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數(shù)控車薄片件夾具及加工
李宏
(廣東機(jī)電職業(yè)技術(shù)學(xué)院廣東廣州510515)
摘要:本文就薄片工件在加工中存在的裝夾、車劉方法、面表高光.及車刀選擇的技術(shù)問越，就自己在實(shí)際加工中的夾具設(shè)計(jì)，加工方法及刁其選擇解決問題方面，作一敘述。
關(guān)健詞:數(shù)拉車床;薄片件;夾具;加工;刀具
引言
利用數(shù)控車床加工薄片零件，因裝夾問題經(jīng)常需要設(shè)計(jì)加工夾具及根據(jù)圖紙要求選擇合理的刀具。如(圖一)所示，材料為防銹鋁合金(LFS)，外徑8100毫米，內(nèi)徑a34毫米.片厚僅4毫米。為音箱裝飾圈，
技術(shù)要求:(1)R4的圓弧面、內(nèi)孔及斜口位高光; (2)表面無刮傷和毛刺; (3)其它面噴細(xì)砂氧化香檳金色。
工件的毛坯尺寸，厚度4.5毫米，中間有一直徑為32毫米的孔，外徑為102毫米，在半徑44毫米處均布4個(gè)直徑4.5毫米的孔的薄圈，用沖床一次沖出。
2.難度分析及工藝流程分析
2.1從零件圖樣要求及材料來看，主要因?yàn)槭潜∑慵浜穸葍H有4毫米，材料為鋁合金，硬度不高，并且批量較大，既要考慮如何保證工件在加工時(shí)的定位精度，又要考慮裝夾方便、可靠、并且不能損傷表面，因此關(guān)鍵是解決零件的定位裝夾問題。
2.2根據(jù)零件圖樣，經(jīng)過工藝分析后，制定出以下加工工藝流程:
2.2.1沖床下料
2.2.2銑床銑R4的圈弧深為2毫米
2.2.3數(shù)控車床車平一側(cè)端面控制厚度4毫米
2.2.4表面噴細(xì)砂氧化香檳金色
2.2.5數(shù)控車床車R4弧面和直徑88毫米的外圓
2.2.6數(shù)控車床惶內(nèi)孔直徑34毫米和孔口直徑39毫米斜口位。
從上述工藝流程來看，在第S步加工時(shí)，如用一般三爪撐著內(nèi)孔的裝夾方法來加工，因?yàn)椴牧陷^薄，車削受力點(diǎn)與加緊力作用點(diǎn)相對(duì)較遠(yuǎn)，剛性不足，引起讓刀和展動(dòng)，而造成R4的圓弧及直徑88毫米處外圓的表面達(dá)不到要求。在第6步加工時(shí)，因?yàn)橐约庸ち薘4的圓弧面，表面不允許劃傷，不可以再裝夾了，就算可以裝夾也會(huì)因?yàn)閯傂圆蛔愕脑蛟斐蓛?nèi)孔和斜口位表面達(dá)不到要求。因此在這兩步加工工序中要考慮如何裝夾定位的問題。
3.夾其設(shè)計(jì)
如何保證零件定位準(zhǔn)確、裝夾方便和加緊可靠呢?根據(jù)運(yùn)動(dòng)學(xué)可知，剛體在空間的任何運(yùn)動(dòng)都可看成是相對(duì)于三個(gè)互相垂直的坐標(biāo)平面，共有六種運(yùn)動(dòng)合成。這六種運(yùn)動(dòng)的可能性稱為六個(gè)自由度·要使工件在空間處于相對(duì)固定不變的位里，就必須限制六個(gè)自由度。限制的方法，用相當(dāng)于六個(gè)支承點(diǎn)的定位元件與工件定位基準(zhǔn)面接觸來限制。我根據(jù)工藝流程的分析經(jīng)過一番考慮.決定該工件采用一面兩銷的定位方案，因一面兩銷定位具有支承面大，支承鋼度好，定位精度高，裝卸工件方便等優(yōu)點(diǎn)，夾具體平面為第一定位基準(zhǔn)，限制了工件的三個(gè)自由度;圓銷為第二定位基準(zhǔn)，限制了工件的兩個(gè)自由度;另一個(gè)根據(jù)六點(diǎn)定位原理，在實(shí)際中我設(shè)計(jì)了如(圖二)所示夾具。
3.1夾具結(jié)構(gòu)(圖二)在第5步用數(shù)控車床車R4弧面和直徑BS毫米的外回時(shí).設(shè)計(jì)了如(圖二)所示的夾具:
3.1.1件1為夾具主體，材料為A3鋼板.最大直徑為I00趕米的臺(tái)階型工件; 3.1.2件2為定位銷，材料為45號(hào)鋼，直徑為4.45毫米，4個(gè)定位銷圓周均布，剛好與薄片工件上的4個(gè)直徑4.5毫米的孔對(duì)應(yīng)配合，使工件在夾具中定位及傳遞切削力;
3.1.3件4,5,6為改裝特制后的壓板組合休，其中件4為軟膠板，直徑80毫米，厚度3毫米，件5用A3鋼板制成，直徑80毫米，厚度l2毫米，件6為活動(dòng)頂尖，件4與件5用強(qiáng)力貓結(jié)劑粘合，然后在與件6的活動(dòng)頂尖頭聯(lián)接并在聯(lián)接處焊接固定。
3.2零件定位裝夾方法及原理(圖二)件1夾持在數(shù)控車床的三爪卡盤上.臺(tái)階處靠卡爪，用百分表打表校正夾具體的外圓及端面，本夾具體以右端面為基準(zhǔn)定位，限制了三個(gè)自由度;工件3的4個(gè)直徑4.5毫米的孔與夾具體上的4個(gè)定位銷對(duì)正套人，一個(gè)定位銷限制了兩個(gè)自由度，對(duì)稱的一個(gè)定位銷限制另一自由度，另兩個(gè)定位銷重復(fù)限制了兩個(gè)自由度，從六點(diǎn)定位原理來看，以上定位出現(xiàn)了重復(fù)定位，但因?yàn)楣ぜ系母鞫ㄎ豢缀蛫A具定位銷的中心距精度很高，為了提高定位支承的穩(wěn)定性，采用了一面四銷定位，通過實(shí)踐加工證明，這樣的
重復(fù)定位可以相容。工件在夾具中定位后一般應(yīng)加緊，使工件在加工過程中保持已獲得的定位不被破壞，本夾具通過壓板壓峨(尾座).使工件3得到較好的定位和夾緊。
3.3夾具結(jié)構(gòu)在第6步用數(shù)控車床車內(nèi)孔直徑34毫米和孔口直徑39毫米斜口位時(shí)，設(shè)計(jì)了夾具:
3.3.1件I為夾具的主體，用A3鋼板制成，最大直徑為200毫米，厚度為20毫米的圓餅型工件，右端面有一直徑36毫米，深為7毫米的孔(零件在惶孔時(shí)以便鎮(zhèn)孔刀可以徨通孔).左端面有一直徑170毫米，深為IO毫米的孔(可用正爪撐夾);
3.3.2件6為定位銷，材料為45號(hào)鋼，直徑為4.45毫米，4個(gè)定位銷圓周均布;
3.3.3件4為軟膠板，外回直徑88毫米.內(nèi)孔直徑勸毫米，厚度1毫米，件5為壓板，用A3鋼板制成，最大直徑為170毫米，厚度為12毫米，中間有一錐孔，小端直徑40毫米，大端直徑70毫米左右.件4與件5用強(qiáng)力貓結(jié)劑粘合;
3.3.4件3為螺絲(對(duì)稱兩個(gè))中心距120毫米，用于件1夾具主體與件5壓板的聯(lián)接。
3.4零件定位裝夾方法及原理件1夾具主體在數(shù)控車床的三卡盤上用反爪夾持，靠卡爪臺(tái)階處，用百分表打表校正夾具體的外圈及端面.本夾具體以右端面為基準(zhǔn)定位，限制了三個(gè)自由度;工件2的4個(gè)直徑4.5毫米的孔與夾具體上的4個(gè)定位銷對(duì)正套人，一個(gè)定位銷限制了兩個(gè)自由度，對(duì)稱的一個(gè)定位銷限制另一自由度，另兩個(gè)定位銷重復(fù)限制了兩個(gè)自由度，從六點(diǎn)定位原理來看.以上定位出現(xiàn)了重復(fù)定位，但因?yàn)楣ぜ系母鞫ㄎ豢缀蛫A具定位銷的中心距精度很高，為了提高定位支承的穩(wěn)定性，采用了一面四銷定位，通過實(shí)踐加工證明，這樣的重復(fù)定位可以相容。工件在夾具中定位后一般應(yīng)加緊，使工件在加工過程中保持已獲得的定位不被破壞，本夾具通過螺絲將壓板連接夾具主體，用壓板壓緊，使工件2得到較好的定位和夾緊。
4.實(shí)際操作
4.1切削用盤及走刀路線選擇
4.1.1外圓粗車時(shí)，主軸轉(zhuǎn)速每分鐘1100-1200轉(zhuǎn)，進(jìn)給速度F200-F350，反偏刀橫裝與刀架上，采用橫向走刀一次加工完成，留梢車余量0.1-0.2毫米。
4.1.2外圓精車時(shí)，主軸轉(zhuǎn)速每分鐘1100-1200轉(zhuǎn)，為取得較好的表面粗糙度選用較低的進(jìn)給速度F30-F45，采用縱向走刀一次加工完成。
4.1.3內(nèi)孔及斜口粗車時(shí)，主軸轉(zhuǎn)速每分鐘1100-1200轉(zhuǎn)，進(jìn)給速度F200-F350,采用橫向走刀由里向外一次加工完成.留精車余量0.1-0.2毫米。
4_1.4內(nèi)孔及料口精車時(shí).主軸轉(zhuǎn)速每分鐘1100-1200轉(zhuǎn)。進(jìn)給速度F30-F45，采用縱向走刀由外向里一次加工完成。
4.2零件加工時(shí)的特殊處理
4.2.1見(圖一)中A,B兩處的倒角去毛刺利用刀具的固有幾何形狀輕碰0.3-0.5毫米。
4.2.2所有刀具均無卷屑植，切屑能順前刀面排離工件，以防切屑纏繞工件而刮傷加工表面。
4.3加工時(shí)的注意事項(xiàng)
4.3.1工件要夾緊，以防在車削時(shí)打滑飛出傷人和扎刀;
4.3.2在車削時(shí)要加注柴油潤(rùn)滑冷卻，以防沮度過高燒壞刀具，使加工表面大不到要求;
4.3.3遵守安全文明生產(chǎn)。
5.結(jié)束
通過實(shí)際加工生產(chǎn).證明加工生產(chǎn)工藝流程、夾具設(shè)計(jì)、刀共及切削用量選用合理.減少了裝夾校正的時(shí)間.減輕了操作者的勞動(dòng)雙度，提高效率.保證了加工后零件的質(zhì)f,平均兩臺(tái)數(shù)控車床每周可加工成品五千件左右。
.考文欲
[1]張恩生主編:《車工實(shí)用技術(shù)手冊(cè)》，江蘇科學(xué)技術(shù)出版社.1999.
f2〕白成軒主編:《機(jī)床夾具設(shè)計(jì)新原理》，機(jī)械工業(yè)出版社.1997.
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(dòng)化
學(xué) 生 姓 名 王 曉 雄
班 級(jí) 機(jī)本0303班
學(xué) 號(hào) 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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