外文翻譯--數(shù)控機(jī)床幾何誤差及其補(bǔ)償方法研究

1、<p>　　畢業(yè)設(shè)計(jì)(論文)外文資料翻譯</p><p>　　系　　部： 機(jī)械工程系 </p><p>　　專 業(yè)： 機(jī)械工程及自動(dòng)化 </p><p>　　姓 名： </p><

2、;p>　　學(xué) 號(hào)： </p><p>　　外文出處： CNC Machine Tool Geometric Error and its Compensation Method </p><p>　　附 件： 1.外文資料翻譯譯文；2.外文原文。 </p><p>　　注：請(qǐng)將該封面與附件裝

3、訂成冊(cè)。</p><p>　　附件1：外文資料翻譯譯文</p><p>　　數(shù)控機(jī)床幾何誤差及其補(bǔ)償方法研究</p><p>　　摘要：對(duì)數(shù)控機(jī)床幾何誤差產(chǎn)生的原因作了比較詳細(xì)的分析，將系統(tǒng)誤差的補(bǔ)償方法進(jìn)行了歸納，并在此基礎(chǔ)上闡述了各類誤差補(bǔ)償方法的應(yīng)用場合，為進(jìn)一步實(shí)現(xiàn)機(jī)床精度的軟升級(jí)打下基礎(chǔ)。 </p><p>　　關(guān)鍵詞：數(shù)控機(jī)床；幾

4、何誤差；誤差補(bǔ)償 </p><p><b>　　前言 </b></p><p>　　提高機(jī)床精度有兩種方法。一種是通過提高零件設(shè)計(jì)、制造和裝配的水平來消除可能的誤差源，稱為誤差防止法 (error prevention)。該方法一方面主要受到加工母機(jī)精度的制約，另一方面零件質(zhì)量的提高導(dǎo)致加工成本膨脹，致使該方法的使用受到一定限制。另一種叫誤差補(bǔ)償法(error com

5、pensation)，通常通過修改機(jī)床的加工指令，對(duì)機(jī)床進(jìn)行誤差補(bǔ)償，達(dá)到理想的運(yùn)動(dòng)軌跡，實(shí)現(xiàn)機(jī)床精度的軟升級(jí)。研究表明，幾何誤差和由溫度引起的誤差約占機(jī)床總體誤差的70%，其中幾何誤差相對(duì)穩(wěn)定，易于進(jìn)行誤差補(bǔ)償。對(duì)數(shù)控機(jī)床幾何誤差的補(bǔ)償，可以提高整個(gè)機(jī)械工業(yè)的加工水平，對(duì)促進(jìn)科學(xué)技術(shù)進(jìn)步，提高我國國防能力，繼而極大增強(qiáng)我國的綜合國力都具有重大意義。 </p><p>　　1幾何誤差產(chǎn)生的原因 </p>

6、;<p>　　普遍認(rèn)為數(shù)控機(jī)床的幾何誤差由以下幾方面原因引起： </p><p>　　1.1 機(jī)床的原始制造誤差 </p><p>　　是指由組成機(jī)床各部件工作表面的幾何形狀、表面質(zhì)量、相互之間的位置誤差所引起的機(jī)床運(yùn)動(dòng)誤差，是數(shù)控機(jī)床幾何誤差產(chǎn)生的主要原因。 </p><p>　　1.2 機(jī)床的控制系統(tǒng)誤差 </p><p>

7、　　包括機(jī)床軸系的伺服誤差（輪廓跟隨誤差），數(shù)控插補(bǔ)算法誤差。 </p><p>　　1.3 熱變形誤差 </p><p>　　由于機(jī)床的內(nèi)部熱源和環(huán)境熱擾動(dòng)導(dǎo)致機(jī)床的結(jié)構(gòu)熱變形而產(chǎn)生的誤差。 </p><p>　　1.4切削負(fù)荷造成工藝系統(tǒng)變形所導(dǎo)致的誤差 </p><p>　　包括機(jī)床、刀具、工件和夾具變形所導(dǎo)致的誤差。這種誤差又稱為“讓

8、刀”，它造成加工零件的形狀畸變，尤其當(dāng)加工薄壁工件或使用細(xì)長刀具時(shí)，這一誤差更為嚴(yán)重。 </p><p>　　1.5 機(jī)床的振動(dòng)誤差 </p><p>　　在切削加工時(shí)，數(shù)控機(jī)床由于工藝的柔性和工序的多變，其運(yùn)行狀態(tài)有更大的可能性落入不穩(wěn)定區(qū)域，從而激起強(qiáng)烈的顫振。導(dǎo)致加工工件的表面質(zhì)量惡化和幾何形狀誤差。 </p><p>　　1.6 檢測系統(tǒng)的測試誤差 <

9、/p><p>　　包括以下幾個(gè)方面： </p><p>　?。?）由于測量傳感器的制造誤差及其在機(jī)床上的安裝誤差引起的測量傳感器反饋系統(tǒng)本身的誤差； </p><p>　?。?）由于機(jī)床零件和機(jī)構(gòu)誤差以及在使用中的變形導(dǎo)致測量傳感器出現(xiàn)的誤差。 </p><p>　　1.7 外界干擾誤差 </p><p>　　由于環(huán)境和運(yùn)

10、行工況的變化所引起的隨機(jī)誤差。 </p><p><b>　　1.8 其它誤差 </b></p><p>　　如編程和操作錯(cuò)誤帶來的誤差。 </p><p>　　上面的誤差可按照誤差的特點(diǎn)和性質(zhì)，歸為兩大類：即系統(tǒng)誤差和隨機(jī)誤差。 </p><p>　　數(shù)控機(jī)床的系統(tǒng)誤差是機(jī)床本身固有的誤差，具有可重復(fù)性。數(shù)控機(jī)床的幾何

11、誤差是其主要組成部分，也具有可重復(fù)性。利用該特性，可對(duì)其進(jìn)行“離線測量”，可采用“離線檢測——開環(huán)補(bǔ)償”的技術(shù)來加以修正和補(bǔ)償，使其減小，達(dá)到機(jī)床精度強(qiáng)化的目的。 </p><p>　　隨機(jī)誤差具有隨機(jī)性，必須采用“在線檢測——閉環(huán)補(bǔ)償”的方法來消除隨機(jī)誤差對(duì)機(jī)床加工精度的影響，該方法對(duì)測量儀器、測量環(huán)境要求嚴(yán)格，難于推廣。 </p><p>　　2幾何誤差補(bǔ)償技術(shù) </p>

12、<p>　　針對(duì)誤差的不同類型，實(shí)施誤差補(bǔ)償可分為兩大類。隨機(jī)誤差補(bǔ)償要求“在線測量”，把誤差檢測裝置直接安裝在機(jī)床上，在機(jī)床工作的同時(shí)，實(shí)時(shí)地測出相應(yīng)位置的誤差值，用此誤差值實(shí)時(shí)的對(duì)加工指令進(jìn)行修正。隨機(jī)誤差補(bǔ)償對(duì)機(jī)床的誤差性質(zhì)沒有要求，能夠同時(shí)對(duì)機(jī)床的隨機(jī)誤差和系統(tǒng)誤差進(jìn)行補(bǔ)償。但需要一整套完整的高精度測量裝置和其它相關(guān)的設(shè)備，成本太高，經(jīng)濟(jì)效益不好。文獻(xiàn)[4] 進(jìn)行了溫度的在線測量和補(bǔ)償，未能達(dá)到實(shí)際應(yīng)用。系統(tǒng)誤差補(bǔ)償

13、是用相應(yīng)的儀器預(yù)先對(duì)機(jī)床進(jìn)行檢測，即通過“離線測量”得到機(jī)床工作空間指令位置的誤差值，把它們作為機(jī)床坐標(biāo)的函數(shù)。機(jī)床工作時(shí)，根據(jù)加工點(diǎn)的坐標(biāo)，調(diào)出相應(yīng)的誤差值以進(jìn)行修正。要求機(jī)床的穩(wěn)定性要好，保證機(jī)床誤差的確定性，以便于修正，經(jīng)補(bǔ)償后的機(jī)床精度取決于機(jī)床的重復(fù)性和環(huán)境條件變化。數(shù)控機(jī)床在正常情況下，重復(fù)精度遠(yuǎn)高于其空間綜合誤差，故系統(tǒng)誤差的補(bǔ)償可有效的提高機(jī)床的精度，甚至可以提高機(jī)床的精度等級(jí)。迄今為止，國內(nèi)外對(duì)系統(tǒng)誤差的補(bǔ)償方法有很多

14、，可分為以下幾種方法： </p><p>　　2.1單項(xiàng)誤差合成補(bǔ)償法 </p><p>　　這種補(bǔ)償方法是以誤差合成公式為理論依據(jù)，首先通過直接測量法測得機(jī)床的各項(xiàng)單項(xiàng)原始誤差值，由誤差合成公式計(jì)算補(bǔ)償點(diǎn)的誤差分量，從而實(shí)現(xiàn)對(duì)機(jī)床的誤差補(bǔ)償。對(duì)三坐標(biāo)測量機(jī)進(jìn)行位置誤差測量的當(dāng)屬利特, 運(yùn)用三角幾何關(guān)系,推導(dǎo)出了機(jī)床各坐標(biāo)軸誤差的表示方法,沒有考慮轉(zhuǎn)角的影響。較早進(jìn)行誤差補(bǔ)償?shù)膽?yīng)是何曼教授

15、，針對(duì)型號(hào)Moore 5-Z(1)的三坐標(biāo)測量機(jī)，在16小時(shí)內(nèi)，測量了工作空間內(nèi)大量的點(diǎn)的誤差，在此過程中考慮了溫度的影響，并用最小二乘法對(duì)誤差模型參數(shù)進(jìn)行了辨識(shí)。由于機(jī)床運(yùn)動(dòng)的位置信號(hào)直接從激光干涉儀獲得，考慮了角度和直線度誤差的影響，獲得比較滿意的結(jié)果。1985年G. Zhang成功的對(duì)三坐標(biāo)測量機(jī)進(jìn)行了誤差補(bǔ)償。測量了工作臺(tái)平面度誤差，除在工作臺(tái)邊緣數(shù)值稍大，其它不超過1μm，驗(yàn)證了剛體假設(shè)的可靠性。使用激光干涉儀和水平儀測量得的

16、21項(xiàng)誤差，通過線性坐標(biāo)變換進(jìn)行誤差合成，并實(shí)施了誤差補(bǔ)償。X-Y平面上測量試驗(yàn)表明，補(bǔ)償前,在所有測量點(diǎn)中誤差值大于20μm的點(diǎn)占20％，在補(bǔ)償后，不超過20％的點(diǎn)的誤差大于2μm，證明精度提高了近10倍。 </p><p>　　除了坐標(biāo)測量機(jī)的誤差補(bǔ)償以外，數(shù)控機(jī)床誤差補(bǔ)償?shù)难芯恳踩〉昧艘欢ǖ某晒?。?977年斯提克教授運(yùn)用矢量圖的方法，分析了機(jī)床各部件誤差及其對(duì)幾何精度的影響，奠定了機(jī)床幾何誤差進(jìn)一步研究的

17、基礎(chǔ)。福勞瑞和其合作者也對(duì)該方法進(jìn)行了研究，得出了機(jī)床幾何誤差的通用模型,對(duì)單項(xiàng)誤差合成補(bǔ)償法作出了貢獻(xiàn)。金奈特更進(jìn)一步將該方法運(yùn)用于在線的誤差補(bǔ)償,獲得了比較理想的結(jié)果。陳特建立了32項(xiàng)誤差模型，其中多余的11項(xiàng)是有關(guān)溫度和機(jī)床原點(diǎn)誤差參數(shù)，對(duì)臥式加工中心的補(bǔ)償試驗(yàn)表明，精度提高10倍。因斯勞特幾乎使用了同張博士一樣的測量方法，對(duì)三坐標(biāo)銑床21項(xiàng)誤差進(jìn)行了測量，運(yùn)用誤差合成法得出了誤差模型，補(bǔ)償后的結(jié)果分別用激光干涉儀和DBB系統(tǒng)進(jìn)行

18、了檢驗(yàn)，證明機(jī)床精度得以提升。 </p><p>　　2.2誤差直接補(bǔ)償法 </p><p>　　這種方法要求精確地測出機(jī)床空間矢量誤差，補(bǔ)償精度要求越高，測量精度和測量的點(diǎn)數(shù)就要求越多，但要詳盡地知道測量空間任意點(diǎn)的誤差是不可能的，利用插值的方法求得補(bǔ)償點(diǎn)的誤差分量，進(jìn)行誤差修正，該種方法要求建立和補(bǔ)償時(shí)一致的絕對(duì)測量坐標(biāo)系。 </p><p>　　1981年,在

19、不同的載荷和溫度條件下，對(duì)機(jī)床工作空間點(diǎn)的誤差進(jìn)行了測量,構(gòu)成誤差矢量矩陣,獲得機(jī)床誤差信息。將該誤差矩陣存入計(jì)算機(jī)進(jìn)行誤差補(bǔ)償。類似的研究主要通過測量機(jī)床工作空間內(nèi)，標(biāo)準(zhǔn)參考件上多個(gè)點(diǎn)的相對(duì)誤差，以第一個(gè)為基準(zhǔn)點(diǎn)，然后換算成絕對(duì)坐標(biāo)誤差，通過插值的方法進(jìn)行誤差補(bǔ)償，結(jié)果表明精度提高了2～4倍。何曼則運(yùn)用三維線性（LVTDS）測量裝置,得到機(jī)床空間27個(gè)點(diǎn)的誤差（分辨率0.25μm，重復(fù)精度1μm），進(jìn)行了類似的工作。進(jìn)一步考慮到溫度的

20、影響，每間隔1.2小時(shí)測量一次，共測量8次，對(duì)誤差補(bǔ)償結(jié)果進(jìn)行了有關(guān)溫度系數(shù)的修。這種方法的不足之處是測量工作量大，存儲(chǔ)數(shù)據(jù)多。目前，還沒有完全合適的儀器，也限制了該方法的進(jìn)一步運(yùn)用和發(fā)展。 </p><p>　　2.3相對(duì)誤差分解、合成補(bǔ)償法 </p><p>　　大多數(shù)誤差測量方法只是得到了相對(duì)的綜合誤差，據(jù)此可以從中分解得到機(jī)床的單項(xiàng)誤差。進(jìn)一步利用誤差合成的辦法，對(duì)機(jī)床誤差補(bǔ)償是可

21、行的。目前，國內(nèi)外對(duì)這方面的研究也取得一定進(jìn)展。 </p><p>　　2000年美國Michigan大學(xué)Jun Ni教授指導(dǎo)的博士生做了這樣的嘗試，運(yùn)用球桿儀(TBB)對(duì)三軸數(shù)控機(jī)床不同溫度下的幾何誤差進(jìn)行了測量，建立了快速的溫度預(yù)報(bào)和誤差補(bǔ)償模型，進(jìn)行了誤差補(bǔ)償。Christopher運(yùn)用激光球桿儀（LBB），在30分鐘內(nèi)獲得了機(jī)床的誤差信息，建立了誤差模型, 在9個(gè)月的時(shí)間間隔內(nèi),對(duì)誤差補(bǔ)償結(jié)果進(jìn)行了5次評(píng)

22、價(jià),結(jié)果表明，通過軟件誤差補(bǔ)償?shù)姆椒梢蕴岣邫C(jī)床的精度，并可保持精度在較長時(shí)間內(nèi)不變。 </p><p>　　誤差合成法，要求測出機(jī)床各軸的各項(xiàng)原始誤差，比較成熟的測量方法是激光干涉儀，測量精度高。用雙頻激光干涉儀進(jìn)行誤差測量，需時(shí)間長，對(duì)操作人員調(diào)試水平要求高。更主要的是對(duì)誤差測量環(huán)境要求高，常用于三坐標(biāo)測量機(jī)的檢測，不適宜生產(chǎn)現(xiàn)場操作。相對(duì)誤差分解、合成補(bǔ)償法，測量方法相對(duì)簡單，一次測量可獲得整個(gè)圓周的數(shù)據(jù)信

23、息，同時(shí)可以滿足機(jī)床精度的檢測和機(jī)床評(píng)價(jià)。目前也有不少的誤差分解的方法，由于機(jī)床情況各異，難以找到合適的通用數(shù)學(xué)模型進(jìn)行誤差分解，并且對(duì)測量結(jié)果影響相同的原始誤差項(xiàng)不能進(jìn)行分解，也難以推廣應(yīng)用。誤差的直接補(bǔ)償法，一般以標(biāo)準(zhǔn)件為對(duì)照獲得空間矢量誤差，進(jìn)行直接補(bǔ)償，少了中間環(huán)節(jié)，更接近機(jī)床的實(shí)用情況。但獲得大量的信息量需要不同的標(biāo)準(zhǔn)件，難以實(shí)現(xiàn)，這樣補(bǔ)償精度就受到限制。 </p><p>　　在國內(nèi)，許多研究機(jī)構(gòu)與高

24、校近幾年也進(jìn)行了機(jī)床誤差補(bǔ)償方面的研究。1986北京機(jī)床研究所開展了機(jī)床熱誤差的補(bǔ)償研究和坐標(biāo)測量機(jī)的補(bǔ)償研究。1997年天津大學(xué)的李書和等進(jìn)行了機(jī)床誤差補(bǔ)償?shù)慕：蜔嵴`差補(bǔ)償?shù)难芯俊?998年天津大學(xué)的劉又午等采用多體系統(tǒng)建立了機(jī)床的誤差模型，給出了幾何誤差的22線、14線 、9線激光干涉儀測量方法，1999年他們還對(duì)數(shù)控機(jī)床的誤差補(bǔ)償進(jìn)行了全面的研究，取得了可喜的成果。1998年上海交通大學(xué)的楊建國進(jìn)行了車床熱誤差補(bǔ)償?shù)难芯俊?99

25、6到2000年在國家自然科學(xué)基金和國家863計(jì)劃項(xiàng)目的支持下，華中科技大學(xué)開展了對(duì)數(shù)控機(jī)床幾何誤差補(bǔ)償以及基于切削力在線辯識(shí)的智能自適應(yīng)控制的研究,取得了一些成果。 </p><p>　　綜上所述：進(jìn)行數(shù)控機(jī)床的誤差補(bǔ)償，誤差測量是關(guān)鍵，誤差模型是基礎(chǔ)。通過誤差的補(bǔ)償，可以有效的提高機(jī)床的精度，為提升我國</p><p><b>　　附件2：外文原文</b></

26、p><p>　　CNC machine tool geometric error and its compensation method </p><p>　　Abstract: The geometric error of CNC machine tools were the cause of a more detailed analysis, the system error compen

27、sation methods were summed up, and on this basis on a variety of methods of error compensation applications, in order to further the achievement of precision machine tools lay the foundation for soft upgrade. </p>

28、<p>　　Keywords: CNC machine tools; geometric error; Error Compensation</p><p><b>　　Foreword </b></p><p>　　Improve the precision machine tool There are two ways. One is by impro

29、ving the part design, manufacture and assembly level to eliminate a possible source of error is called error Prevention Act (error prevention). This method is the main subject on the one hand, the precision machine tool

30、processing constraints, on the other hand, lead to improving the quality of parts processing costs of expansion, with the result that the use of this method are subject to certain restrictions. Another called E</p>

31、<p>　　1 Geometric Error Causes </p><p>　　Generally agreed that the geometric error of CNC machine tools from the following causes: </p><p>　　1.1 Machine Tool original manufacturing error

32、</p><p>　　Machine refers to the composition of the various components work surface geometry, surface quality, the position error between the machine caused by errors in CNC machine tools is the main reason f

33、or the geometric error. </p><p>　　1.2 Machine Control System Error </p><p>　　Including the machine tool axis servo error (follow the outline of error), CNC interpolation algorithm error. </p&

34、gt;<p>　　1.3 THERMAL DEFORMATION </p><p>　　As the machine's internal heat source and environmental thermal disturbances resulting in the structure of machine tool thermal distortion resulting from

35、 errors. </p><p>　　1.4-cutting process system load caused by the deformation caused by error </p><p>　　Including machine tools, cutting tools, workpiece and fixture deformation caused by error.

36、This error also known as "Let's Knife", which resulted in the shape of the processing parts distortion, especially when processing or use of thin-walled workpiece slender tool, this error even more serious.

37、</p><p>　　1.5 machine vibration error </p><p>　　In cutting, the CNC machine tools as a result of process flexibility and the ever-changing process, and its operation there is a greater possibili

38、ty of falling into the hands of unstable region, which aroused strong flutter. Resulting in workpiece surface quality and geometry of the deterioration of the error. </p><p>　　1.6 Detection System test error

39、 </p><p>　　Include the following: </p><p>　　(1) as a result of measurement sensors and its application in machine tool manufacturing error on the installation of sensor error caused by the error

40、 feedback system itself; </p><p>　　(2) as a result of machine tool parts and bodies, as well as in the use of error of deformation lead to sensor error. </p><p>　　1.7 outside interference error

41、</p><p>　　Because of the environment and changes in operating conditions caused by random error. </p><p>　　1.8 Other errors </p><p>　　Such as the programming and operation of an err

42、or caused by error.</p><p>　　The above error may be in accordance with the characteristics and the nature of the error, into two broad categories: namely, system error and random error. </p><p>

43、　　CNC machine tools is the systematic errors inherent machine error, with repeatability. CNC machine tool geometric error is the main component of the also repeatability. Use of the properties may be "off-line measu

44、rement" can be "off-line detection - open-loop compensation" technology to be amended and compensation to smaller, precision machine tools to achieve the purpose of strengthening.Random error with a random

45、, must be used "on-line detection - the closed-loop compensation" approach to the </p><p>　　2 Geometric Error Compensation Technology </p><p>　　For the different types of error, the im

46、plementation of error compensation can be divided into two broad categories. Random error compensation request "line measurement", the error detection devices installed in the machine directly, in the machine w

47、ork, in real time to detect the location of the corresponding error, use this real-time error of processing instructions be amended. Random error compensation of machine tool does not require the nature of the error can

48、be at the same time machine ra</p><p>　　2.1 Synthesis of single error compensation method </p><p>　　The compensation method is based on error of the theoretical basis for the synthetic formula,

49、first of all through direct measurement machine measured the single original error by the error of synthetic formula for calculating compensation point error components in order to achieve the error compensation of machi

50、ne tools. Of coordinate measuring machine for measuring the location of error among Leete, the use of triangular geometry, derived the coordinate axis machine error method, without consi</p><p>　　Apart from

51、the coordinate measuring machine error compensation, the NC machine tool error compensation research has made some achievements. In 1977 Professor Schultschik vector method of analysis of the various components of error

52、of machine tool and its impact on the geometric precision of the effect of laying the machine tool geometric error basis for further study. Ferreira and his collaborators have conducted a study of the method, the geometr

53、ic error of machine tools come to a common model </p><p>　　2.2 Error Compensation Act directly </p><p>　　This approach requires accurate measurement of machine tool space vector error, compensat

54、ion precision higher measuring accuracy and measuring the number of points required more detail but know that any point in space measurement error is not possible, the use of interpolation methods to seek compensation po

55、int of error components for error correction, the approach requires the establishment and compensation consistent absolute measurement coordinate system. </p><p>　　In 1981, Dufour and Groppetti in different

56、load and temperature conditions, the working space of machine-point margin of error was measured, constitutes error vector matrix, was machine error message. The error matrix into a computer error compensation. There are

57、 similar studies ACOkafor et al, by measuring the machine working space, the standard reference piece on the multiple points of relative error to first for the reference point, and then converted into absolute coordinate

58、s error, through </p><p>　　2.3 relative error decomposition, synthetic Compensation Act </p><p>　　Most of error of measurement methods have been only a relatively comprehensive error, which can

59、be machine decomposition single error. Further use of synthetic methods of error of machine tool error compensation is feasible. At present, domestic and international research in this area have also made some progress.

60、</p><p>　　Michigan University of the United States in 2000, Professor Jun Ni guidance Chen Guiquan doctoral made such attempt, the use of clubs Miriam (TBB) of three-axis CNC machine tools at different tempe

61、ratures were measured geometric error, the establishment of a rapid temperature forecasts and error compensation model, carried out error compensation. Christopher uses laser clubs Miriam (LBB), in 30 minutes of the mach

62、ine tool error information, the establishment of error model, in the 9-month time i</p><p>　　Error synthesis requires the axis machine tools to detect the original error, more mature measurement method is la

63、ser interferometer, measurement and high accuracy. Use dual-frequency laser interferometer measurement error, take a long time to debug the level of the operator requirements. More important is the measurement error of t

64、he high environmental requirements, commonly used in the coordinate measuring machine testing, not suitable for the production operation at the scene. Relative error </p><p>　　To sum up: for error compensati

65、on of CNC machine tools, error measurement is the key, error model is the foundation. Through error compensation can effectively improve the accuracy of machine tools, to enhance the level of China's manufacturing in