通過熱量誤差補(bǔ)償來改善數(shù)控機(jī)床的精確度

1、氳洳羼障掉炫恁寂余蜞通過熱量誤差補(bǔ)償來改善數(shù)控機(jī)床的精確度吒氐污遴孥導(dǎo)汀鬢驁峒摘要：通過熱量誤差補(bǔ)償來改變數(shù)控機(jī)床的精度是一種可行的方法。熱量誤差的獲得是通過1-D滾珠排列和建立在錠子轉(zhuǎn)速基礎(chǔ)上的自動(dòng)退刀的表征。通過改變工件的數(shù)控程序，熱量誤差在機(jī)加工以前可以被補(bǔ)償。試驗(yàn)表明直立的加工中心的實(shí)際補(bǔ)償是可行的。亨抻圓蘸齊摳調(diào)儇墟擎關(guān)鍵詞：數(shù)控加工中心, 熱量誤差,補(bǔ)償泫坳康頂鞫高奸嫩舶揖脯岳漲雋阼筋陜鴻譏睇0.引言：睡攬仰炕得耿奔鵒晟霜沱的囈濠瓚?zhàn)糌?fù)行锍篁數(shù)控機(jī)床精確度的改善是生產(chǎn)過程中質(zhì)量控制的根本。熱量誤差已經(jīng)被作為機(jī)器精確度失衡的最大誘因，而且可能也是機(jī)器獲取更高精確度的最大障礙。數(shù)控機(jī)床

2、的熱量誤差可通過機(jī)床本身的結(jié)構(gòu)設(shè)計(jì)和生產(chǎn)技術(shù)的改善而降低。盡管如此，還是有許多物理性限制因素使得精確度不能通過生產(chǎn)和設(shè)計(jì)技術(shù)而單獨(dú)克服。因此，誤差補(bǔ)償技術(shù)是很必要的。在過去的幾年里，對此技術(shù)的研究已經(jīng)獲得重大成果。由于熱量誤差在加工時(shí)隨時(shí)間而變化，許多前人的工作都集中在實(shí)際時(shí)間的的補(bǔ)償比率上。典型的方法是對機(jī)床幾個(gè)有代表性的點(diǎn)進(jìn)行熱量誤差和溫度的同步試驗(yàn)，然后建立一個(gè)與熱量誤差和溫度的試驗(yàn)?zāi)Ｐ蛯Χ喾N變化進(jìn)行回歸分析或是人工網(wǎng)絡(luò)分析。癬蠛赧米搴忱融彬漫嘩在加工期間，誤差是根據(jù)之前建立的模型進(jìn)行預(yù)測并通過在實(shí)際過程中用額外的信號和自由回路進(jìn)行改正的。但是，目前只有很少被報(bào)道的實(shí)際過程補(bǔ)償案例適用于

3、商業(yè)機(jī)床。首先，對機(jī)床的多個(gè)點(diǎn)進(jìn)行熱量誤差和溫度的測量是不可取的。其次，溫度傳感器的線會或多或少影響機(jī)器的運(yùn)轉(zhuǎn)。第三，實(shí)際操作中的誤差補(bǔ)償功能在許多的機(jī)器上是不可用的。肘檗潁董姆茚酒婁榴諦為了改善數(shù)控機(jī)床生產(chǎn)的精確度，有個(gè)方法是值得嘗試的。盡管許多的熱源都能引起熱量誤差，但是環(huán)形軸承的摩擦被認(rèn)為是最主要的熱源。熱量誤差是由1-D滾珠排列來衡量的。一個(gè)自動(dòng)回歸模型是以錠子轉(zhuǎn)速然后被發(fā)展到描述那時(shí)的熱量錯(cuò)誤為基礎(chǔ)的。利用這個(gè)模型，熱量誤差能夠在機(jī)械加工程序制造的時(shí)候被預(yù)測出來。通過對程序的修訂，熱量誤差能夠在加工之前得到補(bǔ)償。那么補(bǔ)償?shù)拇鷥r(jià)就大大的減輕了。陶斬鴣溜爻俚仁虺搿培1.試驗(yàn)工作曛淞軛鼴弟

4、漢鵂屁莖從畀嬡堠戩斡拇一詼圪喟為了達(dá)到補(bǔ)償目的，重要的部分不是每個(gè)機(jī)器的零部件，而是工件的位移。在調(diào)查的線性機(jī)械加工中心中，熱量誤差是由錠子膨脹、錠子固件變形和三個(gè)軸空間的變形一起引起的。由于導(dǎo)桿的伸長和欄的彎曲，熱量誤差并不只是在時(shí)間上的改變，而且還是機(jī)械加工在空間上的變化。統(tǒng)背虔僚哩渲雌卻臬徵為了能夠快速的測量熱量誤差，一些簡單的量規(guī)是可以使用的，例如：滾珠排列。滾珠排列是把一系列的滾珠按相等的間隔固定在頂梁上。由于滾珠的直徑相等，球狀的誤差比較小，因此，滾珠排列被用于熱量誤差測量的一個(gè)參考。大量的之前試驗(yàn)數(shù)據(jù)表明在光軸上的熱量誤差遠(yuǎn)遠(yuǎn)高于在橫軸和縱軸。所以，熱量誤差主要關(guān)注在光軸上。同理

5、，也可以用相同的辦法得到其他兩個(gè)軸上的熱量誤差數(shù)據(jù)。測量的過程如圖1所示：剛開始，滾珠的坐標(biāo)是處在低溫狀態(tài)的，然后錠子在試驗(yàn)狀態(tài)下改變機(jī)器的熱量。滾珠溫度的測量是周期性的。熱量的轉(zhuǎn)移是通過用最初的參考坐標(biāo)減去在新的熱量狀態(tài)下滾珠坐標(biāo)來實(shí)現(xiàn)的。由于這種測量只需要一分鐘，機(jī)器在不同坐標(biāo)下的熱量轉(zhuǎn)移能夠更快更容易的被顯現(xiàn)出來。根據(jù)轉(zhuǎn)動(dòng)速率的變化，熱量誤差和轉(zhuǎn)速是每十分鐘就是一個(gè)循環(huán)。坐標(biāo)的唯一偏離是在低溫狀態(tài)下完成的，而不是在所關(guān)注的獨(dú)立的量規(guī)尺寸下。象激光干涉儀這樣的精確度和準(zhǔn)確度裝置并不做要求。只有四個(gè)測量點(diǎn)z1，z2，z3，z4來覆蓋坐標(biāo)為-50，-150，-250，-350的z坐標(biāo)的工作范圍

6、。在其他的坐標(biāo)中熱量誤差可以通過一個(gè)插值函數(shù)來獲得。綞垂制拋逡靖泖蠼瘁拽上述的試驗(yàn)說明了在錠子位置和工作臺之間的派生位移與錠子和臺之間是一致的。因此熱量誤差z的測量反映了在真正的切割條件下誤差是可以忽略的。析匙咦硇朋崖震羹獗犬為了能夠獲得機(jī)床熱量行為的全面理解以及正確的判斷誤差模型，形成了一種測量方法。錠子轉(zhuǎn)速的多種加載方式是可用的。他們被分為如下三類：1，常規(guī)轉(zhuǎn)速，2，轉(zhuǎn)速范圍，3，真正切割狀態(tài)下的同步轉(zhuǎn)速。此處，由切割過程而引起的熱量作用沒有被考慮進(jìn)來。不過，切割過程對整個(gè)機(jī)床機(jī)構(gòu)的熱量的影響在最終的過程中是可以忽略的。在這種機(jī)床中，最大的熱源來自于z軸。熱量誤差在z方向和不同的x和y坐標(biāo)

7、方向大約是相同的。也就是說x軸和y軸的位置對z軸的熱量誤差沒有重大影響。燦片閃顆篙碧镅魚癯巛煥替豌夯瘡纛贐愆漸超1. 圖1（左）熱量誤差測量 錠子傳感器拋般孥堋寺佘系葙摸互2.1-D 滾珠排列檐測撅慷啾賬嘏墮獺俯圖2（右） 在不同z坐標(biāo)中的熱量誤差言垃洞許箔蕨癱嘮妞踢1. z = - 50 2. z = - 150 3. z = - 250 4. z = - 350藜袁即鍾齜曖懦坑超看圖2 在測試中不同z 坐標(biāo)中熱量轉(zhuǎn)移時(shí)間過程圖的繪制矛黷雍粵嗜市仆垸佬地上圖表明合成的熱量轉(zhuǎn)移明顯是由所在決定的。在z1，z2，z3，z4點(diǎn)上的熱量轉(zhuǎn)移剛開始是一樣的，然后隨著時(shí)間的流逝和溫度的增加而逐漸分離。原

8、因在于最初大量的熱量轉(zhuǎn)移是由于錠子位置的增長造成的，和其他的耐熱時(shí)間較長的機(jī)床部件相比，這個(gè)位置能更快的達(dá)到熱量平衡。然而，隨著時(shí)間的過去，那些象導(dǎo)螺桿和欄這樣由位置決定熱量誤差的部件越來越多的引起合成熱量的轉(zhuǎn)移。結(jié)果，在不同的z坐標(biāo)中熱量的轉(zhuǎn)移具有不同的大小和熱量特性。但是，不同坐標(biāo)中的熱量轉(zhuǎn)移是隨z坐標(biāo)不斷改變的。韌哎芾萵孺逆韓稗諍亓苣儒掘覆莎緬啡睡幸瞥2.熱量誤差的回歸模型膘辱欞口鱺謔傘檫宸賤鲆瓞叱度囟亟皆史贗務(wù)熱量誤差的準(zhǔn)確預(yù)測是精確誤差補(bǔ)償?shù)闹匾h(huán)節(jié)。由于對機(jī)床結(jié)構(gòu)的認(rèn)識和熱源以及界限條件的不充分，根據(jù)熱量傳遞分析得出精確的數(shù)量測量是非常困難的。另外，在眾多的實(shí)用中，利用以經(jīng)驗(yàn)為基礎(chǔ)

9、的誤差模型進(jìn)行回歸分析和網(wǎng)絡(luò)分析來準(zhǔn)確預(yù)測熱量誤差是不可能的。熱量誤差是由多種熱源引起的，而只有錠子引起的熱量被認(rèn)為是最重要的熱源影響因素。外部熱源對機(jī)床精確度的影響能夠通過環(huán)境溫度來控制。根據(jù)已有的數(shù)據(jù)發(fā)現(xiàn)熱量誤差的改變是和時(shí)間成正比的。某一刻的誤差值受其前一刻和錠子的轉(zhuǎn)速影響。這樣，就形成了如下的熱量誤差表現(xiàn)模型。襠隱妹冊旆醒踣脒疼藎z ( t) 地點(diǎn)-t時(shí)間的熱量誤差誑隕憤哥柜往申知欄螂k , m 模型順序另洙灝稱氤率嫘茸照他ai , bi 模型系數(shù)臂誑看瘁瀋銓指嶁皙孕n ( t - i) 在時(shí)間t-i的錠子轉(zhuǎn)速頗閃睡侯彼救嘧湖謫音k和m的順序是有最終的誤差預(yù)測標(biāo)準(zhǔn)準(zhǔn)決定的。系數(shù)ai和b

10、i有人工網(wǎng)絡(luò)分析確定的。這個(gè)模型比其他因?yàn)镃形定閾值信號在各個(gè)結(jié)點(diǎn)上單一輸入的障礙更不容易感光。敉毓嘩枳轉(zhuǎn)卮郫淌繩趕為了能確定模型預(yù)測的精確度，使用了許多新的操作條件。圖4是一個(gè)在新的條件下的預(yù)測結(jié)果，它表明以速度為基礎(chǔ)的自動(dòng)回歸模型能夠在一個(gè)相對穩(wěn)定的環(huán)境下很好的描述熱量誤差。茺睦畚也隊(duì)呦盹隳舅缸圖3 熱量誤差的網(wǎng)絡(luò) 圖4 熱量誤差的預(yù)測 （1）.測量結(jié)果（2）. 預(yù)測結(jié)果翠杜蠢赤鯤麟浹迄榮矢3.熱量誤差的前期補(bǔ)償癩原恃爐怒懷然醯甏茇1.殺含簽鴇鋈鉬涿瓷知磐熱量誤差前期補(bǔ)償?shù)囊?guī)則如圖15所示。只要工件數(shù)控機(jī)床的程序完成，錠子的轉(zhuǎn)速和z坐標(biāo)就能知道。例如，每隔十分鐘，z的熱量誤差就會被模型計(jì)算

11、一次。這樣，就能通過把計(jì)算出來的z加到原來的z上來修改程序。因此，熱量誤差能夠在加工之前得到補(bǔ)償。穡穎輩錸邐峒萄炎燒著誤差補(bǔ)償?shù)挠行允怯稍S多切割試驗(yàn)來證實(shí)的。一些表面是由低于冷啟動(dòng)和一個(gè)小時(shí)不同轉(zhuǎn)速的旋轉(zhuǎn)磨碎的。如圖6所示，用表面磨碎的深度不同來評估在z方向的熱量誤差結(jié)果補(bǔ)償。試驗(yàn)表明這種不同由7m減少到2m。小形竣喋根玻逾盎崽櫨耄諺皈皤芝萍癍牮污測圖 5 通過程序的修正補(bǔ)償熱量誤差袢夯嗔騾噍窳俚遣蜀索荻蓮砦讜瘸舂韋惚鄞度圖 6 補(bǔ)償?shù)挠行院咳箮Z痹黏輥墅肆灑攣?zhàn)裼官p僬枚藤苠嘛鄰4.結(jié)論壙烤熳危滾埤芤盤喉枇撾艦朵逢奧駘縝戥鰩僑以上討論的是改善數(shù)控機(jī)床精確性的一個(gè)新方法。研究的核心是一個(gè)以錠

12、子轉(zhuǎn)速為基礎(chǔ)的誤差模型，而不是以溫度為基礎(chǔ)的傳統(tǒng)方法。通過修正數(shù)控機(jī)床的加工程序，熱量誤差能夠在加工之前得到補(bǔ)償，但并不是在實(shí)際操作中。通過使用這種方法，數(shù)控機(jī)床的精確度能夠大大的提高。笛被寵箋箸富禧檻埕吆葆龍?zhí)鸭武绵ンw摟跡渴艱譽(yù)赦燴毗臬撩砝僉嘧掇伽狻建呤浴寫陜梓傈呻撾瀵驁老靄腰譴覽度嚇炒穸蛸步緙麩覷甘郗參考文獻(xiàn)靛豁亥攔樹樘埠粞停礙1 Chen J S , Chiou G. Quick testing and modeling of thermally-induced errors of CNC machine tools. International Journal of Machine T

13、ools and Manufacture , 1995 , 35(7) 1 0631 074錠嶼睞攘窯榨顧喝肄長2 Chen J S. Computer-aided accuracy enhancement for multi2axis CNC machine tool. International Journal of Machine Tools and Manufacture , 1995 , 35(4) 593605捧池鴦晁氐腡勝攬硌撼3 Donmez M A. A general methodology for machine tool accuracy enhancement by

14、error compensation. Precision Engineering , 1986 , 8 (4) 187196鞋烘火縲帥鲴緩鶼壘皓4 Lo C H. An application of real-time error compensation on a turning center. International Journal of Machine Tools and Manufacture , 1995 , 35(12) 1 6691 682.樘濰鄢尋搗尉陌齒斥洙5 Yang S. The Improvement of thermal error modeling and c

15、ompensation on machine tools by CMAC neural net-work. International Journal of Machine Tools and Manufacture , 1995 , 36(4) 527537躋顴引冊酆淖筮憫賀娓6 李書和1 數(shù)控機(jī)床誤差補(bǔ)償?shù)难芯坎┦繉W(xué)位論文1 天津天津大學(xué),19961鎮(zhèn)揮蜩璋儕渙隘憤在涪陜堪七裉運(yùn)府輥忍局膂楞伽坼捭磚蛙脾瑾蕈霈譖柘顎噱采褶坤愎?jié)馊毱垴牧畏劝匈祮矩肝挂討匍旔揆壅止院塥熇☆@垸幟杭紂纘雷鷗巢觸蘄拼池榱圉涅哿蟻沒鏘胨橛膊尢持醚漠泓熔鮫耍轢昃睦塤藻敷祟痛倘賃靨儕耔暉涵繩殷撂迥繼蝻托頃火粞燙掄譙儕岑

16、鐳梁愫貉緄瑭妹撫仁鍪鲆鷙跛璁悒甩玲馗蓿遁叔妻諭董鋦瀚嬖屜堡另貨字瑚住側(cè)蠻錐管IMPROVING ACCURACY OF CNC MACHINE楮抓繢速寇钚驕軍遮幕TOOLS THROUGH COMPENSATION秦犒崗男鯡噼薪锝熒葙FOR THERMAL ERRORS哄羽掉缸抨鴆瑟銣褰迸Abstract： A method for improving accuracy of CNC machine tools through compensation for the thermal errors is studied. The thermal errors are obtained by 1

17、-D ball array and characterized by an auto regressive model based on spindle rotation speed. By revising the workpiece NC machining program , the thermal errors can be compensated before machining. The experiments on a vertical machining center show that the effectiveness of compensation is good.昃僑交

18、唄黝砼艷困奪查Key words : CNC machine tool Thermal error Compensation蔬焓狻綿氘茨涎圮廁齡0 INTRODUCTION鈄逸鹵它櫞冪陔料甓Improvement of machine tool accuracy is essential to quality cont rol in manufacturing processes. Thermally induced errors have been recognized as the largest cont ributor to overall machine inaccuracy and

19、 are probably the most formidable obstacle to obtaining higher level of machine accuracy. Thermal errors of machine tools can be reduced by the st ructural improvement of the machine tool it self through design and manufacturing technology. However , there are many physical limitations to accuracy w

20、hich can not be overcome solely by production and design techniques. So error compensation technology is necessary. In the past several years , significant effort s have been devoted to the study. Because thermal errors vary with time during machining ,most previous works have concent rated on real-

21、time compensation. The typical approach is to measure the thermal errors and temperature of several representative point s on the machine tools simultaneously in many experiment s , then build an empirical model which correlates thermal errors to the temperature statues by multi-variant regression a

22、nalysis or artificial neural network.During machining , the errors are predicted on-line according to the pre-established model and corrected by the CNC cont roller in real-time by giving additional signals to the feed-drive servo loop.However , very few practical cases of real-time compensation hav

23、e been reported to be applied to commercial machine tools today. Some difficulties hinder it s widespread application. First , it is tedious to measure thermal errors and temperature of many point s on the machine tools. Second ,the wires of temperature sensors influence the operating of the machine

24、 more or less. Third , thereal-time error compensation capability is not available on most machine tools.纜猴播箬琥刨鷸蜣鶴庋In order to improve the accuracy of production-class CNC machine tools , a novel method is proposed. Although a number of heat sources cont ribute to the thermal errors , the f riction

25、of spindle bearings is regarded as the main heat source. The thermal errors are measureed by 1-D ball array and a spindle-mounted probe. An auto regressive model based on spindle rotation speed is then developed to describe the time-variant thermal error. Using this model , thermal errors can be pre

26、dicted as soon as the workpiece NC machining program is made. By modifying the program , the thermal errors are compensated before machining. The effort and cost of compensation are greatly reduced. This research is carried on a JCS2018 vertical machining center.慳詩忱先艙刨選夂各孝1 EXPERIMENTAL WORK椋賑鋟兜丫詘虛壟

27、廂哮For compensation purpose , the principal interest is not the deformation of each machine component , but the displacement of the tool with respect to the workpiece. In the vertical machining center under investigation , the thermal errors are the combination of the expansion of spindle , the disto

28、rtion of the spindle housing , the expansion of three axes and the distortion of the column.類痞已恿翮蹕釤鷦裱字Due to the dimensional elongation of leadscrew and bending of the column , the thermal errors are not only time-variant in the time span but also spatial-variant over the entire machine working spac

29、e.噪脫諷霧類蕙狼鶚瓢秋In order to measure the thermal errors quickly , a simple protable gauge , i. e. , 1-D ball array , is utilized. 1-D ball array is a rigid bar with a series of balls fixed on it with equal space. The balls have the same diameter and small sphericity errors. The ball array is used as a re

30、ference for thermal error measurement . A lot of pre-experiment s show that the thermal errors in z-axis are far larger than those in x-axis and y-axis , therefore major attention is drawn on the thermal errors in z-axis. Thermal errors in the other two axes can be obtained in the same way.噩哌莓輦禁絀阝擋廒

31、佾The measuring process is shown in Fig.1. A probe is mounted on the spindle housing and 1-D ball array is mounted on the working table. Initially , the coordinates of the balls are measured under cold condition. Then the spindle is run at a testing condition over a period of time to change the machi

32、ne thermal status. The coordinates of the balls are measured periodically. The thermal drift s of the tool are obtained by subt racting the ball coordinates under the new thermal status f rom the reference coordinates under initial condition. Because it takes only about 1 min to finish one measureme

33、nt , the thermal drifts of the machine under different z coordinates can be evaluated quickly and easily. According to the rate of change , the thermal errors and the rotation speed are sampled by every 10 min. Since only the drift s of coordinates deviated from the cold condition but not the absolu

34、te dimensions of the gauge are concerned , accuracy and precise inst rument such as a laser interferometer is not required. There are only four measurement point s z 1 ,z 2 , z 3 , z 4 to cover the z-axis working range whose coordinates are - 50 , - 150 , - 250 , - 350 respectively. Thermal errors a

35、t other coordinates can be obtained by an interpolating function.隋跖伴蓯盅焯儕聚戴蚨Previous experiment s show that the thermally induced displacement between the spindle housing and the working table is the same with that between the spindle and table. So the thermal errorsz measured reflect those in real c

36、utting condition with negligible error.湄疊炫瀕熒褥漲鰾嬙噌In order to obtain a thorough impression of the thermal behavior of the machine tool and曹剃猻捂臭抑隧神揄噠identify the error model accurately , a measurement strategy is developed. Various loads of the spindle speed are applied. They are divided into three ca

37、tegories as the following : (1) The constant speed ; (2) The speed spect rum ; (3) The speed simulating real cutting condition. The effect of the heat generated by the cutting process is not taken into account here. However , the influence of the cutting process on the thermal behaviour of the total

38、 machine structure is regarded to be negligible in finishing process.擤癌阼廄曦匍購顰稍刈In this machine , the most significant heat sources are located in the z-axis. Thermal errors in z direction on different x and y coordinates are approximately the same. It implies that the positions of x-carriage and y-c

39、arriage have no strong influence on the z-axis thermal errors.份表鎦蒼援椹瞍叁薟忒Fig.1（L） Thermal error measurement 1.Spindle mounted probe 2.1-D ball array 救鰣?zhí)嗜A駿玲煲轂劃逸庋靄詫畚寬佼濰秣斂碌Fig.2 （R）Thermal errors at different z coordinates 1. z = - 50 2. z = - 150 3. z = - 250 4. z = - 350晝詁靶輩銅柳遑撤岬訌搗鐳湯邗徹昴虜慣邗瀣F(xiàn)ig.2 plot

40、s the time-history of thermal drift z at different z coordinates under a test . It魴謝砌拮莩壬搐成圾缺shows that the resultant thermal drift s are obvious position-dependent . The thermal drift s at z 1 ,z 2 , z 3 , z 4 are coincident initially but separate gradually as time passes and temperature increases.娃

41、霍愈憤貂頁琿菇樓惋The reason is that , initially most of thermal drift s result f rom the position-independent thermal growth of the spindle housing which would rise fast and go to thermal-equilibrium quickly compared to other machine component s with longer thermal-time-constant s. However , as time passes

42、, those position-dependent thermal errors such as the lead screw and the column cont ribute to the resultant thermal drift s of the tool more and more. As a result , the thermal drifts at different z coordinates have different magnitude and thermal characteristics. However , the thermal errors at di

43、fferent coodinates vary with z coordinate continuously.貔傲詡鋌曷肴曾字修繯2 AR MODEL FOR THERMAL ERROR路澀撅匭輯誡檣慝彖瓷Precise prediction of thermal errors is an important step for accurate error compensation.桶鲇輝刊桊簍茭仿絨人Since the knowledge of the machine structure , the heat source and the boundary condition are ins

44、ufficient , a precise quantitative prediction based on theoretical heat transfer analysis is quite difficult . On the other hand , empirical-based error models using regression analysis and neural networks have been demonst rated to predict thermal errors with satisfactory accuracy in much applicati

45、on.蟥觜掠瀑鎵蛟雖住仔怪Thermal errors are caused by various heat sources. Only the influence of the heat caused by the fiction of spindle which is the most significant heat source is considered. The influence of external heat source on machining accuracy can be diminished by environment temperature control.壇莜

46、俗定釵砭螗棰貫何From the obtained data , it is found that thermal errors vary continuously with time. The離燠緄闔哺蜆臥陋謳映value of error at one moment is influenced by that of the previous moment and the rotation speed of spindle. So a model representing the behavior of the thermal errors as written is the form嶁兢呤

47、嗒閌竊令嚦推瀟騷摟冉俐的黑鶉瘰珍倉where z ( t) Thermal error at time t浦沙躔儺浯渴鐮咕鈄螅k , m Order of the model委嵌蟪庾茍褓晝朗傯郅ai , bi Coefficient of the model覽收蘞搠蛑徉毫斑痖媒n ( t - i) Spindle rotation speed at time t - i頁懂馀懇鄙鯉俁怵鷥吹The order k and m are determined by the final prediction-error criterion. The coefficients ai瑭嘞饌喃乳芍榷蟠蘆渺a

48、nd bi are estimated by artificial neural network technique. A neural network is a multiple nonlinear regression equation in which the coefficient s are called weight s and are t rained with an iterative technique called back propagation. It is less sensitive than other modeling technique to individu

49、al input failure due to thresholding of the signals by the sigmoid functions at each node. The neural network for this problem is shown in Fig.3. ( k = 1 , m = 0) . The number of hidded nodes is determined by a trial-and error procedure.凹鹿灄洚乏挨搖尺方亨Using the data obtained (thermal errors and correspon

50、dence speed) , four models for the errors at z 1 , z 2 , z 3 and z 4 are established. Thermal errors at positions other than z 1 , z 2 , z 3 , z 4 are calculated by an interpolating function. So the errors at any z coordinates can be obtained.撿擱翱枸匠衛(wèi)恚獯擄幫In order to verify the prediction accuracy of t

51、he model , a number of new operation conditions are used. Fig14 shows an example of predicted result on a new condition. It shows that the auto regressive model based on speed can descibe thermal errors well in a relative stable environment .閏寅愕岵藕荮篳猞宕于煺湓酴綦姿蒔荏逕釋銅Fig.3 A neural network for thermal err

52、orsFig.4 Thermal error predicting 櫛啡浮蜣墻砑烀麗嘸喂1.Measuring results 2Predicting results俞賭哨寮蟬疤苠坍梧舟3 PRE-COMPENSATION FOR THERMAL ERRORS咄蔚衙近軒譜展邵桃锍The principle of pre-compensation for thermal errors is shown in Fig.5. The spindle rotation speed and the z coordinates are known as soon as the workpiece NC m

53、achining program is made.霜連瓜錢滌嘈劓將樓鎂By , for example , every 10 min , the thermal errors z are calculated by the model. Then the program is corrected by adding the calculated z to the original z . So the thermal errors are compensated before machining.縐格托扉姬骶脧邂縣始The effectiveness of the error compensa

54、tion is verified by many cutting test s. Several surfaces are milled under cold start and after 1 h run with varying speeds. As shown in Fig.6 , the depth difference of the milled surface is used to evaluate the compensation result of the thermal errors in z direction. It shows that the difference i

55、s reduced from 7m to 2m.詵懇業(yè)猿誅含飽擦盜徜Fig.5 Compensation for thermal errors by revising machining program觫委錁奕尷壚猩歇豫沸謁吩篳縉忄脊於耪徊壢Fig.6 The effectiveness of compensation啦滯介樅瑪皿蓄聰些戢榭拿乳仍猢古砷拓跤4 CONCLUSIONS懊錨裊芪以疥呢鉭薏洱A novel method for improving the accuracy of CNC machine tools is discussed. The core of the study

56、 is an error model based on spindle rotation speed but not on temperature like conventional approach. By revising the NC workpiece machining program , the thermal errors can be compensated before machining but not in real-time. By using the method , the accuracy of machine tools can be increased eco

57、nomically.溧善柯坐許鍰濂吧詈雎References侃娉棰賅寰嵯逋楚蛾傯1 Chen J S , Chiou G. Quick testing and modeling of thermally-induced errors of CNC machine tools. International始粒鹼埤勖綴艇退駙耳Journal of Machine Tools and Manufacture , 1995 , 35(7) 1 0631 074劈褊肇場痱健飪蕎銀榀2 Chen J S. Computer-aided accuracy enhancement for multi-axis

58、 CNC machine tool. International Journal of Machine Tools and Manufacture , 1995 , 35(4) 593605鈕俅鯰裙篩醪榜篤灞霽3 Donmez M A. A general methodology for machine tool accuracy enhancement by error compensation. Precision Engineering , 1986 , 8 (4) 187196芐瘟淦城沾息磲呃樓齪4 Lo C H. An application of real-time error compensation on a turning center. International Journal of Machine Tools and Manufacture , 1995 , 35(12) 1 6691 682.舸鹋敲苒嗒酰呷獨(dú)燁盱5 Yang S. The Improvement of thermal error modeling and compensation on machine tools by CMAC neural net