交叉杆型并联机床运动学.doc
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交叉杆型并联机床运动学,摘要目前，叶片、叶轮等复杂不规则曲面零件有不少已采用本身具有多轴联动的特征的并联机床来加工。2009年瑞典艾克斯康公司研制并投入实际生产的新一代并联机床exchon 700已经表明并联机床可以部分代替传统的五轴联动加工中心来加工复杂不规则曲面零件，而且效率和精度相比都有很大优势。由于并联机床本身结构的简单性，其价格比五...
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摘 要
目前，叶片、叶轮等复杂不规则曲面零件有不少已采用本身具有多轴联动的特征的并联机床来加工。2009年瑞典艾克斯康公司研制并投入实际生产的新一代并联机床EXCHON 700已经表明并联机床可以部分代替传统的五轴联动加工中心来加工复杂不规则曲面零件，而且效率和精度相比都有很大优势。由于并联机床本身结构的简单性，其价格比五轴联动加工中心要便宜很多，但是由于技术上的垄断，其实际价格与五轴联动加工中心相比还要昂贵。所以消化和应用并联机床的技术，研究并联机床的有关问题很有意义。
本文的主要研究内容如下：
哈尔滨量具刃具集团生产的6-SPS型七轴六联动交叉杆型并联机床为对象，分析了交叉杆型并联机床的运动学问题和动力学问题，并重点研究了运动学正解的难题和动力学问题。在运动学研究的基础上，探索了并联机床加工复杂曲面、曲线的插补问题和进给伺服控制问题，提出了并联机床数控系统的设计方案。
在运动学研究中，采用李群李代数作为数学工具，提出了并联机床运动学反解的快速而直观的几何算法，为加工复杂曲面问题提供了基本工具。由于李群李代数的引入，并联机床运动学正解可以转化为运动学的反解问题，基本解决了并联机床运动学正解的难题。
在运动学分析的基础上，研究了并联机床插补螺旋线的问题。提出了采用泰勒级数和扩展数字积分法来插补螺旋线的方法，给出了加工精度对于进给速度的限制，并分析了插补算法的流程。在插补算法的基础上，研究了并联机床进给伺服系统的实现问题，拟采用FANUC公司开发的数控位置伺服控制卡来控制并联机床的伺服电机。
并联机床动力学采用李代数和Kane方程来研究，引入了偏速度旋量，建立了旋量形式Kane动力学方程，并探讨了该方程的求解问题。
最后建立虚拟样机，用商业动力学仿真软件Adams进行仿真，将仿真结果与本文采用的运动学正逆解法和动力学问题解法的分析结果进行了对比。
关键词 李群李代数；并联机床；运动学正解；嵌入式数控系统；旋量形式；Kane动力学方程
Abstract
Currently, the parts such as the blade or the impeller with complicated and unformulated curve and surface have already been being manufactured by parallel machine tools which is characteristic of multi-axis linkage for itself. In 2009, EXECHON 700 developed by EXECHON Company in Sweden and applied to the actual production, the new generation of parallel machine tool indicated that parallel machine tools can partly replace the traditional 5-axis linkage machining center in processing of those parts with complicated and unformulated curve and surface，and that it has superiority in efficiency and precision. By virtual of simple structure, the price of the parallel machine tools should be much cheaper than the 5-axis linkage machining center,however,the actual price is more expensive than the 5-axis linkage machining center by view of the technical monopoly. Therefore, the mastering and application of technology on parallel machine tools and research into problems relevant to parallel machine are much significant.
In this thesis, the main research contents as follows:
The cross-pole parallel machine tools of 6－SPS with 7 axes and 6-axis linkage
by the Harbin Measuring & Cutting Tool Group Co., Ltd as subject, the kinematics
and dynamics problems of cross-pole parallel machine tools were studied and analy-
zed, and the forward solution of the kinematics problems and dynamics problems
were studied emphatically. In the basis of solving of kinematics problems, the interp-
olation problem and servo control problem of manufacturing complex curve and sur-
face with parallel machine is explored, then the design scheme of CNC system of the parallel machine tools is provided.
In the research of kinematics problems，with Lie Groups and Lie Algebras, the quick and concrete geometry algorithm in reversed solution of kinematics problems in parallel machine tools was created, providing the basic facility of manufacturing complex curve and surface. As the introduction of Lie Groups and Lie Algebras, the forward solution of the kinematics problems transformed into reverse solution, the i-
ntricate forward solution in parallel machine tool is radically solved.
In the basis of analysis of kinematics problems, the interpolation of helical cur-
ve in parallel machine tools is studied. The study created the method to interpolate the helical curve using Taylor Series and Expand Digital Integral, gave manufacturi-
ng accuracy constraints on the feeding speed, still analyzed the procedures of the int-
erpolation algorithm. In the basis of the solving of interpolation algorithm, the realiz-
ation of servo system of parallel machine tools was studied, in conclusion, to control the servo electric engine with CNC position servo control card made by FANUC.
The dynamics problems of parallel machine were studied by Lie Algebras and Kane equation，the screw form’s Kane dynamics equations were established intr-
oduction of the partial velocity screw, and the solution was also explored.
Finally, the virtual prototype model was designed and simulated in the commer-
cial dynamics simulation software Adams. The simulating results were compared wi-
th the results that came from the solution of kinematics problems and dynamics pro-
blems in this thesis.
Ke..
目前，叶片、叶轮等复杂不规则曲面零件有不少已采用本身具有多轴联动的特征的并联机床来加工。2009年瑞典艾克斯康公司研制并投入实际生产的新一代并联机床EXCHON 700已经表明并联机床可以部分代替传统的五轴联动加工中心来加工复杂不规则曲面零件，而且效率和精度相比都有很大优势。由于并联机床本身结构的简单性，其价格比五轴联动加工中心要便宜很多，但是由于技术上的垄断，其实际价格与五轴联动加工中心相比还要昂贵。所以消化和应用并联机床的技术，研究并联机床的有关问题很有意义。
本文的主要研究内容如下：
哈尔滨量具刃具集团生产的6-SPS型七轴六联动交叉杆型并联机床为对象，分析了交叉杆型并联机床的运动学问题和动力学问题，并重点研究了运动学正解的难题和动力学问题。在运动学研究的基础上，探索了并联机床加工复杂曲面、曲线的插补问题和进给伺服控制问题，提出了并联机床数控系统的设计方案。
在运动学研究中，采用李群李代数作为数学工具，提出了并联机床运动学反解的快速而直观的几何算法，为加工复杂曲面问题提供了基本工具。由于李群李代数的引入，并联机床运动学正解可以转化为运动学的反解问题，基本解决了并联机床运动学正解的难题。
在运动学分析的基础上，研究了并联机床插补螺旋线的问题。提出了采用泰勒级数和扩展数字积分法来插补螺旋线的方法，给出了加工精度对于进给速度的限制，并分析了插补算法的流程。在插补算法的基础上，研究了并联机床进给伺服系统的实现问题，拟采用FANUC公司开发的数控位置伺服控制卡来控制并联机床的伺服电机。
并联机床动力学采用李代数和Kane方程来研究，引入了偏速度旋量，建立了旋量形式Kane动力学方程，并探讨了该方程的求解问题。
最后建立虚拟样机，用商业动力学仿真软件Adams进行仿真，将仿真结果与本文采用的运动学正逆解法和动力学问题解法的分析结果进行了对比。
关键词 李群李代数；并联机床；运动学正解；嵌入式数控系统；旋量形式；Kane动力学方程
Abstract
Currently, the parts such as the blade or the impeller with complicated and unformulated curve and surface have already been being manufactured by parallel machine tools which is characteristic of multi-axis linkage for itself. In 2009, EXECHON 700 developed by EXECHON Company in Sweden and applied to the actual production, the new generation of parallel machine tool indicated that parallel machine tools can partly replace the traditional 5-axis linkage machining center in processing of those parts with complicated and unformulated curve and surface，and that it has superiority in efficiency and precision. By virtual of simple structure, the price of the parallel machine tools should be much cheaper than the 5-axis linkage machining center,however,the actual price is more expensive than the 5-axis linkage machining center by view of the technical monopoly. Therefore, the mastering and application of technology on parallel machine tools and research into problems relevant to parallel machine are much significant.
In this thesis, the main research contents as follows:
The cross-pole parallel machine tools of 6－SPS with 7 axes and 6-axis linkage
by the Harbin Measuring & Cutting Tool Group Co., Ltd as subject, the kinematics
and dynamics problems of cross-pole parallel machine tools were studied and analy-
zed, and the forward solution of the kinematics problems and dynamics problems
were studied emphatically. In the basis of solving of kinematics problems, the interp-
olation problem and servo control problem of manufacturing complex curve and sur-
face with parallel machine is explored, then the design scheme of CNC system of the parallel machine tools is provided.
In the research of kinematics problems，with Lie Groups and Lie Algebras, the quick and concrete geometry algorithm in reversed solution of kinematics problems in parallel machine tools was created, providing the basic facility of manufacturing complex curve and surface. As the introduction of Lie Groups and Lie Algebras, the forward solution of the kinematics problems transformed into reverse solution, the i-
ntricate forward solution in parallel machine tool is radically solved.
In the basis of analysis of kinematics problems, the interpolation of helical cur-
ve in parallel machine tools is studied. The study created the method to interpolate the helical curve using Taylor Series and Expand Digital Integral, gave manufacturi-
ng accuracy constraints on the feeding speed, still analyzed the procedures of the int-
erpolation algorithm. In the basis of the solving of interpolation algorithm, the realiz-
ation of servo system of parallel machine tools was studied, in conclusion, to control the servo electric engine with CNC position servo control card made by FANUC.
The dynamics problems of parallel machine were studied by Lie Algebras and Kane equation，the screw form’s Kane dynamics equations were established intr-
oduction of the partial velocity screw, and the solution was also explored.
Finally, the virtual prototype model was designed and simulated in the commer-
cial dynamics simulation software Adams. The simulating results were compared wi-
th the results that came from the solution of kinematics problems and dynamics pro-
blems in this thesis.
Ke..
