附录1外文翻译原文
外文翻译
宽槽圆柱凸轮数控加工技术研究
摘针传统铣削方法加工圆柱凸轮产生问题提出种针槽宽刀具直径圆柱凸轮槽数控铣削加工方法通分析研究建立种正确坐标转换模型加工出符合求宽槽圆柱凸轮
关键词：数控加工 坐标转换 宽槽圆柱凸轮
圆柱凸轮槽般定规律环绕圆柱面等宽槽圆柱凸轮槽数控铣削加工必须满足求：1圆柱凸轮槽工作面两侧面法截面线必须严格行2圆柱凸轮槽工作段必须等宽保证滚子圆柱凸轮槽中稳运动必条件圆柱凸轮槽宽度时找相应直径立铣刀槽腔中心线进行加工较容易加工出符合述求圆柱凸轮槽现资料介绍目前圆柱凸轮铣削加工种办法实现种方法太局限性实际铣削加工带许困难例旦找槽宽尺寸相等标准刀具时必须刀具进行改制
槽宽尺寸较圆柱凸轮槽难找直径槽宽相等标准刀具相应刀具考虑机床轴输出功率轴工装夹具刚度限制特机床轴结构刀具限制例数控机床轴头7∶2440号锥配JT40工具系统φ20mm立铣刀(直柄锥柄)槽宽38mm圆柱凸轮(文叙述加工凸轮)说法加工必须寻求新加工方法
面根实践验分析研究介绍种直径凸轮槽宽立铣刀圆柱凸轮槽进行数控加工方法称宽槽圆柱凸轮数控加工
加工工艺
圆柱凸轮槽环绕圆柱面等宽槽加工时圆周表面铣削范围360°适带数控回转台立式数控铣床进行加工根圆柱凸轮实际结构选带键心轴作凸轮加工时径周定位基准心轴台肩作轴定位基准心轴前端部螺纹通螺母压紧圆柱凸轮圆柱凸轮轴径尺寸般较克服悬臂加工时切削力造成心轴变形加工程中产生振颤支承尾座数控转台回转轴线轴顶尖顶住心轴中心孔作辅助支承
圆柱凸轮槽底部截面 通常等深般选底圆柱立铣刀加工圆柱凸轮铣削加工前通常实心圆柱体开槽粗加工半精加工精加工等工序槽腔宽度较开槽工序粗加工工序部分刀位轨迹槽腔中心线生成外余刀位轨迹必须槽腔中心线左右两边相应距离等距偏置生成图1示
图 1 圆柱凸轮槽二维展开图
二求解模型
圆柱凸轮槽数控加工中求出道工序中加工两侧表面刀位轨迹中关键圆柱表面凸轮槽通常先圆柱面展开XOS面求出该工序加工两侧表面刀位轨迹展开曲线XS然通坐标转换展开曲线XS转换四坐标机床刀位轨迹面讨加工工序中展开曲线XS求解方法生成刀位轨迹坐标转换方法
1展开曲线XS求解
图2示中Lo圆柱凸轮槽中心线第i道工序LliLri分该工序加工槽腔左右两侧表面展开曲线槽宽Bi加工刀具半径r(显然2r≤Bi)加工槽腔左右侧面刀位轨迹展开曲线CLliCLri设Po槽腔中心线点no槽腔中心线Po点处法矢左右刀位轨迹展开曲线应点PliPri计算方法：
(1)
图 2 圆柱凸轮槽二维展开图
Po点着槽腔中心线移动求出该工序刀位轨迹XOS面展开曲线XS加工工序次改变道工序中槽宽度Bi求出加工需槽腔刀位轨迹展开曲线
2凸轮槽中心线加工坐标转换方法
计算圆柱面展开面进行求出加工圆柱凸轮槽腔刀位轨迹必须面展开曲线转换圆柱面
假设转动轴绕X轴A轴Pi刀位轨迹刀位点二维面展开曲线坐标(xs)四坐标机床坐标(xyza)圆柱凸轮槽腔通常等深z坐标设置需加工深度值加工中变余三坐标构造出坐标转换公式：
(2)
式中R圆柱凸轮轴半径式目前普遍坐标转换公式标准刀具凸轮槽中心线铣削加工圆柱凸轮正确
3式宽槽圆柱凸轮加工中产生问题分析
式推广应宽槽圆柱凸轮数控加工时通坐标转换计算刀位轨迹实际加工中产生问题圆柱凸轮槽加工完毕检验否符合求直径等圆柱凸轮滚子检具进行检验发现加工槽宽窄等卡壳现象仔细观察原加工出槽腔法截面总等宽矩形槽时宽窄喇叭槽弄清楚中原公式(2)表示坐标转换方法进行深入分析研究
图3示公式(1)知加工槽腔两侧表面刀位轨迹线PlPr点槽腔中心线Po等距偏置公式(2)转换PlPr点应转角等Po点转角PlPr应刀轴矢量VlVlPo点应刀轴矢量VoVo行加工出槽腔然成宽窄喇叭槽需等宽矩形槽设截面轴线夹角θ圆柱凸轮轴半径R刀轴矢量VlVlVoVo角度误差：
Δa＝(B2－r)sinθR (3)
图 3 圆柱凸轮槽加工示意图
公式(3)知θ＝0°凸轮槽中心线圆柱轴线垂直时角度误差零槽腔等宽矩形口θ＝90°凸轮槽中心线圆柱轴线行时角度误差达时槽腔喇叭口现象严重0＜θ＜90°时着θ增角度误差越喇叭口现象越严重实际加工出现现象述分析完全致说明公式(3)分析完全正确
4宽槽圆柱凸轮数控加工坐标转换方法
面分析知公式(2)造成凸轮槽宽窄喇叭口原PlPr点应转角两点弧长值SlSr计算SlSr等槽腔中心点Po弧长值So果PlPr点应转角均槽腔中心点Po弧长值So计算消种喇叭槽现象根种思路重新构造坐标转换公式
圆柱面二维展开面设槽腔中心线展开曲线点Po(xoso)加工两侧表面应刀位点展开曲线点Pl(xlsl)Pr(xrsr)坐标转换公式：
(4)
应公式(4)生成刀位轨迹加工圆柱凸轮槽时结果完全符合述设想加工出圆柱凸轮槽已没宽窄喇叭槽现象真正等宽矩形槽
参考文献：
1Chang W CVan Y TResearching Design Trens for the Redesign of Product From Design Studies 200324(2)173_180
2Mou JLiu C RAn error correction method for CNC machine tools using reference partstransactions of NAMRESME1994
3Sutton G PThe machine tool task forch Bal Harbour Bal Habour Hotel1980
4Gene FFranklin Feedback control of Dynamis systems4E
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 1The column cam path working surface namely two sides plane of normal section lines must be strict parallel 2The 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 twodimensional 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
1Launches 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 twodimensional 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
2Along 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 twodimensional surface the coordinates for (xs) on four coordinates engine beds coordinates is (xyza)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
3Has 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 online pl and the pr spot is by the trough cavity middle line in po equalspace 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＝(B2－r)sinθR (3)
a)Cylinder cam slot sketch map b)The AA 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 trumpetshaped object phenomenon is most serious When 0 <θ < 90° along with θincreasing angle error bigger the trumpetshaped 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
4Wide 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 trumpetshaped 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
Twodimensional launches in the plane in the round cylinder supposes the trough cavity middle line to launch in the curve a spot is po (xoSo) processes on two sides surfaces to correspond the knife position spot in to launch in the curve the spot is pl (xlsl) and pr (xrpr) 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：
1Chang W CVan Y TResearching Design Trens for the Redesign of Product From Design Studies 200324(2)173_180
2Mou JLiu C RAn error correction method for CNC machine tools using reference partstransactions of NAMRESME1994
3Sutton G PThe machine tool task forch Bal Harbour Bal Habour Hotel1980
4Gene FFranklin Feedback control of Dynamis systems4E
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附录1外文翻译原文
外文翻译
宽槽圆柱凸轮数控加工技术研究
摘针传统铣削方法加工圆柱凸轮产生问题提出种针槽宽刀具直径圆柱凸轮槽数控铣削加工方法通分析研究建立种正确坐标转换模型加工出符合求宽槽圆柱凸轮
关键词：数控加工 坐标转换 宽槽圆柱凸轮
圆柱凸轮槽般定规律环绕圆柱面等宽槽圆柱凸轮槽数控铣削加工必须满足求：1圆柱凸轮槽工作面两侧面法截面线必须严格行2圆柱凸轮槽工作段必须等宽保证滚子圆柱凸轮槽中稳运动必条件圆柱凸轮槽宽度时找相应直径立铣刀槽腔中心线进行加工较容易加工出符合述求圆柱凸轮槽现资料介绍目前圆柱凸轮铣削加工种办法实现种方法太局限性实际铣削加工带许困难例旦找槽宽尺寸相等标准刀具时必须刀具进行改制
槽宽尺寸较圆柱凸轮槽难找直径槽宽相等标准刀具相应刀具考虑机床轴输出功率轴工装夹具刚度限制特机床轴结构刀具限制例数控机床轴头7∶2440号锥配JT40工具系统φ20mm立铣刀(直柄锥柄)槽宽38mm圆柱凸轮(文叙述加工凸轮)说法加工必须寻求新加工方法
面根实践验分析研究介绍种直径凸轮槽宽立铣刀圆柱凸轮槽进行数控加工方法称宽槽圆柱凸轮数控加工
加工工艺
圆柱凸轮槽环绕圆柱面等宽槽加工时圆周表面铣削范围360°适带数控回转台立式数控铣床进行加工根圆柱凸轮实际结构选带键心轴作凸轮加工时径周定位基准心轴台肩作轴定位基准心轴前端部螺纹通螺母压紧圆柱凸轮圆柱凸轮轴径尺寸般较克服悬臂加工时切削力造成心轴变形加工程中产生振颤支承尾座数控转台回转轴线轴顶尖顶住心轴中心孔作辅助支承
圆柱凸轮槽底部截面 通常等深般选底圆柱立铣刀加工圆柱凸轮铣削加工前通常实心圆柱体开槽粗加工半精加工精加工等工序槽腔宽度较开槽工序粗加工工序部分刀位轨迹槽腔中心线生成外余刀位轨迹必须槽腔中心线左右两边相应距离等距偏置生成图1示
图 1 圆柱凸轮槽二维展开图
二求解模型
圆柱凸轮槽数控加工中求出道工序中加工两侧表面刀位轨迹中关键圆柱表面凸轮槽通常先圆柱面展开XOS面求出该工序加工两侧表面刀位轨迹展开曲线XS然通坐标转换展开曲线XS转换四坐标机床刀位轨迹面讨加工工序中展开曲线XS求解方法生成刀位轨迹坐标转换方法
1展开曲线XS求解
图2示中Lo圆柱凸轮槽中心线第i道工序LliLri分该工序加工槽腔左右两侧表面展开曲线槽宽Bi加工刀具半径r(显然2r≤Bi)加工槽腔左右侧面刀位轨迹展开曲线CLliCLri设Po槽腔中心线点no槽腔中心线Po点处法矢左右刀位轨迹展开曲线应点PliPri计算方法：
(1)
图 2 圆柱凸轮槽二维展开图
Po点着槽腔中心线移动求出该工序刀位轨迹XOS面展开曲线XS加工工序次改变道工序中槽宽度Bi求出加工需槽腔刀位轨迹展开曲线
2凸轮槽中心线加工坐标转换方法
计算圆柱面展开面进行求出加工圆柱凸轮槽腔刀位轨迹必须面展开曲线转换圆柱面
假设转动轴绕X轴A轴Pi刀位轨迹刀位点二维面展开曲线坐标(xs)四坐标机床坐标(xyza)圆柱凸轮槽腔通常等深z坐标设置需加工深度值加工中变余三坐标构造出坐标转换公式：
(2)
式中R圆柱凸轮轴半径式目前普遍坐标转换公式标准刀具凸轮槽中心线铣削加工圆柱凸轮正确
3式宽槽圆柱凸轮加工中产生问题分析
式推广应宽槽圆柱凸轮数控加工时通坐标转换计算刀位轨迹实际加工中产生问题圆柱凸轮槽加工完毕检验否符合求直径等圆柱凸轮滚子检具进行检验发现加工槽宽窄等卡壳现象仔细观察原加工出槽腔法截面总等宽矩形槽时宽窄喇叭槽弄清楚中原公式(2)表示坐标转换方法进行深入分析研究
图3示公式(1)知加工槽腔两侧表面刀位轨迹线PlPr点槽腔中心线Po等距偏置公式(2)转换PlPr点应转角等Po点转角PlPr应刀轴矢量VlVlPo点应刀轴矢量VoVo行加工出槽腔然成宽窄喇叭槽需等宽矩形槽设截面轴线夹角θ圆柱凸轮轴半径R刀轴矢量VlVlVoVo角度误差：
Δa＝(B2－r)sinθR (3)
图 3 圆柱凸轮槽加工示意图
公式(3)知θ＝0°凸轮槽中心线圆柱轴线垂直时角度误差零槽腔等宽矩形口θ＝90°凸轮槽中心线圆柱轴线行时角度误差达时槽腔喇叭口现象严重0＜θ＜90°时着θ增角度误差越喇叭口现象越严重实际加工出现现象述分析完全致说明公式(3)分析完全正确
4宽槽圆柱凸轮数控加工坐标转换方法
面分析知公式(2)造成凸轮槽宽窄喇叭口原PlPr点应转角两点弧长值SlSr计算SlSr等槽腔中心点Po弧长值So果PlPr点应转角均槽腔中心点Po弧长值So计算消种喇叭槽现象根种思路重新构造坐标转换公式
圆柱面二维展开面设槽腔中心线展开曲线点Po(xoso)加工两侧表面应刀位点展开曲线点Pl(xlsl)Pr(xrsr)坐标转换公式：
(4)
应公式(4)生成刀位轨迹加工圆柱凸轮槽时结果完全符合述设想加工出圆柱凸轮槽已没宽窄喇叭槽现象真正等宽矩形槽
参考文献：
1Chang W CVan Y TResearching Design Trens for the Redesign of Product From Design Studies 200324(2)173_180
2Mou JLiu C RAn error correction method for CNC machine tools using reference partstransactions of NAMRESME1994
3Sutton G PThe machine tool task forch Bal Harbour Bal Habour Hotel1980
4Gene FFranklin Feedback control of Dynamis systems4E
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 1The column cam path working surface namely two sides plane of normal section lines must be strict parallel 2The 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 twodimensional 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
1Launches 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 twodimensional 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
2Along 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 twodimensional surface the coordinates for (xs) on four coordinates engine beds coordinates is (xyza)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
3Has 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 online pl and the pr spot is by the trough cavity middle line in po equalspace 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＝(B2－r)sinθR (3)
a)Cylinder cam slot sketch map b)The AA 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 trumpetshaped object phenomenon is most serious When 0 <θ < 90° along with θincreasing angle error bigger the trumpetshaped 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
4Wide 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 trumpetshaped 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
Twodimensional launches in the plane in the round cylinder supposes the trough cavity middle line to launch in the curve a spot is po (xoSo) processes on two sides surfaces to correspond the knife position spot in to launch in the curve the spot is pl (xlsl) and pr (xrpr) 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：
1Chang W CVan Y TResearching Design Trens for the Redesign of Product From Design Studies 200324(2)173_180
2Mou JLiu C RAn error correction method for CNC machine tools using reference partstransactions of NAMRESME1994
3Sutton G PThe machine tool task forch Bal Harbour Bal Habour Hotel1980
4Gene FFranklin Feedback control of Dynamis systems4E
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