum surface roughness. We built Themulti-objective optimal model and gave the optimization results.
(6) Based on tool path that generated by the following three method: traditionalconstant scallop algorithm, self-adaptive tool orientation method and self-adaptivetool orientation method of optimized master cutter path. Combined with the optimalparameter, we conducted the experiment on plastic die-mold steel P1.2738on ahigh-speed5-axis machining center DMU125P, the results show that the tool pathgenerated by self-adaptive tool orientation method of optimized master cutter path canimprove the processing efficiency obviously.
引文
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