宽槽圆柱凸轮数控加工技术的研究
附录1外文翻译及原文 外文翻译 宽槽圆柱凸轮数控加工技术的研究 摘要:针对传统铣削方法加工圆柱凸轮所产生的一些问题，提出了一种针对槽宽大于刀具直径的圆柱凸轮槽的数控铣削加工方法。通过分析研究，建立了一种正确的坐标转换模型，并依此加工出符合要求的宽槽圆柱凸轮。
关键词：数控加工 坐标转换 宽槽圆柱凸轮 圆柱凸轮槽一般是按一定规律环绕在圆柱面上的等宽槽。对圆柱凸轮槽的数控铣削加工必须满足以下要求：1.圆柱凸轮槽的工作面即两个侧面的法截面线必须严格平行；
2.圆柱凸轮槽在工作段必须等宽。这是保证滚子在圆柱凸轮槽中平稳运动的必要条件。当圆柱凸轮槽宽度不大时，可以找到相应直径的立铣刀沿槽腔中心线进行加工，比较容易加工出符合上述要求的圆柱凸轮槽。据现有资料介绍，目前圆柱凸轮的铣削加工都是用这种办法来实现。由于这种方法有太多的局限性，给实际铣削加工带来许多困难。例如一旦找不到与槽宽尺寸相等的标准刀具时，就必须对刀具进行改制。
对于槽宽尺寸较大的圆柱凸轮槽，很难找到直径与槽宽相等的标准刀具。即使有相应的刀具，还要考虑机床主轴输出功率及主轴和工装夹具刚度的限制，特别是机床主轴结构对刀具的限制。例如数控机床主轴头为7∶24的40号内锥，配用JT40的工具系统，则最大只能使用φ20mm的立铣刀(不论直柄还是锥柄)。这对于槽宽为38mm的圆柱凸轮(就是本文所叙述的加工凸轮)来说是无法加工的，必须寻求新的加工方法。
下面根据实践经验和分析研究，介绍一种用直径小于凸轮槽宽的立铣刀对圆柱凸轮槽进行数控加工的方法，称之为宽槽圆柱凸轮的数控加工。
一、加工工艺 圆柱凸轮槽是环绕在圆柱面上的等宽槽，其加工时沿圆周表面铣削的范围往往大于360°，适于用带有数控回转台的立式数控铣床进行加工。根据圆柱凸轮的实际结构，选用带键的心轴作凸轮加工时径向和周向定位基准，以心轴的台肩作轴向定位基准，并用心轴前端部的螺纹通过螺母压紧圆柱凸轮。圆柱凸轮的轴向和径向尺寸一般较大，为了克服由于悬臂加工时切削力所造成的心轴变形和加工过程中产生的振颤，使用一个支承于尾座上的、与数控转台的回转轴线同轴的顶尖顶住心轴中心孔作辅助支承。
圆柱凸轮槽的底部在每一个截面 上通常是等深的，一般选用平底圆柱立铣刀加工。圆柱凸轮铣削加工前通常是一个实心的圆柱体，要经过开槽、粗加工、半精加工、精加工等工序；
由于槽腔宽度较大，因此，除开槽工序及粗加工工序的一部分刀位轨迹可以沿槽腔的中心线生成之外，其余刀位轨、迹则必须是沿槽腔中心线向左、右两边按相应的距离等距偏置生成，如图1所示。
图 1 圆柱凸轮槽的二维展开图 二、求解模型 在圆柱凸轮槽的数控加工中，如何求出每道工序中加工两个侧表面的刀位轨迹是其中的关键。对于圆柱表面上的凸轮槽，通常是先将圆柱面展开，在XOS平面内求出该工序加工两个侧表面的刀位轨迹的展开曲线XS；
然后通过坐标转换，将展开曲线XS转换为四坐标机床上的刀位轨迹。下面讨论任一加工工序中展开曲线XS的求解方法，以及生成最后刀位轨迹的坐标转换方法。
1.展开曲线XS的求解 如图2所示，其中Lo为圆柱凸轮槽的中心线，对于第i道工序，Lli和Lri分别为该工序将要加工的槽腔的左、右两个侧表面展开曲线，此槽宽为Bi，加工刀具半径为r(显然2r≤Bi)，加工此槽腔左、右侧面的刀位轨迹展开曲线为CLli和CLri，设Po为槽腔中心线上的一个点，no为槽腔中心线在Po点处的法矢，那么左、右刀位轨迹展开曲线上对应点Pli和Pri的计算方法为：
(1) 图 2 圆柱凸轮槽的二维展开图 将Po点沿着槽腔中心线移动，即可以求出该工序刀位轨迹在XOS平面内的展开曲线XS；
按照加工工序，依次改变每道工序中的槽宽度Bi，即可求出加工所需槽腔所有刀位轨迹的展开曲线。
2.沿凸轮槽中心线加工的坐标转换方法 以上计算是在圆柱面的展开平面内进行的，为了求出加工圆柱凸轮槽腔的刀位轨迹，必须将平面内的展开曲线转换到圆柱面上。
假设转动轴为绕X轴的A轴，Pi为刀位轨迹上的一个刀位点，它在二维平面展开曲线上的坐标为(x,s)，在四坐标机床上的坐标为(x,y,z,a)。由于圆柱凸轮槽腔通常是等深的，因此，z坐标在设置为所需要加工的深度值之后，在加工中是不变的；
对于其余三个坐标，构造出以下坐标转换公式：
(2) 式中，R为圆柱凸轮轴的半径。上式是目前普遍使用的坐标转换公式，对于用标准刀具沿凸轮槽中心线铣削加工圆柱凸轮是正确的。
3.对上式在宽槽圆柱凸轮加工中产生问题的分析 当将上式推广应用于宽槽圆柱凸轮的数控加工时，通过坐标转换计算的刀位轨迹在实际加工中却产生了一些问题。在圆柱凸轮槽加工完毕后，为了检验是否符合要求，用直径等于圆柱凸轮滚子的检具进行检验，却发现所加工的槽宽窄不等、有卡壳的现象。仔细观察，原来加工出来的槽腔的法截面并不总是上下等宽的矩形槽，而有时是上宽下窄的喇叭槽。为了弄清楚其中的原因，对公式(2)所表示的坐标转换方法进行了深入的分析和研究。
如图3所示，由公式(1)可知，加工槽腔两个侧表面的刀位轨迹线上的Pl和Pr点是由槽腔中心线上的Po等距偏置而得，按公式(2)转换之后，Pl和Pr点对应的转角并不等于Po点的转角，也即Pl和Pr对应的刀轴矢量VlVl与Po点对应的刀轴矢量VoVo不平行，因此，加工出来的槽腔自然就成了上宽下窄喇叭槽，而不是所需要的上下等宽的矩形槽。设截面与轴线的夹角为θ，圆柱凸轮轴的半径为R，刀轴矢量VlVl与VoVo的角度误差为：
Δa＝(B/2－r)sinθ/R (3) 图 3 圆柱凸轮槽加工示意图 由公式(3)可知，当θ＝0°，也即凸轮槽中心线与圆柱轴线垂直时，角度误差为零，即槽腔是上下等宽的矩形口；
当θ＝90°，也即凸轮槽中心线与圆柱轴线平行时，角度误差达到最大，此时槽腔的喇叭口现象最严重；
当0＜θ＜90°时，随着θ的增大，角度误差越大，喇叭口现象也就越严重。实际加工出现的现象与上述分析完全一致，这说明公式(3)的分析是完全正确的。
4.宽槽圆柱凸轮数控加工的坐标转换方法 由上面的分析可知，公式(2)造成凸轮槽为上宽下窄喇叭口的主要原因是，Pl和Pr点对应的转角是按照这两个点自己的弧长值Sl和Sr来计算的，而Sl和Sr是不等于槽腔中心点Po的弧长值So。因此，如果Pl和Pr点对应的转角均按照槽腔中心点Po的弧长值So来计算，就可以消除这种喇叭槽现象。根据这种思路，重新构造坐标转换公式。
在圆柱面的二维展开平面上，设槽腔中心线展开曲线上的一个点为Po(xo,so)，加工两个侧表面上对应刀位点在展开曲线上的点为Pl(xl,sl)和Pr(xr,sr)，那么，坐标转换公式为：
(4) 应用公式(4)生成的刀位轨迹加工圆柱凸轮槽时，结果完全符合上述的设想，加工出来的圆柱凸轮槽已经没有了上宽下窄的喇叭槽现象，而是真正的上下等宽矩形槽。
参考文献：
1.Chang 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. 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 tool 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 Coordinates 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 surface 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 diameter 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. Because 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 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 tool 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 this 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 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 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 axial 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 spindle 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 and 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, Therefore, 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 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, usually 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 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 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 knife 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: (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 working 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, in 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-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 the 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 the 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 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 originally 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 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 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 trough 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 cam 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 column 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 phenomenon 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 narrow 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 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 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) produces 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.Chang 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.
