混联结构并联机床的研究
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摘要
并联机床(Parallel Machine Tool)又称为虚拟轴机床(Virtual Axis Machine Tool)，是90年代中期问世的数控机床新结构，是机构学理论、机器人技术与数控技术结合的产物，其原型是并联机器人操作机。并联机床与传统五坐标数控机床相比有如下优点：①刚度重量比大②响应速度快③加工精度高④环境适应能力强⑤技术的附加值高。并联机床具有“硬件简单、软件复杂”的特点，是一种技术附加值很高的机电一体化产品，具有广阔的应用前景。本文以四种混联型并联机床为主要研究对象，对混联型并联机床的机型结构设计、位置分析、奇异位形、工作空间、运动学模型、动力学模型、精度分析、刚度分析、灵巧性分析、插补算法、虚拟样机及加工仿真等问题进行了较全面而深入的研究。
针对传统数控机床和现有并联机床不足之处，借鉴了传统数控机床和现有并联机床的优点，将串联结构与并联结构有机融合，通过机型综合，提出了三种混联结构并联机床的新机型，并申请了发明专利。这三种混联结构并联机床具有结构简单、加工灵活、加工精度高、加工速度快、加工工艺性好、位置与姿态解耦和数控编程方便等优点，可以满足大型具有复杂曲面类零件的多轴联动数控加工的要求。
采用动平台四个铰心的绝对坐标作为输出变量，用结式消元法对2RPS+2TPS型并联机床进行了位置正解分析，得到了其7次的一元输入输出方程，由此得到了全部位置正解。消元过程中引入了数字-符号方法，将结构参数处理为数值量，将关节变量处理为符号量，将数字、符号推导过程转化为了矩阵运算过程，由于结构参数以数值量的形式出现在方程推导中，降低了符号推导的难度，符号推导不需要复杂的符号处理软件的支持。所得位置正解均满足原始方程且无增根。基于结式消元法分别对1PS+3TPS型、1PT+2TPS型和1PPS+4TPS型并联机床进行了位置正解分析，获得了封闭形式的解析解。论文中给出了混联结构并联机床位置反解的方法。对于以上混联结构并联机床机型，文中均给出了位置分析的数值实例。
提出了一种求解6-SPS型并联机床主进给机构工作空间的解析方法，该方法以曲面分析为基础，通过分析得到了6-SPS型并联机床主进给机构工作空间
四川大学博士学位论文
的拓扑逻辑结构图，结合主进给机构的运动特性，得到了主进给机构工作空间
边界曲面的曲面方程。在此基础上，描绘出了6－SPS型并联机床工作空问边界
曲面的投影视图及截面曲线图。分析计算结果表明6SPS型并联机床的理论工
作空间是山3O张曲面片包围而成的闭包。建立了二重八面体变几何析架并联机
床位置分析的输入输出方程，推导出了其奇异位形判别解析表达式，并用同伦
连续法对所建立的奇异位形判别方程组进行了求解，得到了奇异位形的全部解。
由曲面分析方法得到了其工作空间边界曲面的曲面方程，描绘出了二重八面体
变几何析架并联机床工作空间边界曲面的投影视图及截面曲线图。分析结果表
明二重八面体变几何析架并联机床的理论工作空间是由6张曲面片包围而成的
闭包。分别推导出了Znys＋ZTPS型、IPS＋3TPS型和 IPT＋ZTPS型并联机床奇
异仓形判别的解析表达式，得到了奇异曲面方程，并由边界曲面分析方法得到
了 lPS＋3TPS型和 IPT＋ZTPS型并联机床的工作空间，文中给出了以上混联结
构并联机床奇异位形与工作空间分析的数值实例。
针对叩旬TPS型并联机床的实际加工要求，提出了灵活度指针。该灵活
度指针选取为刀尖参考点服务区的面积与服务半球面积的比值。提出了基于曲
面分析的灵活度计算方法，并分析了结构参数、运动学参数对机床主进给机构
灵活度的影响。分析计算结果表明：IPS旬TPS型型并联机床的主进给机构灵
巧性好，可以实现大倾角加工。以r＋3TPS型并联机床为对象，提出了一种
精度建模方法，该方法将精度建模的问题转化对应的“虚拟机构”的运动分析
问题。建立了 IPS＋3TPS型并联机床主进给机构的驱动误差、结构误差及球铰
间隙误差与刀尖参考点位姿误差之间的关系式。利用空间向量链模型推出了并
联机床系统位姿误差与主进给机构安装误差立柱尺寸误差及工作台运动误差间
关系的综合表达式，得到了＊＋3TPS型并联机床的误差模型，为该型并联机
床的精度补偿提供了理论基础。文中给出了误差分析的数值实例。建立了
IPS＋3TPS型并联机床刚度分析和弹性动力学分析的有限元模型，研究了参数
变化对主进给机构刚度和固有频率的影响。计算结果表明：IPS伺TPS型型并
联机床与6－SPS型井联机床相比，Z方向刚度与之相当而X、Y方向的刚度优
于后者；加大中间腿的截面积可以大大提高并联机床的刚度。以上研究结果为－
优化并联机床的结构参数，提高其结构抗震性和切削稳定性奠定了基础。
推导出了ZRPS＋ZTPS型及m＋3TPS型并联机床运动学分析的一阶和二阶
影响系数矩阵，得到了其运动学模型。基于数值－符号运算，采用凯恩动力学方
程，建立了moTPS型并联机床解析的动力学模型，得到了动力学模型矩阵
一 四I；！大学博士学位论文
Parallel machine tools(PMTs), Which came forth in the middle of l990s, are
also called virtual axis machine tools(VAMTs). PMT is an aPPlication of spatial
multi-loop parallel machanism in the field of NC machine tool, is an combination
Otheome of mechanism theory robotic technology and numerical control technology,
the PrototyPe of PMTs is parallel robotic manipulators. PMTs enjoy following
advdsges over tr8ditional five-coordinates NC machine tools: high stiffness weight
ratio, high feed speed, high machining precision, high additional technology value et
ai. PMT has the characteristic of hardWare simple and software complex, is an
electromechanic product with high additional technology value, has very vast
aPPlication vistas in industry.
Aiming at the deficiency of traditional NC machine tool and parallel machine
tool, the advantages of traditiona NC machine tool and parallel machine tool are
used fOr reference, three hybrid type PMT, which combine serial structure with
parallel structUre, are proposed in this dissertation tbIough type synthesis, Invention
Patents have been aPplied for them. This three hybrid type PMTs possess such
advantages as: simple structUre, good dexterity high machining precision, high
machinillg speed, position decouPling wth orientation, easy NC programming et al,
can meet the need of numerical colltrol machining fOr large pwts with complex
Wes. Prototype synthsis, displacement analysis, singularity configuration,
worksPace, kinematic model, dynamic model, dexterity analysis, accuracy analysis,
stifness analysis, interpolation algorithm, machining simulation are studied deeply
and systematically for hybrid tyPe PMTs in this dissertation.
Absolute coordinates of spherical joints on movable platfOrm are chosen as
unknwn, a direct displacemeat analysis which is based on resultan eliminatiom
methOd for 2nyS+2TPS tyPe PMTs is presented, the 7th degree inPut-outPul closed
form equation with one wtwn is obtained, and all of the roots fOr all unknowns
are gained. Numeric-symbolic technique is introduced in the procedure of resultant
elimination, procedure of number-spobol manipulation is transformed into that of
matrix manipulation. Because joini variables are treated as symbols and all structure
paramCters are treated as real nuxnbers, the comPlexity of derivation for input-outPut
eqUaion is reduced. The soluton is verified with a numerical example, its rsults
withoot extraneous roots agree with the original eqUaions. Forward displacement
analysis for lPS+3TPS,lPT+2TPS, lPPS+4TPS type PMTs are performed based on
result elimation method. Closed form solutions for forward displacement of these
hybrid type PMTs are derived, numerical examples are given for illustration.
Method of inverse displacement analysis for hybrid twe PMTS is a1so given.
An analytical method, which is based on surface analysis, for workspace -
analysis of 6-SPS type PMTs is proposed in this dissertation. Topological diagram
of workspace for 6-SPS type PMTs is derived, the equations of workspace
boundny surfaces for 6-SPS type PMTs are also derived based on the kinematic
characteristic of the PMTs. The projection and section curve graPhs of workspace
boundary surfaces for 6-SPS tyPe PMTs are drawn. Results of analysis show that the
theoretic workspace of 6-SPS trpe PMTs is enveloped by 30 surface patchs. InPut
and outPut ewtons of disPlacement analysis for double-octahedron variable
geometry miss PMTs are established, analytical expressions for determining
singuledty configuration are derived. These analy'tical expressions are solved using
homotOpy cofitinuation algorithJns, all solotions of singularity configuration are
obtained. A numerical exarnple of singularity configuration analysis for
double-octahedron variable geometry trUss PMTs is given., the equations of
worksPace boundary surfaces for double-octahedron variable geometry truss PMTs
are derived based on surface analysis method. The projection and section curve
g
针对传统数控机床和现有并联机床不足之处，借鉴了传统数控机床和现有并联机床的优点，将串联结构与并联结构有机融合，通过机型综合，提出了三种混联结构并联机床的新机型，并申请了发明专利。这三种混联结构并联机床具有结构简单、加工灵活、加工精度高、加工速度快、加工工艺性好、位置与姿态解耦和数控编程方便等优点，可以满足大型具有复杂曲面类零件的多轴联动数控加工的要求。
采用动平台四个铰心的绝对坐标作为输出变量，用结式消元法对2RPS+2TPS型并联机床进行了位置正解分析，得到了其7次的一元输入输出方程，由此得到了全部位置正解。消元过程中引入了数字-符号方法，将结构参数处理为数值量，将关节变量处理为符号量，将数字、符号推导过程转化为了矩阵运算过程，由于结构参数以数值量的形式出现在方程推导中，降低了符号推导的难度，符号推导不需要复杂的符号处理软件的支持。所得位置正解均满足原始方程且无增根。基于结式消元法分别对1PS+3TPS型、1PT+2TPS型和1PPS+4TPS型并联机床进行了位置正解分析，获得了封闭形式的解析解。论文中给出了混联结构并联机床位置反解的方法。对于以上混联结构并联机床机型，文中均给出了位置分析的数值实例。
提出了一种求解6-SPS型并联机床主进给机构工作空间的解析方法，该方法以曲面分析为基础，通过分析得到了6-SPS型并联机床主进给机构工作空间
四川大学博士学位论文
的拓扑逻辑结构图，结合主进给机构的运动特性，得到了主进给机构工作空间
边界曲面的曲面方程。在此基础上，描绘出了6－SPS型并联机床工作空问边界
曲面的投影视图及截面曲线图。分析计算结果表明6SPS型并联机床的理论工
作空间是山3O张曲面片包围而成的闭包。建立了二重八面体变几何析架并联机
床位置分析的输入输出方程，推导出了其奇异位形判别解析表达式，并用同伦
连续法对所建立的奇异位形判别方程组进行了求解，得到了奇异位形的全部解。
由曲面分析方法得到了其工作空间边界曲面的曲面方程，描绘出了二重八面体
变几何析架并联机床工作空间边界曲面的投影视图及截面曲线图。分析结果表
明二重八面体变几何析架并联机床的理论工作空间是由6张曲面片包围而成的
闭包。分别推导出了Znys＋ZTPS型、IPS＋3TPS型和 IPT＋ZTPS型并联机床奇
异仓形判别的解析表达式，得到了奇异曲面方程，并由边界曲面分析方法得到
了 lPS＋3TPS型和 IPT＋ZTPS型并联机床的工作空间，文中给出了以上混联结
构并联机床奇异位形与工作空间分析的数值实例。
针对叩旬TPS型并联机床的实际加工要求，提出了灵活度指针。该灵活
度指针选取为刀尖参考点服务区的面积与服务半球面积的比值。提出了基于曲
面分析的灵活度计算方法，并分析了结构参数、运动学参数对机床主进给机构
灵活度的影响。分析计算结果表明：IPS旬TPS型型并联机床的主进给机构灵
巧性好，可以实现大倾角加工。以r＋3TPS型并联机床为对象，提出了一种
精度建模方法，该方法将精度建模的问题转化对应的“虚拟机构”的运动分析
问题。建立了 IPS＋3TPS型并联机床主进给机构的驱动误差、结构误差及球铰
间隙误差与刀尖参考点位姿误差之间的关系式。利用空间向量链模型推出了并
联机床系统位姿误差与主进给机构安装误差立柱尺寸误差及工作台运动误差间
关系的综合表达式，得到了＊＋3TPS型并联机床的误差模型，为该型并联机
床的精度补偿提供了理论基础。文中给出了误差分析的数值实例。建立了
IPS＋3TPS型并联机床刚度分析和弹性动力学分析的有限元模型，研究了参数
变化对主进给机构刚度和固有频率的影响。计算结果表明：IPS伺TPS型型并
联机床与6－SPS型井联机床相比，Z方向刚度与之相当而X、Y方向的刚度优
于后者；加大中间腿的截面积可以大大提高并联机床的刚度。以上研究结果为－
优化并联机床的结构参数，提高其结构抗震性和切削稳定性奠定了基础。
推导出了ZRPS＋ZTPS型及m＋3TPS型并联机床运动学分析的一阶和二阶
影响系数矩阵，得到了其运动学模型。基于数值－符号运算，采用凯恩动力学方
程，建立了moTPS型并联机床解析的动力学模型，得到了动力学模型矩阵
一 四I；！大学博士学位论文
Parallel machine tools(PMTs), Which came forth in the middle of l990s, are
also called virtual axis machine tools(VAMTs). PMT is an aPPlication of spatial
multi-loop parallel machanism in the field of NC machine tool, is an combination
Otheome of mechanism theory robotic technology and numerical control technology,
the PrototyPe of PMTs is parallel robotic manipulators. PMTs enjoy following
advdsges over tr8ditional five-coordinates NC machine tools: high stiffness weight
ratio, high feed speed, high machining precision, high additional technology value et
ai. PMT has the characteristic of hardWare simple and software complex, is an
electromechanic product with high additional technology value, has very vast
aPPlication vistas in industry.
Aiming at the deficiency of traditional NC machine tool and parallel machine
tool, the advantages of traditiona NC machine tool and parallel machine tool are
used fOr reference, three hybrid type PMT, which combine serial structure with
parallel structUre, are proposed in this dissertation tbIough type synthesis, Invention
Patents have been aPplied for them. This three hybrid type PMTs possess such
advantages as: simple structUre, good dexterity high machining precision, high
machinillg speed, position decouPling wth orientation, easy NC programming et al,
can meet the need of numerical colltrol machining fOr large pwts with complex
Wes. Prototype synthsis, displacement analysis, singularity configuration,
worksPace, kinematic model, dynamic model, dexterity analysis, accuracy analysis,
stifness analysis, interpolation algorithm, machining simulation are studied deeply
and systematically for hybrid tyPe PMTs in this dissertation.
Absolute coordinates of spherical joints on movable platfOrm are chosen as
unknwn, a direct displacemeat analysis which is based on resultan eliminatiom
methOd for 2nyS+2TPS tyPe PMTs is presented, the 7th degree inPut-outPul closed
form equation with one wtwn is obtained, and all of the roots fOr all unknowns
are gained. Numeric-symbolic technique is introduced in the procedure of resultant
elimination, procedure of number-spobol manipulation is transformed into that of
matrix manipulation. Because joini variables are treated as symbols and all structure
paramCters are treated as real nuxnbers, the comPlexity of derivation for input-outPut
eqUaion is reduced. The soluton is verified with a numerical example, its rsults
withoot extraneous roots agree with the original eqUaions. Forward displacement
analysis for lPS+3TPS,lPT+2TPS, lPPS+4TPS type PMTs are performed based on
result elimation method. Closed form solutions for forward displacement of these
hybrid type PMTs are derived, numerical examples are given for illustration.
Method of inverse displacement analysis for hybrid twe PMTS is a1so given.
An analytical method, which is based on surface analysis, for workspace -
analysis of 6-SPS type PMTs is proposed in this dissertation. Topological diagram
of workspace for 6-SPS type PMTs is derived, the equations of workspace
boundny surfaces for 6-SPS type PMTs are also derived based on the kinematic
characteristic of the PMTs. The projection and section curve graPhs of workspace
boundary surfaces for 6-SPS tyPe PMTs are drawn. Results of analysis show that the
theoretic workspace of 6-SPS trpe PMTs is enveloped by 30 surface patchs. InPut
and outPut ewtons of disPlacement analysis for double-octahedron variable
geometry miss PMTs are established, analytical expressions for determining
singuledty configuration are derived. These analy'tical expressions are solved using
homotOpy cofitinuation algorithJns, all solotions of singularity configuration are
obtained. A numerical exarnple of singularity configuration analysis for
double-octahedron variable geometry trUss PMTs is given., the equations of
worksPace boundary surfaces for double-octahedron variable geometry truss PMTs
are derived based on surface analysis method. The projection and section curve
g
引文
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