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學(xué)生實(shí)習(xí)報(bào)告
（限1500字以上）
院（系）：機(jī)械工程學(xué)院專業(yè)：機(jī)械設(shè)計(jì)制造及其自動化 班級： 0303 姓名：王曉雄
一、實(shí)習(xí)的主要內(nèi)容
生產(chǎn)實(shí)習(xí)是機(jī)械類專業(yè)教學(xué)中的一項(xiàng)重要實(shí)踐環(huán)節(jié)。其目的是使學(xué)生了解和掌握本專業(yè)基本生產(chǎn)實(shí)際知識，培養(yǎng)學(xué)生理論聯(lián)系實(shí)際及初步的獨(dú)立工作能力，為后續(xù)有關(guān)課程的學(xué)習(xí)打下基礎(chǔ)。實(shí)習(xí)可分為兩個(gè)階段：第一階段為見習(xí)實(shí)習(xí)；第二階段為結(jié)合專業(yè)方向的生產(chǎn)實(shí)習(xí)。實(shí)習(xí)內(nèi)容是使學(xué)生接觸和了解機(jī)械制造的生產(chǎn)過程，學(xué)習(xí)到有關(guān)主要工種加工方法的基本知識，為學(xué)好金屬工藝學(xué)、機(jī)械制造基礎(chǔ)奠定必要的感性知識基礎(chǔ)，同時(shí)也為學(xué)習(xí)其他技術(shù)基礎(chǔ)課建立一些實(shí)踐基礎(chǔ)。
實(shí)習(xí)目的是使學(xué)生了解各類機(jī)械的運(yùn)轉(zhuǎn)和工作原理，并結(jié)合本專業(yè)的需要和目的，了解和觀察本專業(yè)涉及到的各類機(jī)械的組成結(jié)構(gòu)、運(yùn)轉(zhuǎn)機(jī)構(gòu)和工作原理以及生產(chǎn)過程，為課程設(shè)計(jì)和畢業(yè)設(shè)計(jì)打下基礎(chǔ)。結(jié)合專業(yè)方向的生產(chǎn)實(shí)習(xí)應(yīng)根據(jù)專業(yè)特點(diǎn)，有針對性的到一些工礦企業(yè)單位進(jìn)行。
2007年初我在深圳現(xiàn)代精密塑膠模具公司實(shí)習(xí)：
1參加由公司組織的理論知識的學(xué)習(xí)，由有經(jīng)驗(yàn)的領(lǐng)導(dǎo)、工程師授課，學(xué)習(xí)公司的文化、以及公司的發(fā)展前景、主要產(chǎn)品的生產(chǎn)流程和必要的技術(shù)要求以及一些改進(jìn)方向、公司必須保留和更新發(fā)展的技術(shù)核心等等。
2在有經(jīng)驗(yàn)的師傅的指導(dǎo)下，親自動手拆裝模具、維修模具以及學(xué)習(xí)模具的結(jié)構(gòu)組成以及工藝技術(shù)要求、模具的裝拆的方法和技巧、同時(shí)也要求設(shè)計(jì)一些簡單實(shí)用的模具，為以后設(shè)計(jì)或改進(jìn)大型模具做準(zhǔn)備。
3參加由公司有經(jīng)驗(yàn)的技術(shù)員指導(dǎo)的模具設(shè)計(jì)，學(xué)習(xí)如何根據(jù)模具的用途設(shè)計(jì)一些實(shí)用的模具，以及設(shè)計(jì)制造模具時(shí)應(yīng)該注意的主要問題和細(xì)節(jié)。
二、實(shí)習(xí)取得的經(jīng)驗(yàn)及收獲
畢業(yè)實(shí)習(xí)是一門專業(yè)實(shí)踐課，是機(jī)械類各專業(yè)學(xué)生學(xué)習(xí)了各門專業(yè)課程之后，在進(jìn)行畢業(yè)設(shè)計(jì)或畢業(yè)論文時(shí)必不可少的實(shí)踐教學(xué)環(huán)節(jié)。它對于培養(yǎng)我們的動手能力有很大的意義，而且可以使我們了解傳統(tǒng)的機(jī)械制造工藝和現(xiàn)代機(jī)械制造技術(shù)。我國現(xiàn)行的教育體制，使得通過高考而進(jìn)入大學(xué)的大學(xué)生的動手實(shí)踐能力比較薄弱。因此，處于學(xué)校和社會過渡階段的大學(xué)就承擔(dān)了培養(yǎng)學(xué)生實(shí)踐能力的任務(wù)。畢業(yè)實(shí)習(xí)就是培養(yǎng)學(xué)生實(shí)踐能力的有效途徑。通過實(shí)習(xí)掌握了模具的一些基本知識，如模具的組成結(jié)構(gòu)、如何根據(jù)用戶的需要去設(shè)計(jì)一些簡單的模具、在模具設(shè)計(jì)時(shí)的工藝、公差、粗造度、等如何選擇和應(yīng)用有了初步的理解。
我們機(jī)械制造及自動化專業(yè)所學(xué)習(xí)的重點(diǎn)在于各種機(jī)械成型設(shè)備，本次實(shí)習(xí)就是為了讓我們能夠?qū)τ谖覀兯鶎W(xué)過的各種儀器、設(shè)備有一個(gè)感性的直觀的認(rèn)識，從而把書本上的理論和現(xiàn)實(shí)中的傳統(tǒng)技術(shù)和已經(jīng)被應(yīng)用于實(shí)際的最新發(fā)展的高新技術(shù)聯(lián)系與結(jié)合起來，進(jìn)一步鞏固和深化所學(xué)的理論知識，彌補(bǔ)以前單一理論教學(xué)的不足,為后續(xù)專業(yè)課學(xué)習(xí)和畢業(yè)設(shè)計(jì)打好基礎(chǔ)。
三、存在的不足及建議
通過實(shí)習(xí)我本人感覺到還有很多不足的地方：
1、專業(yè)知識還不是很扎實(shí)，特別是公差方面的，為了讓設(shè)計(jì)出來的產(chǎn)品達(dá)到要求而一味的加大精度，給制造帶來了難度；
2、實(shí)際操作能力不夠，現(xiàn)在是技術(shù)更新的時(shí)候，公司都引進(jìn)了很多先進(jìn)的生產(chǎn)設(shè)備，但自己對這些高新設(shè)備束手無策；
3、初到公司缺乏工作經(jīng)驗(yàn)，很多的工作感到無從下手，沒有一個(gè)完整的頭緒，很難單獨(dú)去接受一個(gè)實(shí)際的課題。
通過實(shí)習(xí)我想對學(xué)校一點(diǎn)建議：
雖然自己只工作了兩個(gè)月，但還是感覺到了學(xué)校和公司之間有很大的差距。如果能縮小這種差距的話，對以后學(xué)校就業(yè)將有很大優(yōu)勢，更對學(xué)生能夠很快融入工作環(huán)境打下堅(jiān)實(shí)的基礎(chǔ)。我就以過來人的身份建議學(xué)校能夠更加注重學(xué)生的實(shí)際動手能力，加強(qiáng)學(xué)生的實(shí)踐能力的培養(yǎng)，如增加學(xué)生的在校實(shí)習(xí)的機(jī)會和延長學(xué)生的實(shí)踐活動的時(shí)間，更加注重在老師的指導(dǎo)下讓學(xué)生真正的參與到實(shí)踐中去。畢業(yè)設(shè)計(jì)期間學(xué)校是否能考慮組織學(xué)生到生產(chǎn)現(xiàn)場去參觀實(shí)習(xí)，讓學(xué)生接受最為直接的設(shè)計(jì)基本知識，比憑空去設(shè)想更有效果。
湖南工業(yè)大學(xué)
機(jī)械工程學(xué)院
機(jī)械加工工藝過程卡片
產(chǎn)品型號
ZG65拔叉
零（部）件圖號
12-37-112
產(chǎn)品名稱
副變速拔叉
零（部）件名稱
共（2）頁
第（ ）頁
材料牌號
ZG65
毛坯種類
鑄件
毛坯外型尺寸
生產(chǎn)類型
大批量
每臺件數(shù)
1
備注
工序號
工序名稱
工 序 內(nèi) 容
車間
工段
設(shè)備
工 藝 裝 備
工時(shí)
夾具
刃具
量具
輔具
準(zhǔn)備
單件
1
鑄造
鑄造、清沙
2
熱處理
正火
3
車削
車拔叉頭端面
C366——1回轉(zhuǎn)式六角車床
YT15外圓車刀
卡尺
鉆、鏜削
鉆、鏜、鉸Φ14H9孔
Z515鉆床
Φ6.5標(biāo)準(zhǔn)錐柄麻花鉆
Φ14H9孔用塞規(guī)
車削
孔口倒角
C366——1回轉(zhuǎn)式六角車床
YT15外圓車刀
4
鉗工
校正拔叉腳
鉗工臺
5
銑削
粗銑拔叉腳兩端面
X62W臥式銑床
專用夾用
YT15三面刃銑刀
0~200/0.02mm游標(biāo)卡尺
6
銑削
銑拔叉腳內(nèi)側(cè)面
X62W臥式銑床
專用夾具
YT15三面刃銑刀
0~200/0.02mm游標(biāo)卡尺
7
銑削
銑操縱槽
X62W臥式銑床
專用夾具
YT15三面刃銑刀
0~200/0.02mm游標(biāo)卡尺
8
鉆削
鉆Φ8.7孔
Z515鉆床
鉆用夾具
Φ8.7錐柄麻花鉆
0~200/0.02mm游標(biāo)卡尺
9
鉗工
去毛刺
鉗工臺
10
熱處理
拔叉腳局部淬火
11
鉗工
校正拔叉腳
鉗工臺
12
磨削
磨拔叉腳兩端面
M7120A平面磨床
專用夾具
砂輪
0~200/0.02mm游標(biāo)卡尺
13
清洗
14
檢驗(yàn)
設(shè)計(jì)（日期）
審核（日期）
標(biāo)準(zhǔn)化（日期）
會簽（日期）
王曉雄
標(biāo)記
處數(shù)
更改文件號
簽字
日期
處數(shù)
更改文件號
簽字
日期
湖南工業(yè)大學(xué)畢業(yè)設(shè)計(jì) 2007
拖拉機(jī)撥叉銑專機(jī)（臥式）
摘要：
本文主要介紹了X62W型臥式拖拉機(jī)撥叉銑專機(jī)的性能參數(shù)、結(jié)構(gòu)原理，帶輪、彈簧夾頭的設(shè)計(jì)計(jì)算，刀具的選擇和使用，電機(jī)的選擇以及使用，零件的加工工藝過程以及各種標(biāo)準(zhǔn)件的選擇。X62W型臥式拖拉機(jī)撥叉銑專機(jī)是一臺半自動臥式銑專機(jī)，它是以現(xiàn)役的X62W型臥式銑床為基礎(chǔ)設(shè)計(jì)出的新型半自動臥式銑撥叉專機(jī)。工件以其主軸孔定位，定位心軸置于圓盤工作臺上，圓盤工作臺主軸呈臥式安置；它的工作過程是：人工上料——自動定位——自動夾緊——自動銑削，銑畢自動松開工件后由操作者取下。?這種專機(jī)工作它可以克服現(xiàn)有X62W型臥式銑床工人勞動強(qiáng)度大，生產(chǎn)率低等缺點(diǎn)。X62W型臥式拖拉機(jī)撥叉銑專機(jī)的工作節(jié)拍為每分鐘20件，并且具有工作安全、可靠，結(jié)構(gòu)緊湊，運(yùn)行平穩(wěn)，產(chǎn)品質(zhì)量穩(wěn)定，操作維護(hù)簡單等多種優(yōu)點(diǎn)。改造后的X62W型臥式拖拉機(jī)撥叉銑專機(jī)在生產(chǎn)實(shí)踐中將會得到有效的應(yīng)用，而且會取得了良好的效果，在滿足生產(chǎn)急需的前提下為企業(yè)創(chuàng)造了顯著的經(jīng)濟(jì)效益。
關(guān)鍵詞：撥叉銑專機(jī)、帶輪、彈簧夾具
Design of the milling machine for transmission fork of transmission(horizontal)
Summary: This text mainly introduces the parameters and structure principle of X62W type horizontal milling machine for fork of transmission, with wheel and spring chuck design calculate, choice and use of cutter and electrical machinery, preparation method course and choices of different standard component of part. X62W type horizontal milling machine for transmission fork of transmission is one set of semi-automatic horizontal mill special plane. It regard current X62W type miller as the half automatic on that stir the fork special airplane. The workpiece fixing with its sipindle hole. The spolting spindle is placed in disc worktable. Its working process is: anticipate on the artificial- automatic position- automatic clamp- automatic milling, after milling unclamped the work piece automatically and taken down the workpiece by the operator. Use this kind of special airplane works can overcome the current X62W type miller much disadvantage such as big labor strength bi, low productivity. The X62W type horizontal milling machine for fork of transmission’s work tempo is 20piece every minute. And have the work safety, dependable, construction tightly packed, circulate steady, product quantity stability, operation and maintenance simple etc. various advantages. The reconstructing of X62W type horizontal milling machine for fork of transmission would getting application effectively, and will obtain the good result, It will creats evidence economic performance for the business enterprise at the need of the premise bottom.
Keywords：Dial fork mill special plane, solid pulley, spring chuck.
目 錄 1 前 言 1 2 總體方案論 證 3 2 1 被加工零件分 析 3 2 2 毛坯的選 擇 3 2 3 基準(zhǔn)選 擇 5 2 4 擬訂機(jī)械加工工藝路 線 5 2 5 確定機(jī)械加工余量 工序尺寸及公 差 7 2 6 選擇機(jī)床設(shè)備及工藝裝 備 7 3 金屬切削用量的選擇與計(jì) 算 8 3 1 刀具的選 擇 8 3 2 切削用量的選擇以及計(jì) 算 8 4 機(jī)械傳動裝置的總體設(shè) 計(jì) 9 4 1 分析和擬訂傳動裝 置 9 4 2 減速機(jī)的選 擇 9 4 3 帶輪的設(shè)計(jì)計(jì) 算 10 5 彈簧夾頭的特點(diǎn)以及設(shè)計(jì)計(jì) 算 14 5 1 彈簧夾頭的介 紹 15 5 2 彈簧夾頭的夾緊力的影響因 素 15 6 軸的強(qiáng)度校 核 16 6 1 求軸上載 荷 16 6 2 繪制彎矩圖和扭矩 圖 16 6 3 彎矩合成強(qiáng)度校 核 16 6 4 疲勞強(qiáng)度安全系 數(shù) 16 7 結(jié) 論 21 參考文 獻(xiàn) 22 致 謝 23 附 錄 24
湖南工業(yè)大學(xué)
外文翻譯
專 業(yè) 機(jī)械設(shè)計(jì)制造及其自動化
學(xué) 生 姓 名 王 曉 雄
班 級 機(jī)本0303班
學(xué) 號 26030336
指 導(dǎo) 教 師 黃 開 友
MULTI-OBJECTIVE OPTIMAL FIXTURE LAYOUT
DESIGN IN A DISCRETE DOMAIN
Diana Pelinescu and Michael Yu Wang
Department of Mechanical Engineering
University of Maryland
College Park, MD 20742 USA
E-mail: yuwang@eng.umd.edu
Abstract
This paper addresses a major issue in fixture layout design:to evaluate the acceptable fixture designs based on several quality criteria and to select an optimal fixture appropriate with practical demands. The performance objectives considered are related to the fundamental requirements of kinematic localization and total fixturing (form-closure) and are defined as the workpiece localization accuracy and the norm and distribution of the locator contact forces. An efficient interchange algorithm is uaed in a multiple-criteria optimization process for different practical cases, leading to proper trade-off strategies for performing fixture synthesis.
I. INTRODUCTION
Proper fixture design is crucial to product quality in terms of precision and accuracy in part fabrication and assembly. Fixturing systems, usually consisting of clamps and locators, must be capable to assure certain quality performances, besides of positioning and holding the workpiece throughout all the machining operations. Although there are a few design guidelines such as 3-2-1 rule, automated systems for designing fixtures based on CAD models have been slow to evolve.
This article describes a research approach to automated design of a class of fixtures for 3D workpieces. The parts considered to be fixtured present an arbitrary complex geometry, and the designed fixtures are limited to the minimum number of elements required, i.e. six locators and a clamp. Furthermore, the fixels are modeled as non-frictional point contacts and are restricted to be applied within a given collection of discrete candidate locations. In general, the set of fixture locations available is assumed to be a potentially very large collection; for example, the locations might be generated by discretizing
the exterior surfaces of the workpiece. The goal of the fixture design is to determine first, from the proposed discrete domain, the feasible fixture configurations that satisfy the form-closure constraint. Secondly, the sets of acceptable fixture designs are evaluated on several criteria and optimal fixtures are selected. The performance measures considered in this work are the localization accuracy, and the norm and distribution of the locator contact forces. These objectives cover the most critical error sources encountered in a fixture design, the position errors and the unwanted stress in the part-fixture elements due to an overloaded or unbalanced force system.
The optimal fixture design approach is based on a concept of optimum experiment design. The algorithm developed evaluates efficiently the admissible designs exploiting the recursive properties in localization and force analysis. The algorithm produces the optimal fixture design that meets a set of multiple performance requirements.
II. RELATED WORK
Literature on general fixturing techniques is substantial, e.g., [1]. The essential requirement of fixturing is the century-old concept of form closure [2], which has been
extensively studied in the field of robotics in recent years [3, 4]. There are several formal methods for analyzing performance of a given fixture based on the popular screw theory, dealing with issues such as kinematic closure [5], contact types and friction effects [6]. A different analysis approach based on the geometric perturbation technique was reported in [7]. An automatic modular fixture design procedure based on this method was developed in [8] to include geometric access constraints in addition to kinematic closure. The problem of designing modular fixtures gained more attention lately [9]. There has also been extensive research in fixture designs, focusing on workpiece and fixture structural
rigidity [6], tool accessibility and path clearance [7]. The problem of fixture synthesis has been largely studied for the case of a fixed number of fixture elements (or fixels) [8, 10], particularly in the application to robotic manipulation and grasping for its obvious easons [3, 4]. This article aims to be an extension of the results on the fixture design issues previously reported in [14].
III. FIXTURE MODEL
The fundamental performance of a fixture is characterized by the kinematic constraints imposed on the workpiece being held by the fixture. The kinematic conditions are well understood [3, 4, 5, 7, 12]. For a fixture of n locators (i = 1, 2, … , n), the fixture can be represented by:
dy=GTdq
where define small perturbations in the locator positions and the location of the workpiece respectively. The fixture design
is defined by the locator matrixi where and ni and ri denote the surface normal and position at the ith contact point on the workpiece surface. The problem of fixture design requires the synthesis of a fixturing scheme to meet a given set of performance requirements.
IV. QUALITY PERFORMANCE CRITERIA FOR A FIXTURE
A. Accurate Localization
An essential aspect of fixture quality is to position with precision the workpiece into the fixturing system. In general the workpiece positional errors are due to the geometric variability of the part and the locators set-up errors. This paper will focus only on the workpiece positional errors due to the locator positioning errors. As an extension of the fixture model equation (eq.1), the locator positioning errors dy can be related with the workpiece localization error dq as follows:
Clearly, for given source errors the workpiece positional accuracy depends only on the locator locations being independent from the clamping system, the Fisher information matrix M = GGT characterizing completely the system errors. It has been shown [12] that a suitable criterion to achieve high localization accuracy is to maximize the determinant of the information matrix (Doptimality), i.e., max(det M).
B. Minimal Locator Contact Forces
Another objective in planning a fixture layout might be to minimize all support forces at the locator contact regions throughout all the operations with complete kinematic restraint or force-closure. Locator contact forces in response to the clamping action are given as:
Normalizing these forces with respect to the clamping intensity we obtain:
The force-closure condition requires these forces to be always positive for each locator i of a set of n locators:
Computing the norm of the locator contact forces:
leads to an appropriate design objective, i.e. min
Note that this objective indicates both locator and clamp positions to be determined in the optimization process.
C. Balanced Locator Contact Forces
Another significant issue in designing a fixture is that the total force acting on the workpiece have to be distributed as uniformly as possible among the locator contact
regions. If p represents the mean reactive force in response to the clamp action, then we define the dispersion of the locator contact forces as:
Therefore, minimizing the defined dispersion represents an objective for a balanced force-closure: min(d).
V. OPTIMAL FIXTURE DESIGN WITH INTERCHANGE ALGORITHMS
As mentioned earlier, by generating on the exterior surface of the workpiece to be fixtured a set of discrete locations defined as position and orientation, we create a potential collection for the fixture elements. For example, using the information contained in the part CAD model, a discrete vector collection (unitary, normal vectors) can be generated as uniformly as possible on those surfaces accessible to the fixture components (fig.1).
Figure 1: Part CAD model and global collection of candidate locations for the fixture elements.
The fixture design layout will select from this collection optimal candidates for locators and clamps with respect to the performance objectives and to the kinematic closure condition. Dealing with a large number of candidate locations the task of selecting an appropriate set of fixels is very complex.
As already introduced in [12, 14] an effective method for finding the desired fixture with regard to one of the previous quality objectives is the optimal pursuit method with an interchange algorithm. Due to its own limitations and to the fact that the objectives are functions with many extremes, the exchange procedure may not end up to a unique optimized fixture configuration, but to several improved designs depending on the initial layout. Therefore the solution offered by the multiple interchange with random initialization algorithm is overwhelming favorable, fact that recommends this procedure over the single interchange algorithms. The algorithm can be described as a sequence of three phases:
Phase 1: Random generation of initial sets of locators.
The starting layout is generated by a random selection of distinct sets, each consisting from 6 locators out of the list of N candidate locations. If the clamp is pre-determined, a
valid selection is obtained through a simultaneous check for all kinematic constraints. A big initial set of proposed ocators is preferred, giving the opportunity of finding a convergent optimal solution. However from the efficiency point of view the designer has to balance the algorithm between the accuracy of the final solution and the computation time.
Phase 2: Improvement by interchange.
The interchange algorithm's goal is to pursue for an improvement of the initial sets of locators with respect to one of the objectives. Basically, this is done iteratively by exchanging one by one the proposed locators with candidate locations from the global collection. It is also essential to consider the form-closure restraint during the exchange procedure. The process will continue as long as an improvement of the objective function is registered. Studying the effect of interchange on the proposed quality measures leads us to some efficient algebraic properties. For example, an interchange between a current locator j (j = 1,2,…,6) and a candidate location k (k = 1,2, … ,N-6) yields changes in the optimized function such that:
Thus, at each interchange the pair is selected such that the significant term that controls the function evolution is improving, e.g. max p 2jk and min Δpc , easing the iterative process.
Phase 3: Selecting the optimal solution.
Applying the interchange algorithm for each initial set of locators we will end up with several distinct solutions on the configuration scheme of the fixture, the best fixture design corresponds evidently to the maximum improvement of the objective function. It should be emphasized that this algorithm can be used sequentially for different objective functions. Depending on the objective pursued the best solution can be evident (for a single objective) or might need the designer's final decision (for multiple objectives).
VI. MULTI-OBJECTIVE FIXTURE LOCATOR OPTIMIZATION
In many applications the clamp is already fixed given some practical considerations. Then with the clamp predefined, the best fixture with respect to a certain performance criterion is constructed by selecting a suitable set of locators such that a significant improvement of the objective-function is registered. Using the random interchange algorithm we can analyze the impact of the optimization process on the fixture characteristics, as well as we can select the best optimized fixture solution for a specific criterion. In analyzing the effect of random interchange algorithm on several parts, there can be made the following statistical and empirical observations.
A. Multi-objective trade-offs
In some applications both localization quality and a minimum force dispersion are important. In this case we may have to use a 2-step algorithm: first max(det M) and secondly min(d). The proposed order is a consequence of the above observations. First, maximizing the determinant will automatically decrease the dispersion. Next, a decreasing in dispersion leads in a decreasing in determinant value. Therefore, during the second phase of the algorithm tradeoffs between the two objectives occur. To solve the multi-objective optimization problem the interchange algorithm is applied successively for both objectives. With the clamp pre-defined, a rigorous check for form-closure is needed after each exchange step.
A following set of plots present the results when the design requirements of precision localization and uniform contact forces are considered simultaneously. Fig. 2 and Fig. 3 illustrate the global changes of the fixture characteristics during the 2-step algorithm performed on an initial collection of distinct random sets of locators, with the clamp pre-fixed. It can be noticed the advantages of using max(det M) objective as a first step: while the determinant is increasing, the norm and the dispersion of the forces are decreasing, fact benefic for the overall quality of the fixture. Furthermore the solutions are convergent, such that the candidate set of locators for the next step will be significantly reduced. On the other hand, in the second phase, when applying min(d) optimization on sets of locators with a high determinant value the only trend in the determinant evolution is a decreasing one. Therefore, during the second phase of the algorithm tradeoffs between the two objectives occur, fact expressed also through the Pareto-line plot (Fig. 3). In this case the final decision has to be left for the designer to determine the best fixture scheme.
Figure 2: Changes upon the fixture characteristics applying the 2-step optimization algorithm on an initial collection of random sets of locators.
Figure 3: Behavior during a 2-step random interchange algorithm for a collection of locator sets.
As an example, the behavior of a single initial set of locators is studied during the interchange processes of the 2-step algorithm (Fig. 4), confirming the previous remarks. The trade-off zone is decisive in the multiobjective design. The resultant configurations of the fixture after each successive phase are presented in Fig. 5. It can be noticed that the first objective moves the locators close to the boundaries as far as possible from each other, while the second one reorients them to the surfaces' interior.
Figure 4: General behavior of a 2-step interchange.
Figure 5: Fixture configurations during a 2-step algorithm: (a) initial, (b) after max(det M), and (c) after min(d) respectively.
B. Designer decision in finalizing the fixture
During the second phase of the algorithm a fairly significant decrease in the determinant value is registered, so few solutions will be acceptable for the multi-objective problem. In order to overcome these problems, an active designer control during min(d) interchange procedure is recommended. Essentially, the modifications consist in controlling the exchange procedure, such that the determinant of the improved locators must be permanently greater than a certain bound, simultaneously with the check for the form-closure condition. Even considering a tight bound for the determinant, more solutions are acceptable for the design than in the uncontrolled min(d) optimization case (fig. 6).
As an example, the behavior of a single set of locators is studied during the interchange process of a 2- step algorithm controlled for two different bounds of the determinant value, emphasizing the fact that in the trade off zone the designer decision is decisive in finalizing the fixture configuration (fig. 7).
Figure 6: Second phase of a 2-step random interchange algorithm: uncontrolled min(d); controlled min(d).
Figure 7: General behavior during a 2-step algorithm applied on a single set of locators. (a) for B1 and (b) for B2.
VII. OPTIMAL FIXTURE CLAMPING
This section deals with a more complicated problem: to search simultaneously for the optimal clamp and locators in order to achieve a required fixture quality. Varying the
clamp, it is obvious that the number of combinations for possible clamp-locators candidates is increasing very much. It will be shown that this problem is manageable
for the precise localization objective. For the other objectives we will have to restrain the search of the optimal clamp inside of a small set of proposed locations, such that the optimization procedure could be handled.
A. Optimal Clamp from a Set of Clamps
In some applications the clamps have certain preferred locations, therefore the need to choose the best clamp from a proposed collection might be raised. For example, let's consider that a collection of preferred clamps is given, and an optimal fixture design with respect to the highly precise localization objective is needed. It is obvious that applying a random interchange procedure successively for each clamp, we find optimal fixture configurations for each specified clamp. Comparing the determinant values offered by these fixture schemes (fig. 8), we end up by selecting an optimal clamp and its corresponding locators, constructing the best- improved fixture design (fig. 9).
Figure 8: Clamp selection from a collection of clamps for single-objective design.
Figure 9: The initial collection of proposed clamps; the best clamp and the corresponding locators.
B. Optimal Clamp from a Set of Clamps
Furthermore, by extension, the selection of the optimal clamp from a set of proposed locations with regard to the multi-objective design problem can be considered. It consists of mainly applying the random 2-step interchange algorithm consecutively for each proposed clamp.
By collecting the results after applying this procedure for all the clamps, we can compare their different behavior, and select the most appropriate one. It is obvious that an optimal clamp allows only small fluctuations of the determinant while the force dispersion is decreasing significantly (fig. 10). As an example, Fig. 11 illustrates the final fixture design consisting of the best clamp selected from a proposed collection with respect to the multi-objectives and the corresponding optimal locators.
Figure 11: The initial collection of proposed clamps; the best clamp and the corresponding locators.
VIII. CONCLUSIONS
This article focuses on optimal design of fixture layout for 3D workpieces with an optimal random interchange algorithm. The quality objectives considered include accurate workpiece localization, minimal and balanced contact forces. The paper focuses on multi-criteria optimal design with a hierarchical approach and a combined-objective approach. The optimization processes make use of an efficient interchange algorithm. Examples are used to illustrate empirical observations with respect to the design approaches and their effectiveness.
The work described here is yet complete. Since the inter-relationship between the locators and the clamps has a determinant role on the fixture quality measures, a more coherent and complete approach to study the influence of the clamp and search of the optimal clamp position is needed in future works.
IX. REFERENCES
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[3] B. Mishra, J. T. Schwartz, and M. Sharir, "On the existence and synthesis of multifinger positive grips", Robotics Report 89, Courant Institute of Mathematical Sciences, New York University, 1986.
[4] X. Markenscoff, L. Ni, and C. H. Papadimitriou, "The geometry of grasping", International Journal of Robotics Research, vol. 9, no. 1, pp. 61-74, 1990.
[5] Y.-C. Chou, V. Chandru, and M. M. Barash, "A mathematical approach to automate