方臺面數(shù)控回轉(zhuǎn)工作臺設計【600×600】,600×,600,方臺面數(shù)控回轉(zhuǎn)工作臺設計【600×,600】,臺面,數(shù)控,回轉(zhuǎn),工作臺,設計 X-Y數(shù)控工作臺設計 學 生： 學 號： 專 業(yè)： 班 級： 指導教師： (600×600)方臺面數(shù)控回轉(zhuǎn)工作臺設計 目錄 一、課程設計目的…………………………………………………………………4 二、設計任務………………………………………………………………………4 三、設計主要步驟……………………………………………………………………5 1、確定設計總體方案………………………………………………………………5 （1）、機械傳動部件的選擇……………………………………………………5 （2）、控制系統(tǒng)的設計…………………………………………………………6 2、機械傳動部件的計算與選型……………………………………………………6 （1）、導軌上移動部件的重量估算……………………………………………6 （2）、計算切削力………………………………………………………………6 （3）、滾珠絲杠傳動的設計計算及校驗………………………………………7 (4)、步進電機的選用…………………………………………………………10 （5）、滾動導軌的設計計算……………………………………………………15 3、其余附件的選擇…………………………………………………………………16 四、控制系統(tǒng)的設計………………………………………………………………17 五、總結(jié)體會…………………………………………………………………………19 六、參考文獻………………………………………………………………………19 一、設計的目的 《數(shù)控機床》課程設計是一個重要的實踐性教學環(huán)節(jié)，要求學生綜合的運用所學的理論知識，獨立進行的設計訓練，主要目的： 1、 通過設計，使學生全面地、系統(tǒng)地了解和掌握數(shù)控機床的基本組成及其思想知識，學習總體的方案擬定、分析與比較的方法。 2、 通過對機械系統(tǒng)的設計，掌握幾種典型傳動元件與導向元件的工作原理、設計計算及選用的方式 3、 通過對機械系統(tǒng)的設計，掌握常用伺服電機的工作原理、計算控制方法與控制驅(qū)動方式 4、 培養(yǎng)學生獨立分析問題和解決問題的能力，學習并樹立“系統(tǒng)設計”的思想 5、 鍛煉提高學生應用手冊和標準、查閱文獻資料及撰寫科技論文的能力 二、設計任務 設計X-Y數(shù)控工作臺，主要參數(shù)如下： 設計一臺數(shù)控回轉(zhuǎn)工作臺并開發(fā)其控制、驅(qū)動系統(tǒng)，工作臺臺面600×600mm，分辨率為δ=5分/step，承受最大載荷Tmax=1800Nm。 三、設計主要步驟 1、確定設計總方案 ⑴、機械傳動部件的選擇 ①、 絲杠螺母副的選擇 步進電動機的旋轉(zhuǎn)運動需要通過絲杠螺母副轉(zhuǎn)換成直線運動，需要滿足初選0.005mm脈沖當量，因為定位精度±0.01mm，對于機械傳動要有一定的精度損失，大約是1/3-1/2的定位精度，現(xiàn)取為1/2，滑動絲杠副無法做到，只有選用滾珠絲桿副才能達到要求，滾珠絲桿副的傳動精度高、動態(tài)響應快、運轉(zhuǎn)平穩(wěn)、壽命長、效率高、預緊后可消除反向間隙。 同時選用內(nèi)循環(huán)的形式，因為這樣摩擦損失小，傳動效率高，且徑向尺寸結(jié)構(gòu)緊湊，軸向剛度高。 由于定位精度不高，故選擇的調(diào)隙方式是墊片調(diào)隙式，這種調(diào)隙方式結(jié)構(gòu)簡單，剛性好，裝卸方便。 由于工作臺轉(zhuǎn)速不高，故可以采用一般的安裝方法，即一端固定，一端游動的軸承配置形式。 ②、導軌副的選用 要設計數(shù)控銑床工作臺，需要承受的載荷不大，而且脈沖當量小，定位精度高，因此選用直線滾動導軌副，它具有摩擦系數(shù)小，不易爬行，傳動效率高，結(jié)構(gòu)緊，安裝預緊方便等優(yōu)點。 ③、伺服電機的選用 選用步進電動機作為伺服電動機后，可選開環(huán)控制，也可選閉環(huán)控制。任務書所給的精度對于步進電動機來說還是偏低，為了確保電動機在運動過程中不受切削負載和電網(wǎng)的影響而失步，決定采用開環(huán)控制，任務書初選的脈沖當量尚未達到0.001mm，定位精度也未達到微米級，空載最快移動速度也只有2300mm/min,故本設計不必采用高檔次的伺服電機，因此可以選用混合式步進電機，以降低成本，提高性價比。 ④、減速裝置的選用 選擇了步進電動機和滾珠絲桿副以后，為了圓整脈沖當量，放大電動機的輸出轉(zhuǎn)矩，降低運動部件折算到電動機轉(zhuǎn)軸上的轉(zhuǎn)動慣量，可能需要減速裝置，且應有消間隙機構(gòu)，如果要選用減速裝置，則應選用無間隙齒輪傳動減速箱。 ⑵、控制系統(tǒng)的設計 ①、設計的X-Y工作臺準備用在數(shù)控銑床上，其控制系統(tǒng)應該具有輪廓控制，兩坐標直線插補與圓弧插補的基本功能，所以控制系統(tǒng)設計成連續(xù)控制型。 ②、對于步進電動機的開環(huán)控制系統(tǒng)，選用MCS-51系列的8位單片機AT89S52作為控制系統(tǒng)的CPU，能夠滿足任務書給定的相關(guān)指標。 ③、要設計一臺完整的控制系統(tǒng)，在選擇CPU之后，還要擴展程序存儲器，I/O接口電路，D/A轉(zhuǎn)換電路，串行接口電路等。 ④、選擇合適的驅(qū)動電源，與步進電動機配套使用。 2、機械傳動部件的計算和選擇 （1）、導軌上移動部件的重量估算 按照下導軌上面移動部件的重量來進行估算。包括工件、夾具、工作平臺、上層電動機、減速箱、滾珠絲杠副、直線滾動導軌副、導軌座等，估計重量約為3700N。 （2）、計算切削力 根據(jù)設計任務，加工材料為碳素鋼或有色金屬及如下參數(shù)： 設零件的加工方式為立式加工，采用硬質(zhì)合金銑刀，工件材料為碳素鋼。由【5】中的表中，可知d=15mm的硬質(zhì)合金立銑刀最大的切削參數(shù)如下： 每齒進給量fz=0.1mm 銑刀轉(zhuǎn)速n=300r/min 由【2】中P200,查得立銑時切削力計算公式為： 代如上式得： 采用立銑刀進行圓柱銑削時，各銑削力之間的比值可由【2】中查得，各銑削力之間的比值范圍如下： =(1.0~1.2) 取1.1 /=(0.2~0.3) 取0.25 /=（0.35~0.4） 取0.38 考慮逆銑時的情況，因為逆銑的情況的受力最大的情況，為了安全考慮這種最危險的工況。由此可估算三個方向的銑削力分別為： 考慮立銑，則工作臺受到垂直方向的銑削力，受到水平方向的銑削力分別為和 今將水平方向較大的銑削力分配給工作臺的縱向，則縱向銑削力，徑向銑削力為。 Fx=Ff=1803N Fy=Ffn=410N Fz=Fe=623N （3）、滾珠絲杠傳動設計計算及校驗 ①、 最大工作載荷的計算 已知移動部件總重量G=3700N，按滾動導軌計算，由【3】中，取顛覆力影響系數(shù)K=1.1，滾動導軌上的摩擦系數(shù)查【1】中P194可知u=0.0025—0.005,現(xiàn)取u=0.005，求得滾珠絲杠副的最大工作載荷： =1.1×1803+0.005×(410+623+3700) =2007N ②、最大計算動載荷的確定 設工作臺在承受最大銑削力時的最快進給速度v=950mm/min，初選絲杠導程P=5mm,則此時絲杠轉(zhuǎn)速=v/P=190r/min。 預計滾珠絲杠的工作五年,每天工作八小時，由此得使用壽命為T=5×360 ×8=14400h，根據(jù)【1】中P110，公式5—4得： 其中 T——使用壽命 14400 h N——循環(huán)次數(shù) ——滾珠絲杠的當量轉(zhuǎn)速 190r/min 求得：≈164 （） 查【1】中P110，表5-1、5-2得，受中等沖擊載荷取值范圍，現(xiàn)取，滾道硬度為60HRC時，硬度影響系數(shù)取值，由【1】中， 代入數(shù)據(jù)得：≈14281N ②、 規(guī)格型號的初選 根據(jù)計算出的最大動載荷和初選的絲杠導程，查網(wǎng)上生產(chǎn)該型號的生產(chǎn)廠家的資料，選擇濟寧博特精密絲杠制造有限公司生產(chǎn)的GDM系列2005-3型滾珠絲杠副，為內(nèi)循環(huán)固定反向器雙螺母墊片預緊式滾珠絲杠副，其公稱直徑為20mm，導程為5mm，循環(huán)滾珠為3圈×2系列，精度等級取5級。 滾珠絲杠螺母副幾何參數(shù) （單位mm） 名 稱 符 號 計算公式和結(jié)果 絲杠滾道 公稱直徑 20 螺距 P 5 接觸角 鋼球直徑 3.175 螺紋滾道法面半徑 偏心距 螺紋升角 絲桿 絲杠外徑 19.3 絲杠底徑 螺桿接觸直徑 絲杠螺母 螺母螺紋外徑 螺母內(nèi)徑（內(nèi)循環(huán)） 表一 ④、傳動效率的計算 將公稱直徑d0=20mm,導程P=5mm,代入λ=arctan[P/(d0)]，得絲杠螺旋升角λ=4°33′。將摩擦角ψ=10′，代入η=tanλ/tan(λ+ψ),得傳動效率η=96.4%。 ⑤、剛度的驗算 X-Y工作臺上下兩層滾珠絲杠副的支承均采用“一端固定，一端游動”的軸承配置形式。由【1】中P109，可知這種安裝適用于較高精度、中等載荷的絲杠，一端采用深溝球軸承，一端采用一對背對背角接觸球軸承,這樣能承受集中力偶。 絲杠螺母的剛度的驗算可以用接觸量來校核。 a、滾珠絲杠滾道間的接觸變δ，查【3】中相關(guān)公式，根據(jù)公式，求得單圈滾珠數(shù)Z=20；該型號絲杠為雙螺母，滾珠的圈數(shù)列數(shù)為32，代入公式Z圈數(shù)列數(shù)，得滾珠總數(shù)量=120。絲杠預緊時，取軸向預緊力/3=669N。查【3】中相關(guān)公式，得， 滾珠與螺紋滾道間接觸變形 ==0.0014。因為絲杠有預緊力，且為軸向負載的1/3，所以實際變形量可以減少一半，取=0.0007mm。 b、 絲杠在工作載荷作用下的抗拉壓變形 絲杠采用的是一端采用深溝球軸承，一端采用一對背對背角接觸球軸承的配置形式，軸承的中心距a=560mm,鋼的彈性模量E=2.110MPa,由表一中可知，滾珠直徑=3.175mm,絲杠底徑=16.2mm，則絲杠的截面積S==206.12,由【7】中，式3-35 其中， 最大工作載荷=2007N 中心距a=560mm 彈性模量E=2.110MPa 截面積S==206.12 代入以上數(shù)據(jù)，得 =0.026mm c、則，絲杠的有效行程為500mm，由【3】中知，5級精度滾珠絲杠有效行程在400~500mm時，行程偏差允許達到30um，可見絲杠剛度足夠。 ⑥、穩(wěn)定性的驗算 根據(jù)【3】 。 取支承系數(shù)=2； 由絲杠底徑d2=16.2mm求得截面慣性矩3380.88； 壓桿穩(wěn)定安全系數(shù)K取3（絲杠臥式水平安裝）； 滾動螺母至軸向固定處的距離L=a取最大值560mm。 代入公式，得P=14481kg,f=14481N大于=14281N，故不會失穩(wěn)，滿足使用要求。 ⑦、臨界轉(zhuǎn)速的驗算 對于絲杠有可能發(fā)生共振，需驗算其臨界轉(zhuǎn)速，不會發(fā)生共振的最高轉(zhuǎn)速為臨界轉(zhuǎn)速，由【1】中P111式5-10得： 其中 20-1.2×3.175=16.2mm 為臨界轉(zhuǎn)速計算長度 為絲杠支承方式系數(shù)=3.927（一端固定，一端游動） 代入數(shù)據(jù)得： 臨界轉(zhuǎn)速遠大于絲杠所需轉(zhuǎn)速，故不會發(fā)生共振。 ⑧、滾珠絲杠的選型及安裝連接尺寸的確定 由以上驗算可知，選用GDM2005型的絲杠，完全符合滿足所需要求，故確定選用該型號， 由表一可知絲杠所需的安裝連接尺寸 （4）、步進電機的選用 步進電動機的計算和選型 a、步進電動機轉(zhuǎn)軸上的總轉(zhuǎn)動慣量的計算。 總轉(zhuǎn)動慣量J主要包括電動機轉(zhuǎn)子的轉(zhuǎn)動慣量、滾珠絲杠上一級移動部件等折算到電動機軸上的轉(zhuǎn)動慣量。 ⅰ、滾珠絲杠的轉(zhuǎn)動慣量J 由【1】中P134式5-28得： 式中 D為絲杠公稱直徑D=20mm L為絲杠長度L=560mm 代入數(shù)據(jù)，得：J=0.77×20×560×10=6.9×10kg.㎡ ⅱ、滾珠絲杠上一級移動部件等折算到電動機軸上的轉(zhuǎn)動慣量 由【1】中式5-29得： 其中 M為工作臺的（包括工件）的質(zhì)量M= S為絲杠螺距S=5mm 代入數(shù)據(jù)，得： ⅲ、初選常州寶馬前楊電機電器有限公司的90YG5502型混合式步進電動機，可知其轉(zhuǎn)子的轉(zhuǎn)動慣量 所以=6.9×10+2.4×10+4×10=7.09×10 N·m 驗算慣量匹配，電動機軸向慣量比值應控制在一定的范圍內(nèi)，既不應太大也不應太小，即伺服系統(tǒng)的動態(tài)特性取決于負載特性。為使該系統(tǒng)慣量達到較合理的配合，一般比值控制在1/4——1之間， 由此可見:,符合慣量匹配要求。 ②、步進電機軸上的等效負載轉(zhuǎn)矩M的計算 a、承受的負載轉(zhuǎn)矩在不同工況下是不同的，考慮最大切削負載時電動機所需力矩，由【1】中P132式5-25得： 其中 其中: 為折算到電動機軸上的總慣量==7.09×10 T系統(tǒng)時間常數(shù)，由任務書知為T=0.4S 切削時的轉(zhuǎn)速為300r/min 得： 其中： 為導軌摩擦力 S為絲杠螺距S=5mm i為齒輪降速比，已計算出為1 η為傳動鏈總效率，η=0.7—0.8，取0.8 代入數(shù)據(jù) 得： 其中： 為最大軸向載荷， 為滾珠絲杠未預緊時的效率，=0.95≥0.9 其余數(shù)據(jù)同上 代入數(shù)據(jù) 得： 其中：進給方向的最大切削力 其余參數(shù)同上。 代入數(shù)據(jù)得： N·m 由此都得到等效負載轉(zhuǎn)矩 N·m b、快速空載時電動機所需力矩M 由【1】中P132式5-24得： 加速力矩其中： 其余參數(shù)同上 入數(shù)據(jù)得： 力矩摩擦其中：u為導軌副的摩擦因數(shù)，滾動導軌取 u=0.005 其余參數(shù)同上。 代入數(shù)據(jù)得：N·m 附加摩擦力矩： 其余參數(shù)同上 代入數(shù)據(jù)得： N·m 所以可知快速空載時點擊所需力矩： =0.02+0.021+0.065 =0.106 N·m 比較和，取其較大者，就是最大等效負載，即：==1.93N.m ③、步進電機的初選 考慮到步進電機的驅(qū)動電源受電網(wǎng)的影響較大，當輸入電壓降低時，其輸入轉(zhuǎn)矩也會下降，可能會造成丟步，甚至堵轉(zhuǎn)，因此按最大等效負載M考慮一定的安全系數(shù)λ，取λ=2，則步進電機的最大靜轉(zhuǎn)矩應滿足： N·m 由所選的電機型號參數(shù)可知，最大轉(zhuǎn)矩 N·m，可知滿足要求。 ④、確定選型的步進電機的參數(shù) 所選電動機參數(shù)如下圖所示： 圖2 外形尺寸安裝接線圖和和矩頻特性如圖3所示 圖3 圖4 （5）、滾動導軌的設計計算 ①、工作載荷的計算 工作載荷是影響導軌副壽命的重要因素，對于水平布置的十字工作臺多采用雙導軌、四滑塊的支承形式?？紤]最不利的情況，即垂直于臺面的工作載荷全部由一個滑塊承擔，則單滑塊所承受的最大垂直方向載荷為： 其中，移動部件重量G=800N,外加載荷F==623N 代入上式，得：N ② 、小時額定工作壽命的計算 預期工作臺的工作壽命為5年，一年365天，取工作時間為360天，每天工作8小時，因此得到小時額定工作壽命 ③、距離額定壽命計算 由公式，從而得到 式中，為小時額定工作壽命。 n為移動件每分鐘往復次數(shù)（4—6）取5 S為移動件行程長度，由加工范圍為600mm×300mm取900mm 代入數(shù)據(jù) 得： ④、額定動載荷計算 由公式 從而得到： 式中：為額定動載荷 L為距離工作壽命，由上式可知為7776km F為滑塊的工作載荷，由上式可知為1548N 代入數(shù)據(jù)得： ⑤、產(chǎn)品選型 根據(jù)額定動載荷，選擇滾動導軌，查滾動導軌生產(chǎn)廠家，選用南京工藝裝備制造有限公司的GGB25BA型，相關(guān)尺寸如下圖4所示， 圖5 可知其額定動載荷C=17.7KN，大于16.649KN，故可知滿足要求。 ⑥、安裝連接尺寸。 對于導軌的安裝按照如圖5所示相關(guān)尺寸安裝。 3、其余附件的選擇 1、聯(lián)軸器的選擇 剛性聯(lián)軸器結(jié)構(gòu)比較簡單，制造容易， 免維護，超強抗油以及耐腐蝕，即使承受負載時也無任何回轉(zhuǎn)間隙，即便是有偏差產(chǎn)生負荷時，剛性聯(lián)軸器還能剛性傳遞扭矩。適用于安裝底座剛性好、對中精度較高、沖擊載荷不大、對減振要求不高的中小功率軸系傳動。根據(jù)選出的電機和絲杠的參數(shù)，選用沈陽光宇科技有限公司的LK13-C32-1012型剛性聯(lián)軸器。 四、控制系統(tǒng)的設計 根據(jù)任務書的要求，設計控制系統(tǒng)的時主要考慮以下功能： （1） 接受操作面板的開關(guān)與按鈕信息； （2） 接受限位開關(guān)信號； （3） 控制X，Y向步進電動機的驅(qū)動器； （4） 與PC機的串行通信。 CPU選用MCS-51系列的8位單片機AT89S52，采用8279，和W27C512，6264芯片做為I/O和存儲器擴展芯片。W27C512用做程序存儲器，存放監(jiān)控程序；6264用來擴展AT89S52的RAM存儲器存放調(diào)試和運行的加工程序；8279用做鍵盤和LED顯示器借口，鍵盤主要是輸入工作臺方向，LED顯示器顯示當前工作臺坐標值；系統(tǒng)具有超程報警功能，并有越位開關(guān)和報警燈；其他輔助電路有復位電路，時鐘電路，越位報警指示電路。 1、 進給控制系統(tǒng)原理框圖 圖6 2、 驅(qū)動電路流程設計 步進電機的速度控制比較容易實現(xiàn)，而且不需要反饋電路。設計時的脈沖當量為0.005mm，步進電機每走一步，工作臺直線行進給0.005mm。步進電機驅(qū)動電路中采用了光電偶合器，它具有較強的抗干擾性，而且具有保護CPU的作用，當功放電路出現(xiàn)故障時，不會將大的電壓加在CPU上使其燒壞。 圖7 步進電機驅(qū)動電路圖 該電路中的功放電路是一個單電壓功率放大電路，當A相得電時，電動機轉(zhuǎn)動一步。電路中與繞組并聯(lián)的二極管D起到續(xù)流作用，即在功放管截止是，使儲存在繞組中的能量通過二極管形成續(xù)流回路泄放，從而保護功放管。與繞組W串聯(lián)的電阻為限流電阻，限制通過繞組的電流不至超過額定值，以免電動機發(fā)熱厲害被燒壞。 由于步進電機采用的是五相十拍的工作方式（五個線圈A、B、C、D、E），其正轉(zhuǎn)時通電順序為：A-AB-B-BC-C-CD-D-DE-E-EA-A……….其反轉(zhuǎn)的通電順序為：A-AE-E-ED-D-DC-C-CB-B-BA-A………。 3、驅(qū)動電源的選用，及驅(qū)動電源與控制器的接線方式 設計中X、Y向步進電動機均為90BYG5502型，生產(chǎn)廠家為常州寶馬前楊電機電器有限公司。查步進電動機的資料，選擇與之匹配的驅(qū)動電源為BD28Nb型，輸入電壓為50V AC，相電流為3A，分配方式為五相十拍。該驅(qū)動電源與控制器的接線方式如圖8所示： 圖8 五、總結(jié)體會 我覺得本次課程設計是對過去所學專業(yè)知識的一個全面的綜合的運用。在設計的過程中我全面地溫習了以前所學過的知識，包括機械設計基礎和機械制圖方面的基礎知識，還有剛學過的數(shù)控機床和機電一體化系統(tǒng)設計，經(jīng)過復習整理所學得專業(yè)知識使得設計思路清晰系統(tǒng)。通過設計使我更加接近生產(chǎn)實際，鍛煉了將理論運用于實際的分析和解決實際問題的能力，鞏固、加深了有關(guān)機械設計方面的知識。 在此過程中我不僅運用了以前所學的各個學科方面的知識，而且學到了課本以外的知識。在此次設計過程中遇到了不少問題，也走了不少彎路，通過此次設計實踐讓我學會虛心求教，細心體察，大膽實踐。任何能力都是在實踐中積累起來的，都會有一個從不會到會，從不熟練到熟練的過程，人常說“生活是最好的老師”就是說只有在生活實踐中不斷磨練，才能提高獨立思考和解決問題的能力；同時也培養(yǎng)了自己優(yōu)良的學風、高尚的人生、團結(jié)和合作的精神；學會了勤奮、求實的學習態(tài)度。 還有很重要的一點是讓我體會到了一個設計者的精神。在設計過程中既要自己不斷思考、創(chuàng)造，又要注意借用現(xiàn)有的資料，掌握了查閱和使用標準、規(guī)范、手冊、圖冊、及相關(guān)技術(shù)資料的基本技能以及計算、繪圖、數(shù)據(jù)處理等方面的能力。 通過對通用機械零件、常用機械傳動或簡單機械的設計，掌握了一般機械設計的程序和方法，有助于樹立正確的工程設計思想，培養(yǎng)獨立、全面、科學的機械設計能力。 最后對在整個設計過程中對老師認真、耐心輔導表示衷心的感謝！ 六、參考文獻 【1】、文懷興、夏田 .《數(shù)控機床系統(tǒng)設計》 北京：北京化工出版社，2008. 【2】、韓榮第 .《金屬切削原理與刀具》 哈爾濱：哈爾濱工業(yè)大學出版社，2007. 【3】、李洪 .《機床設計手冊》北京：遼寧科學技術(shù)出版社，1999. 【4】、陳家芳.《金屬切削工藝手冊》 上海：上?？茖W技術(shù)出版社, 2005. 【5】、楊建明. 《數(shù)控加工工藝與編程》北京：北京理工大學出版社，2009. 【6】、張新義.《經(jīng)濟型數(shù)控機床系統(tǒng)設計》北京：機械工業(yè)出版社，2000 【7】張建民.機電一體化系統(tǒng)設計[M].北京：高等教育出版社.2001 【8】張訓文.機電一體化系統(tǒng)設計與應用[M].北京：北京理工大學出版社.2006 【9】張立勛等.機電一體化系統(tǒng)設計[M].哈爾濱：哈爾濱工程大學出版社. 18 英文翻譯 【附】英文原文 翻譯文獻：Five-axis milling machine tool kinematic chain design and analysis 作者：E.L.J. Bohez 文獻出處：International Journal of Machine Tools & Manufacture 42 (2002) 505–520 翻譯頁數(shù)： Five-axis milling machine tool kinematic chain design and analysis 1. Introduction The main design specifications of a machine tool can be deduced from the following principles: ● The kinematics should provide sufficient flexibility in orientation and position of tool and part. ● Orientation and positioning with the highest possible speed. ● Orientation and positioning with the highest possible accuracy. ● Fast change of tool and workpiece. ● Save for the environment. ● Highest possible material removal rate. The number of axes of a machine tool normally refers to the number of degrees of freedom or the number of independent controllable motions on the machine slides.The ISO axes nomenclature recommends the use of a right-handed coordinate system, with the tool axis corresponding to the Z-axis. A three-axis milling machine has three linear slides X, Y and Z which can be positioned everywhere within the travel limit of each slide. The tool axis direction stays fixed during machining. This limits the flexibility of the tool orientation relative to the workpiece and results in a number of different set ups. To increase the flexibility in possible tool workpiece orientations, without need of re-setup, more degrees of freedom must be added. For a conventional three linear axes machine this can be achieved by providing rotational slides. Fig. 1 gives an example of a five-axis milling machine. 2. Kinematic chain diagram To analyze the machine it is very useful to make a kinematic diagram of the machine. From this kinematic (chain) diagram two groups of axes can immediately be distinguished: the workpiece carrying axes and the tool carrying axes. Fig. 2 gives the kinematic diagram of the five-axis machine in Fig. 1. As can be seen the workpiece is carried by four axes and the tool only by one axis.The five-axis machine is similar to two cooperating robots, one robot carrying the workpiece and one robot carrying the tool.Five degrees of freedom are the minimum required to obtain maximum flexibility in tool workpiece orientation,this means that the tool and workpiece can be oriented relative to each other under any angle. The minimum required number of axes can also be understood from a rigid body kinematics point of view. To orient two rigid bodies in space relative to each other 6 degrees of freedom are needed for each body (tool and workpiece) or 12 degrees. However any common translation and rotation which does not change the relative orientation is permitted reducing the number of degrees by 6. The distance between the bodies is prescribed by the toolpath and allows elimination of an additional degree of freedom, resulting in a minimum requirement of 5 degrees. 3.Literature review One of the earliest (1970) and still very useful introductions to five-axis milling was given by Baughman [1] clearly stating the applications. The APT language was then the only tool to program five-axis contouring applications. The problems in postprocessing were also clearly stated by Sim [2] in those earlier days of numerical control and most issues are still valid. Boyd in Ref. [3] was also one of the early introductions. Beziers’ book [4] is also still a very useful introduction. Held [5] gives a very brief but enlightening definition of multi-axis machining in his book on pocket milling. A recent paper applicable to the problem of five-axis machine workspace computation is the multiple sweeping using the Denawit-Hartenberg representation method developed by Abdel-Malek and Othman [6]. Many types and design concepts of machine tools which can be applied to five-axis machines are discussed in Ref. [7] but not specifically for the five-axis machine. he number of setups and the optimal orientation of the part on the machine table is discussed in Ref. [8]. A review about the state of the art and new requirements for tool path generation is given by B.K. Choi et al. [9]. Graphic simulation of the interaction of the tool and workpiece is also a very active area of research and a good introduction can be found in Ref. [10]. 4. Classification of five-axis machines’ kinematic structure Starting from Rotary (R) and Translatory (T) axes four main groups can be distinguished: (i) three T axes and two R axes; (ii) two T axes and three R axes; (iii) one T axis and four R axes and (iv) five R axes. Nearly all existing five-axis machine tools are in group (i). Also a number of welding robots, filament winding machines and laser machining centers fall in this group. Only limited instances of five-axis machine tools in group (ii) exist for the machining of ship propellers. Groups (iii) and (iv) are used in the design of robots usually with more degrees of freedom added. The five axes can be distributed between the workpiece or tool in several combinations. A first classification can be made based on the number of workpiece and tool carrying axes and the sequence of each axis in the kinematic chain. Another classification can be based on where the rotary axes are located, on the workpiece side or tool side. The five degrees of freedom in a Cartesian coordinates based machine are: three translatory movements X,Y,Z (in general represented as TTT) and two rotational movements AB, AC or BC (in general represented as RR).Combinations of three rotary axes (RRR) and two linear axes (TT) are rare. If an axis is bearing the workpiece it is the habit of noting it with an additional accent. The five-axis machine in Fig. 1 can be characterized by XYABZ. The XYAB axes carry the workpiece and the Z-axis carries the tool. Fig. 3 shows a machine of the type XYZAB
, the three linear axes carry the tool and the two rotary axes carry the workpiece. 5. Workspace of a five-axis machine Before defining the workspace of the five-axis machine tool, it is appropriate to define the workspace of the tool and the workspace of the workpiece. The workspace of the tool is the space obtained by sweeping the tool reference point (e.g. tool tip) along the path of the tool carrying axes. The workspace of the workpiece carrying axes is defined in the same way (the center of the machine table can be chosen as reference point).These workspaces can be determined by computing the swept volume [6].Based on the above-definitions some quantitative parameters can be defined which are useful for comparison, selection and design of different types of machines. 6.Selection criteria of a five-axis machine It is not the objective to make a complete study on how to select or design a five-axis machine for a certain application. Only the main criteria which can be used to justify the selection of a five-axis machine are discussed. 6.1. Applications of five-axis machine tools The applications can be classified in positioning and contouring. Figs. 12 and 13 explain the difference between five-axis positioning and five-axis contouring. 6.1.1. Five-axis positioning Fig. 12 shows a part with a lot of holes and flat planes under different angles, to make this part with a three axis milling machine it is not possible to process the part in one set up. If a five-axis machine is used the tool can process. More details on countouring can be found in Ref. [13]. Applications of five-axis contouring are: (i) production of blades, such as compressor and turbine blades; (ii) injectors of fuel pumps; (iii) profiles of tires; (iv) medical prosthesis such as artificial heart valves; (v) molds made of complex surfaces. 6.1.2. Five-axis contouring Fig. 13 shows an example of five-axis contouring, tomachine the complex shape of the surface we need to control the orientation of the tool relative to the part during cutting. The tool workpiece orientation changes in each step. The CNC controller needs to control all the five-axes simultaneously during the material removal process. More details on countouring can be found in Ref. [13]. Applications of five-axis contouring are: (i) production of blades, such as compressor and turbine blades; (ii) injectors of fuel pumps; (iii) profiles of tires; (iv) medical prosthesis such as artificial heart valves; (v) molds made of complex surfaces. 6.2. Axes configuration selection The size and weight of the part is very important as a first criterion to design or select a configuration. Very heavy workpieces require short workpiece kinematic chains. Also there is a preference for horizontal machine tables which makes it more convenient to fix and handle the workpiece. Putting a heavy workpiece on a single rotary axis kinematic chain will increase the orientation flexibility very much. It can be observed from Fig. 4that providing a single horizontal rotary axis to carry the workpiece will make the machine more flexible. In most cases the tool carrying kinematic chains will be kept as short as possible because the toolspindle drive must also be carried. 6.3.five-axes machining of jewelry A typical workpiece could be a flower shaped part as in Fig. 14. This application is clearly contouring. The part will be relatively small compared to the tool assembly. Also small diameter tools will require a high speed spindle. A horizontal rotary table would be a very good option as the operator will have a good view of the part (with range 360°). All axes as workpiece carrying axes would be a good choice because the toolspindle could be fixed and made very rigid. There are 20 ways in which the axes can be combined in the workpiece kinematic chain (Section 4.2.1). Here only two kinematic chains will be considered. Case one will be a T
T
T
R
R
kinematic chain shown in Fig. 15. Case two will be a R
R
T
T
T
kinematic chain shown in Fig. 16. For model I a machine with a range of X=300mmY=250 mm, Z=200 mm, C=n 360° and A=360°, and a machine tool table of 100 mm diameter will be considered. For this kinematic chain the tool workspace is a single point. The set of tool reference points which can be selected is also small. With the above machine travel ranges the workpiece workspace will be the space swept by the center of the machine table. If the centerline of the two rotary axes intersect in the reference point, a prismatic workpiece workspace will be obtained with as size XYZ or 300×250×200 mm3. If the centerlines of the two rotary axes do not intersect in the workpiece reference point then the workpiece workspace will be larger. It will be a prismatic shape with rounded edges. The radius of this rounded edge is the excentricity of the bworkpiece reference point relative to each centerline. Model II in Fig. 15 has the rotary axes at the beginning of the kinematic chain (R
R
T
T
T
). Here also two different values of the rotary axes excentricity will be considered. The same range of the axes as in model I is considered. The parameters defined in Section 5 are computed for each model and excentricity and summarized in Table 1. It can be seen that with the rotary axes at the end of the kinematic chain (model I), a much smaller machine tool workspace is obtained. There are two main reasons for this. The swept volume of the tool and workpiece WSTOOLWSWORK is much smaller for model I. The second reason is due to the fact that a large part of the machine tool workspace cannot be used in the case of model I, because of interference with the linear axes. The workspace utilization factor however is larger for the model I with no excentricity because the union of the tool workspace and workpiece workspace is relatively smaller compared with model I with excentricity e=50 mm. The orientation space index is the same for both cases if the table diameter is kept the same. Model II can handle much larger workpieces for the same range of linear axes as in model I. The rotary axes are here in the beginning of the kinematic chain, resulting in a much larger machine tool workspace then for model I. Also there is much less interference of the machine tool workspace with the slides. The other 18 possible kinematicchain selections will give index values somewhat in between the above cases. 6.4. rotary table selection Two machines with the same kinematic diagram (T
T
R
R
T) and the same range of travel in the linear axes will be compared (Fig. 17). There are two options for the rotary axes: two-axis table with vertical table (model I), two-axis table with horizontal table (model II). Tables 2 and 3 give the comparison of the important features. It can be observed that reducing the range of the rotary axes increases the machine tool workspace. So model I will be more suited for smaller workpieces with operations which require a large orientation range, typically contouring applications. Model II will be suited for larger workpieces with less variation in tool orientation or will require two setups. This extra setup requirement could be of less importance then the larger size. The horizontal table can use pallets which transform the internal setup to external setup. The larger angle range in the B-axes 105 to +105, Fig. 17. Model I and model II T
T
R
R
T machines. compared to 45 to +20, makes model I more suited for complex sculptured surfaces, also because the much higher angular speed range of the vertical angular table. The option with the highest spindle speed should be selected and it will permit the use of smaller cutter diameters resulting in less undercut and smaller cutting forces. The high spindle speed will make the cutting of copper electrodes for die sinking EDM machines easier. The vertical table is also better for the chip removal. The large range of angular orientation, however, reduces the maximum size of the workpiece to about 300 mm and 100 kg. Model II with the same linear axes range as model I, but much smaller range in the rotation, can easily handle a workpiece of double size and weight. Model II will be good for positioning applications. Model I cannot be provided with automatic workpiece exchange, making it less suitable for mass production. Model II has automatic workpiece exchange and is suitable for mass production of position applications. Model I could, however, be selected for positioning applications for parts such as hydraulic valve housings which are small and would require a large angular range. 7.New machine concepts based on the Stewart platform Conventional machine tool structures are based on Carthesian coordinates. Many surface contouring applications can be machined in optimal conditions only with five-axis machines. This five-axis machine structure requires two additional rotary axes. To make accurate machines, with the required stiffness, able to carry large workpieces, very heavy and large machines are required. As can be seen from the kinematic chain diagram of the classical five-axis machine design the first axis in the chain carries all the subsequent axes. So the dynamic responce will be limited by the combined inertia. A mechanism which can move the workpiece without having to carry the other axes would be the ideal. A new design concept is the use of a ‘HEXAPOD’. Stewart [16] described the hexapod principle in 1965. It was first constructed by Gough and Whitehall [20] in 1954 and served as tire tester. Many possible uses were proposed but it was only applied to flight simulator platforms. The reason was the complexity of the control of the six actuators. Recently with the amazing increase of speed and reduction in cost of computing, the Stewart platform is used by two American Companies in the design of new machine tools. The first machine is the VARIAX machine from the company Giddings and Lewis, USA. The second machine is the HEXAPOD from the Ingersoll company, USA. The systematic design of Hexapods and other similar systems is discussed in Ref. [17]. The problem of defining and determining the workspace of virtual axis machine tools is discussed in Ref. [18]. It can be observed from the design of the machine that once the position of the tool carrying plane is determined uniquely by the CL date (point + vector), it is still possible to rotate the tool carrying platform around the tool axis. This results in a large number of possible length combinations of the telescopic actuators for the same CL data. 8.Conclusion Theoretically there are large number of ways in which a five-axis machine can be built. Nearly all classical Cartesian five-axis machines belong to the group with three linear and two rotational axes or three rotational axes and two linear axes. This group can be subdivided in six subgroups each with 720 instances.If only the instances with three linear axes are considered there are still 360 instances in each group. The instances are differentiated based on the order of the axes in both tool and workpiece carrying kinematic chain.If only the location of the rotary axes in the tool and workpiece kinematic chain is considered for grouping five-axis machines with three linear axes and two rotational axes, three groups can be distinguished. In the first group the two rotary axes are implemented in the workpiece kinematic chain. In the second group the two rotary axes are implemented in the tool kinematic chain. In the third group there is one rotary axis in each kinematic chain. Each group still has twenty possible instances. To determine the best instance for a specific application area is a complex issue. To facilitate this some indexes for comparison have been defined such as the machine tool workspace, workspace utilization factor, orientation space index, orientation angle index and machine tool space efficiency. An algorithm to compute the machine tool workspace and the diameter of the largest spherical dome which can be machined on the machine was outlined. The use of these indexes for two examples was discussed in detail. The first example considers the design of a five-axis machine for jewelry machining. The second example illustrates the selection of the rotary axes options in the case of a machine with the same range in linear axes. 翻譯題名：Five-axis milling machine tool kinematic chain design and analysis 期刊與作者：E.L.J. Bohez 出版社： International Journal of Machine Tools & Manufacture 42 (2002) 505–520 ● 英文譯文 摘要： 現(xiàn)如今五軸數(shù)控加工中心已經(jīng)非常普及。大部分機床的運動學分析都 基于笛卡爾直角坐標系。本文羅列了現(xiàn)有的概念設計與實際應用，這些從理論上都基于自由度的綜合。一些有用的參數(shù)都有所規(guī)定，比如工件使用系數(shù)，機床空間效率，方向空間搜索以及方向角等。每一種概念，它的優(yōu)缺點都有所分析。選擇的標準及機器參數(shù)設置的標準都給出來了。據(jù)于Stewart平臺的新概念最近行業(yè)內(nèi)已有介紹并作簡短討論。 1.緒論 設計一臺數(shù)控機床主要要遵循以下規(guī)則： 1，刀具和工件在空間方向上要有足夠的靈活性。 2，方向和位置的改變要盡可能的快。 3，方向和位置的改變要盡可能的準確。 4，刀具和工件快速變、換。 5，環(huán)保 6，切削材料速度快 一臺數(shù)控機床的軸的數(shù)目通常取決于其自由度數(shù)目或者獨立控制運動的導軌數(shù)目。國際標準委員會推薦通過右手笛卡兒坐標系來命名坐標軸，刀具相應的為Z軸。一個三軸銑床有三條導軌，X,Y,Z向，它們可用來在長度范圍內(nèi)可以在任意位置移動。加工過程中刀具軸的位置始終不變。這就限制了刀具相對于工件在方向上變化的靈活性，并且導致許多偏差的出現(xiàn)。為了盡可能的提高刀具相對于工件的靈活性，無需重啟，必須要加入多個自由度。對于傳統(tǒng)三軸機床來說這可以通過提供旋轉(zhuǎn)滑臺來實現(xiàn)。圖1給出了一個五軸銑床的例子。 圖1 五軸數(shù)控機床 1.運動鏈圖表 通過制作機器的運動鏈圖表對于機器的分析來說十分有用。通過運動簡圖可知兩組軸可以迅速的區(qū)分開：工件裝夾軸和刀具軸。圖2給出了圖1.五軸機床的運動鏈簡圖。由圖上可以看出工件由四根軸承載，刀具僅在一根軸上。這個五軸機床與兩工位操作機器人很相似，一個機器人夾住工件，另一個夾住刀具。為了獲得刀具工件方向上的最大自由，五個自由度已是最低要求，這就意味著工件和刀具可以在任意角度位置相對定位。最低需求的軸數(shù)也可以通過剛體運動學的方法來分析。兩個剛體在空間確定相對位置，每個剛體需要6個到12個自由度。然而由于任意的移動或轉(zhuǎn)動并不改變相對位置就允許將自由度減少到6.兩個剛體之間的距離通過刀具軌跡來描述，并且允許去掉一個額外的自由度，結(jié)果也就是5個自由度。 圖2 運動鏈圖 2.參考文獻 最早（1970年）到目前并且仍就有參考價值的對五軸數(shù)控銑床的介紹之一是由 Baughman提出的并清楚的闡述了它的應用（附錄1有他的介紹）。APT語言隨后成為唯一的五軸輪廓加工的編程語言之一。后處理階段的問題也在數(shù)控發(fā)展的早期由Sim清楚的表述出來（附錄2有對他的介紹），并且大部分問題到現(xiàn)在仍然有效。Boyd（詳見附錄3）也是最早引進數(shù)控機床的先驅(qū)之一。Beziers的書（見附錄4）也是非常有用的介紹。Held（見附錄5）在他的小型銑削加工的書里對多軸機床也有非常簡短但啟發(fā)性的定義。目前一篇適用于解決五軸數(shù)控機床工作空間計算的文章，通過使用Denawit-Hartenberg發(fā)表并由 Abdel-Malek and Othman（見附錄6）改進的算法 應用于多弧段切削。許多對機床的類型和概念設計，這些可以被應用于五軸機床，Ref都有討論（見附錄8）.關(guān)于對刀具路徑生成的技巧和新需求由B.K. Choi et al給出（見附錄9）。工件與刀具的圖像模擬也是研究的熱點并且可以在Ref（見附錄10）的書是一個好的入門讀物。 3.五軸機床運動結(jié)構(gòu)的分類 從R軸（旋轉(zhuǎn)軸）和T軸（移動軸）劃分大致可以分為四大部分：（i）3個移動軸和2個轉(zhuǎn)動軸；（ii）2個T軸和3個R軸；（