复杂曲面加工运动创成与加工区域研究
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摘要
目前，世界经济正以惊人的速度迅速发展，人们对各种产品的性能要求越来越高。随着科技的不断进步，具有复杂曲面特征的产品相继出现，并且大量地应用在航空航天、模具、工具等领域。因此复杂曲面已经成为近年来的研究热点。本文在国家重点基础研究发展计划（973计划）项目的支持下，以轴对称非球面和自由曲面为研究对象，分别对轴对称非球面加工机床运动创成、自由曲面加工机床运动创成以及抛物面和双曲面的加工范围开展研究工作，并进行了相关仿真实验来验证理论分析的正确性。
采用解析法研究了轴对称非球面加工机床运动创成。从轴对称非球面构型特征出发，应用坐标变换方法，获得刀具和工件的数学描述，解析刀具与工件的位姿关系，建立刀具相对于工件的位姿矩阵，提出所需的运动单元，创成设计轴对称非球面加工机床运动功能方案，优化设计结果，并给出对应运动结构式的机床结构布局图。在满足刀具轴线始终保持铅垂方向的情况下，得到30种轴对称非球面加工机床运动构型；而在满足刀具轴线与工件切削点法线方向始终保持一致的情况下，得到18种轴对称非球面加工机床运动构型。
采用解析法研究了自由曲面加工机床运动创成。根据自由曲面的特征，将其划分为八种基本型面，从八种基本型面构型出发，解析刀具与工件的位姿关系，建立刀具相对于工件的位姿矩阵，提出所需的运动单元，创成设计各基本型面加工机床运动功能方案。针对包含多种基本型面的自由曲面，综合必要的运动方案，明确了自由曲面对应的运动构型，给出了自由曲面加工机床构型的选择原则及方法，提出并优化可能的机床结构布局。
详细研究了面向机床构型的轴对称非球面加工范围。采用坐标变换方法，建立了加工轴对称非球面的数学模型。针对轴对称非球面中最典型的抛物面，分析了工件参数、刀具参数、刀具切削状态参数以及机床构型参数之间的函数关系，从而推导了刀具位于铅垂方向的位置、抛物面最大矢高、最大口径、摆角范围及刀杆伸出最小长度等关键技术指标的变化规律。提出了一种面向机床构型的轴对称非球面加工范围的典型算法，通过输入非球面基本结构参数和机床运动范围参数，在加工之前便能很快捷地判断出机床是否能够完成所选轴对称非球面的加工任务。仿真实验验证了该算法的有效性。
详细分析了双曲面加工干涉区域。建立了加工双曲面的数学模型，通过对双曲面参数特征的分析，发现了双曲面上任意点的切线斜率极限值以及刀具轴线斜率极限值的变化规律，据此推导出双曲面参数、刀具参数与偏心率平方之间的函数关系，推演了加工双曲面不发生干涉的参数准则，同时明确了切削角与偏心率平方满足不同函数关系对应的干涉区域。当参数位于可能干涉的区域时，计算出保证加工不发生干涉所允许的双曲面最大口径和最大矢高，通过仿真实验，验证了理论分析的正确性，为加工双曲面的参数选取提供依据。
Nowadays, development speed of world economy is surprising. The performancerequirements of products are becoming higher and higher. With the scientific andtechnological progress, the products with complex surface have come into world,which were applied in the fields of aerospace, die, tool, etc.. Therefore, complexsurface becomes research focus in recent years. Under financial support of theprojects named National Basic Research Program of China, this thesis investigatesmotion generation for machining axisymmetric aspheric surface, motion generationfor machining free-form surface, dimensional range of machining parabolic surfaceand hyperboloidal surface. And the simulation experiment is accomplished, whichshows the validity of theoretical analysis.
Based on analysis method, motion generation for machining axisymmetricaspheric surface is researched. Based on the configuration characteristic ofaxisymmetric aspheric surface, the mathematical description of tool and workpiece isobtained with coordinate transformation method. The relationship of position andorientation between tool and workpiece is analyzed. The matrix of positon andorientation between tool and workpiece is set up. The essential movement units areproposed. The movement function scheme of the machine tool for machiningaxisymmetric aspheric surface is generated. The results of design are optimized andthe structural configurations of the machine tool are obtained according to theexpression of movement structure. As the rotational axis of the tool is always vertical,30optimized structural configurations are obtained. And as the rotational axis of thetool coincides with the normal at cutting point of workpiece,18optimized structuralconfigurations are obtained.
Based on analysis method, motion generation for machining free-form surface isresearched. Free-form surface is divided into eight basic surfaces by differentcurvature. Based on the configuration characteristic of eight basic surfaces, therelationship of position and orientation between tool and workpiece surface isanalyzed. The matrix of position and orientation between tool and workpiece surfaceis set up. The essential movement units are proposed. The motion schemes of themachine tool for machining eight basic surfaces are generated. The motion schemesare synthetized for machining free-form surface with multiple basic surfaces. Thebasic modules and the necessary motions for generating free-form surface are clarified. Selection principle and method of motion configuration for machining free-formsurface is presented. And the possible structural configurations of the machine tool areproposed and optimized.
The dimensional range of machining axisymmetric aspheric surface for machinetool is researched. Based on coordinate transformation method, the mathematicalmodel for machining axisymmetric aspheric surface is set up. Parabolic surface isstudied. The functional relationships between workpiece parameter, tool parameter,cutting state parameter and machine tool performance parameter are analyzed. Thevariation laws of key technical indexes such as the position of tool locating in verticaldirection, the maximum vector height and aperture of parabolic surface, swing rangeof tool, the minimum arbor distance of tool locating tool carrier in lateral are deduced.An algorithm on dimensional range of machining axisymmetric aspheric surface formachine tool is presented. It can be estimated swiftly that whether the machine toolcould do it before machining axisymmetric aspheric surface by means of inputtingstructure parameters of axisymmetric aspheric surface and motion ranges of machinetool. The simulation experiment results show the validity of the algorithm.
Interference area for machining hyperboloidal surface is discussed. Themathematical model for machining hyperboloidal surface is set up. Based on theanalysis of parameter characteristics of hyperboloidal surface, the variation law of theslope limit value of tangent at arbitrary point on hyperboloidal surface and the slopelimit value of the axis of tool is discovered. Based on the discovery, the functionalrelationship between parabola parameter, tool parameter and the square of eccentricityis obtained. The parameter criterion that there is no interference as machininghyperboloidal surface is deduced. The interference areas corresponding to differentfunctional relationships between cutting angle and the square of eccentricity areclarified. As the parameters are in the possible interference area, the maximum vectorheight and aperture of hyperboloidal surface are calculated. The simulationexperiment results showed the validity of theoretical analysis, which facilitates theparameter selection for machining hyperboloidal surface.
采用解析法研究了轴对称非球面加工机床运动创成。从轴对称非球面构型特征出发，应用坐标变换方法，获得刀具和工件的数学描述，解析刀具与工件的位姿关系，建立刀具相对于工件的位姿矩阵，提出所需的运动单元，创成设计轴对称非球面加工机床运动功能方案，优化设计结果，并给出对应运动结构式的机床结构布局图。在满足刀具轴线始终保持铅垂方向的情况下，得到30种轴对称非球面加工机床运动构型；而在满足刀具轴线与工件切削点法线方向始终保持一致的情况下，得到18种轴对称非球面加工机床运动构型。
采用解析法研究了自由曲面加工机床运动创成。根据自由曲面的特征，将其划分为八种基本型面，从八种基本型面构型出发，解析刀具与工件的位姿关系，建立刀具相对于工件的位姿矩阵，提出所需的运动单元，创成设计各基本型面加工机床运动功能方案。针对包含多种基本型面的自由曲面，综合必要的运动方案，明确了自由曲面对应的运动构型，给出了自由曲面加工机床构型的选择原则及方法，提出并优化可能的机床结构布局。
详细研究了面向机床构型的轴对称非球面加工范围。采用坐标变换方法，建立了加工轴对称非球面的数学模型。针对轴对称非球面中最典型的抛物面，分析了工件参数、刀具参数、刀具切削状态参数以及机床构型参数之间的函数关系，从而推导了刀具位于铅垂方向的位置、抛物面最大矢高、最大口径、摆角范围及刀杆伸出最小长度等关键技术指标的变化规律。提出了一种面向机床构型的轴对称非球面加工范围的典型算法，通过输入非球面基本结构参数和机床运动范围参数，在加工之前便能很快捷地判断出机床是否能够完成所选轴对称非球面的加工任务。仿真实验验证了该算法的有效性。
详细分析了双曲面加工干涉区域。建立了加工双曲面的数学模型，通过对双曲面参数特征的分析，发现了双曲面上任意点的切线斜率极限值以及刀具轴线斜率极限值的变化规律，据此推导出双曲面参数、刀具参数与偏心率平方之间的函数关系，推演了加工双曲面不发生干涉的参数准则，同时明确了切削角与偏心率平方满足不同函数关系对应的干涉区域。当参数位于可能干涉的区域时，计算出保证加工不发生干涉所允许的双曲面最大口径和最大矢高，通过仿真实验，验证了理论分析的正确性，为加工双曲面的参数选取提供依据。
Nowadays, development speed of world economy is surprising. The performancerequirements of products are becoming higher and higher. With the scientific andtechnological progress, the products with complex surface have come into world,which were applied in the fields of aerospace, die, tool, etc.. Therefore, complexsurface becomes research focus in recent years. Under financial support of theprojects named National Basic Research Program of China, this thesis investigatesmotion generation for machining axisymmetric aspheric surface, motion generationfor machining free-form surface, dimensional range of machining parabolic surfaceand hyperboloidal surface. And the simulation experiment is accomplished, whichshows the validity of theoretical analysis.
Based on analysis method, motion generation for machining axisymmetricaspheric surface is researched. Based on the configuration characteristic ofaxisymmetric aspheric surface, the mathematical description of tool and workpiece isobtained with coordinate transformation method. The relationship of position andorientation between tool and workpiece is analyzed. The matrix of positon andorientation between tool and workpiece is set up. The essential movement units areproposed. The movement function scheme of the machine tool for machiningaxisymmetric aspheric surface is generated. The results of design are optimized andthe structural configurations of the machine tool are obtained according to theexpression of movement structure. As the rotational axis of the tool is always vertical,30optimized structural configurations are obtained. And as the rotational axis of thetool coincides with the normal at cutting point of workpiece,18optimized structuralconfigurations are obtained.
Based on analysis method, motion generation for machining free-form surface isresearched. Free-form surface is divided into eight basic surfaces by differentcurvature. Based on the configuration characteristic of eight basic surfaces, therelationship of position and orientation between tool and workpiece surface isanalyzed. The matrix of position and orientation between tool and workpiece surfaceis set up. The essential movement units are proposed. The motion schemes of themachine tool for machining eight basic surfaces are generated. The motion schemesare synthetized for machining free-form surface with multiple basic surfaces. Thebasic modules and the necessary motions for generating free-form surface are clarified. Selection principle and method of motion configuration for machining free-formsurface is presented. And the possible structural configurations of the machine tool areproposed and optimized.
The dimensional range of machining axisymmetric aspheric surface for machinetool is researched. Based on coordinate transformation method, the mathematicalmodel for machining axisymmetric aspheric surface is set up. Parabolic surface isstudied. The functional relationships between workpiece parameter, tool parameter,cutting state parameter and machine tool performance parameter are analyzed. Thevariation laws of key technical indexes such as the position of tool locating in verticaldirection, the maximum vector height and aperture of parabolic surface, swing rangeof tool, the minimum arbor distance of tool locating tool carrier in lateral are deduced.An algorithm on dimensional range of machining axisymmetric aspheric surface formachine tool is presented. It can be estimated swiftly that whether the machine toolcould do it before machining axisymmetric aspheric surface by means of inputtingstructure parameters of axisymmetric aspheric surface and motion ranges of machinetool. The simulation experiment results show the validity of the algorithm.
Interference area for machining hyperboloidal surface is discussed. Themathematical model for machining hyperboloidal surface is set up. Based on theanalysis of parameter characteristics of hyperboloidal surface, the variation law of theslope limit value of tangent at arbitrary point on hyperboloidal surface and the slopelimit value of the axis of tool is discovered. Based on the discovery, the functionalrelationship between parabola parameter, tool parameter and the square of eccentricityis obtained. The parameter criterion that there is no interference as machininghyperboloidal surface is deduced. The interference areas corresponding to differentfunctional relationships between cutting angle and the square of eccentricity areclarified. As the parameters are in the possible interference area, the maximum vectorheight and aperture of hyperboloidal surface are calculated. The simulationexperiment results showed the validity of theoretical analysis, which facilitates theparameter selection for machining hyperboloidal surface.
引文
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