面向数字孪生的产品表面模型表达与生成方法

产品数字孪生模型被认为是实现物理世界和虚拟世界深度融合的一种潜在的有效解决方法。针对产品全生命周期过程对数字孪生几何模型合理准确表达的实际应用需求,提出以非理想表面模型为载体实现数字孪生模型的几何参考表达方法。引入新一代产品几何技术规范,给出了通过几何要素及相关操作实现非理想表面模型信息的完整表达方案;分析了面向数字孪生的产品非理想表面模型的两种映射生成方法和模型创建流程,通过在离散网格模型上增加几何误差信息的方式生成规范表面模型;根据逆向建模的思想,通过实际测量离散点云数据并采用离散几何及小波分析等手段进行多尺度表面形貌误差表征,从而生成认证表面模型。最后通过某零件实例分析验证了所提方法的可行性。     

新一代GPS标准中非理想表面模型的建模方法

本文重点研究在新一代产品几何技术规范标准下如何将非理想表面模型以离散数学的方法表达出来。利用马尔科夫链蒙特卡洛仿真技术(MCMC)和基于主成分分析(PCA)的全局建模法来实现考虑几何约束和公差规范的具有随机误差的非理想表面模型的仿真分析;利用统计形状分析方法(SSA)和基于广义Darboux结构的局部建模法来实现在制造过程中产生的系统误差的非理想表面模型的仿真分析;并引入平均非理想表面模型概念及其统计分析方法对产品变形趋势进行预测。最后以实际工件为对象,通过本文提出的方法得到了其非理想表面模型的仿真结果,并对其仿真效果进行了综合分析,分析结果证明了本文提出方法的正确性和可行性。     

基于离散傅里叶变换的分形粗糙表面轮廓合成与研究

针对使用离散傅里叶变换合成的分形粗糙表面轮廓,分别研究轮廓的分形参数(分形维数D、尺度系数C)与传统表征参数的联系,分形参数对轮廓空域几何形貌的影响以及分形参数对轮廓滤波的影响。结果表明,若假设分形轮廓的功率谱密度函数严格满足幂律关系,则可由Parseval定理获得轮廓分形参数与其方均根偏差Rq的定量关系但此时,轮廓的其余传统表征参数为随机值,且相互之间线性无关;分形维数D影响轮廓高低频成分的能量比随着D的增加,轮廓高频成分的能量增加,轮廓空域几何形貌显得凹凸不平;分形维数D相同时,尺度系数C越大,轮廓的方均根偏差越大;在为获得光滑分形轮廓进行滤波时,分形维数D较小的轮廓,可以保留更多的能量。     

球头铣刀数控加工表面形貌几何仿真的研究

几何仿真是建立铣削力预测模型的基础,而传统的几何仿真只考虑刀具的平动而忽略其转动。本文在同时考虑刀具平动和转动的基础上,利用工件Z-Map表示模型和刀刃离散表示法,提出了一种球头铣刀三轴数控铣削的微观几何仿真算法。该算法鲁棒性好、适用范围广,不仅能高效而准确地仿真铣削表面形貌,而且能准确提供切屑的轮廓,为建立精确的切削力预测模型提供了重要的几何参数。     

表面微观形貌的分形表征及模拟

最后的研究表明，机械加工表面的微观形貌具有自仿射性和多尺度性，因而表面形貌的高度分布方差、斜率和曲率的方差工现进唯一的。基于分形几何理论，用Ｗｅｉｅｒｓｔｒａｓ－Ｍａｎｄｅｌｂｒｏｔ分形函数来表征表面的微观形貌，所得到的参数是不依赖于测量尺度而变的“固有”参数。根据分形几何建立的表面轮廓的数学模型可对表面轮廓进行模拟，为建立三维表面形貌的评定参数提供理论依据。     

小波变换在粗糙表面几何形貌表征中的应用

粗糙表面几何形貌对于表面特性如摩擦、磨损、润滑、腐蚀疲劳等具有重大的影响,表面几何形貌能否及时准确地被表征具有重要的工程意义．简要叙述小波变换的特点,重点介绍目前小波变换在表面粗糙度评定、表面形貌分离与重构以及表面形貌分形维数提取等方面的应用,提出了目前小波变换在表面几何形貌表征中存在的不足,以及今后小波技术在表面形貌中发展的新趋势．     

巴特沃思小波在表面形貌信号分离中的应用

为了快速准确地分析工程表面,提出了一种基于巴特沃思小波的滤波方法。首先,讨论了小波滤波器的低通幅度传输特性,并以此作为选择适合表面形貌分析小波滤波器的依据。然后,介绍了巴特沃思小波滤波器的构造原理,并给出了它的快速实现算法;综合其优良的传输特性和高效的实现算法,以巴特沃思小波作为表面分析的滤波器,对实际表面轮廓进行了多层分解。最后,利用巴特沃思小波建立了表面轮廓评定的基准线,并给出了确定小波分解层数的方法。实验结果表明,巴特沃思小波能够快速准确地实现表面轮廓的多尺度分析,稳定可靠地提取表面中线;在普通计算机上提取11200点数据表面中线仅耗时60ms,利用该中线计算所得R值相对误差仅比利用高斯中线所得R值相对误差大0.12%。     

金刚石车削工件表面轮廓的仿真与分析

对振动情况下加工的工件表面的三维形貌进行了仿真 ,并从理论上对工件表面形貌的径向、周向与刀具螺旋轨迹方向的截面轮廓进行了分析。结果表明 :不同的截面轮廓分别载有不同的表面特征信息 ,利用这些特征有助于对刀具与工件间的相对振动进行辨识。采用有关文献中的试验数据对仿真结果进行了验证     

表面形貌评定方法对比分析

表面形貌特征直接影响了零件的使用功能和技术性能,为了能合理地对表面形貌特征参数进行评估,分析了传统的最小二乘拟合法和经典的高斯滤波法对表面轮廓参数的评估,讨论了最小二乘拟合和高斯滤波法在评估中所存在的不足。根据表面形貌的综合成分,建立表面形貌的数学模型,首次运用B样条小波分析实现了表面形貌数学模型的小波构建。通过小波的分解与重构原理,分离出表面形貌评定基准线。通过工程实例对比分析,验证了B样条小波对表面形貌多尺度分析的合理性,其结果与实际值的误差最小。     

基于HHT的新一代GPS动态测量误差分析和滤波技术研究

针对新一代GPS的轮廓信号和几何误差成分特点,引入一种具有自适应能力的非平稳信号分析新方法——希尔伯特-黄变换(Hilbert-Huang Transform,HHT)用于轮廓滤波和几何误差成分分析。研究了HHT中固有模态函数(Intrinsic Mode Function,IMF)的特点,指出各阶IMF分量按特征时间尺度从小到大的顺序排列,构建了基于经验模态分解(Empirical Mode Decomposition,EMD)的滤波器并将其用于轮廓滤波。分析了EMD分解中剩余项的特点,根据各阶IMF的瞬时频率和幅值函数以及Hilbert-Huang谱,确定了各周期性分量以及非周期性趋势项。几何误差仿真信号分析结果表明,与小波神经网络方法的相比,HHT方法获取的初始阶段信号更好;对实测轮廓曲线,采用HHT和小波变换进行了滤波试验验证,结果表明HHT方法获取的轮廓曲线更平滑。     

机械加工表面轮廓分形维数对数小波谱计算方法

为了提高接触表面的建模精度,利用小波的多尺度分析能力,对表面轮廓进行多尺度小波分解,提出了计算机械加工表面轮廓分形维数的对数小波谱法以及有效分解尺度概念,并认为轮廓只在有效分解尺度上具有分形特征;通过M-B函数模拟生成不同分形维数、不同采样区间的分形轮廓;应用对数小波谱法计算了模拟轮廓的分形维数,进而与功率谱密度法（PSD法）等5种方法的计算结果进行了分析比较,结果表明：对数小波谱法能很好地处理分形的多尺度特征,并且选用sym4小波时计算精度最高,误差在0.15%以内;最后应用对数小波谱法对一实际机械加工表面轮廓分形维数进行了计算,说明了其实用性。     

Realistic simulation of surface defects in five-axis milling using the measured geometry of the tool

Managing macro- and micro-geometry of surfaces during manufacturing processes is a key factor for their following uses. Indeed, micro-geometry and surface topography are directly linked to the performances of functions (contact, friction, lubrication, etc.) by texture parameters to ensure the desired local geometry. Common models for simulation of surface topography are based on ideal geometry of the machining tool and cannot represent surface defects. The actual prediction and simulation of defects are one step forward in a competitive context. In this paper, the realistic model proposed aims to simulate and predict as finely as possible local defects of machined surfaces taking into account the actual edge geometry of the cutting tool. The combined use of the machining kinematics and of the measured geometry of the cutting edges leads to the representation of the geometrical envelope of the surface using a Zbuffer technique. Simulation assessment is carried out by the analysis of 3D surface topography parameters such as surface complexity and relative area and by a comparison of simulation results to an experimental case of study.     

铣削加工表面几何特征的仿真研究

基于坐标矩阵的齐次变换和矢量运算法则,建立了铣削加工过程中刀具的运动轨迹方程,并在工件离散、刀具离散和加工过程离散的基础上,设计了铣削表面形貌仿真算法,并基于MATLAB的GUI功能开发了铣削加工表面形貌仿真系统。验证结果表明,仿真结果与实验结果一致性程度高,可应用于实际铣削加工表面几何形貌的预测和分析之中。     

Deviation modeling of manufactured surfaces from a perspective of manufacturing errors

Assembly analysis, as an important step in the product design stage, provides verifications of product design with specific requirements. The manufactured surfaces that participate in the analysis result from different manufacturing methods and show inconsistency with the designed surfaces due to the effects of numerous manufacturing errors. These deviations have a vital impact on the assembly analysis results and make a big difference on the final product design process. Therefore, consideration of such manufactured surface deviations in assembly analysis is critical in order to achieve an effective product design. In this paper, a general surface deviation modeling and representation approach based on curvilinear coordinate system is proposed. Different curvilinear coordinate systems for various manufacturing methods are defined on nominal product surfaces. By introducing the deviation dimension in the orthogonal direction of the curvilinear coordinates, deviation coordinate systems are formed. The deviation coordinate system could be used to describe deviation surfaces resulting from numerous manufacturing errors with deviation functions. As an example, non-ideal planar surfaces in the face milling process are modelled with the proposed method. With the generated non-ideal planar surfaces, the sealing performance analysis of an assembly is implemented. The validity of the proposed method and its applicability in simulation are verified in the end.     

Geometry simulation and evaluation of the surface topography in five-axis ball-end milling

Limited by the factors such as dynamic vibrations, cutting heat, and the use of coolant, it is difficult to measure or evaluate the surface quality in real time. Geometry simulation of the surface topography became the main method used in engineering to estimate and control the quality of the surface machining. This paper proposed a new method for geometry simulation and evaluation of a milled surface. Allowing for the coherency in geometric variations management process, the proposed method is developed based on the skin model of a workpiece. To make the simulated surface topography more realistic, the effects of locating errors, spindle errors, geometrical errors of the machine tool, and cutting tool deflections are included. And a new method is adopted to evaluate the milled surface, in which the roughness of the surface is characterized by the modal coefficients, instead of the R _a , R _z , and R _q values. At the end of this paper, measurements and cutting tests are carried out to validate the proposed method.     

分形表面特征信息的复合评定方法

提出一种表面特征信息的复合评定方法,识别和分析不同尺度下的表面特征信息分量,理解工程表面宏观功能特性。许多工程表面具有统计自相似和自组织等分形特性,针对这种分形工程表面,提出一种基于小波的表面特征模型。利用小波的变焦特性,观察和分析不同尺度下的工程表面形貌。采用分形维方法,确定特征信息的小波分量尺度,从原始表面形貌中提取粗糙度、形状误差和波纹度等特征信息。     

提高虚拟车削仿真质量的工件建模方法

根据车削加工工件的几何外形和成形特点 ,提出了包含加工误差信息的回转体类工件半剖轮廓多边形建模方法和记录、组织加工误差信息的刀具轨迹法。在虚拟加工中 ,刀具扫描体被简化表示为刀具扫描体轮廓多边形 ,简化了仿真计算。同时还对加工过程仿真和反映加工误差的已加工表面形貌的构建等关键问题进行了研究。该建模方法在VMIS虚拟加工与检测系统中获得了应用     

A novel robust Gaussian filtering method for the characterization of surface generation in ultra-precision machining

A lot of research work has been focused on the study of the surface generation mechanisms in order to predict the surface topography and provide the optimal machined parameters based on the experiential understanding of relationship of machined conditions and surface features. Although the formation of novel geometrical product specification (GPS) and verification framework system promotes the relevant research work to new characterization methods and draft of international standards, relative little research work was conducted on the application of surface characterization techniques to ultra-precision machining which is very important to evaluate the surface quality. In this paper, a novel robust Gaussian filtering method (RGF) is proposed and used to characterize the surface topography of ultra-precision machined surfaces. Cubic B-spline and M-estimation are used to make the method reliable and robust. Based on the property comparisons of classical weighting functions, a novel auto-developed robust weighting function (ADRF) is defined to improve the robustness of RGF. To verify the characterization feasibility of the proposed method, computer simulation is used and then the real ultra-precision machined surfaces are analyzed. The experimental results indicate that the RGF method cannot only separate the surface components effectively on the whole measured area and but also eliminates the influence of freak outliers.     

装配误差传递建模及其精度可靠性评估

研究了刚体零件的装配误差建模以及装配精度可靠性评估方法。将零件误差分成位置误差和方向误差,并采用误差矢量加以描述。综合考虑尺寸误差和形位误差,将装配过程误差分成零件内误差和配合面误差,给出主动配合面和被动配合面的定义。针对典型配合面类型,分析误差组成及其计算方法。采用位姿变换矩阵法建立装配误差模型,分析误差在零件内部以及配合面间的传递过程,计算装配总误差并据此确定装配误差的概率分布。给出装配精度可靠度的定义,通过仿真获得装配精度的可靠度指标。以某测量平台的装配过程为例,完成装配过程误差分析和装配精度可靠度评估,验证模型的有效性。