數(shù)控機(jī)床相關(guān)畢業(yè)設(shè)計(jì)翻譯---通過(guò)熱量誤差補(bǔ)償來(lái)改善數(shù)控機(jī)床的精確度

1、<p>　　IMPROVING ACCURACY OF CNC MACHINE</p><p>　　TOOLS THROUGH COMPENSATION</p><p>　　FOR THERMAL ERRORS</p><p>　　Abstract： 　A method for improving accuracy of CNC machine tools

2、 through compensation for the thermal errors is studied. The thermal errors are obtained by 1-D ball array and characterized by an auto regressive model based on spindle rotation speed. By revising the workpiece NC machi

3、ning program , the thermal errors can be compensated before machining. The experiments on a vertical machining center show that the effectiveness of compensation is good.</p><p>　　Key words : CNC machine too

4、l 　　Thermal error 　　Compensation</p><p>　　0 　INTRODUCTION</p><p>　　Improvement of machine tool accuracy is essential to quality cont rol in manufacturing processes. Thermally induced errors have

5、 been recognized as the largest cont ributor to overall machine inaccuracy and are probably the most formidable obstacle to obtaining higher level of machine accuracy. Thermal errors of machine tools can be reduced by th

6、e st ructural improvement of the machine tool it self through design and manufacturing technology. However , there are many physical limitations to accur</p><p>　　In order to improve the accuracy of producti

7、on-class CNC machine tools , a novel method is proposed. Although a number of heat sources cont ribute to the thermal errors , the f riction of spindle bearings is regarded as the main heat source. The thermal errors are

8、 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 pr

9、edicted as soon </p><p>　　1 　EXPERIMENTAL WORK</p><p>　　For compensation purpose , the principal interest is not the deformation of each machine component , but the displacement of the tool with

10、 respect to the workpiece. In the vertical machining center under investigation , the thermal errors are the combination of the expansion of spindle , the distortion of the spindle housing , the expansion of three axes a

11、nd the distortion of the column.</p><p>　　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 ove

12、r the entire machine working space.</p><p>　　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 ba

13、lls fixed on it with equal space. The balls have the same diameter and small sphericity errors. The ball array is used as a reference for thermal error measurement . A lot of pre-experiment s show that the thermal errors

14、 in z-axis are far larger than those in x-axis and y-axis , therefore major attention is drawn on the thermal errors i</p><p>　　The measuring process is shown in Fig.1. A probe is mounted on the spindle hous

15、ing 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

16、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 refer</p><p&g

17、t;　　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 errorsΔz measured reflect those

18、 in real cutting condition with negligible error.</p><p>　　In order to obtain a thorough impression of the thermal behavior of the machine tool and</p><p>　　identify the error model accurately ,

19、 a measurement strategy is developed. Various loads of the spindle speed are applied. They are divided into three categories as the following : (1) The constant speed ; (2) The speed spect rum ; (3) The speed simulating

20、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 machine structure is re

21、garded to be negligible</p><p>　　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 i

22、mplies that the positions of x-carriage and y-carriage have no strong influence on the z-axis thermal errors.</p><p>　　Fig.1（L） 　Thermal error measurement 　　 1.Spindle mounted probe 　2.1-D ball array 　　</

23、p><p>　　Fig.2 （R）　Thermal errors at different z coordinates 　1. z = - 50 　2. z = - 150 　3. z = - 250 　4. z = - 350</p><p>　　Fig.2 plot s the time-history of thermal drift Δz at different z coordin

24、ates under a test . It</p><p>　　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 p

25、asses and temperature increases.</p><p>　　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 th

26、ermal-equilibrium quickly compared to other machine component s with longer thermal-time-constant s. However , as time passes , those position-dependent thermal errors such as the lead screw and the column cont ribute to

27、 the resultant thermal drift s of the tool more and more. As a result , the thermal drifts at different z coordinat</p><p>　　2 　AR MODEL FOR THERMAL ERROR</p><p>　　Precise prediction of thermal

28、errors is an important step for accurate error compensation.</p><p>　　Since the knowledge of the machine structure , the heat source and the boundary condition are insufficient , a precise quantitative predi

29、ction 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

30、 satisfactory accuracy in much application.</p><p>　　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 sour

31、ce is considered. The influence of external heat source on machining accuracy can be diminished by environment temperature control.</p><p>　　From the obtained data , it is found that thermal errors vary cont

32、inuously with time. The</p><p>　　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 wri

33、tten is the form</p><p>　　where 　Δz ( t) ———Thermal error at time t</p><p>　　k , m ———Order of the model</p><p>　　ai , bi ———Coefficient of the model</p><p>　　n ( t -

34、i) ———Spindle rotation speed at time t - i</p><p>　　The order k and m are determined by the final prediction-error criterion. The coefficients ai</p><p>　　and bi are estimated by artificial neur

35、al 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

36、 than other modeling technique to individual 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

37、 hidded nodes is dete</p><p>　　Using the data obtained (thermal errors and correspondence speed) , four models for the errors at z 1 , z 2 , z 3 and z 4 are established. Thermal errors at positions other th

38、an z 1 , z 2 , z 3 , z 4 are calculated by an interpolating function. So the errors at any z coordinates can be obtained.</p><p>　　In order to verify the prediction accuracy of the model , a number of new op

39、eration 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 .</p&

40、gt;<p>　　Fig.3 A neural network for thermal errors　Fig.4 Thermal error predicting 　　</p><p>　　1.Measuring results 2Predicting results</p><p>　　3 　PRE-COMPENSATION FOR THERMAL ERRORS</p

41、><p>　　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 machining program is made.</p><p&

42、gt;　　By , for example , every 10 min , the thermal errors Δz are calculated by the model. Then the program is corrected by adding the calculated Δz to the original z . So the thermal errors are compensated before machini

43、ng.</p><p>　　The effectiveness of the error compensation 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

44、difference of the milled surface is used to evaluate the compensation result of the thermal errors in z direction. It shows that the difference is reduced from 7μm to 2μm.</p><p>　　Fig.5 　Compensation for th

45、ermal errors by revising machining program</p><p>　　Fig.6 　The effectiveness of compensation</p><p>　　4 　CONCLUSIONS</p><p>　　A novel method for improving the accuracy of CNC machin

46、e tools is discussed. The core of the study 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

47、compensated before machining but not in real-time. By using the method , the accuracy of machine tools can be increased economically.</p><p>　　References</p><p>　　1 　Chen J S , Chiou G. Quick te

48、sting and modeling of thermally-induced errors of CNC machine tools. International</p><p>　　Journal of Machine Tools and Manufacture , 1995 , 35(7) ∶1 063～1 074</p><p>　　2 　Chen J S. Computer-ai

49、ded accuracy enhancement for multi-axis CNC machine tool. International Journal of Machine Tools and Manufacture , 1995 , 35(4) ∶593～605</p><p>　　3 　Donmez M A. A general methodology for machine tool accurac

50、y enhancement by error compensation. Precision Engineering , 1986 , 8 (4) ∶187～196</p><p>　　4 　Lo C H. An application of real-time error compensation on a turning center. International Journal of Machine Too

51、ls and Manufacture , 1995 , 35(12) ∶1 669～1 682.</p><p>　　5 　Yang S. The Improvement of thermal error modeling and compensation on machine tools by CMAC neural network. International Journal of Machine Tools

52、 and Manufacture , 1995 , 36(4) ∶527～537</p><p>　　6 　李書和1 數(shù)控機(jī)床誤差補(bǔ)償?shù)难芯俊肹博士學(xué)位論文]1 天津∶天津大學(xué),19961</p><p>　　通過(guò)熱量誤差補(bǔ)償來(lái)改善數(shù)控機(jī)床的精確度</p><p>　　摘　要：通過(guò)熱量誤差補(bǔ)償來(lái)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(guò)1-D滾珠排列和

53、建立在錠子轉(zhuǎn)速基礎(chǔ)上的自動(dòng)退刀的表征。通過(guò)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。</p><p>　　關(guān)鍵詞：　數(shù)控加工中心, 熱量誤差,補(bǔ)償</p><p><b>　　0.引言：</b></p><p>　　數(shù)控機(jī)床精確度的改善是生產(chǎn)過(guò)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

54、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)床的熱量誤差可通過(guò)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(guò)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(guò)去的幾年里，對(duì)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(duì)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

55、誤差和溫度的試驗(yàn)?zāi)Ｐ蛯?duì)多種變化進(jìn)行回歸分析或是人工網(wǎng)絡(luò)分析。</p><p>　　在加工期間，誤差是根據(jù)之前建立的模型進(jìn)行預(yù)測(cè)并通過(guò)在實(shí)際過(guò)程中用額外的信號(hào)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(guò)程補(bǔ)償案例適用于商業(yè)機(jī)床。首先，對(duì)機(jī)床的多個(gè)點(diǎn)進(jìn)行熱量誤差和溫度的測(cè)量是不可取的。其次，溫度傳感器的線會(huì)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。</p>

56、<p>　　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(lái)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(cè)出來(lái)。通過(guò)對(duì)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。</p><p>&l

57、t;b>　　1.試驗(yàn)工作</b></p><p>　　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(zhǎng)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。</p><p>　　為了能夠快速的測(cè)量熱量誤差，一些簡(jiǎn)單的量規(guī)是可以使

58、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(cè)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，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(cè)量的過(guò)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(cè)量是周期性的。熱量的轉(zhuǎn)移是通過(guò)

59、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(lái)實(shí)現(xiàn)的。由于這種測(cè)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(lái)。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(cè)量點(diǎn)z1，z2，z3，z4來(lái)覆蓋坐標(biāo)為-50，-150，-250，-350的z坐標(biāo)的工作范圍。在其他的坐標(biāo)中熱量誤差可以

60、通過(guò)一個(gè)插值函數(shù)來(lái)獲得。</p><p>　　上述的試驗(yàn)說(shuō)明了在錠子位置和工作臺(tái)之間的派生位移與錠子和臺(tái)之間是一致的。因此熱量誤差Δz的測(cè)量反映了在真正的切割條件下誤差是可以忽略的。</p><p>　　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(cè)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。

61、此處，由切割過(guò)程而引起的熱量作用沒有被考慮進(jìn)來(lái)。不過(guò)，切割過(guò)程對(duì)整個(gè)機(jī)床機(jī)構(gòu)的熱量的影響在最終的過(guò)程中是可以忽略的。在這種機(jī)床中，最大的熱源來(lái)自于z軸。熱量誤差在z方向和不同的x和y坐標(biāo)方向大約是相同的。也就是說(shuō)x軸和y軸的位置對(duì)z軸的熱量誤差沒有重大影響。</p><p>　　圖1（左）　熱量誤差測(cè)量 錠子傳感器</p><p>　　2.1-D 滾珠排列</p>&l

62、t;p>　　圖2（右） 在不同z坐標(biāo)中的熱量誤差</p><p>　　1. z = - 50 　2. z = - 150 　3. z = - 250 　4. z = - 350</p><p>　　圖2 在測(cè)試中不同z 坐標(biāo)中熱量轉(zhuǎn)移時(shí)間過(guò)程圖的繪制</p><p>　　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

63、樣的，然后隨著時(shí)間的流逝和溫度的增加而逐漸分離。原因在于最初大量的熱量轉(zhuǎn)移是由于錠子位置的增長(zhǎng)造成的，和其他的耐熱時(shí)間較長(zhǎng)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(guò)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(lái)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。</p><p>　　2.熱量誤差的回歸模型&

64、lt;/p><p>　　熱量誤差的準(zhǔn)確預(yù)測(cè)是精確誤差補(bǔ)償?shù)闹匾h(huán)節(jié)。由于對(duì)機(jī)床結(jié)構(gòu)的認(rèn)識(shí)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(cè)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)的誤差模型進(jìn)行回歸分析和網(wǎng)絡(luò)分析來(lái)準(zhǔn)確預(yù)測(cè)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(duì)機(jī)床精確度的影響能夠通過(guò)環(huán)境溫度來(lái)控制。根據(jù)已有的數(shù)據(jù)發(fā)現(xiàn)熱量誤差的

65、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。</p><p>　　Δz ( t) 地點(diǎn)----t時(shí)間的熱量誤差</p><p>　　k , m ——— 模型順序</p><p>　　ai , bi ———模型系數(shù)</p><p>　　n ( t - i) ———在時(shí)間t-i的錠子轉(zhuǎn)

66、速</p><p>　　k和m的順序是有最終的誤差預(yù)測(cè)標(biāo)準(zhǔn)準(zhǔn)決定的。系數(shù)ai和bi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(hào)在各個(gè)結(jié)點(diǎn)上單一輸入的障礙更不容易感光。</p><p>　　為了能確定模型預(yù)測(cè)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(cè)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(duì)穩(wěn)定的環(huán)境下很好的描述熱量誤差。</p><

67、;p>　　圖3 熱量誤差的網(wǎng)絡(luò) 圖4 熱量誤差的預(yù)測(cè) （1）.測(cè)量結(jié)果（2）. 預(yù)測(cè)結(jié)果</p><p>　　3.熱量誤差的前期補(bǔ)償</p><p><b>　　1.</b></p><p>　　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

68、分鐘，Δz的熱量誤差就會(huì)被模型計(jì)算一次。這樣，就能通過(guò)把計(jì)算出來(lái)的Δz加到原來(lái)的z上來(lái)修改程序。因此，熱量誤差能夠在加工之前得到補(bǔ)償。</p><p>　　誤差補(bǔ)償?shù)挠行允怯稍S多切割試驗(yàn)來(lái)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(lái)評(píng)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7μm減少到2μm。</p><p>　　圖 5 通過(guò)

69、程序的修正補(bǔ)償熱量誤差</p><p>　　圖 6 補(bǔ)償?shù)挠行?lt;/p><p><b>　　4.結(jié)論</b></p><p>　　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(guò)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(guò)使用這種

70、方法，數(shù)控機(jī)床的精確度能夠大大的提高。</p><p><b>　　參考文獻(xiàn)</b></p><p>　　1 　Chen J S , Chiou G. Quick testing and modeling of thermally-induced errors of CNC machine tools. International Journal of Machine

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72、5(4) ∶593～605</p><p>　　3 　Donmez M A. A general methodology for machine tool accuracy enhancement by error compensation. Precision Engineering , 1986 , 8 (4) ∶187～196</p><p>　　4 　Lo C H. An appl

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