工件自由度判斷的幾何定理及應(yīng)用
發(fā)布時(shí)間：2018-08-25 12:46
【摘要】：機(jī)床夾具是零件加工中重要的工藝裝備,其設(shè)計(jì)質(zhì)量直接影響到零件的加工質(zhì)量和效率,而工件自由度的正確判斷是夾具設(shè)計(jì)最基本的內(nèi)容,傳統(tǒng)判斷工件自由度的方法是六點(diǎn)定位原則,它只能夠感性地判斷工件在夾具中的自由度,難以解決一些疑難定位問題,例如對于復(fù)雜曲面定位、異面組合定位的工件,用傳統(tǒng)的方法判斷其自由度往往會(huì)因?yàn)槿鄙倬唧w的規(guī)則而導(dǎo)致錯(cuò)判而使夾具設(shè)計(jì)失敗。我們認(rèn)為傳統(tǒng)方法有兩個(gè)問題沒有得到很好的解決,其一,對工件自由度的分析與判斷未能夠抽象成數(shù)學(xué)法則,不便于計(jì)算機(jī)輔助夾具設(shè)計(jì)對工件自由度的判斷;其二,在工程實(shí)踐中經(jīng)常會(huì)遇到各種不規(guī)則工件定位,往往夾具限制工件某方向的自由度并不是坐標(biāo)軸方向,而是空間其它任意方向,傳統(tǒng)方法難以適應(yīng)。經(jīng)過研究發(fā)現(xiàn)工件在夾具中的自由度完全取決于工件定位法線的數(shù)量及其幾何關(guān)系,為此本文提出定位法線與定位法面概念,由定位法線的數(shù)量及其幾何關(guān)系推導(dǎo)出一組判斷工件自由度的幾何定理,從而實(shí)現(xiàn)了對工件自由度的理性判斷,為生產(chǎn)實(shí)際、教學(xué)、計(jì)算機(jī)輔助夾具設(shè)計(jì)提供一種具體、簡單易行的方法。本文的主要研究內(nèi)容如下:(1)探討了工件在定位元件中自由度被限制的根本原因,從力學(xué)的角度出發(fā),建立了工件定位的力學(xué)模型;同時(shí),從運(yùn)動(dòng)學(xué)的角度也建立相應(yīng)的運(yùn)動(dòng)學(xué)模型。(2)將實(shí)際生產(chǎn)中工件在夾具中的定位轉(zhuǎn)移至工件定位的力學(xué)模型和運(yùn)動(dòng)學(xué)模型中,研究分析工件的自由度限制情況。(3)提出定位法線、定位法面和轉(zhuǎn)動(dòng)定位法面的基本概念,進(jìn)而總結(jié)出判斷工件自由度的幾何定理,并給出相應(yīng)的理論證明;結(jié)合幾何定理,總結(jié)出判斷工件過定位的具體方法,大大提高判斷工件定位狀態(tài)的效率。(4)利用幾何定理給出常用定位元件對工件自由度的限制個(gè)數(shù);給出工件定位具體實(shí)例,結(jié)合幾何定理判斷工件自由度限制情況,對不合理的定位給出相應(yīng)改進(jìn)方案。(5)結(jié)合矩陣和函數(shù)的知識(shí)實(shí)現(xiàn)判斷工件自由度的程序化,為計(jì)算機(jī)輔助夾具設(shè)計(jì)中判斷工件定位狀態(tài)提供了相應(yīng)的基礎(chǔ)理論依據(jù);舉出工件定位實(shí)例,對提出理論的正確性進(jìn)行驗(yàn)證。本文的主要研究結(jié)論如下:(1)工件在夾具中的自由度完全取決于工件在夾具中定位法線的數(shù)量及其幾何關(guān)系。(2)用幾何定理容易處理各種疑難自由度分析,可有效避免欠定位與過定位,為改進(jìn)不合理的定位方案提供重要理論依據(jù)。(3)利用定位法線的等效,可將法線復(fù)雜的空間關(guān)系簡化,從而便于使用幾何定理判斷工件的自由度限制情況。(4)用幾何定理分析判斷工件自由度更具理性且簡單直觀,適合計(jì)算機(jī)輔助判斷工件的自由度。
[Abstract]:Jig is an important process equipment in the machining of parts, and its design quality directly affects the machining quality and efficiency of the parts, and the correct judgment of the degree of freedom of the workpiece is the most basic content of the fixture design. The traditional method of judging the degree of freedom of a workpiece is the six-point positioning principle. It can only judge the degree of freedom of the workpiece in the fixture sensitively. It is difficult to solve some difficult localization problems, for example, for the workpiece with complex surface localization and cross-plane combination localization. The traditional method of judging the degree of freedom often leads to the failure of fixture design due to the lack of specific rules. We think that two problems have not been solved well in the traditional method. One is that the analysis and judgment of the degree of freedom of the workpiece can not be abstracted into the mathematical rule, which is not convenient for the computer aided fixture design to judge the degree of freedom of the workpiece. In engineering practice, various kinds of irregular workpiece positioning are often encountered. It is often difficult to adapt the traditional methods to restrict the degree of freedom of the workpiece in one direction, not in the axis direction, but in any other direction of the space. It is found that the degree of freedom of the workpiece in the fixture depends entirely on the number of the normal alignment of the workpiece and its geometric relationship. In this paper, the concepts of the normal alignment and the normal plane are proposed in this paper. A set of geometric theorems for judging the degree of freedom of workpiece are deduced from the quantity of orientation normal and its geometric relationship, and the rational judgment of degree of freedom of workpiece is realized, which provides a concrete method for production practice, teaching and computer aided fixture design. A simple and easy method. The main contents of this paper are as follows: (1) the fundamental reason of the degree of freedom of the workpiece in the positioning element is discussed, and the mechanical model of the workpiece positioning is established from the point of view of mechanics, at the same time, The kinematics model is also established from the point of view of kinematics. (2) the positioning of the workpiece in the fixture is transferred to the mechanical model and the kinematics model of the workpiece positioning, and the degree of freedom limitation of the workpiece is studied and analyzed. (3) the localization normals are proposed. The basic concepts of locating normal plane and rotating positioning normal surface are summarized, then the geometric theorem of judging the degree of freedom of workpiece is summarized, and the corresponding theoretical proof is given, and the concrete method of judging the overpositioning of workpiece is summarized according to the geometric theorem. It greatly improves the efficiency of judging the position state of workpiece. (4) the limited number of degrees of freedom of workpiece is given by using geometric theorem, the concrete example of workpiece location is given, and the limit of degree of freedom of workpiece is judged according to geometric theorem. The corresponding improvement scheme for the unreasonable positioning is given. (5) programming the degree of freedom of the workpiece is realized by combining the knowledge of matrix and function, which provides the corresponding basic theoretical basis for judging the position state of the workpiece in the computer-aided fixture design; An example of workpiece location is given to verify the correctness of the proposed theory. The main conclusions of this paper are as follows: (1) the degree of freedom of the workpiece in the fixture depends entirely on the number of normal lines located in the fixture and its geometric relationship. (2) it is easy to deal with the analysis of various difficult degrees of freedom by using geometric theorems. It can effectively avoid underpositioning and over-positioning, and provide an important theoretical basis for improving unreasonable positioning schemes. (3) by using the equivalence of normal alignment, the complex spatial relationship of normal lines can be simplified. It is convenient to use geometric theorem to judge the degree of freedom of workpiece. (4) it is more rational and simple to judge the degree of freedom of workpiece by using geometric theorem, which is suitable for computer aided judgment of degree of freedom of workpiece.
【學(xué)位授予單位】：太原科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TG75
[Abstract]:Jig is an important process equipment in the machining of parts, and its design quality directly affects the machining quality and efficiency of the parts, and the correct judgment of the degree of freedom of the workpiece is the most basic content of the fixture design. The traditional method of judging the degree of freedom of a workpiece is the six-point positioning principle. It can only judge the degree of freedom of the workpiece in the fixture sensitively. It is difficult to solve some difficult localization problems, for example, for the workpiece with complex surface localization and cross-plane combination localization. The traditional method of judging the degree of freedom often leads to the failure of fixture design due to the lack of specific rules. We think that two problems have not been solved well in the traditional method. One is that the analysis and judgment of the degree of freedom of the workpiece can not be abstracted into the mathematical rule, which is not convenient for the computer aided fixture design to judge the degree of freedom of the workpiece. In engineering practice, various kinds of irregular workpiece positioning are often encountered. It is often difficult to adapt the traditional methods to restrict the degree of freedom of the workpiece in one direction, not in the axis direction, but in any other direction of the space. It is found that the degree of freedom of the workpiece in the fixture depends entirely on the number of the normal alignment of the workpiece and its geometric relationship. In this paper, the concepts of the normal alignment and the normal plane are proposed in this paper. A set of geometric theorems for judging the degree of freedom of workpiece are deduced from the quantity of orientation normal and its geometric relationship, and the rational judgment of degree of freedom of workpiece is realized, which provides a concrete method for production practice, teaching and computer aided fixture design. A simple and easy method. The main contents of this paper are as follows: (1) the fundamental reason of the degree of freedom of the workpiece in the positioning element is discussed, and the mechanical model of the workpiece positioning is established from the point of view of mechanics, at the same time, The kinematics model is also established from the point of view of kinematics. (2) the positioning of the workpiece in the fixture is transferred to the mechanical model and the kinematics model of the workpiece positioning, and the degree of freedom limitation of the workpiece is studied and analyzed. (3) the localization normals are proposed. The basic concepts of locating normal plane and rotating positioning normal surface are summarized, then the geometric theorem of judging the degree of freedom of workpiece is summarized, and the corresponding theoretical proof is given, and the concrete method of judging the overpositioning of workpiece is summarized according to the geometric theorem. It greatly improves the efficiency of judging the position state of workpiece. (4) the limited number of degrees of freedom of workpiece is given by using geometric theorem, the concrete example of workpiece location is given, and the limit of degree of freedom of workpiece is judged according to geometric theorem. The corresponding improvement scheme for the unreasonable positioning is given. (5) programming the degree of freedom of the workpiece is realized by combining the knowledge of matrix and function, which provides the corresponding basic theoretical basis for judging the position state of the workpiece in the computer-aided fixture design; An example of workpiece location is given to verify the correctness of the proposed theory. The main conclusions of this paper are as follows: (1) the degree of freedom of the workpiece in the fixture depends entirely on the number of normal lines located in the fixture and its geometric relationship. (2) it is easy to deal with the analysis of various difficult degrees of freedom by using geometric theorems. It can effectively avoid underpositioning and over-positioning, and provide an important theoretical basis for improving unreasonable positioning schemes. (3) by using the equivalence of normal alignment, the complex spatial relationship of normal lines can be simplified. It is convenient to use geometric theorem to judge the degree of freedom of workpiece. (4) it is more rational and simple to judge the degree of freedom of workpiece by using geometric theorem, which is suitable for computer aided judgment of degree of freedom of workpiece.
【學(xué)位授予單位】：太原科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TG75
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