本文選題：李群李代數(shù) + 并聯(lián)機(jī)床�。� 參考：《江蘇科技大學(xué)》2011年碩士論文

【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(lái)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(lái)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(wèn)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(wèn)題和動(dòng)力學(xué)問(wèn)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(wèn)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(wèn)題和進(jìn)給伺服控制問(wèn)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(wèn)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(wèn)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(wèn)題。提出了采用泰勒級(jí)數(shù)和擴(kuò)展數(shù)字積分法來(lái)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(wèn)題,擬采用FANUC公司開(kāi)發(fā)的數(shù)控位置伺服控制卡來(lái)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(lái)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(wèn)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(wèn)題解法的分析結(jié)果進(jìn)行了對(duì)比。
[Abstract]:At present, the leaves, Many complicated irregular curved surface parts, such as impeller, have been machined using parallel machine tools with their own characteristics of multi-axis linkage. The new generation parallel machine tool EXCHON 700, developed and put into production by Accom Company of Sweden in 2009, has shown that Parallel machine tools can partly replace traditional five-axis machining centers for machining complex irregular curved surfaces. And efficiency and precision have great advantages. The price of parallel machine tool is much cheaper than that of five-axis linkage machining center because of its simple structure, but because of the technical monopoly, its actual price is more expensive than that of five-axis linkage machining center. So it is very meaningful to digest and apply the technology of parallel machine tool and study the related problems of parallel machine tool. The main contents of this paper are as follows: In this paper, the kinematics and dynamics problems of 6-SPS type seven axis and six linkage cross rod parallel machine tool produced by Harbin measuring tool Group are analyzed, and the problems of kinematics forward solution and dynamics are emphatically studied. On the basis of kinematics research, the problems of machining complex curved surface, interpolation of curve and feed servo control are explored, and the design scheme of NC system of parallel machine tool is put forward. In kinematics research, using Li Qun lie algebra as mathematical tool, a fast and intuitionistic geometric algorithm for kinematics inverse solution of parallel machine tool is proposed, which provides a basic tool for machining complex surface problem. Because of the introduction of Li Qun lie algebra, the forward kinematics solution of the parallel machine tool can be transformed into the inverse solution of the kinematics, which basically solves the problem of the forward kinematics solution of the parallel machine tool. On the basis of kinematics analysis, the problem of interpolation helix of parallel machine tool is studied. The method of interpolation helix by Taylor series and extended digital integration method is proposed. The limit of machining precision to feed speed is given and the flow chart of interpolation algorithm is analyzed. On the basis of interpolation algorithm, the realization of feed servo system of parallel machine tool is studied, and the servo motor of parallel machine tool is controlled by the NC position servo control card developed by FANUC company. The dynamics of parallel machine tool is studied by using the lie algebra and Kane equation. The partial velocity spinor is introduced. The Kane dynamic equation in the form of spinor is established and the solution of the equation is discussed. Finally, a virtual prototype is built and simulated by commercial dynamics simulation software Adams. The simulation results are compared with the results of kinematics forward and inverse solution and dynamic problem solution.
【學(xué)位授予單位】：江蘇科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2011
【分類號(hào)】：TH113

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