用表面反应来测量圆柱形钢SCM440的磨削力和表面粗糙度的方法

1、期季羧挖琳缟尝襻芒氵伽衄犒庭浠纲坦露缍撅胤佥潮拦烈罕瘙孑用表面反应来测量圆柱形钢SCM440的磨削力和表面粗糙度的方法麾仕九匣陕哪裤瞒茫秣杈拚踮猩 摘要：这项研究的目的是为了有效的分析在磨削过程中的磨削力和表面粗糙度圆柱形工件，材料是钢SCM440,l利用表面反应的方法。传感器用来测量主轴驱动马达的电力，通过磨削参数的变化来测量和分析粗糙度。用实验数据建立一个模型，预测磨削力和粗糙度。通过单独的改变磨削率绘制数学模型的轮廓线。在工业中测量磨削条件是很容易的。泔魏酣藉站鲕单淤丌齑礅不铡嗽关键词：磨削力，表面粗糙度，圆柱形磨棒，表面反应方法摞调拷薪歹讯蟊鄙胆胴庠鹏寂殪 简介：不少实验更多的说明充分

2、和有效的磨削过程是与车削和铣削很不同。由于砂轮表面的不均匀，每次磨削工件时是不一样的。尽管努力的尝试，但是砂轮和工件间的磨削过程还没搞清楚。所以绘制了许多统计模型和计算机模型。不但这些模型很复杂，很难描述磨削过程，而且增加了优化磨削的难度，很难验证磨削参数之间的相互影响和磨削结果。汐颧嘟瞳宝颓芄枫榛泼蚍峒赣罹 在过去的几十年中Malkin调查和研究了磨削监测结果和磨削现象如切削机理、磨削能以及磨削参数之间的相互影响。在他的研究中，那是很明显的：切削机理很复杂，很难重复磨削过程而获得相同的磨削条件。Shaji刊登了Taguchi方法。用石墨作润滑剂估算磨削表面的参数。影响切削表面参数的参数如砂轮

3、速度，工件转速，切削深度，打磨模型还有切削力被统计。Kwak先生用Taguchi方法显示了不同的切削参数引起磨削表面几何误差。同样用表面反映方法也可以估算磨削表面的几何误差。峁狭骞拐敛懑荔耻芩盖功雁笕舂 在本论文中，用圆柱形钢SCM440作磨削棒料，用表面反映方法来预测切削力和表面粗糙度和帮助选择磨削条件。况蘧鲕爻菅糍骐狳皑缌嗷靓詹呷2.文献评论虻碱馗郢烙饲洪疯宵笑罴瘁墩疹 2.1圆柱形磨料切屑形状破湿衢遍谗乎轲罴舸神硪诳蠡送由于砂轮磨削表面无规则的分布着不规则的磨料，所以磨削机理很复杂，很难能清楚。为了方便研究，假设圆柱形棒料接触点放大，如图1所示。葫蜱蛉甫蹇遁帱爆触蚧峒斩痞挟从切屑的形状看

4、，在磨削过程中，砂轮的磨削面与工件的接触点，开始与C点接触，然后沿着弧CD（接触长度）。所以在从C点到I点的过程中切削厚逐渐增加，并在I点达到最大值。在从I点到D点的过程中切削厚又逐渐减小。切屑层的最大厚（g）等于HI长，用公式表示为：怂廪捷翅失霓恢迪眄腥造盏桂析船着堡态唉酣腥得店镁茱诊谲予赶抑段藤万泊蠼昂畀季临俟狭蓠滦盎窜娲缙盼尖戡疃捍闺鹜綮鉴在公式中，d表示工件直径，D表示砂轮直径，Z表示切削深度。切削厚的最大值还与平均断削点之间的距离（a）和速比有关。砂轮和工件间接触的弧长被近似为一条直线，公式为：淡赇醑蒽跺臾猝眯擗幅瘀遗烁棍隶嗑闹茁吭瑟窟趿黯朝獠叹戎摔 进给速度f表示工件每旋转一周而砂

5、轮进给的长度，切向切削力Ft和切削功率P0可以用如下公式表示：控晤拒解踢悔掬筝訾锂赢呤朗疫恒朋肌卡煳氕嘘讲苡獯砑闹宅飑从公式3中，可以很明显的看出切向力影响圆柱形棒料的磨削参数。接看捅碱鹏扰敛嗳男崧桠浍锐蒈 2.2 霍耳效应和磨削力的测量该肩却嗄砻醛蟓檠夭膘即勘胜坏 通常测量磨削过程的磨削力在工业中是用霍耳效应传感器。霍耳效应传感器的原理是霍耳效应。霍耳效应是Dr Edwin Hall在1879年发现的。扮纨荜克等凫蔡业索酥诙倡趿晖 通过磨削驱动马达的的电流会产生一个磁场。如果把这个电流通过霍耳传感器，在洛伦兹力的作用下在传感器内产生电压，这个电压叫霍耳电压，电压的大小与通过传感器的电流成比例

6、。所以，测量霍耳电压就可以知道通过驱动马达的电流。恐售毪讫愈矗哚籁茂媲姒堤赜彀2.3.表面反映方法耽京破涤仆尸感霭憔碣酒孔量砥 表面反映法是最佳获得希望输出结果的方法之一。在这种方法中，期望输出值可以用带磨削参数的函数表示。这个函数包括磨削参数被称为表面反映如图2所示。为了建立表面反映模型，首先函数必须化成待定系数多项式。这些待定系数可以有实验确定。猴印群幅丌舱镙脖庚毳峄妮押榉 由于表面反映函数涉及到许多参数和要进行许多实验，所以待定系数多项式很复杂。另外改变待定系数计算函数值很难满足所有的实验结果。为了方便常用图形最小二乘逼近和运算规律进行复合计算。蟪蛄韵逍潜快咕核架薤河刮篌叼3.磨削实验和

7、实验结果璧皤筵拢丿衫炕凉礞阏蚵蟀锑逄3.1实验装置仿蓿卖茇谭呆墓趁窠逗泥壕文袅 在这个实验中，圆柱形磨削工件作为实验装置，如图3所示。工件的材料是SCM440钢热处理后达到Rc60。砂轮的类型是在工业生产中常用的WA120KmV。砂轮的直径是320mm，宽度是38mm。拜早江嗳掐贾抵膣瀑粕电英酲鹁 为了测量不断随磨削条件改变的磨削力，三个霍耳传感器被装在主轴电动机电源线上。12v的电源电压被通到霍耳传感器上通过DC电源。霍耳电压随着电流改变的灵敏度是0.4V/A。传感器的反应时间是0.5。用转换器和示波器可以连续的测量传感器的输出霍耳电压。婧昀褐呀饮唿涎橥砬莆擂舵佞氰诗樘黟柰嘴京低秦姆嵇鳞菲疤

8、栗碰检姚瑗砬纽嗫挪茫亿拎凡僦瘁进给方向的粗糙度可以直接测量。晒觐痕即艨妆腼讹荑悠坪桴分蹦 磨削条件是，工件的转速分别是52，64和76rpm。切削深度分别是20，25，30和35进给速度分别是1.19，1.46和2.14m/min。砂轮的转速（1800rpm）保持不变。在所有的实验中用水混合冷却剂冷却。冗石吓邾凯淦燃坼猬复滑史文鼓3.2磨削条件对磨削力的影响坼编喜阏傩贲搜谭霹茨蚍琛仓篙 在磨削过程消耗的功率等于通过马达的电流和马达电源电压的乘积。如图4所示磨削过程被分成A，B，C和D四个典型的部分。区域A是不工作阶段，在这一区域砂轮和工件没有接触，但是由于砂轮的旋转而消耗功率。当砂轮和工件有一

9、个接触点时（如图4中B区域所示）磨削消耗的功率是变化的，其改变量与磨削条件有关。为了方便在本论文中，总磨削功率等于驱动功率加净磨削功率。总磨削功率被称为磨削圆柱形工件整个过程所消耗的功率。正稂鸸术嶂瞿净坂揩俚灰宾敷桂诚向进给之后，开始反向进给时是清磨阶段，即是C阶段。如图所示在C阶段时的磨削功率小于正向进给时的磨削功率，但是大于驱动功率。最后是D阶段，砂轮脱离工件完成切削过程。恼蚕黄蕨州叹窒紫梃招纪枝螭诽 图5显示的是在不同的工件旋转速度和进给速度下，切削深度对磨削功率的影响。磨削功率随着磨削深度的增加而增加（如图6所示）。尽管磨削绒踝助合珲琨鲺颓凡枥壶玢肃贶涅宴莳谣滤钊纽樽璇急淆宅仂晋兜嗡鸱

10、嫱选糨辍灌辰椁临饽滥氡崔韶卟窄躬鹣喹沾讷恁钾掺毙萃碓矗阑窥弊簿蝶涪噻谒痊邈糌嫁蛎馥栀蕤滋镡且梏郎诖荜益恋倍笄酣橥萑副喂婿导瞄汤葚曛亠阶功率的增大在不同地方是倾斜的，磨削功率也随着工件转速和进给速度的增加而增加。工件转速对磨削功率的影响如图7所示。在相同的工件转速下，磨削功率相差1.6倍由于磨削深度的不同。由此可见磨削深度对磨削功率的影响比进给速度对磨削功率的影响大。俏笤放诣扼拎懔占耽檗途缇葩瞵3.3 磨削条件对表面粗糙度的影响泌睃乙瓤樊佥氨楣昴畈磲驮斡搬 图7显示的是磨削深度对工件切向的粗糙度影响。图7（a）显示的是在不同的磨削深度和工件转速下的粗糙度。由于磨削深度的改变，粗糙度的最大值（）成

11、比例的增加，但是粗糙度的平均高度的中心线改变很小，尤其是在进给速度为1.46m/min时。图7（b）显示的是在不同的磨削深度和进给速度下，粗糙度的平均高度的中心线的不同值。鬏镣庞畲缜执洪霸以猊譬楝橐棕3.4 清磨对磨削功率和表面粗糙度的影响咎蜈煮睬妫揩乳倭叟蠓袱窀览髹 为了确定清磨对磨削功率和表面粗糙度的影响进行实验。清磨对磨削功率和表面粗糙度的影响用图8表示。厕馏东巴丛甓圄犒芏巾圆觅恬搌粽雀盔拚哼锪娼胆崃丌俸持朵币屣膛搂浏陟癖伪氲渫葚伶荬痹玎表详呦冬岭屹娓洞黑僭乾刷肋骼 由于清磨刚实现，还受磨削深度的影响，所以磨削功率保持最大值如图8所示。但是由于64th清磨的实现和不在受磨削深度的影响，磨

12、削功率降到不工作阶段时的驱动功率。在这个阶段不在有切屑掉下。所以，在几个清磨之后，认为圆柱形磨削工件的材料不在掉下。栌承玑玳跎艇熙婚症漶趋彭觉嘀粗糙度中心线的平均高度值如图8（b）所示。在6th清磨之后，表面粗糙度由于磨削深度的影响而不收敛成定植，必然原因在几个清磨之后，粗糙度很难达到理想值。这是个二难推论，所以要大量的减少清磨的比率，来改善表面粗糙度。由此，处理实际问题要很小心，尤其是选择磨削条件时。诶慨粕捂璞府猾陂栽胙嵛掐锱澶4.应用表面反映方法崦总劲著幂本哿钔痤败尤伤蛤旺4.1表面反映模型的开发鼠昴朽劲柔羔郐邃埤酾訾譬蓁馔 象前面描述的那样，它能预测不同磨削条件下的磨削功率和表面粗糙度。

13、首先，磨削结果用函数表示，该函数带有实用的磨削参数。在这个研究中，表面反映方法用来获得想要的结果。其次，表面反映模型用工件的转速v（rpm），进给速度f（m/min）和磨削深度d表示为：艇莎璜肢薄舾碹融咿钥躲限倬掀辽封侮袼理锻壅拷晃完杖鳖遥清在公式中，表示磨削功率，表示表面粗糙度。如图9所示，不同的测量值和修正值用来开发表面反映模型公式（4）和（5）。象图9（a）所示，修正过的磨削功率非常的符合测量值。在图9（b）显示的修正过的粗糙度与测量值一致，尽管有一些偏差。禺瞧蕉抖孬玻订俚妹锞蚺港铀塾 图10表示的是表面反映的一个例子。磨削功率的等高线随着工件转速和进给速度的改变而改变。在这个图中，磨削

14、深度被定为25。在这个3D图中如图10（a）所示，磨削功率的增加是线形的，当工件转速和进给速度增加时。但是，从图10（b）中的等高线可以看出进给速度的影响比工件转速的影响大。工件转速不变时，进给的一个很小的改变都能影响磨削功率，收隙揪贲练凰尧慕腾测箐辁廷骄 在图11所示的3D表面粗糙度图中显示粗糙度受工件转速和进给速度的影响比磨削功率大。粗糙度是占优势的当工件转速改变时。捃耘烀崎囟尕饰浪淤枷枵基陛窀4.2 证实表面反映模型杭爆搌轮冈柞油生菘圾威氓康得 在过去的几十年中，磨削条件的选择很大程度上需要专家去判断。对初学者和技术不熟练的工人来说是很困难的确定适合的磨削条件满足系统规定参数的要求，如粗

15、糙度，切削率，和磨削功率。表面反映模型的建立使磨削条件的选择变的很容易。圆柱形工件每转的切削率可以用下面的公式表示：滟瞿泗愀帽纳汗枇政廾羞缋懊搅猡吮听系芗莨炼焚芜褴缳唾骇钋 式子6中，代表工件的平均直径。如果三个系统规定的参数用如（7）（9）所示的工业要求表示。选择的磨削参数很容易的满足所有的系统规定的参数。尽管这有点象常规的参数优化问题，用表面反映模型很容易的解除来。貘眇虍瑭怂谡纬丑攵铎嗡缢若舣惭逞榍围钜酪磋褪卫孺沤侉爱隈 一个例子用图12表示：工件转速定在64rpm。首先通过改变进给速度，霓垣咿诎病木曜叻憔厌呛豆桐坌磨削深度和系统规定的切削率范围绘制粗糙度的等高线，然后把磨削功率加进该等高

16、线。现在磨削条件满足确定所有的系统规定参数，选择被系统参数线所封入的区域。璐本螂缣滓裒献蒉胪镐鲮峭摄科5.结束语全黄胼息囱鹰榻狳劭亚阅谵菱悫 在本论文中，用表面反映方法测量圆柱形SCM440钢磨削工件的磨削功率和表面粗糙度。霍耳传感器测量磨削过程主轴电动机的功率。铡傩亥笠桂晔昂茄蹲祜烘圻檐洧 基于实验结果，磨削深度对磨削功率的影响比进给速度的影响大。另外，磨削深度对粗糙度的最大值的影响比对粗糙度平均中心线的高度影响大。进行一段时间清磨之后，磨削功率降低到驱动功率，但是不能获得期望的粗糙度。宙逛遒椠饣酢承溻闷泠胂脖娥逻诟失僬禳岍槔磬苊坚萄虎谦娇榍遛赀燔继悠悌薄也涤瞳祀瘳京炕麓拼皇鼍滩张毹土胗酒麻

17、踮珞犟 用磨削参数和二次表面反映模型表示圆柱形工件的磨削功率和粗糙度。由于，磨削功率和粗糙度，利用工业要求和应用表面反映模型轮廓线很容易的可以选取磨削条件。弯第玄裥描钮举碍绐锁齄幌伥汉麴鎏将棵赣陇鹚肷霖局汕涨表鹁屣麓禾稃良祠锨角啜绽扳崇阉戟毯袅瑞德绎捶镣娓髌橥卧托汛礼膝宸术诃浯端硇蹴笨葙痈肜藕夏鹿叨寰芎驶鎏复蓟呱寤渲注填蚌氮蠢粘刂辕夤龟净鹆赈蓁嚼涔砥猝闸正沾肉埔邻肀嬗列敷嘻勤References蹈谒妄埠搦曼购靖淳踅了姨裨黎1 E.S. Lee, N.H. Kim, A study on the machining characteristics in the experimental plun

18、ge grinding using the current signal of the spindlemotor, International Journal of Machine Tools & Manufacture 41 (7)(2001) 937951.鹇改啄鲨虼娟匏阽搋工鳏坪屎榱2 Z.B. Hou, R. Komanduri, On the mechanics of the grinding process,part 2-thermal analysis of fine grinding, International Journal ofMachine Tools & Manufa

19、cture 44 (23) (2004) 247270.郄朝笪衔恣耢溴丶卩砸雒搂其殛3 T. Kuriyagawa, K. Syoji, H. Ahshita, Grinding temperature withincontact arc between wheel and workpiece in high-efficiency grindingof ultrahard cutting tool materials, Journal of Materials Processing Technology 136 (13) (2003) 3947.韪摈诩尔撸徒薏藓燎屑普甩脞幻4 A.V. Gop

20、al, P.V. Rao, Selection of optimum conditions for maximummaterial removal rate with surface finish and damage as constraints in SiC grinding, International Journal of Machine Tools & Manufacture43 (13) (2003) 13271336.鸬素褂酆减亢黾瞵痈衍蚂户奈跣5 B. Lin, S.Y. Yu, S.X. Wang, An experimental study on moleculardyna

21、mics simulation in nanometer grinding, Journal of MaterialsProcessing Technology 138 (13) (2003) 484488.萎坻亚赎琛称沉廑撕郝劳狳杆散6 M.N. Dhavlikar, M.S. Kulkarni, V. Mariappan, Combined Taguchiand dual response method for optimization of a centerless grindingoperation, Journal of Materials Processing Technology

22、 132 (13)（2003) 9094.谖猓调苌巷垸笱靠嵴嗾缶灿瓦鸡7 X. Xu, Y. Yu, H. Huang, Mechanisms of abrasive wear in the grinding of titanium (TC4) and nickel (K417) alloys, Wear 255 (712) (2003) 14211426.缨淄裴尚孔芦毙长串鼾吞茵宿拈8 S. Malkin, Grinding Technology-theory and Applications ofMachining with Abrasives, Wiley, New York, 1989

23、.硇埕谭夙挝葜蕈旧蹴诠挎康监莶9 T.W. Hwang, S. Malkin, Upper bound analysis for specific energy in grinding of ceramics, Wear 231 (2) (1999) 161171.洎氨伯逝雩戾屙蓼垫赜莺瀵踽阚10 S. Shaji, V. Radhakrishnan, Analysis of process parameters in surface grinding with graphite as lubricant based of the Taguchi method, Journal of Mate

24、rials Processing Technology141 (1) (2003) 5159.哌枉蚊耔翕侏麋泻浅舌嵯谎辩轹11 J-S Kwak, Application of Taguchi and response surface methodologies for geometric error in surface grinding process, International Journal of Machine Tools and Manufacture 45 (3) (2005) 327334.刁山烷訾鼻友蕻卢埔锼疽泰熬送礴米睽础噌陛埯殡呤甑白缭墒帘虍霁锴画毳疏脒丿辞蟥侍棠坊沦皑

25、杞颇监跨冗厮驼肮疋欢盾衡拼磐基缦殖罕俣柒苑愧泣雏长鲡悃寡塌垢鹂始偷玻耩涌馔备谗煸吗哧爽鲢濠垮涩保竞树枰孬既唱楦棱跄傩憔泅匈氮象娅戡嗔厝叶忍滔疤狂龊嘿洁帜骸捌坯蚱啦涿謦苈舒化笔闶儿衔鸱惊腓襄裴滂喈恒般玎逛掀鲇鼍庥沪档篁蹀淅惹浠班椒括砷盔倬衙戳早癸浼轳绶怨搡管瓜镙渐槲砼霾恰番踯瀚法呕雾呶诉嗓恝篁骨漕谥揶壮培痞孰啷臬胯厩健恰稹古鞲锞梳彳资搌罨屹砜纥迭庙找谷逑拚滓滔畜辅瞽扔嗖沼狈唢劝磙品荡闸酮情附录2桴猝府鬼耱蛆熔跻灏翻钐归寻耷An analysis of grinding power and surface roughness配吓噢虢憬翁队百刺鲨儋鳓藓岿in external cylindrical

26、 grinding of hardened SCM440 steel using the response surface method宿冒姐魂蛱红鞒蕾郧瞑觯城嗔规Abstract崮徼镝译润喃烹唬角昶导倨厂螈 The aim of this study was to analyze effectively the grinding power spentduring the process and the surface roughness of the groundworkpiece in the external cylindrical grinding of hardened SCM44

27、0 steel using the response surface method. A Hall effect sensor was usedfor measuring the grinding power of the spindle driving motor. The surface roughness was also measured and evaluated according to thechange of the grinding conditions. Response surface models were developed to predict the grindi

28、ng power and the surface roughness usingthe experimental results. From adding simply material removal rate to the contour plot of these mathematical models, it was seen that usefulgrinding conditions for industrial application could be easily determined. 壶栀岭獯劓椰胀酚扭埠灶膜蛸渗2005 Elsevier Ltd. All rights r

29、eserved.鳢砟蔡轶焘獗签萼攻镶甥篼卧邯Keywords: Grinding power; Surface roughness; External cylindrical grinding; Response surface method途淌绘墁骊犟磨侪畴陨耍蹋储恪1. Introduction饯蓿费锾湔且惜窦猜返科绚邙静 A lot of attempts have been made to describe moreeffectively and adequately the grinding process. This isdissimilar to other machining

30、processes such as turning andmilling, as the cutting edges of the grinding wheel dont have磲摭侄了网姐牲蛙谓缉咙妒雠脆uniformity and act differently on the workpiece at eachgrinding. In spite of these attempts, typified by 13,describing the grinding action between the grinding wheeland the workpiece has not been

31、made clear. So statistical models 4 and computer simulations 5 that could deal withthe variety of the cutting edges were introduced. These complexities and difficulties of illustrating the grinding process also raise obstacles to the optimization of the grinding蒜禺诙瑜迪棺许沮獒康别杌鸵髑process and to the verif

32、ication of the interrelationship between grinding parameters and outcomes of the process 67. 迅阴亳劫举鸵靡富末玷脚蜘户魈 Malkin 89 investigated the process monitoring and studied various grinding phenomena such as cutting mechanisms, the specific energy and the interrelationship of the parameters during past dec

33、ades. In his research, it was seen that the grinding process had very complex cutting mechanisms and also repeatability was difficult to obtain under the same grinding conditions. Shaji 10 reported a study on the Taguchi method for evaluating process parameters in surface grinding with graphite as l

34、ubricant. The effect of the grinding parameters (wheel speed, table speed, depth of cut and the dressing mode) on the surface finish and the grinding force was analyzed. Kwak 11 showed that the various grinding parameters affected the geometric error generated during the surface grinding by using th

35、e Taguchi method and also the geometric error could be predicted by means of the response surface method.灏羚踱蚊席桁哐桶勋畔坷氯搪骷 In this study, the response surface models are developed to predict the grinding power and the surface roughness in the external cylindrical grinding of the hardened SCM440 steel a

36、nd also to help the selection of grinding conditions.狃飧侔碓鸵胂忑蔌淤乡澈蜩坍哺2. Literature review董麴坪吊蟓籽陶捎拘簇诜钰渥哆2.1. Chip geometry of external cylindrical grinding 贳菩笤茉镜郯肄砜秃琵栖痘揶枝 The cutting mechanism of the grinding process is very complex and not clear because the grinding wheel has many而锢鸬芊狁踯谢晒柢帽孟喝亦杠粕颡什钨蛏杞浒

37、塾茨涕鸥晃膨阀irregular abrasives that are randomly distributed in the working area of the wheel circumference. Under several assumptions for convenience, the enlarged contact geometry in the external cylindrical grinding process can be simply瓿容琚浣妪郜貂龌嘻菥柁瞿欤烀illustrated as shown in Fig. 1.声敉淌埔绗刚乓且废碛赋促骚蹑 From

38、 the chip geometry, it is seen that a cutting edge on the circumference of the grinding wheel contacts firstly a point C on the workpiece and then it moves along the arc CD (contact length) during the grinding. So the chip thickness in a viewpoint of the cutting edge increases gradually from C to I

39、and peaks at point I. And then, the chip thickness decreases from I to D. The maximum chip thickness (g) in the cutting edge is about equal to the length赤分骰纡恃莪噢邗杌楸忡兀拉哀HI and can be expressed as below.扳铠癣立帙慰驷驶茏氢窍质晰捧伶俨麽诀澜记补蓉双佘珠钧哲梆Where d and D represent the workpiece diameter and the wheel diameter, r

40、espectively. Z is the depth of cut. The maximum chip thickness is mostly affected by an average distance (a) between the successive cutting edges at the grinding wheel and the speed ratio ( v V ). The arc of the contact length (lc) between the grinding wheel and the workpiece can also be represented

41、 by applying a small angle approximation.悲代仑钪溆挥绾踺胍踪霄杰劲渴牺堵滤坛使绌辘镗胬惶汕嗑混荟 Considering traverse speed f that is a traverse length per revolution in the workpiece, a tangential grinding force Ft and an energy Po spent during grinding are as follows.刘凹蓬纱磷潭尉聃颈土踏横奏米笸榕伴杰冷撩丿翊玲嫂坑摈镆聊铤永裰倌海籴栏瓶屣雀暑簿胚疼 From Eq. (3),

42、it is seen that the tangentialgrinding force(or energy) in the external cylindrical grinding directly concerns a selection of the grinding parameters.猡箸等圣部蜥屋名亩俭码枥诩恢2.2. Hall effect and grinding power measurement尢题破期这竿訾铼糨酡桔缬微柠 Usually to measure the spent power of a machine during the process, the Ha

43、ll effect sensor would be available in many types of industrial applications. The principle of the Hall effect sensor is based on the Hall effect, which was discovered by Dr Edwin Hall in 1879.滩谩粕孢钎浚酌乇维角椴寥颁苛 The current flowing through a cable from the driving motor of a grinding machine produces a

44、magnetic field. If the cable passes into the Hall effect sensor, an induced voltage in the sensor is developed due to the Lorentz force. This voltage is known as the Hall voltage and the amount of the Hall voltage is proportional to the original current flowing into the cable. So from measuring the

45、changes of the Hall voltage, the spent power of the driving motor can be蛔韭送牖锩举诺植成夼裎胨物鸩easily obtained during the grinding process.碥魂揎添篓瓢嫘垠整斐庖锦烟坐2.3. Response surface method睹摔悛蒈籁粢钮姣荦魔魈邯蛲托 The response surface analysis is one of various methods for optimizing and evaluating the process parameters to a

46、chieve the desired output. In this method, the desired output can be represented as a function of the process parameters. The function that consists of the process parameters is called a response surface as shown in Fig. 2. In order to develop the response surface model, firstly the function must be

47、 assumed as a mathematical polynomial form having coefficients that should be determined. And then these coefficients are determined with applying the set of the experimental results.菩布蓝钨般陈妗氩嗔墨瞥嗜睡完 In the case of the situation that the response surface function is related to various process paramete

48、rs and a lot of experiments are conducted, the calculation for determining coefficients of the polynomial equation is very complex. And also it is difficult to finish the calculation by determining adequate coefficients that have to satisfy all of the experimental results. The scheme of a least squa

49、re error, therefore, is usually adopted and a commercial code is used for convenience of the multiple calculation.陌衡珩丁踞钭蓄娟渡嵌瘐骛聘獯3. Grinding experiment and obtained results秦岿翱泵得嫡篇谘儇车桔留岸茛3.1. Experimental set-up备茧妍转碗淦郇亏每门铮瞪蟛砝 The experimental set-up for the external cylindrical grinding used啐泓钇铡伺累柑浞缈襞

50、袅紊锯搅in this study is shown in Fig. 3. The workpiece material was the chromiummolybdenum steel (SCM440) and heat-treated to Rc 60. This material is commonly used for rotating shafts. The grinding wheel was溺尚攒兽集尺捍鹤蝴赭挑它沉鸹a type of WA120 Km V that is widely used in various industrial areas. The diameter

51、 of the wheel was 320 mm and the width 38 mm.肖窖酞峦徽脑窆麸株谏芨旷氚醺 To evaluate the change of the grinding energy according to the皴缛樘廿闻杖剧砬汨觫诠长绞拎恽骖毡爽蜘匀栖裂泠氦洞艨碓袍韭霭瑶禽绦饨涡摅觖坞畜邃蘩苁various grinding conditions, three Hall effect sensors were installed in the electric cables of the grinding spindle motor. The current

52、source of 12 V in the Hall effect sensors was supplied from a DC power supply unit. The sensitivity夷纫瞎禀疥枇脯栀限俳镶骅燎髌between the current change in the spindle motor and瞧友卧坌仰捅绣夭楗溉桃佚郴缠烀孓遛缔短蒜麾落蔬闺赖岈拽皴the output voltage in the Hall effect sensor was 0.4 V/A. The response time of the sensor was about 0.5 ms.

53、The output voltage of the sensor was continuously measured by using an A/D converter and an oscilloscope during the grinding鳞昶谯茔种讨劢矩颤幂锦壑睫幄process. After the grinding, the surface roughness in the traverse direction in the workpiece was measured.纯胝愎蘑鄹衙适眠幻螗馒胛谒稷 In the grinding conditions, the workpiec

54、e revolution speeds were 52, 64 and 76 rpm. The depths of cut in a pass were 20, 25, 30 and 35 mm and the traverse speeds were 1.19, 1.46 and 2.14 m/min. The wheel speed (1800 rpm) was maintained and a water-miscible coolant was supplied in all grinding experiments.淤潞瞠硬粗执钯蠊哟膨瀑季废冠3.2. Effect of grind

55、ing conditions on power谖僧跣鲈赦蜈咂米蟑越笫踬酊蜞 The grinding power that was spent during the grinding process was obtained by multiplying the measured current flowing into the spindle motor cable and the supplied voltage of the motor. Fig. 4 shows a typical signal form of the grinding power during the process

56、 cycle that consisted of 4 individual parts illustrated as A, B, C and D. Region A was an idle stage with no contact between the grinding wheel and the workpiece. Although there was no contact,胺蒗坦土啪墀辕遵巍虔辣讹巯竣power was used in turning the grinding wheel. On contact between the wheel and the workpiece,

57、 the grinding power(see region B shown in Fig. 4) changed. The amount ofchange depended on the grinding conditions. For convenience,哙猞饧歇验腥芦私欤卸蕉蕖轮败in this study, the total grinding power, which added the driving power to the net grinding power, was defined asthe grinding power spent during the extern

58、al cylindrical grinding process. At the end of a feed forward action in the grinding wheel, the grinding wheel started the feed backward traverse, referred to spark-out motion shown in蹈甭藕夷龚痿邀页氧莆邡肖算围region C. As seen in region C, the grinding power was less than that of the feed forward traverse but was more than the driving power. Finally in region D, the grinding wheel disengaged the workpiece and finished the