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Method of fabricating artificial rock specimens based on extrusion free forming(EFF)3D printing
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作者 Xiaomeng Shi Tingbang Deng +2 位作者 Sen Lin Chunjiang Zou Baoguo Liu 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第4期1455-1466,共12页
Three-dimensional(3D)printing technology has been widely used to create artificial rock samples in rock mechanics.While 3D printing can create complex fractures,the material still lacks sufficient similarity to natura... Three-dimensional(3D)printing technology has been widely used to create artificial rock samples in rock mechanics.While 3D printing can create complex fractures,the material still lacks sufficient similarity to natural rock.Extrusion free forming(EFF)is a 3D printing technique that uses clay as the printing material and cures the specimens through high-temperature sintering.In this study,we attempted to use the EFF technology to fabricate artificial rock specimens.The results show the physico-mechanical properties of the specimens are significantly affected by the sintering temperature,while the nozzle diameter and layer thickness also have a certain impact.The specimens are primarily composed of SiO_(2),with mineral compositions similar to that of natural rocks.The density,uniaxial compressive strength(UCS),elastic modulus,and tensile strength of the printed specimens fall in the range of 1.65–2.54 g/cm3,16.46–50.49 MPa,2.17–13.35 GPa,and 0.82–17.18 MPa,respectively.It is capable of simulating different types of rocks,especially mudstone,sandstone,limestone,and gneiss.However,the simulation of hard rocks with UCS exceeding 50 MPa still requires validation. 展开更多
关键词 Artificial rock 3D printing Extrusion free forming(EFF) Similarity analysis Mechanical properties
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Free form deformation and symmetry constraint‐based multimodal brain image registration using generative adversarial nets
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作者 Xingxing Zhu Mingyue Ding Xuming Zhang 《CAAI Transactions on Intelligence Technology》 SCIE EI 2023年第4期1492-1506,共15页
Multi‐modal brain image registration has been widely applied to functional localisation,neurosurgery and computational anatomy.The existing registration methods based on the dense deformation fields involve too many ... Multi‐modal brain image registration has been widely applied to functional localisation,neurosurgery and computational anatomy.The existing registration methods based on the dense deformation fields involve too many parameters,which is not conducive to the exploration of correct spatial correspondence between the float and reference images.Meanwhile,the unidirectional registration may involve the deformation folding,which will result in the change of topology during registration.To address these issues,this work has presented an unsupervised image registration method using the free form deformation(FFD)and the symmetry constraint‐based generative adversarial networks(FSGAN).The FSGAN utilises the principle component analysis network‐based structural representations of the reference and float images as the inputs and uses the generator to learn the FFD model parameters,thereby producing two deformation fields.Meanwhile,the FSGAN uses two discriminators to decide whether the bilateral registration have been realised simultaneously.Besides,the symmetry constraint is utilised to construct the loss function,thereby avoiding the deformation folding.Experiments on BrainWeb,high grade gliomas,IXI and LPBA40 show that compared with state‐of‐the‐art methods,the FSGAN provides superior performance in terms of visual comparisons and such quantitative indexes as dice value,target registration error and computational efficiency. 展开更多
关键词 freeform deformation Generative adversarial nets Multi‐modal brain image registration Structural representation Symmetry constraint
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REVERSE ENGINEERING BASED ON COMPUTER VISION FOR FREE FORM SURFACE 被引量:1
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作者 Lai Xinmin Lin Zhongqin School of Mechanical Engineering, Shanghai Jiaotong University Huang Tian Zhang Dawei Zeng Ziping Tianjin University 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 1999年第4期241-246,共6页
The key issues such as vision sensor, sampling planning are studied for reverse engineering. For the developed sensor, the low sensitivity to the incident angle and the high linearity between the output and the input ... The key issues such as vision sensor, sampling planning are studied for reverse engineering. For the developed sensor, the low sensitivity to the incident angle and the high linearity between the output and the input are carried out. During digitizing, the adaptive sampling planning method based on the curvature of surface and the slope of tangent line of measured point is proposed. After integrating the vision sensor, CNC milling and relevant software, the reverse engineering system based on computer vision is developed. The experiment shows that this system is reliable and efficient. 展开更多
关键词 REVERSE engineering COMPUTER VISION Sampling PLANNING free form surface
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双刀盘铣齿机床与Free-form型机床的加工运动等效转换 被引量:1
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作者 王志永 李文强 张宇 《机械工程学报》 EI CAS CSCD 北大核心 2024年第21期312-319,共8页
为了实现在国产数控螺旋锥齿轮加工机床上采用单刀盘加工直齿锥齿轮,基于空间运动学原理,在保证工件轴线与刀盘轴线相对位置及相对运动关系不变的前提下,将双刀盘铣齿机床中刀盘与工件的相对位置和相对运动关系等效转换至Free-form型机... 为了实现在国产数控螺旋锥齿轮加工机床上采用单刀盘加工直齿锥齿轮,基于空间运动学原理,在保证工件轴线与刀盘轴线相对位置及相对运动关系不变的前提下,将双刀盘铣齿机床中刀盘与工件的相对位置和相对运动关系等效转换至Free-form型机床,得到以时间为自变量的Free-form型机床各数控轴的运动表达式;通过Matlab计算每个加工时刻Free-form型机床运动轴的位置坐标点并编写数控加工程序;基于Vericut仿真软件,建立了Free-form型机床加工环境并对加工过程进行仿真,仿真结果验证了运动转换方法和数控加工程序的正确性;在实际Free-form型机床上进行了铣齿加工实验,利用齿轮测量中心对实验工件的实际齿面相对于理论齿面的齿形误差进行了检测,齿形误差在10.8μm以内;利用滚动检查机对齿轮副的接触区进行检验,实际啮合接触区与TCA结果基本一致。仿真加工和实际切齿加工实验的结果验证了机床加工运动等效转换方法的正确性。 展开更多
关键词 双刀盘铣齿机床 free-form型机床 运动转换 机床调整参数 直齿锥齿轮
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融合卷积CR-FFD与偏置Transformer胶囊网络的单视图三维物体重建
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作者 连远锋 赵泽欣 《计算机辅助设计与图形学学报》 北大核心 2025年第4期623-634,共12页
针对复杂拓扑结构物体单视图三维重建过程中二维图像与三维形状之间难以准确映射的问题,提出一种融合卷积Catmull-Rom样条自由形变(CR-FFD)与偏置Transformer胶囊网络的单视图三维重建方法.首先通过Catmull-Rom样条基函数对点云模型控... 针对复杂拓扑结构物体单视图三维重建过程中二维图像与三维形状之间难以准确映射的问题,提出一种融合卷积Catmull-Rom样条自由形变(CR-FFD)与偏置Transformer胶囊网络的单视图三维重建方法.首先通过Catmull-Rom样条基函数对点云模型控制点进行插值,保持点云模型形变局部拓扑结构的一致性;然后提出卷积神经网络最小二乘求逆解法,通过非线性参数映射加速求解过程;最后设计偏置注意力Transformer胶囊网络增强局部特征表达能力,捕获点云形状的细粒度特征.实验结果表明,在ShapeNet数据集上,所提方法的EMD指标平均值为3.84, CD指标平均值为3.71;在Pix3D数据集上, EMD指标平均值为5.51, CD指标平均值为5.39;与已有的单视图点云三维重建方法相比,该方法有效地提升单视图的三维重建结果,能够从不同角度保持重建的一致性. 展开更多
关键词 CATMULL-ROM样条 自由形变 三维重建 胶囊网络 偏置注意力
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基于空间运动学的传统机床与Free-form型机床运动转换方法的研究 被引量:22
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作者 王小椿 吴联银 +1 位作者 李彬 张艳红 《机械工程学报》 EI CAS CSCD 北大核心 2001年第4期93-98,共6页
从空间运动学的观点来看 ,为保持加工过程中刀具与工件之间的相对位置不变 ,传统机床与Free form型机床的运动转换只需进行 2次矢量旋转即可简单实现。然而现有的CNC系统不可能在加工时对齿面的每一点进行转换 ,因为这满足不了实时性的... 从空间运动学的观点来看 ,为保持加工过程中刀具与工件之间的相对位置不变 ,传统机床与Free form型机床的运动转换只需进行 2次矢量旋转即可简单实现。然而现有的CNC系统不可能在加工时对齿面的每一点进行转换 ,因为这满足不了实时性的要求 ,而且也无必要。因此作者提出了一种简单的方法 ,即只在齿面参考点进行转换 ,通过空间相对运动高阶加速度的分析 ,就可得到Free form机床的所有调整参数 ,文中推导了这种转换方法的精确转化公式。与其他方法相比 ,介绍的方法概念清晰 ,计算量小 ,更加简便而准确。最后给出了计算实例以验证本文方法理论和算法的正确性 ,其TCA分析结果表明 。 展开更多
关键词 free-form型铣齿机 摇台 参数调整 空间运动学 运动转换
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传统机床与Free-Form型机床运动的等效转换 被引量:16
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作者 魏冰阳 任东锋 +1 位作者 方宗德 周彦伟 《机械科学与技术》 CSCD 北大核心 2004年第4期425-428,共4页
给出了基于空间坐标系变换把普通铣齿机调整参数转换成Free form型机床调整参数的原理与方法。在两种机床坐标系下保持刀盘相对工件的运动关系不变 ,通过耦合两种机床下的坐标系使两种机床的运动关系完全等效 ,由此原理推出了普通铣齿机... 给出了基于空间坐标系变换把普通铣齿机调整参数转换成Free form型机床调整参数的原理与方法。在两种机床坐标系下保持刀盘相对工件的运动关系不变 ,通过耦合两种机床下的坐标系使两种机床的运动关系完全等效 ,由此原理推出了普通铣齿机向Free form型机床转换的显式转换公式 ,该公式适用于任意一种传统的加工方法和机床。最后通过实例 ,利用TCA进行了分析验证。本文提出的转换方法概念清晰 ,转换简单 ,不会引起转换误差 ,是一种针对两类机床完全等效的转换方法。 展开更多
关键词 free-form 型铣齿机 调整参数 坐标变换
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刀倾型机床调整参数转化为Free-Form型机床调整参数的原理 被引量:12
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作者 张艳红 吴联银 +1 位作者 魏洪钦 王小椿 《机械科学与技术》 CSCD 北大核心 2000年第5期782-784,共3页
从空间几何角度分析了从刀倾型机床调整参数转化为 Free- Form型机床调整参数的原理 ,提出一种新的仅需要两次矢量旋转的简单的转化方法 ,并推导出了以显式表达的转化公式 ,通过求导 ,可获得 Free- Form型机床各运动轴高次泰勒展开多项... 从空间几何角度分析了从刀倾型机床调整参数转化为 Free- Form型机床调整参数的原理 ,提出一种新的仅需要两次矢量旋转的简单的转化方法 ,并推导出了以显式表达的转化公式 ,通过求导 ,可获得 Free- Form型机床各运动轴高次泰勒展开多项式系数的精确解法。该转化方法原理清晰 ,转换简单 ,其显式表达的转化公式可以满足数控系统实时插补的要求 ,有别于其它的转化方法。 展开更多
关键词 刀倾型机床 调整参数 free-form型铣齿机
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基于FreeForm与3ds Max建模的三维打印 被引量:8
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作者 赵正旭 张廷廷 《计算机应用》 CSCD 北大核心 2016年第A01期180-183,共4页
针对三维打印机对产品设计与制作周期的要求较高,传统的专业建模软件对于普通大众来说可实现性较差,不利于推广三维打印技术的问题,对比了传统建模软件与Free Form触觉建模系统的建模特点,提出了一种将Free Form系统和3ds Max软件相结... 针对三维打印机对产品设计与制作周期的要求较高,传统的专业建模软件对于普通大众来说可实现性较差,不利于推广三维打印技术的问题,对比了传统建模软件与Free Form触觉建模系统的建模特点,提出了一种将Free Form系统和3ds Max软件相结合的建模方式。首先,在Free Form系统中设计具有自由曲面特性的基本黏土模型,并将设计完的模型按比例缩减10%后以STL格式导出;其次,将模型导入到3ds Max软件中,利用复合建模方法继续对模型进行外观设计和尺寸处理;最后,将模型重新加载到Free Form系统中进行模型修复和细节加工,输出经过近似处理的STL格式的三维模型。实验结果表明,该建模方法相对于传统专业建模软件下的建模,提高了建模速度,缩短了产品制作周期,建立的模型经Maker Bot Desktop软件切片处理后,可成功地转化为x3g格式的打印模型,并能在三维打印机上正确打印。 展开更多
关键词 free form 3ds MAX 触觉 建模 三维打印
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摇台磨齿机与Free-form型数控磨齿机加工调整参数转换的运动分析法 被引量:1
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作者 周凯红 唐进元 严宏志 《中国机械工程》 EI CAS CSCD 北大核心 2009年第11期1265-1269,共5页
基于保持加工过程中刀具与工件之间的相对运动和相对位置不变的原则,论述用Free—form型数控磨齿机等效替代刀倾型摇台磨齿机展成螺旋锥齿轮的方法。通过分析加工参考点处刀具与轮坯相对运动的高阶加速度,推导了显式表达的两类机床加工... 基于保持加工过程中刀具与工件之间的相对运动和相对位置不变的原则,论述用Free—form型数控磨齿机等效替代刀倾型摇台磨齿机展成螺旋锥齿轮的方法。通过分析加工参考点处刀具与轮坯相对运动的高阶加速度,推导了显式表达的两类机床加工参数的转换公式。通过对一个实例的计算及两类机床所展成齿面的接触分析结果的比较,证明所提出的计算公式精确高效,能满足数控机床实时控制的要求。 展开更多
关键词 准双曲面齿轮 齿面接触分析 机床调整参数 free-form型磨削机床
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基于优化算法的Free-form型机床各轴运动方程及其对齿面误差的影响 被引量:1
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作者 唐进元 王智泉 李友元 《国防科技大学学报》 EI CAS CSCD 北大核心 2011年第5期64-68,共5页
以No.116铣齿机为例,通过推导传统摇台型机床、Free-form型机床中的坐标变换矩阵,根据运动等效转换的原则,应用最小二乘优化原理,用多项式拟合出Free-form型机床各轴的运动方程。通过算例分析,传统摇台型机床与Free-form型机床中的坐标... 以No.116铣齿机为例,通过推导传统摇台型机床、Free-form型机床中的坐标变换矩阵,根据运动等效转换的原则,应用最小二乘优化原理,用多项式拟合出Free-form型机床各轴的运动方程。通过算例分析,传统摇台型机床与Free-form型机床中的坐标变换矩阵高度吻合,用各轴运动方程在CATIA软件中虚拟加工出的螺旋锥齿轮齿面与理论齿面上的点的距离在0.009mm以内,且该值可控制在0.00001mm以内,验证了该转换方法的正确性。在此基础上,分析了Free-form型机床各轴运动误差对齿面误差的影响,发现B轴为对齿面影响最大的轴,为提高Free-form型机床的制造精度提供了部分理论依据。 展开更多
关键词 螺旋锥齿轮 优化算法 传统摇台型机床 free-form型机床 各轴运动方程 齿面误差
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摇台磨齿机与Free-form型数控磨齿机加工调整参数的转换方法 被引量:1
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作者 周凯红 唐进元 曾韬 《制造技术与机床》 CSCD 北大核心 2008年第9期100-103,共4页
现有的Free-form型螺旋锥齿轮磨齿机的CNC系统不可能在加工齿面每一点时完全转换传统摇台螺旋锥齿轮磨齿机的展成运动,因为这满足不了实时性的要求,而且也无必要。因此作者提出了一种只在齿面参考点进行两次矢量旋转的简单的转化方法,... 现有的Free-form型螺旋锥齿轮磨齿机的CNC系统不可能在加工齿面每一点时完全转换传统摇台螺旋锥齿轮磨齿机的展成运动,因为这满足不了实时性的要求,而且也无必要。因此作者提出了一种只在齿面参考点进行两次矢量旋转的简单的转化方法,并推导出了以显式表达Free-form型机床加工调整参数的精确计算公式。与其他方法相比,介绍的方法概念清晰,计算量小,更加简便而准确并可以满足数控系统实时插补的要求。 展开更多
关键词 free-form型磨齿机 刀倾型机床 调整参数
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STUDY OF NON-CONTACT MEASUREMENT OF FREE-FORM SURFACES
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作者 徐玉春 张国雄 +2 位作者 解则晓 冯国馨 王春海 《Transactions of Tianjin University》 EI CAS 2001年第4期226-228,共3页
A non contact three dimensional measurement method is presented in this paper.This system consists of a laser triangulation probe,a probe head and a coordinate measuring machine (CMM).The measurement principle of th... A non contact three dimensional measurement method is presented in this paper.This system consists of a laser triangulation probe,a probe head and a coordinate measuring machine (CMM).The measurement principle of the system is discussed,and a system calibration method employing a reference ball is proposed.The geometric model involving four frames is established to calculate the data points based on the reading of the laser probe and position information from the CMM.A measuring experiment for gesso free form surface using this system is carried out. 展开更多
关键词 free form surface coordinate measuring machine PH10 probe head laser triangulation probe CALIBRATION
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Free-form型机床的切齿优化(一)——优化模型的建立
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作者 张艳红 郭九生 王小椿 《机械传动》 CSCD 2002年第1期28-30,共3页
分析了Free -from型机床的参数形式 ,并建立了优化的数学模型。该模型在原来二阶预控 ,三阶优化的基础上又进一步对 4阶参数进行优化 ,啮合性能进一步提高。利用参数线投影法 。
关键词 free-form型机床 切齿优化 优化模型 参数线投影法 齿轮加工
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Free-form型机床切齿优化(二)——混合进化遗传算法
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作者 张艳红 郭九生 王小椿 《机械传动》 CSCD 2002年第2期26-28,共3页
针对Free -form型机床优化目标函数多维及非线性的特性 ,提出了一种混合进化遗传算法。该方法把遗传算法的全局搜索能力与参数线投影法的局部搜索能力结合起来。并在十进制为基因串的编码基础上 ,对遗传算子做了改进 ,使计算量减少 ,目... 针对Free -form型机床优化目标函数多维及非线性的特性 ,提出了一种混合进化遗传算法。该方法把遗传算法的全局搜索能力与参数线投影法的局部搜索能力结合起来。并在十进制为基因串的编码基础上 ,对遗传算子做了改进 ,使计算量减少 ,目标直观 ,优化性能显著提高。最后的例子也鲜明地表示出该优化方法的先进性。 展开更多
关键词 free-form型机床 混合进化遗传算法 优化 切齿
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基于Free-form型锥齿轮机床的齿面制造技术
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作者 吴训成 《机床与液压》 北大核心 2006年第2期32-34,共3页
介绍了一种基于Free-form型机床切齿加工理论的点啮合齿面制造技术。提供了Free-form型机床3轴联动切齿加工基本方程及详细的计算公式。直接以工件齿轮的转角为运动参数,将机床其它各轴的运动表达为工件齿轮转角的函数。阐明了机床运动... 介绍了一种基于Free-form型机床切齿加工理论的点啮合齿面制造技术。提供了Free-form型机床3轴联动切齿加工基本方程及详细的计算公式。直接以工件齿轮的转角为运动参数,将机床其它各轴的运动表达为工件齿轮转角的函数。阐明了机床运动函数及其它切齿参数的确定方法。 展开更多
关键词 锥齿轮 齿面 制造技术 freeform型锥齿轮机床
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An investigation on adaptively machining the leading and tailing edges of an SPF/DB titanium hollow blade using free-form deformation 被引量:11
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作者 Zhengcai ZHAO Jiuhua XU +1 位作者 Yucan FU Zhiqiang LI 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2018年第1期178-186,共9页
Titanium hollow blades are characterized with lightweight and high structural strength, which are widely used in advanced aircraft engines nowadays. Superplastic forming/diffusion bonding (SPF/DB) combined with nume... Titanium hollow blades are characterized with lightweight and high structural strength, which are widely used in advanced aircraft engines nowadays. Superplastic forming/diffusion bonding (SPF/DB) combined with numerical control (NC) milling is a major solution for manufacturing titanium hollow blades. Due to the shape deviation caused by multiple heat and pressure cycles in the SPF/DB process, it is hard to manufacture the leading and tailing edges by the milling process. This paper presents a new adaptive machining approach using free-form deformation to solve this problem. The actual SPF/DB shape of a hollow blade was firstly inspected by an on-machine measurement method. The measured point data were matched to the nominal SPF/DB shape with an improved ICP algorithm afterwards, by which the point-pairs between the measurement points and their corresponding points on the nominal SPF/DB shape were established, and the maximum modification amount of the final nominal shape was constrained. Based on the displacements between the point-pairs, an accurate FFD volume was iteratively calculated. By embedding the final nominal shape in the deformation space, a new final shape of the hollow blade was built. Finally, a series of measurement and machining tests was performed, the results of which validated the feasibility of the proposed adaptive machining approach. 展开更多
关键词 Adaptive machining Blade geometry free-form deformation Reconstruction TITANIUM
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Accurate Evaluation of Free-form Surface Profile Error Based on Quasi Particle Swarm Optimization Algorithm and Surface Subdivision 被引量:13
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作者 WEN Xiulan ZHAO Yibing +2 位作者 WANG Dongxia ZHU Xiaochun XUE Xiaoqiang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2013年第2期406-413,共8页
Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for ... Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface. 展开更多
关键词 profile error evaluation free-form surface quasi particle swarm optimization surface subdivision
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Study of the Contact Force in Free-form Surfaces Compliant EDM Polishing by Robot 被引量:2
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作者 ZHAN Jian-ming 1, ZHAO Ji 2, XU Shu-xin 1, ZHU Pei-xi ng 1 (1. College of Mechanical Science and Engineering, Jilin University, Changchun 130022, China 2. Office of Education Administration, Jilin University, Changchun 130012, Chin a) 《厦门大学学报(自然科学版)》 CAS CSCD 北大核心 2002年第S1期69-,共1页
With an elastic negative pole being driven by ultra so nic vibration and being moved along the surface of work-piece compliantly by ro bot, a new kind of effective EDM, the compliant EDM, cuts the electrically condu c... With an elastic negative pole being driven by ultra so nic vibration and being moved along the surface of work-piece compliantly by ro bot, a new kind of effective EDM, the compliant EDM, cuts the electrically condu ctive materials away and polishes work-piece of free-form surface. The study o f the contact force between the end of polishing tool and the surface of work-p iece is the key for the compliant EDM to study its cutting mechanism and to make better use of it. This paper makes a model for the contact force and verifies i t by experiments and simulation based on the theory of elastic body kinetics and dynamic stress concentration. The research work shows that this contact force i s caused by both the electrical impulsion of EDM and the mechanical force of ult rasonic vibration, the discharge frequency of compliant EDM has a much more clos er connection with the vibration frequency of polishing tool rather than the fre quency of ultrasonic vibration. 展开更多
关键词 ROBOT compliant EDM polishing free-form surfac es contract force
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Closed form solutions for free vibrations of rectangular Mindlin plates 被引量:7
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作者 Yufeng Xing Bo Liu The Solid Mechanics Research Center, Beihang University,100191 Beijing, China 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第5期689-698,共10页
A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three c... A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate. 展开更多
关键词 Mindlin plate free vibration Closed form solution Separation of variable
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