摘 要
目前，葉片、葉輪等復(fù)雜不規(guī)則曲面零件有不少已采用本身具有多軸聯(lián)動(dòng)的特征的并聯(lián)機(jī)床來加工。2009年瑞典艾克斯康公司研制并投入實(shí)際生產(chǎn)的新一代并聯(lián)機(jī)床EXCHON 700已經(jīng)表明并聯(lián)機(jī)床可以部分代替?zhèn)鹘y(tǒng)的五軸聯(lián)動(dòng)加工中心來加工復(fù)雜不規(guī)則曲面零件，而且效率和精度相比都有很大優(yōu)勢(shì)。由于并聯(lián)機(jī)床本身結(jié)構(gòu)的簡(jiǎn)單性，其價(jià)格比五軸聯(lián)動(dòng)加工中心要便宜很多，但是由于技術(shù)上的壟斷，其實(shí)際價(jià)格與五軸聯(lián)動(dòng)加工中心相比還要昂貴。所以消化和應(yīng)用并聯(lián)機(jī)床的技術(shù)，研究并聯(lián)機(jī)床的有關(guān)問題很有意義。
本文的主要研究?jī)?nèi)容如下：
哈爾濱量具刃具集團(tuán)生產(chǎn)的6-SPS型七軸六聯(lián)動(dòng)交叉桿型并聯(lián)機(jī)床為對(duì)象，分析了交叉桿型并聯(lián)機(jī)床的運(yùn)動(dòng)學(xué)問題和動(dòng)力學(xué)問題，并重點(diǎn)研究了運(yùn)動(dòng)學(xué)正解的難題和動(dòng)力學(xué)問題。在運(yùn)動(dòng)學(xué)研究的基礎(chǔ)上，探索了并聯(lián)機(jī)床加工復(fù)雜曲面、曲線的插補(bǔ)問題和進(jìn)給伺服控制問題，提出了并聯(lián)機(jī)床數(shù)控系統(tǒng)的設(shè)計(jì)方案。
在運(yùn)動(dòng)學(xué)研究中，采用李群李代數(shù)作為數(shù)學(xué)工具，提出了并聯(lián)機(jī)床運(yùn)動(dòng)學(xué)反解的快速而直觀的幾何算法，為加工復(fù)雜曲面問題提供了基本工具。由于李群李代數(shù)的引入，并聯(lián)機(jī)床運(yùn)動(dòng)學(xué)正解可以轉(zhuǎn)化為運(yùn)動(dòng)學(xué)的反解問題，基本解決了并聯(lián)機(jī)床運(yùn)動(dòng)學(xué)正解的難題。
在運(yùn)動(dòng)學(xué)分析的基礎(chǔ)上，研究了并聯(lián)機(jī)床插補(bǔ)螺旋線的問題。提出了采用泰勒級(jí)數(shù)和擴(kuò)展數(shù)字積分法來插補(bǔ)螺旋線的方法，給出了加工精度對(duì)于進(jìn)給速度的限制，并分析了插補(bǔ)算法的流程。在插補(bǔ)算法的基礎(chǔ)上，研究了并聯(lián)機(jī)床進(jìn)給伺服系統(tǒng)的實(shí)現(xiàn)問題，擬采用FANUC公司開發(fā)的數(shù)控位置伺服控制卡來控制并聯(lián)機(jī)床的伺服電機(jī)。
并聯(lián)機(jī)床動(dòng)力學(xué)采用李代數(shù)和Kane方程來研究，引入了偏速度旋量，建立了旋量形式Kane動(dòng)力學(xué)方程，并探討了該方程的求解問題。
最后建立虛擬樣機(jī)，用商業(yè)動(dòng)力學(xué)仿真軟件Adams進(jìn)行仿真，將仿真結(jié)果與本文采用的運(yùn)動(dòng)學(xué)正逆解法和動(dòng)力學(xué)問題解法的分析結(jié)果進(jìn)行了對(duì)比。
關(guān)鍵詞 李群李代數(shù)；并聯(lián)機(jī)床；運(yùn)動(dòng)學(xué)正解；嵌入式數(shù)控系統(tǒng)；旋量形式；Kane動(dòng)力學(xué)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..