方向機殼鉆夾具設計【鉆4-φ13孔】【說明書+CAD】

方向機殼鉆夾具設計【鉆4-φ13孔】【說明書+CAD】,鉆4-φ13孔,說明書+CAD,方向機殼鉆夾具設計【鉆4-φ13孔】【說明書+CAD】,方向,機殼,夾具,設計,13,說明書,CAD 蘇州職業(yè)大學畢業(yè)設計 序 言 隨著我國機械工業(yè)技術的迅速發(fā)展，制造技術已成為當代科學技術發(fā)展最為重要的領域之一，它是產(chǎn)品更新，生產(chǎn)發(fā)展，市場競爭的重要的手段。從一定意義上講，機械制造技術的發(fā)展水平?jīng)Q定著其它產(chǎn)業(yè)的發(fā)展水平。而夾具成為加工的重要基礎。所以夾具的發(fā)展將嚴重影響我國機械制造及加工水平。 我這次所設計的是一種方向機殼體的鉆夾具。它是專門為HFC方向機殼體的鉆孔工序設計的專用夾具。工件在夾具當中的定位和夾緊，夾具在機床上的定位，及機床的選擇在設計說明書當中都有詳細的說明。 本書在自己的努力和指導老師及同學的幫助下，通過查閱大量的相關資料。使得這次課程設計得到圓滿的成功。在此對他們表示衷心的感謝。由于我的水平有限，在設計當中難免有不足之處，還請各位老師多多的指導。 編者：施蕓 目 錄 一、設計目的﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍4 二、機床的選擇﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍5 三、鉆床夾具的選擇﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍6 四、鉆模板的選擇﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍7 五、鉆套的選擇﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍8 六、鉆套導引孔尺寸和公差的確定﹍﹍﹍﹍﹍﹍﹍﹍10 七、鉆套高度及鉆套與工件距離﹍﹍﹍﹍﹍﹍﹍﹍﹍11 八、工件在夾具中的定位﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍12 九、定位誤差的分析與計算﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍18 十、工件的夾緊﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍20 小節(jié)﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍22 參考文獻﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍﹍23 一、設計目的 為了安裝需要，要在HFC方向機殼體側面上鉆四個Φ13的孔。工件如下圖。因為沒有現(xiàn)成的夾具可用，所以特為此道工序設計一個夾具。 二、機床的選擇 根據(jù)所須加工孔的孔徑，其基本尺寸為φ13的四個孔。適合該機床的主要有三種機床，數(shù)據(jù)如下： 型 號 最大鉆削直徑 主軸端面至工作臺最大距離 工作臺面積 主 軸 孔莫氏錐度號 最大行 程 轉 速 Z518 18 600 350×350 2 145 330-3040 ZQ4015 15 475 250×300 2 100 480-4100 Z535 35 750 450×500 4 225 68-1100 考慮到工件的裝卸，及工作臺的面積，經(jīng)各方面的比較，決定采用Z535立式鉆床。 三、鉆床夾具的選擇 鉆床夾具的類型很多，根據(jù)被加工孔的分布情況可分為： a 固定式鉆模： 這類鉆模在使用過程當中，是固定在鉆床的工作臺面上的，但用于立式鉆床時一般只能加工單孔。 b 回轉式鉆模： 用于加工分布在同一圓周上的徑向孔系，或加工工件上同一圓周上的平行孔系。 c 翻轉式鉆模： 這類鉆模沒有轉軸和分度裝置。在使用過程當中需要用手進行翻轉。主要加工小型工件上分布幾個方向上的孔。 d 蓋板式鉆模： 這類鉆模沒有夾具體，鉆模板上除了鉆套以外，還有定位元件和夾緊裝置。加工時，鉆模板象蓋子一樣覆蓋在工件上。 e 滑柱式鉆模： 這是一種帶有升降鉆模板的通用可調夾具。 根據(jù)工件的特殊構造，決定采用蓋板式鉆模。它的特點是結構簡單輕巧，清除切屑方便。對于體積大而笨重工件的小孔的加工，采用蓋板式鉆模最為適宜。對于中小批生產(chǎn)，凡鉆鉸后立即進行倒角，等工序時，采用蓋板式鉆模也極為方便。但蓋板式鉆模每次需要從工件上裝卸，比較費事，所以不宜用于大批大量生產(chǎn)。 四、 選擇鉆模板 鉆模板是供安裝鉆套用的。要求具有一定的強度和剛度，以防止由于變形而影響鉆套的位置精度和導向精度。 常用的有以下幾種： a固定式鉆模板： 直接固定在夾具體上，而不可移動的。因此所獲得的位置精度高，但裝卸工件不是很方便。 b鉸鏈式鉆模板： 鉆模板與夾具為鉸鏈連接。由于鉸鏈處必然有間隙，因而加工孔的位置精度比固定式鉆模低。 c可卸式鉆模板： 當裝卸工件必須將鉆模板取下，則應采取可卸式鉆模板。但由于裝卸鉆模板比較的費時費力，且鉆孔的位置精度較低，故一般在使用其他類型鉆模板不便于安裝工件時采用。 d懸掛式鉆模板： 該鉆模板適用于大批大量生產(chǎn)中鉆削同一方向上的平行孔系，可在立式鉆床上配合多軸傳動或在組合機床上使用。 由于該工件構造獨特，所需要加工的孔的位置精度不是很高，且是小批量的生產(chǎn)。故決定采用可卸式鉆模板。 五、 鉆套的選擇 在鉆床夾具當中，通常是用鉆套實現(xiàn)刀具的對準，加工中只需要將鉆頭對準鉆套，所鉆孔的位置精度就能達到工序要求。當然鉆套還有增強刀具剛度的作用。 由于是加工同一平面上的不同位置的相同尺寸孔，故只需要選用一種鉆套。 鉆套的四種形式： a固定式鉆套： 固定式鉆套分為A型無肩的，B型有肩的。帶肩的主要用于鉆模板較薄時，用以保持鉆套必要的導引長度。鉆套外圓以H7/r6或H7/n6配合直接壓入夾具體或鉆模板中這種鉆套的缺點是磨損后不易更換，因此主要用于中小批生產(chǎn)用的鉆床夾具上或用來加工孔距小和孔距精度要求較高的孔。為防止切屑進入鉆套孔內，鉆套的上下端應以稍突出鉆模板為宜，一般不能低于鉆模板。 b可換鉆套： 可換鉆套的實際功用和固定鉆套一樣，在批量較大時，磨損后可立即更換。為了避免鉆模板的磨損，鉆套不直接壓配在夾具體或鉆模板，而是以H7/g6或H6/g5的配合裝進襯套的內孔中，并用防轉螺釘防止在加工過程中刀具、切屑與鉆套內孔的摩擦力使鉆套產(chǎn)生轉動，或退刀時隨刀具抬起，襯套外圓與夾具體或鉆模板的配合采用H7/n6或H7/r6。 c 快換鉆套： 快換鉆套是供同一個孔需經(jīng)多個加工工步所用的。由于在加工過程當中，需要依次更換，取出鉆套，以適應不同加工刀具的需要，宜采用快換鉆套。 d 特殊鉆套： 是根據(jù)具體情況自行設計的，以補充標準鉆套性能的不足。 經(jīng)過比較，結合工件的結構，決定采用固定鉆套的A型無肩鉆套。（數(shù)量為四個） 六、鉆套導引孔尺寸和公差的確定 在選用標準結構的鉆套時，鉆套導引孔的尺寸與公差需要由下面原則確定： 1） 鉆套導引孔直徑的基本尺寸，應等于所導引刀具的最大極限尺寸，以防止卡住和咬死。 2） 鉆套導引孔與刀具的配合，應按基軸制選用，這是因為這類刀具的結構和尺寸均已標準化。 3） 鉆套導引孔與刀具之間應保證有一定的配合間隙，以防卡死。導引孔的公差帶根據(jù)所導引刀具的種類和加工精度要求選定，鉆孔和擴孔選F7，F(xiàn)8；粗較時選G7；精較是選G6。 4） 標準鉆頭的最大尺寸就是所加工孔的基本尺寸，故鉆頭導引孔的基本尺寸與加工孔的基本尺寸相同，公差取F7。 5） 若刀具加工時不是用切削部分而是用導柱部分引導，則可按基孔制的相應配合H7/f7，H7/g6，或H6/g5選取。 故鉆套導引孔的基本尺寸與所加工孔的基本尺寸相同，公差取F7。 七、鉆套高度選擇和鉆套與工件距離 1） 鉆套高度 鉆套高度由孔距精度、工件材料、孔加工精度、刀具耐用度、工件表面形狀等因素決定。鉆孔距精度在±0.25mm或是自由尺寸公差時，鉆套的高度取H=（1.5～2.5）d。鉆套內徑采用基軸制F8的公差。所以H=（1.5～2.5）d=（1.5～2.5）×13=19.5～32.5mm 加工IT6～IT7級精度，孔距在12mm以上的孔或加工工件孔距精度要求在±0.10～±0.15mm時，鉆套的高度取H=（2.5～3.5）d鉆套內徑采用基軸制G7的公差。 H=（2.5～2）d=（2.5～3.5）×13=32.5～45.5mm 由于該零件加工孔精度不怎么高，故鉆套高度取27mm. 2） 鉆套與工件的距離 鉆套與工件間留有一定的距離h，如果h太大會增大鉆頭的傾斜量使鉆套不能很好的導向。h過小，切屑排出困難，不僅會增大工件加工表面的粗糙度，有時還可能將鉆頭折斷。 H值可按下面經(jīng)驗公式選?。? 加工鑄鐵、黃銅時，h=（0.3～0.7）d； 加工鋼件時，h=（0.7～1.5）d； 由于工件是鑄鐵，故取 h=（0.3～0.7）d=（0.3～0.7）×13=3.9～9.1mm取7.5mm。 八、工件在夾具中的定位 1 工件定位原理 目前一般習慣上把工件定位范疇內的位置不確定性稱為自由度。由于工件在空間直角中，有六個方向的不定度，限制工件在某一方向的不定度，工件在夾具中某一方向的位置就可以確定。工件在夾具中定位的任務就是通過定位元件限制工件的不定度。以滿足工序的加工精度要求，工件在夾具中的定位通常有四種分別如下： A 完全定位：工件在夾具中，六個不定度都被限制，稱為完全定位。 B 部分定位：六個不定度沒有被完全限制時稱為部分定位。 C 欠定位：工件實際限制的自由度少于工序加工要求應予以限制的不定度的個數(shù)，產(chǎn)生定位不足現(xiàn)象稱欠定位。 D 重復定位：工件在夾具中定位，若幾個定位支承點重復限制同一個或幾個不定度時，稱重復定位。一般來說：對工件上形狀精度和位置精度很底的毛坯表面作為定位表面時，是不允許出現(xiàn)重復定位的。對于用已加工過的工件表面或精度較高的毛坯表面作為定位表面時，為提高工件定位的穩(wěn)定性和剛度，在一定的條件下是允許采用重復定位的。 2 確定定位方案 根據(jù)零件的特殊結構及已加工的的各個表面。具體的方案如下： 1） 工件應限制的自由度： X ，Y 方向的移動自由度，X， Y ，Z方向的轉動自由度。 2） a以已加工的底面為基準面，限制 X ，Y方向的轉動自由度，Z方向的移動自由度。 b 以中間孔套入一根長芯軸，限制X， Y方向的轉動和移動自由度。 c 以后面的已加工的孔為基準套入一定位軸，限制Z 方向的自由度。 所以出現(xiàn)了重復定位的情況。但由于是采用已加工面為基準，所以對該定位方案是合理的。 3 定位元件的選擇與設計 工件在夾具中位置的確定，主要是通過各種類型的定位元件實現(xiàn)的。一般的定位元件有： 1） 平面定位元件：固定支承、可調支承、自位支承、輔助支承 固定支承：支承點的位置固定不變的定位元件。如各種固定支承釘。 可調支承：支承點的位置可調節(jié)的定位元件。如可擰動的螺釘。 自位支承：支承點的位置在工件定位過程當中，隨工件定位基準面位置變化而自動與之相適應的定位元件（如球面三點式自位支承），這類支承在結構上均需設計成活動或浮動的。 輔助支承：這類支承只起提高工件支承剛性或起輔助作用的定位元件而不起定位作用。 2） 圓孔表面定位元件 這類定位元件常用于圓孔表面。一般定位元件有：定位銷、剛性心軸、錐度心軸等。 3） 外圓表面定位元件 這類定位元件常用于外圓表面定位。一般有：定位套、支承板、V型塊等。 定位套對工件外圓表面主要實現(xiàn)定心定位；支承板實現(xiàn)對外圓表面的支承定位；V型塊則實現(xiàn)對外圓表面的定心對中定位。 4 ）錐面定位元件 主要用于加工軸類零件或某些要求精度定心的零件時，以工件上的錐孔作為定位基準?？商岣吖ぜS向的定位精度。 根據(jù)工件的結構的特殊性，在工件所加工的孔的平面上，該部分類似懸臂梁，受到鉆刀向下的力，及鉆削工件時所引起的扭轉力距和重力的合力的作用。工件受到重力的作用會下垂，而使工件定位基準脫離定位元件。同時還會引起工件的振動，導致刀具的損壞，最終影響加工質量。根據(jù)這一特點，決定采用輔助支承?？梢栽诠ぜ杓庸た椎南虏吭O置輔助支承。先預定位，然后在夾緊力的作用下再實現(xiàn)與主要定位元件全部接觸的準確定位。該支承部件為球面支柱。考慮要加工四個孔，且孔的位置不是對稱的，分布較大，故采用兩個 這樣的支柱，具體如上圖。 對于工件的后部，由于采用了一個定位軸，所以要保證定位軸的定位。決定一端用定位螺釘，一端用壓緊螺釘。 4 導向元件的選擇 導向元件的作用是用來確定刀具與工件的相對位置，起到正確導引刀具的作用。另外還可以當定位元件使用。這類元件包括各種鉆模板、鉆套、鉸套和導向支承等。 1）鉆模板 前面我們已經(jīng)選用了可卸式鉆模板。但普通的可卸式鉆模板還不能滿足我們所加工孔的要求，所以要另外設計。由于所加工的孔是不對稱的兩組平行孔。通過分析發(fā)現(xiàn)它們之間的連線的垂線與中間的孔成164°角。為保證加工時的精度，可以把鉆模板設計成三角形花鍵連接的形式，設計的一個寬鍵齒中心線剛好與這一垂線成164°角?；ㄦI用拉床或插床加工，熱處理后用磨削的方法提高定心面的精度。外三角花鍵齒用銑床加工，熱處理后也可用磨削的方法提高定心面和齒側面的精度。具體設計如下： 三角花鍵 根據(jù)Dg=32 查表6-74內花鍵弧齒槽寬和外花鍵弧齒厚偏差取m=2 齒數(shù)：z=14 模數(shù)：m=2 分度圓：df=dg-2(0.6+ξ)m=32-2(0.6+0.1)×2=29.2mm 齒頂圓直徑：dd= df+2(0.4+ξ)m=29.2+2(0.4+0.1)m=31.2mm 齒根圓直徑: dg=df -2(0.6-ξ)m=29.2-2(0.6-0.1)×2=26.6mm 公稱圓：D=df +2×(0.4+ξ)m=29.2+2×（0.4+0.1）×2=31.2mm 內花鍵齒根圓弧起始點直徑：dq=(z+1.1)m=(14+1.1)2=30.2mm 內花鍵齒槽寬：s=(π/2+2ξtanα)=(3.14/2+tan45°×2×0.1)=3.54 內花鍵齒槽角：β=90°-203°/z=90°-203°/14=76.5° 外花鍵基圓:dj=df+2×(0.4+ξ)m=29.2+2×(0.4+0.1)×2=31.2mm 內花鍵齒根高：h"1=(0.6+ξ)× m=(0.6+0.1)×2=1.4 內花鍵齒頂高：h′1=(0.4-ξ)×m=(0.4-0.1)×2=0.6 外花鍵齒根高：h"=(0.4+ξ)m=(0.4+0.1)×2=1 外花鍵齒頂高：h′=(0.6-ξ)m=(0.6-0.1)×2=1 內花鍵齒頂圓直徑：Dg=df+2×(0.6+ξ)m=29.2+2(0.6+0.1)×2= 32 分度圓周節(jié)：t=πm=3.14×2=6.28 內外表面光潔度的粗糙度必須在3.2～1.6之間。 而芯軸也就設計成相應的情況。具體如下圖： 九、定位誤差的分析與計算 1 定位誤差 定位誤差是由于定位不準而造成某一工序在工序尺寸（通常指加工表面對工序基準的距離尺寸）或位置要求方面的加工誤差。對某一定位方案，經(jīng)分析計算其可能產(chǎn)生的定位誤差，只要小于工件有關尺寸或位置公差的1/3～1/5。一般即認為此定位方案能滿足該工序的加工精度的要求。 工件在夾具中的位置是由定位元件確定的，當工件上的定位表面一旦與夾具上的定位元件接觸或配合，作為一個整體的工件的位置也就確定了。但對于一批工件來說，由于在各個工件的有關表面之間，彼此在尺寸及位置上均有著在公差范圍內的差異。夾具本身和各個定位元件之間也具有一定的尺寸和位置公差。這樣一來，工件雖已定位，但每個被定位元件的某些具體表面都會有自己的位置變動量，從而造成在工序尺寸和位置要求方面的加工誤差。 2 定位誤差的組成及計算方法 定位誤差是指一批工件在用調整法加工時，僅僅由于定位不準而引起工序尺寸或位置要求的最大可能變動范圍。即定位誤差主要是由基準誤差和基準不重合誤差兩項組成。所以在設計夾具時，對任何一個定位方案，可通過一批工件定位時的兩個極端位置，直接計算出工序基準的最大變動范圍，既為該定位方案的定位誤差。 在工件內孔直徑最大而定位銷直徑最小的條件下，當工件相對于定位銷O1O2向上處于最高位置O1且工件外圓尺寸最小時，工序尺寸為最小值Hmin ，當工件相對于定位銷沿OO2 向下處于最底位置O2是工件外圓尺寸最大時，工序尺寸為最大值Hmax,此時工序尺寸H的定位誤差可知： δ定位 =A1A2=Hmax–Hmin=O1O2+1/2d-1/2(d-Td)=O1O2 +1/2Td 根據(jù)定位誤差產(chǎn)生的原因也可按定位誤差的組成進行計算： δ定位=δ位置+δ不重=O1O2 +1/2Td 在工件的裝夾配合當中，由于芯軸與工件采用的是H7/k6過渡配合，故認為O1O2基本為0。所以： δ定位=0.5Td 即為芯軸公差的一半。 十、工件的夾緊 夾緊裝置是保持工件在定位中所獲得的既定位置，以便在切削力，重力，慣性力等外力作用下不發(fā)生移動和振動確保加工質量和生產(chǎn)安全。 1 夾緊裝置的組成 分析該工件的夾緊由于采用蓋板式鉆模板，工件裝卸都必須手動實現(xiàn)且工件的體積和重量不是很大。故在這里采用手動即可實現(xiàn)工件的夾緊。 2 夾緊力的計算 1）夾緊力的方向 由于在整個加工過程是以工件底面為準，鉆模板壓在上面，所以上面可以用螺母直接夾緊。 根據(jù)所加工材料及孔的尺寸查表8-37鉆頭的磨鈍標準及耐用度得 后刀面最大磨損極限：0.5～0.8mm，T=3600 刀具切削速度： V=27.91/51.62=0.52 m/s 查表10-3鉆孔時切削速度計算公式得： Cv=14.7 Zv=0.25 Yv=0.55 m=0.125 f=0.3mm/r 查表10-4 鉆削時軸向力，扭距及功率的計算公式 F=9.81×42.7×13×0.3×1=3471.57N M=9.81×0.021×13×0.3×1 =13.29N·m Pm=2Mv/d=2×13.29/13 =2.04k N 令F =Fw，將Fw向中心簡化,芯軸有軸向力Fw和旋轉力矩T ,當鉆削在如圖的孔時,所受力矩最大,故計算這一個便可: T =FwL=3471.5×157=545000N·mm 預緊力: Fp= kuF/uc=1.2×3471.57/0.15=27800N 根據(jù)芯軸許用應力公式對芯軸來進行校驗: 查表11-6螺栓,螺釘,螺柱和螺母的力學性能等級 = [σ]=σs/s=480/1.5=320 MP D=4×1.3×2.78×10000/3.14×320=12mm 考慮到安全性取M14的螺母。由于橫向載荷較小，在這里不作計算。 設計小結 “不積跬步，無以至千里；不積小流，無以成江河”。這次的設計使我認識到基礎知識積累及實踐的重要。設計中遇到了很多問題，使設計進度舉步維艱，其根本原因還是在于對基礎知識的模糊的理解。現(xiàn)在我認識到低年級時對基礎課的怠慢是多么愚蠢的事?！凹埳系脕斫K覺淺，絕之此事需躬行”以前認為很簡單的事情，做起來發(fā)現(xiàn)并不是那樣。實踐出真知，這次的設計使我認識到了實踐動手的重要性，堅定了我投身制造一線的想法。 然而亡羊補牢未為晚。通過系統(tǒng)復習以前的課程，查閱各種資料，以及向老師和同學尋求幫助，我的畢業(yè)設計終于完稿了。在此我要特別感謝吳彥紅老師，樊十全老師，文建萍老師的悉心指導；感謝方向機廠趙書記和陳師傅的鼎力相助；感謝同學的熱情幫助。當然，由于自身水平有限，不足之處在所難免，敬請各位老師批評指正。 參考文獻 1.機床夾具零部件 第一機械工業(yè)部機床研究所 1965 2.吳克堅主編 機械原理 高等教育出版社 1989 3.劉鴻文主編 材料力學 高等教育出版社 1991 4.吳宗澤主編 機械設計高等教育出版社 1990 5、成大先主編，機械設計手冊 [M] 1994年4月第三版第五卷，化學工業(yè)出版社。 6.林文煥主編 機床夾具設計 中國鐵道出版局 1987 7.王秀倫主編 機床夾具設計 國防工業(yè)出版社 1983 8.編輯委員會編 機械工程手冊 機械工業(yè)出版社 1979 9.李家寶編 夾具設計 機械工業(yè)出版社 1964 10.唐用中編 組合夾具組裝技術 國防工業(yè)出版社 1979 11.長春第一汽車制造廠工裝設計室編 機床夾具設計原理 1976 12.湖南大學機制教研室編 機床夾具 湖南人民出版社 1976 13東北重型機械學院 機床夾具設計手冊 上?？茖W技術出版社1990 14齊民 機械工程材料 大連理工大學出版社2003 15機械工程師手冊第二版編輯委員會 機械工程師手冊 機械工業(yè)出版社 14 ORIGINAL ARTICLEFast collision detection approach to facilitate interactivemodular fixture assembly design in a virtual environmentGaoliang Peng&Xin Hou&Chong Wu&Tianguo Jin&Xutang ZhangReceived: 27 May 2008 /Accepted: 21 April 2009 /Published online: 9 May 2009#Springer-Verlag London Limited 2009Abstract Collision detection is a fundamental componentto simulate realistic and natural object behaviors in virtualreality-based system. In this paper, a hybrid method ofspace decomposition and bounding volume approach ispresented to assist modular fixture assembly design in avirtual environment. Based on characteristics of modularfixture, a novel space decomposition methodology at objectlevel is proposed, which is achieved by automaticallypartitioning the checking space into cells according to theoriented bounding boxes of assembled elements after theinitial approximate collision detection using the intersectionchecking method based on separation plane-based bound-ing box. Then the pairs of candidate objects are determinedfor narrow phase exact polygons overlap tests. Results fromseveral performance tests on modular fixture design systemshow that an important advantage of this proposed methodcompared with other universal algorithms is its simpleinformation representation and low preprocessing cost.Keywords Collisiondetection.Virtualassembly.Modularfixture.Spacedecomposition.Boundingvolume1 IntroductionVirtual reality (VR) became a very common mean duringthe development of the industrial products. The aidprovided by VR is noticeable, since the user can interactwith the virtual prototype in a very natural way 13. VRholds great potential in manufacturing applications to solveproblems before fatal mistakes occur in practical manufac-turing so that great costs are prevented. VR applicationshave gained increasing attention internationally.Fixture design takes a significant part of the total time(cost) necessary for technical and technological productionpreparation. The design of a fixture is a highly complex andintuitive process, which requires knowledge and experience4. Modular fixtures are one of the important aspects ofmanufacturing. Proper fixture design is crucial to productquality with regard to the precision, accuracy, and finish ofthe machined part. Modular fixture is a system ofinterchangeable and highly standardized componentsdesigned to securely and accurately position, hold, andsupport the workpiece throughout the machining process5. Traditionally, fixture designers rely on experiences oruse trial-and-error methods to determine an appropriatefixture scheme.Since the potentially high degree of “reality” experi-enced in a virtual environment (VE), the VR-based modularfixture design has the advantages of designing a fixture in anatural and instructive manner, providing better match tothe working conditions, reducing lead-time, and generallyproviding a significant enhancement to fixture productivityand economy 6. In order to achieve this goal, the VRsystem must be able to simulate realistic and natural objectbehaviors. First of all, as a basic requirement of fixturedesign, there should be no collision between fixture,component and machine tool 7, 8; the objects notInt J Adv Manuf Technol (2010) 46:315328DOI 10.1007/s00170-009-2073-0G. Peng (*):X. Hou:T. Jin:X. ZhangSchool of Mechanical and Electrical Engineering,Harbin Institute of Technology,Harbin, Chinae-mail: C. WuSchool of Management, Harbin Institute of Technology,Harbin, Chinapenetrating into others must be guaranteed. Therefore, a fastinteractive collision detection (CD) algorithm is fundamen-tal in such a VR system.However, collision checking for a complex VE iscomputationally intensive. Researchers have addressedsome “universal” algorithms to reduce the computationalcosts. But these algorithms often need auxiliary datastructures and require intensive preprocessing time cost.In addition, the implementation of such algorithm is verycomplicated. Therefore, based on the well study of modularfixture characteristics and practical requirements, wedevelop a “special” CD algorithm to keep the associatedcosts as low as possible for VR-based modular fixtureassembly design.The paper is organized as follows. A review of relatedwork of the existing CD algorithms is presented inSection 2. Section 3 gives an overview of our proposedalgorithm. In Section 4, we describe the space subdivisionmodel used in our algorithm. Section 5 provides the detailsabout the broad phase of our proposed algorithm, in whichirrelevant objects are discarded and a set of objects that canpossibly collide are determined. The narrow phase for exactpolygon based overlap tests is described in Section 6.Section 7 presents some experimental results of ouralgorithm, and finally, in Section 8, we give concludingremarks and outline directions for future extensions of thiswork.2 Related workDuring the past few years, a great deal of effort has beenmade to solve the CD problem for various types ofinteractive 3D graphics and scenarios. For a workspacefilled with n objects, the most obvious problem is the O(n2)problem of detecting collisions between all objects, whichis time consuming and not bearable if the number n is large.Thus, some necessary techniques are needed to reduce thecomputational costs. Generally, a CD algorithm consists oftwo main steps, namely broad phase and narrow phase 9.The first phase aims to filter out pairs of objects which areimpossible to interact and determine which objects in theentire workspace potentially interact. The second phase isto perform a more accurate test to identify collisionbetween those selected object parts in the first phase,moreover if necessary, to find the pairs of contactingprimitive geometric elements (polygons), and to calculatethe overlapping distance.For a CD algorithm, it is critical to reduce the number ofpairs of objects or primitives that need to be checked.Therefore, a number of different techniques have been usedto make coarse grain detection, among which spacedecomposition and bounding volumes is most popular.In space decomposition methods, the environment issubdivided into space grids using hierarchical spacesubdivision. Objects in the environment are clusteredhierarchically according to the regions that they fall into.These objects are then checked for intersection by testingfor overlapping grid cells exploiting spatial partitioningmethods like Octrees 10, 11, BSP-trees 12, k-d trees13, etc. Using such decompositions in a hierarchicalmanner can further speed up the collision detection processbut leads to extremely high storage requirements.Bounding volume (BV) approach is used in previouscomputer graphics algorithms to speed up computation andrendering process. The BVof a geometric object is a simplevolume enclosing the object. Typically, BV types are axis-aligned boxes (AABBs) 14, spheres 15, and orientedbounding boxes (OBB) 16.Since AABBs method is simple to compute and allowsefficient overlap queries, it is often used in hierarchy, but italso may be a particularly poor approximation of the setthat they bound, leaving large “empty corners.” Thesystems utilizing AABBS include I-COLLIDE 17, Q-COLLIDE 18, and SOLID 19, etc.Bounding sphere is another natural choice to approxi-mate an object as it is particularly simple to test pairs foroverlap, and the update for a moving object is trivial.However, spheres are similar to AABBs as they can be poorapproximations to the convex hull of contained objects.In comparison, an OBB is a rectangular bounding box atarbitrary orientations in 3D space. In an ideal case, theOBB can be repositioned such that it is able to enclose anobject as tightly as possible. In other words, the OBB is thesmallest possible bounding box of arbitrary orientation thatcan enclose the geometry in question. This approach is verygood at performing fast rejection tests. A system calledRAPID 20 for interference detection based on OBB hasbeen built, which approximates geometry better thanAABBs. The shortcomings of OBB-tree against sphere treelie in its slowness to update and orientation sensitive 9.Most CD-related researches are involved in “universal”algorithms, and few literatures are found to develop CDapproach in a special application like virtual assembly.Actually, a fast and interactive collision detection algorithmis fundamental to a virtual assembly environment, whichallows designers to move parts or components to performassembly and disassembly operations.Figueiredo 21 presented a faster algorithm for thebroad and narrow phases of the collision detectionalgorithm of determining precise collisions between surfa-ces of 3D assembly models in virtual prototype environ-ments. The algorithm used the overlapping AABB and theR-tree data structure to improve performance in both thebroad and narrow phases of the collision detection. Thisapproach is for such a VE with objects dispersed in the316Int J Adv Manuf Technol (2010) 46:315328space. In addition, the R-tree data structure is very memoryintensive.Stephane 22 worked on continuous collision detectionmethods and constraints to deal with rigid polyhedralobjects for desktop virtual prototyping. Whereas such a4D method is only useful for handling the path of knownmoving objects. Especially, the algorithm is so computa-tionally intensive that it has to run on high-end computers.Collision detection is a critical problem in multi-axisnumerical control (NC) machining with complex machiningenvironments. There has been much previous work oninterference detection and avoidance in NC machiningsimulation. Wang 23 developed a graphics-assistedcollision detection approach for multi-axis NC machining.In this method, a combination of machining environmentculling and a two-phase collision detection strategy wasused.Researches surveyed above provided various efficienttechniques to carry out collision detection for polygonalmodels. However, these popular algorithms aimed atgeneral polygonal models, most of which need expensivepretreatments or large system memory or both of them inorder to improve the performance and meet real-timerequirements. Therefore, when these algorithms are utilizedin desktop VR application system such as modular fixturedesign, the requirement of real time cannot be wellguaranteed.Few CD researches can be found in the area ofcomputer-aided fixture design. Hu 24 presented analgorithm of fast interference checking between themachining tool and fixture units, as well as between fixtureunits, to replace the visually checked method. Moreover, inKumars work 25, in order to automate interference-freemodular fixture assembly design, the machining interferencedetection is accomplished through the use of cutter-sweptsolid based on cutter-swept volume approach. However,these algorithms are only capable of static interferencechecking and applied in CAD software packages.The research presented in this paper makes a solution tothese issues by addressing a “special” collision detectionalgorithm for VR-based modular fixture design. Theproposed algorithm uses the hybrid approach of spacedecomposition and bounding volume method to get highperformance.3 Algorithm overview3.1 Requirements for proposed algorithmWe aimed to develop a desktop VR-based modular fixtureassembly design system, in which the designer can selectsuitable fixture elements and put them together to generatea fixture structure, like “building blocks.” Without physicalfixture elements, he/she can test different structure schemesand finally design a feasible fixture configuration that meetsthe fixturing function requirements. In order to retain highdegree of “reality” in engineering application, there arethree main requirements for a CD algorithm to performmodular fixture configuration design:1.Precise and fast: During the simulation of assemblyand disassembly operations, finding precise collisionsis an important task for achieving realistic behavior26. When the user interactively assembles a part or acomponent, the “flying” object may collide with staticmodels, thus the system must find out the “colliding”event immediately. The interval between two checkingpoints should be near enough to achieve betterperformance. Otherwise, when objects move very fast,they may appear before checking, which will reduce theimmersive feelings. Therefore, the proposed systemcarries out a CD checking task in each rendering loopof VE. In addition, in modular fixture assembly designprocess, the designer selects elements and assemblesthem to right position or disassembles them to changethe fixture configuration. Once an element is assembledor disassembled, the “static” environment models areupdated. Accordingly, the CD checking model needsrestructure. So the preprocess should not take too long;otherwise, the performance of proposed system will beimpaired severely for certain “smooth feel” cannot beachieved.2.Low system requirements: Finding collisions in a 3Denvironment is time-consuming. In some cases, it caneasily consume up to 50% of the total run time 21.However, in modular fixture design workspace, thereare some other time-consuming tasks, such as designprocess control and reasoning, automatic geometricconstraints recognition and solving, etc. In spite of thecomplexity of the 3D virtual prototypes due tothousands of polygons, the designed CD checkingprocedure must be done in real time with relativelylow system resource demands.3.Low hardware cost: In order to achieve wider engi-neering applications, the proposed modular fixtureassembly system is designed to run on common PClike popular CAD commercial software. Althoughmuch research has engaged in developing hardware-accelerated CD algorithms, which utilize special graph-ic hardware, like graphics processing unit, to deal withthe computing collisions, thus the systems CPU can befreed. Nevertheless, we did not plan to adopt this kindof method and optimize performance only fromsoftware implementation. The objective of this researchis to develop a CD algorithmInt J Adv Manuf Technol (2010) 46:315328317Taking into account all above requirements, unfortunate-ly, these objectives usually are in conflict. To meet theprecise demand, we must increase checking frequencywhich will enormously increase the computational com-plexity and the memory bandwidth requirement. So, howcan a balance be reached with regard to these? In otherwords, how can the utilization of system resources beminimized yet the performance optimized without the helpof extra hardware? It is the start point of our algorithm.3.2 Modular fixture analysisThe objective of this research is to develop a CD algorithmfor assisting in modular fixture assembly design operationsin VE. To simplify the algorithm and to gain highperformance, the characteristics of modular fixture shouldbe well studied.1.Process of modular fixture assembly design: The tasksof modular fixture assembly design are to select theproper fixture elements and assemble them to aconfiguration one by one according to the designedfixturing plan. Thus, the CD problem in VR-basedmodular fixture assembly design can be stated as: theintersection checking between one moving object(assembling element or unit) with the static environ-ment objects (assembled elements) at discrete time.2.Fixture element shape: Modular fixture elements withregular shape can be classified into three types, namely,block, cylinder, and block-cylinder 27. Other compli-cated assembly units can be regarded as compositionsof these three meta-elements. It is well known that theOBB is tighter than the AABB and sphere. Moreover,when an object changes its position and orientation inVE, its OBB does not need to rebuild. Therefore, wecan construct OBBs of modular fixture elements off-line and store them as attributes of element models.During the assembly design process, such attributes canbe retrieved directly; thus, complex work for construct-ing bounding volume in run time can be avoided.3.Fixture element layout: A modular fixture system oftenconsists of supporting units, locating units, and clamp-ing units. These units lie out on the base plate andprovide corresponding functions at certain positions. AsFig. 1 shows, in the projection view parallel to the baseplate, the units are arranged in some kind of “regions.”In addition, to meet the height requirement of fixturingpoint, a unit often utilizes a number of supportingelements severed as blocking up objects. Therefore, atthe direction perpendicular to the baseplate, theelements lay out hierarchically. Accordingly, we candecompose the space with regard to elements layoutfeature.3.3 Algorithm flowchartAccording to the above characteristics of modular fixture,the proposed algorithm is designed to decrease thecomplexity and meet the requirements of VR-basedmodular fixture assembly design. As Fig. 2 shows, at thepreprocessing stage, once an element or component isassembled or disassembled, the Layer-based ProjectionModel (LPM) is established in terms of OBBs of thoseassembled elements. Such an LPM is used for the CDchecking when a new object is assembled.Just like the traditional CD method, proposed algorithmconsists of two steps, namely, broad phase and narrowphase. The broad phase is responsible for filtering pairs ofobjects that cannot intersect. At this stage, it determinespairs of objects in the same subspace, whose silhouettes inLPM overlap and their OBBs intersect. These pairs ofobjects are candidates for exact polygon-based collisiontests in the next narrow phase. During the broad phase, the(a)default view(b)downtown view Fig. 1 Modular fixture structure318Int J Adv Manuf Technol (2010) 46:315328test may cease at any time if no intersection is found, whichhelps to reject many noncollision or trivial collision cases.In the narrow phase, the collision detection algorithm willcalculate detailed intersection between geometrical meshesof the objects. If no intersection polygons are found, thecollide will not occur, and the active object can keep onmoving. Otherwise, whenever overlaps are detected, relatedreactions (for proposed system, it highlights objects anddoes back-tracking) may arise.4 Space decomposition for identifyingneighboring objectsConsidering the fact that most regions of the “universe” areoccupied by only a few objects or left empty, it means thatcollision only happens among objects that are close enough.So we can use this phenomenon to filter out most of “far-away” objects. Space decomposition is the commonapproach to be used for this intention. It first splits the“universe” into cells and then does further collision tests forobjects in the same cell. In order to keep generality, most ofexisting space subdivision approaches are based on a set ofpolygons. Such a “polygon-oriented” approach is socomputationally intensive to deal with large number ofpolygons. Since standard components are almost withrelatively regular shapes, we plan to develop an “object-oriented” space decomposition method.4.1 Space decomposition modelAfter the baseplate is arranged, the remaining work is toassemble the fixture elements or units onto the baseplate.As the assembling elements or units move to the assembledposition, collisions may happen between active object andthe assembled elements that have been fixed in the spacearound the baseplate. Hence, the CD checking processneeds start-up only after the active object enters into thisspace. Firstly, as Fig. 3a shows, we define a valid collisionspace noted as , which is a cuboid whose bottom face isdecided by the baseplate, and its height would change alongwith the assembling operation. The top of is determinedby the vertex coordinates of OBBs. is defined toguarantee that all the assembled elements are inside.After the checking space is identified, we need todecompose the space into a number of cells. How can weorganize these cells into proper structure and represent therelevant information to facilitate interaction checking? Inliterature, some