【摘要】：機(jī)構(gòu)的誤差傳遞建模是貫穿操作裝備設(shè)計(jì)、制造以及服役的一個(gè)關(guān)鍵問題,對于預(yù)測裝備的定位精度、實(shí)現(xiàn)誤差參數(shù)標(biāo)定與補(bǔ)償?shù)染哂兄陵P(guān)重要的作用。因此,建立準(zhǔn)確、高效的誤差傳遞模型是實(shí)現(xiàn)操作裝備高精度作業(yè)的基礎(chǔ)。構(gòu)件的尺寸和變形誤差是影響操作機(jī)構(gòu)末端定位精度的主要因素。它們分別由零部件的制造及裝配誤差和外載作用下的結(jié)構(gòu)變形所導(dǎo)致,因此現(xiàn)有精度分析方法分別將其歸結(jié)為機(jī)構(gòu)的尺寸誤差分析和結(jié)構(gòu)變形計(jì)算兩個(gè)獨(dú)立的范疇,通過尺寸誤差和結(jié)構(gòu)變形的線性疊加獲得操作機(jī)構(gòu)的末端位姿誤差。然而,當(dāng)具有閉環(huán)拓?fù)錁?gòu)型的操作機(jī)構(gòu)中存在過約束時(shí),不滿足公共約束的尺寸誤差需要通過構(gòu)件結(jié)構(gòu)變形進(jìn)行協(xié)調(diào),即構(gòu)件結(jié)構(gòu)變形與尺寸誤差之間存在耦合關(guān)系。因此,將尺寸誤差和結(jié)構(gòu)變形相分離的誤差建模方法無法準(zhǔn)確反映過約束機(jī)構(gòu)的誤差傳遞規(guī)律,需要綜合考慮上述兩類誤差因素,建立同時(shí)適用于開鏈機(jī)構(gòu)、閉環(huán)機(jī)構(gòu)以及并聯(lián)過約束機(jī)構(gòu)的統(tǒng)一誤差傳遞建模方法。針對上述問題,本文基于局部指數(shù)映射,分別將尺寸誤差和結(jié)構(gòu)變形轉(zhuǎn)化為等效關(guān)節(jié)的位置誤差和變形誤差,建立了操作機(jī)構(gòu)的尺寸和變形誤差到末端位姿誤差的傳遞模型,實(shí)現(xiàn)了尺寸和變形誤差的統(tǒng)一建模。在此基礎(chǔ)上建立了尺寸誤差參數(shù)的獨(dú)立性判別準(zhǔn)則和解析分離算子,以及過約束誤差子空間的判別與分離方法,為操作機(jī)構(gòu)的誤差建模與分析、尺寸參數(shù)標(biāo)定與補(bǔ)償以及精度設(shè)計(jì)提供了理論基礎(chǔ)。全文的理論和應(yīng)用研究成果歸納如下:□構(gòu)件尺寸誤差在開鏈機(jī)構(gòu)中的傳遞規(guī)律研究基于機(jī)器人運(yùn)動(dòng)學(xué)建模的局部指數(shù)積公式,建立了滿足完備性和連續(xù)性要求的開鏈機(jī)構(gòu)尺寸誤差到末端位姿誤差的誤差映射模型,推導(dǎo)了構(gòu)件尺寸誤差的獨(dú)立性判別準(zhǔn)則,提出了誤差參數(shù)獨(dú)立分量和冗余分量的解析分離算法,得到了僅含有獨(dú)立參數(shù)的最小誤差映射模型,揭示了構(gòu)件尺寸參數(shù)誤差在開鏈機(jī)構(gòu)中的傳遞規(guī)律,為尺寸和變形誤差的統(tǒng)一建模提供了基礎(chǔ)。與現(xiàn)有方法相比,本文所建立的尺寸誤差建模方法具有更好的通用性,適用于相鄰關(guān)節(jié)軸線存在平行、垂直等特殊關(guān)系的開鏈機(jī)構(gòu)。另外,能夠通過解析方式消除模型中的冗余誤差分量,得到具有最小誤差參數(shù)的系統(tǒng)誤差傳遞模型。研究結(jié)果表明,開鏈機(jī)構(gòu)具有確定的獨(dú)立誤差參數(shù),與具體的建模方法無關(guān)�！鯓�(gòu)件結(jié)構(gòu)變形的關(guān)節(jié)運(yùn)動(dòng)誤差等效方法研究借鑒機(jī)器人末端剛度矩陣綜合的思想,進(jìn)行了構(gòu)件結(jié)構(gòu)剛度矩陣的中心主軸分解,提出了構(gòu)件結(jié)構(gòu)變形的關(guān)節(jié)運(yùn)動(dòng)誤差等效方法,將構(gòu)件的結(jié)構(gòu)變形誤差轉(zhuǎn)化為等效關(guān)節(jié)的運(yùn)動(dòng)誤差,實(shí)現(xiàn)了操作機(jī)構(gòu)中構(gòu)件結(jié)構(gòu)剛度和變形誤差的解析建模,為構(gòu)件尺寸誤差與結(jié)構(gòu)變形的統(tǒng)一表征提供了有效的描述方式。采用關(guān)節(jié)運(yùn)動(dòng)誤差等效的方式表征構(gòu)件的結(jié)構(gòu)變形,可以建立各等效關(guān)節(jié)運(yùn)動(dòng)誤差與構(gòu)件尺寸誤差之間的映射關(guān)系,從而為實(shí)現(xiàn)與過約束尺寸誤差相耦合的變形誤差分離提供了可能�！醪僮鳈C(jī)構(gòu)尺寸與變形誤差傳遞的統(tǒng)一建模方法借助構(gòu)件結(jié)構(gòu)剛度的關(guān)節(jié)等效模型,分別將尺寸誤差和結(jié)構(gòu)變形轉(zhuǎn)化為等效關(guān)節(jié)的位置誤差和變形誤差,采用關(guān)節(jié)誤差傳遞的方式建立構(gòu)件尺寸和變形誤差統(tǒng)一表征,實(shí)現(xiàn)了操作機(jī)構(gòu)尺寸和變形誤差傳遞的統(tǒng)一建模。研究表明,對于開鏈機(jī)構(gòu)和非過約束閉環(huán)機(jī)構(gòu),構(gòu)件尺寸誤差和結(jié)構(gòu)變形相互獨(dú)立,其末端位姿誤差可通過兩者線性疊加得到。對于過約束操作機(jī)構(gòu),其構(gòu)件尺寸誤差和結(jié)構(gòu)變形之間存在耦合關(guān)系,位于過約束誤差子空間上的不相容尺寸誤差需要通過構(gòu)件的結(jié)構(gòu)變形進(jìn)行協(xié)調(diào)。與現(xiàn)有方法相比,論文所建立的操作機(jī)構(gòu)尺寸和變形誤差統(tǒng)一傳遞模型具有通用性,同時(shí)適用于開鏈、閉環(huán)非過約束和閉環(huán)過約束機(jī)構(gòu)。特別地,對于過約束操作機(jī)構(gòu),能夠分離得到系統(tǒng)的過約束誤差子空間,并通過內(nèi)力平衡方程和變形協(xié)調(diào)條件,最終確定由協(xié)調(diào)變形所引起的末端位姿誤差。□操作機(jī)構(gòu)誤差傳遞模型的區(qū)域映射求解算法根據(jù)誤差因素的有界不確定特性,提出了由輸入誤差區(qū)域到輸出誤差區(qū)域傳遞的機(jī)構(gòu)區(qū)域誤差映射模型,借助獨(dú)立誤差約束集形態(tài)和的閔可夫斯基法則,建立了基于運(yùn)動(dòng)幾何包絡(luò)理論的輸出誤差區(qū)域邊界推進(jìn)求解算法,得到了操作機(jī)構(gòu)末端誤差區(qū)域的確切邊界,以輸出誤差區(qū)域的形式更加準(zhǔn)確地描述了操作機(jī)構(gòu)的末端定位精度特性�！醪僮鳈C(jī)構(gòu)誤差建模與分析的應(yīng)用研究應(yīng)用論文的理論研究成果,得到了一般串聯(lián)工業(yè)機(jī)器人尺寸誤差傳遞的最小參數(shù)模型,實(shí)現(xiàn)了支線客機(jī)前起落架執(zhí)行機(jī)構(gòu)末端誤差區(qū)域的準(zhǔn)確預(yù)測,解決了六自由度并聯(lián)調(diào)姿平臺尺寸誤差參數(shù)的標(biāo)定與補(bǔ)償,實(shí)現(xiàn)了空間三自由度過約束并聯(lián)旋壓機(jī)構(gòu)尺寸與變形耦合誤差的分離計(jì)算,驗(yàn)證了論文所建立的誤差傳遞建模方法的通用性和有效性。
[Abstract]:Error transfer modeling of mechanism is a key problem throughout the design, manufacture and service of operational equipment. It plays an important role in predicting the positioning accuracy of equipment and realizing the calibration and compensation of error parameters. Dimension and deformation errors are the main factors affecting the positioning accuracy of the end of the manipulator. They are caused by the manufacturing and assembling errors of the parts and the structural deformation under the action of external loads. Therefore, the existing accuracy analysis methods can be divided into two separate categories: the dimension error analysis of the mechanism and the structural deformation calculation. However, when there are over-constraints in the operating mechanism with closed-loop topology, the dimension errors which do not satisfy the common constraints need to be coordinated by the structural deformation of the component, that is, there is a coupling relationship between the structural deformation and the dimensional error. The error modeling method of separating dimension error and structural deformation can not accurately reflect the error transfer law of over-constrained mechanism. It is necessary to consider the above two error factors comprehensively and establish a unified error transfer modeling method for both open-chain mechanism, closed-loop mechanism and parallel over-constrained mechanism. Dimensional error and structural deformation are transformed into position error and deformation error of equivalent joint respectively by partial exponential mapping. The transfer model from dimension and deformation error of manipulator to position error of end is established, and the unified modeling of dimension and deformation error is realized. The separation operator and the method of distinguishing and separating over-constrained error subspace are analyzed, which provide theoretical basis for error modeling and analysis, dimension parameter calibration and compensation, and precision design. The local exponential product formula of robot kinematics modeling is established. The error mapping model from the dimension error to the position error of the end of the open-chain mechanism satisfying the requirements of completeness and continuity is established. The independence criterion of the dimension error of the component is deduced. The analytical separation algorithm of the independent component of the error parameter and the redundant component is proposed. The algorithm contains only the error components. The minimal error mapping model with independent parameters reveals the transfer rule of dimension parameter errors in open-chain mechanisms and provides a basis for the unified modeling of dimension and deformation errors. In addition, the redundant error components in the model can be eliminated analytically, and the system error transfer model with minimum error parameters can be obtained. The results show that the open-chain mechanism has definite independent error parameters and is independent of the specific modeling methods. Based on the idea of robot end stiffness matrix synthesis, the central principal axis decomposition of component structure stiffness matrix is carried out, and the joint motion error equivalent method of component structure deformation is proposed. The structural deformation error of component is transformed into the motion error of equivalent joint, and the structural stiffness and change of component in operating mechanism are realized. Analytical modeling of form error provides an effective description for the unified characterization of component dimension error and structural deformation. By using the equivalent method of joint motion error to characterize the structural deformation of components, the mapping relationship between the equivalent joint motion error and component dimension error can be established, thus realizing the phase of over-constrained dimension error. _Unified modeling method of dimension and deformation error transfer of manipulator mechanism transforms dimension error and structure deformation into position error and deformation error of equivalent joint respectively by means of joint equivalent model of structural stiffness of component, and establishes dimension and deformation of component by joint error transfer. The research shows that the dimension error and structure deformation are independent of each other for open-chain mechanism and non-over-constrained closed-loop mechanism, and the end pose error can be obtained by linear superposition of them. Comparing with the existing methods, the unified transfer model of the dimension and deformation errors of the operating mechanism established in this paper is universal and applicable to open-chain, closed-loop non-over-constrained and closed-loop over-constrained systems. In particular, for over-constrained manipulators, the over-constrained error subspace of the system can be separated and the end pose error caused by coordinated deformation can be determined by the internal force balance equation and the deformation coordination condition. The region mapping algorithm for solving the error transfer model of the manipulator is bounded according to the error factors. Based on the Minkowski's law of the sum of independent error constraints, a boundary-propulsion algorithm of output error region based on the envelope theory of kinematic geometry is established, and the accuracy of the error region at the end of the manipulator is obtained. 鍒囪竟鐣，

本文編號：2244744