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1、外文翻譯 寬槽圓柱凸輪數(shù)控加工技術(shù)的研究 摘要:針對(duì)傳統(tǒng)銑削方法加工圓柱凸輪所產(chǎn)生的一些問題，提出了一種針對(duì)槽寬大于刀具直徑的圓柱凸輪槽的數(shù)控銑削加工方法。通過分析研究，建立了一種正確的坐標(biāo)轉(zhuǎn)換模型，并依此加工出符合要求的寬槽圓柱凸輪。 關(guān)鍵詞：數(shù)控加工　坐標(biāo)轉(zhuǎn)換　寬槽圓柱凸輪 圓柱凸輪槽一般是按一定規(guī)律環(huán)繞在圓柱面上的等寬槽。對(duì)圓柱凸輪槽的數(shù)控銑削加工必須滿足以下要求：1.圓柱凸輪槽的工作面即兩個(gè)側(cè)面的法截面線必須嚴(yán)格平行；2.圓柱凸輪槽在工作段必須等寬。這是保證滾子在圓柱凸輪槽中平穩(wěn)運(yùn)動(dòng)的必要條件。當(dāng)圓柱凸輪槽寬度不大時(shí)，可以找到相應(yīng)直徑的立銑刀沿槽腔中心線進(jìn)行加工，比較容易加工出

2、符合上述要求的圓柱凸輪槽。據(jù)現(xiàn)有資料介紹，目前圓柱凸輪的銑削加工都是用這種辦法來實(shí)現(xiàn)。由于這種方法有太多的局限性，給實(shí)際銑削加工帶來許多困難。例如一旦找不到與槽寬尺寸相等的標(biāo)準(zhǔn)刀具時(shí)，就必須對(duì)刀具進(jìn)行改制。 對(duì)于槽寬尺寸較大的圓柱凸輪槽，很難找到直徑與槽寬相等的標(biāo)準(zhǔn)刀具。即使有相應(yīng)的刀具，還要考慮機(jī)床主軸輸出功率及主軸和工裝夾具剛度的限制，特別是機(jī)床主軸結(jié)構(gòu)對(duì)刀具的限制。例如數(shù)控機(jī)床主軸頭為7∶24的40號(hào)內(nèi)錐，配用JT40的工具系統(tǒng)，則最大只能使用φ20mm的立銑刀(不論直柄還是錐柄)。這對(duì)于槽寬為38mm的圓柱凸輪(就是本文所敘述的加工凸輪)來說是無法加工的，必須尋求新的加工方法。

3、 下面根據(jù)實(shí)踐經(jīng)驗(yàn)和分析研究，介紹一種用直徑小于凸輪槽寬的立銑刀對(duì)圓柱凸輪槽進(jìn)行數(shù)控加工的方法，稱之為寬槽圓柱凸輪的數(shù)控加工。 一、加工工藝 圓柱凸輪槽是環(huán)繞在圓柱面上的等寬槽，其加工時(shí)沿圓周表面銑削的范圍往往大于360°，適于用帶有數(shù)控回轉(zhuǎn)臺(tái)的立式數(shù)控銑床進(jìn)行加工。根據(jù)圓柱凸輪的實(shí)際結(jié)構(gòu)，選用帶鍵的心軸作凸輪加工時(shí)徑向和周向定位基準(zhǔn)，以心軸的臺(tái)肩作軸向定位基準(zhǔn)，并用心軸前端部的螺紋通過螺母壓緊圓柱凸輪。圓柱凸輪的軸向和徑向尺寸一般較大，為了克服由于懸臂加工時(shí)切削力所造成的心軸變形和加工過程中產(chǎn)生的振顫，使用一個(gè)支承于尾座上的、與數(shù)控轉(zhuǎn)臺(tái)的回轉(zhuǎn)軸線同軸的頂尖頂住心軸中心孔作輔助支承

4、。 圓柱凸輪槽的底部在每一個(gè)截面 上通常是等深的，一般選用平底圓柱立銑刀加工。圓柱凸輪銑削加工前通常是一個(gè)實(shí)心的圓柱體，要經(jīng)過開槽、粗加工、半精加工、精加工等工序；由于槽腔寬度較大，因此，除開槽工序及粗加工工序的一部分刀位軌跡可以沿槽腔的中心線生成之外，其余刀位軌、跡則必須是沿槽腔中心線向左、右兩邊按相應(yīng)的距離等距偏置生成，如圖1所示。 圖 1　圓柱凸輪槽的二維展開圖 二、求解模型 在圓柱凸輪槽的數(shù)控加工中，如何求出每道工序中加工兩個(gè)側(cè)表面的刀位軌跡是其中的關(guān)鍵。對(duì)于圓柱表面上的凸輪槽，通常是先將圓柱面展開，在XOS平面內(nèi)求出該工序加工兩個(gè)側(cè)表面的刀位軌跡的展開曲線XS

5、；然后通過坐標(biāo)轉(zhuǎn)換，將展開曲線XS轉(zhuǎn)換為四坐標(biāo)機(jī)床上的刀位軌跡。下面討論任一加工工序中展開曲線XS的求解方法，以及生成最后刀位軌跡的坐標(biāo)轉(zhuǎn)換方法。 1.展開曲線XS的求解 　　如圖2所示，其中Lo為圓柱凸輪槽的中心線，對(duì)于第i道工序，Lli和Lri分別為該工序?qū)⒁庸さ牟矍坏淖?、右兩個(gè)側(cè)表面展開曲線，此槽寬為Bi，加工刀具半徑為r(顯然2r≤Bi)，加工此槽腔左、右側(cè)面的刀位軌跡展開曲線為CLli和CLri，設(shè)Po為槽腔中心線上的一個(gè)點(diǎn)，no為槽腔中心線在Po點(diǎn)處的法矢，那么左、右刀位軌跡展開曲線上對(duì)應(yīng)點(diǎn)Pli和Pri的計(jì)算方法為： 　　(1) 圖 2　圓柱凸輪槽的二維展開

6、圖 ? ? 將Po點(diǎn)沿著槽腔中心線移動(dòng)，即可以求出該工序刀位軌跡在XOS平面內(nèi)的展開曲線XS；按照加工工序，依次改變每道工序中的槽寬度Bi，即可求出加工所需槽腔所有刀位軌跡的展開曲線。 2.沿凸輪槽中心線加工的坐標(biāo)轉(zhuǎn)換方法 　　以上計(jì)算是在圓柱面的展開平面內(nèi)進(jìn)行的，為了求出加工圓柱凸輪槽腔的刀位軌跡，必須將平面內(nèi)的展開曲線轉(zhuǎn)換到圓柱面上。 假設(shè)轉(zhuǎn)動(dòng)軸為繞X軸的A軸，Pi為刀位軌跡上的一個(gè)刀位點(diǎn)，它在二維平面展開曲線上的坐標(biāo)為(x,s)，在四坐標(biāo)機(jī)床上的坐標(biāo)為(x,y,z,a)。由于圓柱凸輪槽腔通常是等深的，因此，z坐標(biāo)在設(shè)置為所需要加工的深度值之后，在加工中是不變的；對(duì)

7、于其余三個(gè)坐標(biāo)，構(gòu)造出以下坐標(biāo)轉(zhuǎn)換公式： ??????????????? ?? (2) 式中，R為圓柱凸輪軸的半徑。上式是目前普遍使用的坐標(biāo)轉(zhuǎn)換公式，對(duì)于用標(biāo)準(zhǔn)刀具沿凸輪槽中心線銑削加工圓柱凸輪是正確的。 　 3.對(duì)上式在寬槽圓柱凸輪加工中產(chǎn)生問題的分析 　　當(dāng)將上式推廣應(yīng)用于寬槽圓柱凸輪的數(shù)控加工時(shí)，通過坐標(biāo)轉(zhuǎn)換計(jì)算的刀位軌跡在實(shí)際加工中卻產(chǎn)生了一些問題。在圓柱凸輪槽加工完畢后，為了檢驗(yàn)是否符合要求，用直徑等于圓柱凸輪滾子的檢具進(jìn)行檢驗(yàn)，卻發(fā)現(xiàn)所加工的槽寬窄不等、有卡殼的現(xiàn)象。仔細(xì)觀察，原來加工出來的槽腔的法截面并不總是上下等寬的矩形槽，而有時(shí)是上寬下窄的喇叭槽。為了弄清楚其中的原

8、因，對(duì)公式(2)所表示的坐標(biāo)轉(zhuǎn)換方法進(jìn)行了深入的分析和研究。 如圖3所示，由公式(1)可知，加工槽腔兩個(gè)側(cè)表面的刀位軌跡線上的Pl和Pr點(diǎn)是由槽腔中心線上的Po等距偏置而得，按公式(2)轉(zhuǎn)換之后，Pl和Pr點(diǎn)對(duì)應(yīng)的轉(zhuǎn)角并不等于Po點(diǎn)的轉(zhuǎn)角，也即Pl和Pr對(duì)應(yīng)的刀軸矢量VlVl與Po點(diǎn)對(duì)應(yīng)的刀軸矢量VoVo不平行，因此，加工出來的槽腔自然就成了上寬下窄喇叭槽，而不是所需要的上下等寬的矩形槽。設(shè)截面與軸線的夾角為θ，圓柱凸輪軸的半徑為R，刀軸矢量VlVl與VoVo的角度誤差為： Δa＝(B/2－r)sinθ/R　　(3) 圖 3　圓柱凸輪槽加工示意圖 由公式(3)可知，當(dāng)θ＝

9、0°，也即凸輪槽中心線與圓柱軸線垂直時(shí)，角度誤差為零，即槽腔是上下等寬的矩形口；當(dāng)θ＝90°，也即凸輪槽中心線與圓柱軸線平行時(shí)，角度誤差達(dá)到最大，此時(shí)槽腔的喇叭口現(xiàn)象最嚴(yán)重；當(dāng)0＜θ＜90°時(shí)，隨著θ的增大，角度誤差越大，喇叭口現(xiàn)象也就越嚴(yán)重。實(shí)際加工出現(xiàn)的現(xiàn)象與上述分析完全一致，這說明公式(3)的分析是完全正確的。 4.寬槽圓柱凸輪數(shù)控加工的坐標(biāo)轉(zhuǎn)換方法 由上面的分析可知，公式(2)造成凸輪槽為上寬下窄喇叭口的主要原因是，Pl和Pr點(diǎn)對(duì)應(yīng)的轉(zhuǎn)角是按照這兩個(gè)點(diǎn)自己的弧長(zhǎng)值Sl和Sr來計(jì)算的，而Sl和Sr是不等于槽腔中心點(diǎn)Po的弧長(zhǎng)值So。因此，如果Pl和Pr點(diǎn)對(duì)應(yīng)的轉(zhuǎn)角均按照槽

10、腔中心點(diǎn)Po的弧長(zhǎng)值So來計(jì)算，就可以消除這種喇叭槽現(xiàn)象。根據(jù)這種思路，重新構(gòu)造坐標(biāo)轉(zhuǎn)換公式。 在圓柱面的二維展開平面上，設(shè)槽腔中心線展開曲線上的一個(gè)點(diǎn)為Po(xo,so)，加工兩個(gè)側(cè)表面上對(duì)應(yīng)刀位點(diǎn)在展開曲線上的點(diǎn)為Pl(xl,sl)和Pr(xr,sr)，那么，坐標(biāo)轉(zhuǎn)換公式為： ?????????? 　　(4) ??? 應(yīng)用公式(4)生成的刀位軌跡加工圓柱凸輪槽時(shí)，結(jié)果完全符合上述的設(shè)想，加工出來的圓柱凸輪槽已經(jīng)沒有了上寬下窄的喇叭槽現(xiàn)象，而是真正的上下等寬矩形槽。 參考文獻(xiàn)： 1.Chang W C,Van Y T.Researching Design Trens

11、for the Redesign of Product From Design Studies 2003.24(2):173_180 2.Mou J,Liu C R.An error correction method for CNC machine tools using reference parts.transactions of NAMRE/SME,1994. 3.Sutton G P.The machine tool task forch. Bal Harbour Bal Habour Hotel,1980. 4.Gene F.Franklin Feedback cont

12、rol of Dynamis .systems,4E. 英文原文 Wide Trough Column Cam Numerical Control Processing Research Summary: Some questions produces which in view of the traditional milling method processing column cam, proposed one kind in view of the trough spaciously in the cutting too

13、l diameter column cam path numerical control milling processing method. Through the analysis research, has established one kind of correct coordinates transformation model, and processes according to this conforms to the request wide trough column cam. Keywords: Numerical control processing Coordin

14、ates Transformation width trough column cam Main Text The column cam path is generally surrounds according to the certain rule in the round cylinder and so on the wide trough. Must satisfy below to the column cam path numerical control milling processing requests: 1.The column cam path working sur

15、face namely two sides plane of normal section lines must be strict parallel; 2.The column cam path must wait for the width in the work section. This is guarantees the roller in the column cam path the steady motion essential condition. When column cam path width not big, may find the corresponding d

16、iameter the end mill to carry on the processing along the trough cavity middle line, compared with is easy to process conforms to the above request column cam path. According to the existence information introduced that, at present the column cam milling processing all is realizes with this means. B

17、ecause this method has too many limitations, brings many difficulties for the actual milling processing. For example when cannot find with the trough width size equal standard cutting tool, must carry on to the cutting tool changes the system. Regarding the trough width size big column cam path, is

18、 very difficult to find the diameter and the trough width equal standard cutting tool. Even if has the corresponding cutting tool, but also must consider the engine bed main axle output and the main axle and the work clothes jig rigidity limit, specially engine bed main axle structure to cutting too

19、l limit. For example the numerical control engine bed host axle neck is 7: 24 40 inner cones, uses for parts JT40 the tool system, then most greatly only can use φ20mm end mill (no matter straight handle bit holder). This regarding the trough width is the 38mm column cam (is processing cam which thi

20、s article narrates) said is unable to process, must seek the new processing method. Under and analyzes the research according to the experience, introduced one kind is smaller than the cam path width end mill with the diameter to carry on the numerical control processing to the column cam path the

21、method, calls it the width trough column cam numerical control processing. First, Processing craft The column cam path is surrounds in the round cylinder and so on the width trough, when its processing often is bigger than 360°. along the circumference surface milling scopeIs suitable for with to

22、have the numerical control rotary abutment the vertical numerical control milling machine to carry on the processing. According to the column cam actual structure, selects the belt key the spindle makes when the cam processing the radial direction and the week to the localization datum, makes the ax

23、ial localization datum by the spindle ledge, and the nose thread contracts the column cam with the spindle in front of through the nut. The column cam axial and the radial direction size is generally big, in order to overcome because the bracket processes time the cutting force creates in the spindl

24、e distortion and the processing process produces inspires trembles, uses a supporting on the tailstock, withstands the spindle center bore with the numerical control turnplate rotation spool thread coaxial apex to make the auxiliary supporting. The column cam path base on each section usually is an

25、d so on deep, selects the flat base column end mill processing generally. Before the column cam milling processing usually is a solid circular cylinder, must pass through working procedure and so on slot, rough machining, half precision work, precision work; Because the trough cavity width is big, T

26、herefore, except the trough working procedure and a rough machining working procedure part of knives positions path may along beside the trough cavity middle line production, other knife position paths then must be along the trough cavity center alignment left, are right nearby two according to the

27、Corresponding . Figure 1 column cam path two-dimensional developed view Second, Solution model In the column cam path numerical control processing, how extracts in each working procedure to process two sides surfaces the knife position path is key. Regarding the periphery on cam path, usual

28、ly is launches first the round cylinder, extracts this working procedure in the XOS plane to process two sides surfaces the knife position path to launch curve XS; Then transforms through the coordinates, will launch the curve XS transformation will be on four coordinates engine beds knife position

29、path. Under discusses no matter what in a processing working procedure launches curve XS the solution method, as well as production final knife position path coordinates transformation method. 1.Launches curve XS the solution Like chart 2 shows, Lo is the column cam path middle line, regarding the

30、 i working procedure, Lli and Lri respectively the trough cavity which is going to process be this working procedure left, the right two sides surface launches the curve, this width is Bi, processes the cutting tool radius is r (obviously 2r ≤ Bi), processes this cavity to be left, the right side k

31、nife position path launches the curve is CLli and CLri ,supposes Po is in a trough cavity middle line spot, Po is the trough cavity middle line in the Po place law arrow, Then is left, the right knife position path launches in the curve corresponding points pli and the pri computational method is:

32、 (1) Figure 2 column cam path two-dimensional developed view Po along the trough cavity middle line migration, namely may extract this working procedure knife position path to launch curveXS in the XOS plane; According to the processing working procedure, changes in each wor

33、king procedure in turn trough width Bi, then extracts the processing to need the trough cavity all knives position path to launch the curve. 2.Along cam path middle line processing coordinates transformation method Above the computation is launches in the plane in the round cylinder to carry on, i

34、n order to extract the processing column cam path cavity the knife position path, must launch the plane in the curve to transform to the round cylinder in. The supposition rotating axis for circles Xaxis A axis, pi is in a knife position path knife position spot, it launches in the curve in the two

35、-dimensional surface the coordinates for (x,s), on four coordinates engine beds coordinates is (x,y,z,a).。Because the column cam path cavity usually is and so on deep, therefore, the z coordinates in establish after depths which needs to process, in the processing is invariable; Below ?? (2) In th

36、e formula, R is the column cam shaft radius. The previous type is the present universal use coordinates transformation formula, regarding uses the standard cutting tool to process the column cam along the cam path middle line milling is correct. 3.Has the question analysis to the previous type in t

37、he width trough column cam processing When applies the previous type promotion in the width trough column cam numerical control processing, has had some questions actually through the coordinates transformation computation knife position path in the actual processing. Finished after the column cam

38、path processing, in order to examine whether conforms to the requirement, with the diameter was equal to the column cam bowl examines has carries on the examination, discovered actually processes the trough width does not wait for the phenomenon which, has jams. The careful observation, processes or

39、iginally on trough cavity plane of normal section not always inferior width rectangular trough, but sometimes is on under the width the narrow loudspeaker trough. In order to clarify reason, (2) expressed the coordinates transformation method to the formula to carry on the thorough analysis and the

40、research. Like chart 3 shows, (1) may know by the formula, processes the trough cavity two sides surfaces knife position path on-line pl and the pr spot is by the trough cavity middle line in po equal-space bias but, (2) transforms after the formula, pl and the pr point correspondence corner is not

41、 equal to a Po corner, also is pl and pr corresponding cutter bar vector vlvl and po point correspondence cutter bar vector vovo not parallel, therefore, processes the trough cavity has become on under naturally the width the narrow loudspeaker trough, but is not on inferior width rectangular troug

42、h which needs. Supposes the section and the spool thread included angle for theta, the column cam shaft radius is R, cutter bar vector VlVl and VoVo theangle error is: δa＝(B/2－r)sinθ/R (3) a)Cylinder cam slot sketch map b)The A-A cuts to face enlarge the sketch map Chart 3 Column c

43、am path processing schematic drawing (3) may know by the formula, whenθ= 0°, when is the cam path middle line and the column spool thread vertical, the angle error is a zero, namely the trough cavity is on the inferior width rectangular mouth; Whenθ= 90°, when is the cam path middle line and the co

44、lumn spool thread parallel, the angle error achieved biggest, this time the trough cavity trumpet-shaped object phenomenon is most serious; When 0 <θ < 90°, along with θincreasing, angle error bigger, the trumpet-shaped object phenomenon is also more serious. The actual processing appears the phenom

45、enon is completely consistent with the above analysis, this explained formula (3) the analysis is entirely accurate. 4.Wide trough column cam numerical control processing coordinates transformation method May know by the above analysis, the formula (2) creates the cam path for on width under the n

46、arrow trumpet-shaped object main reason is, pl and the pr point correspondence corner is defers to these two, but sl and sr which selects own arc length value sl and sr calculates are is not equal to trough cavity central point po arc length value so. Therefore, if pl and the pr point correspondence

47、 corner defers to trough cavity central point po arc length value so to calculate, may eliminate this kind of loudspeaker trough phenomenon. According to this kind of mentality, again structure coordinates transformation formula. Two-dimensional launches in the plane in the round cylinder, supposes

48、 the trough cavity middle line to launch in the curve a spot is po (xo,So), processes on two sides surfaces to correspond the knife position spot in to launch in the curve the spot is pl (xl,sl) and pr (xr,pr), then, the coordinates transformation formula is: 　　(4) The application formula (4) produ

49、ces when knife position path processing column cam path, the result conforms to the above tentative plan completely, processes the column cam path already did not have on under the width the narrow loudspeaker trough phenomenon, but was the true on inferior wide rectangle trough. Reference： 1.Chan

50、g W C,Van Y T.Researching Design Trens for the Redesign of Product From Design Studies 2003.24(2):173_180 2.Mou J,Liu C R.An error correction method for CNC machine tools using reference parts.transactions of NAMRE/SME,1994. 3.Sutton G P.The machine tool task forch. Bal Harbour Bal Habour Hotel,1980. 4.Gene F.Franklin Feedback control of Dynamis .systems,4E. 14