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企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第1 页 车间 工序号工序名称材料牌号机加工030粗车40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数卧式车床CA61401夹具编号夹具名称切削液车夹具工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01三爪装夹左端毛坯,车右端面以及72外圆，留精加工余量外圆车刀560700.481.510.07020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第 页 车间 工序号工序名称材料牌号机加工040粗车40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数卧式车床CA61401夹具编号夹具名称切削液车夹具工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01掉头，三爪装夹右端外圆,车左端面以及84外圆，留精加工余量外圆车刀560700.481.510.07020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第3 页 车间 工序号工序名称材料牌号机加工050精车40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数卧式车床CA61401夹具编号夹具名称切削液车夹具工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01车右端面以及72外圆及倒角，达到图纸尺寸外圆车刀560700.50.510.05020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第4 页 车间 工序号工序名称材料牌号机加工060精车40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数卧式车床CA61401夹具编号夹具名称切削液车夹具工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01车左端面以及84外圆及倒角，达到图纸尺寸外圆车刀560700.50.510.05020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第5 页 车间 工序号工序名称材料牌号机加工060扩40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数卧式车床CA61401夹具编号夹具名称切削液钻夹具工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01扩30的通孔至2828钻头450168020.220.08020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第6页 车间 工序号工序名称材料牌号机加工080镗40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数卧式车床CA61401夹具编号夹具名称切削液钻夹具工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01镗38H7孔，达到图纸尺寸镗刀800500.5220.6020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第7页 车间 工序号工序名称材料牌号机加工090镗40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数卧式车床CA61401夹具编号夹具名称切削液钻夹具工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01镗50孔镗刀800500.5220.4020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第8页 车间 工序号工序名称材料牌号机加工100滚齿40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数滚齿机Y3150E1夹具编号夹具名称切削液滚齿工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01滚齿（Z=26)滚刀672890.45116020304编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工序卡产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共9 页第页 车间 工序号工序名称材料牌号机加工110滚齿40Cr毛坯种类毛坯外形尺寸每毛坯可制作数每台件数锻件11设备名称设备型号设备编号同时加工件数滚齿机Y3150E1夹具编号夹具名称切削液滚齿工位夹具编号工位器具名称工序工时准终单件工步号工步名称工艺装备主轴转速(r/min)切削速度(m/min)进给量(mm/r)背吃刀量(mm)进给次数工时/min机动单件01滚齿（Z=22)滚刀672890.451150203编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期企业名称机械加工工艺过程卡片产品型号零件图号01-01产品名称双联齿轮零件名称双联齿轮共1 页第 1页材料牌号40Cr毛坯种类锻件毛坯外形尺寸每毛坯可制作数 1每台件数1备注工序号工序名称工序内容车间工段设备工艺装备工时/min010锻造锻造准终单件020热处理正火，去应力退火热处理030粗车三爪装夹左端毛坯,车右端面以及72外圆，留精加工余量机加工车沈阳一机CA6140外圆车刀0.07040粗车掉头，三爪装夹右端外圆,车左端面以及84外圆，留精加工余量机加工车沈阳一机CA6140外圆车刀0.07050精车车右端面以及72外圆及倒角，达到图纸尺寸机加工车沈阳一机CA6140外圆车刀0.05060精车车车左端面以及84外圆及倒角，达到图纸尺寸机加工车沈阳一机CA6140外圆车刀0.05070扩扩30的通孔至28机加工钻沈阳一机CA614028钻头0.08080镗镗38H7孔，达到图纸尺寸机加工镗沈阳一机CA6140镗刀0.6090镗镗50孔机加工镗沈阳一机CA6140镗刀0.4100滚齿滚齿（Z=26)机加工滚齿滚齿机Y3150E滚刀6110滚齿滚齿（Z=22)机加工滚齿滚齿机Y3150E滚刀5120钳去毛刺机加工130检验140入库编制 (日期)审核 (日期)标准化 (日期)会签 (日期)标记处数更改文件号签字日期标记处数更改文件号签字日期机 械 技 术 学 院毕 业 设 计 论 文双联齿轮机械加工工艺及三维造型设计学生姓名： 指导教师姓名： 所在班级： 所在专业： 论文提交日期： 2015.4 论文答辩日期： 2015 答辩委员会主任： 主答辩人： xxxx 系2无锡职业技术学院毕业设计论文独创性声明本人声明所呈交的毕业设计论文是我个人在指导老师指导下进行的研制工作及取得的研制成果。尽我所知，除了文中特别加以标注和致谢的地方外，论文中不包含其他人已经发表或撰写过的研究成果，也不包含为获得无锡职业技术学院或其它教育机构的毕业文凭或证书而使用过的材料。与我一同工作的同志对本论文所做的任何贡献均已在论文中作了明确的说明并表示了谢意。学生签名： 日期：2015.4.1无锡职业技术学院毕业设计论文使用授权声明无锡职业技术学院及其图书馆、档案室有权保留本人所送毕业设计论文：双联齿轮机械加工工艺及三维造型设计的复印件和电子文档，可以采用影印、缩印或其他复制手段保存本论文。本人电子文档的内容和纸质论文的内容相一致。除此以外，允许本论文被查阅和借阅，可以公布（包括刊登）论文的全部或部分内容。论文的公布（包括刊登）授权无锡职业技术学院机械技术学院办理。学生签名： 指导教师签名： 日期：2015.4.118双联齿轮机械加工工艺及三维造型设计摘要 双联齿轮零件加工工艺及夹具设计是包括零件加工的工艺设计、工序设计部分。在工艺设计中要首先对零件进行分析，了解零件的工艺再设计出毛坯的结构，并选择好零件的加工基准，设计出零件的工艺路线；接着对零件各个工步的工序进行尺寸计算，关键是决定出各个工序的工艺装备及切削用量并在以后设计中注意改进。关键词 工艺，工序，切削用量 Double gear machining technology and three-dimensional designabstract Double gear parts and fixture design process includes parts machining process design, process design part. In the process of designing the parts to be the first analysis to understand the parts of the process re-design the structure of the blank, and select the machining datum good parts, the design process route parts; then the part of each step of the process to calculate the size of a key is to determine the technical equipment and cutting the amount of each process and attention to improving the design in the future.Key words technology, processes, cutting the amount of目 录第1章 序 言1第2章 零件的分析22.1零件的形状22.2零件的工艺分析3第3章 工艺规程设计53.1 确定毛坯的制造形式53.2定位基准的选择零件表面加工方法的选择53.3 制定工艺路线53.4 选择加工设备和工艺装备73.4.1 机床选用73.4.2 选择刀具83.4.3 选择量具83.5 机械加工余量、工序尺寸及毛坯尺寸的确定8第4章 确定切削用量及基本时间104.1 工序切削用量的及基本时间的确定104.2 工序切削用量的及基本时间的确定124.3 工序切削用量及基本时间的确定124.4 工序切削用量及基本时间的确定14总 结16致 谢17参 考 文 献18无锡职业技术学院毕业设计论文双联齿轮机械加工工艺及三维造型设计 第1章 序 言机械制造业是制造具有一定形状位置和尺寸的零件和产品，并把它们装备成机械装备的行业。机械制造业的产品既可以直接供人们使用，也可以为其它行业的生产提供装备，社会上有着各种各样的机械或机械制造业的产品。我们的生活离不开制造业，因此制造业是国民经济发展的重要行业，是一个国家或地区发展的重要基础及有力支柱。从某中意义上讲，机械制造水平的高低是衡量一个国家国民经济综合实力和科学技术水平的重要指标。双联齿轮零件加工工艺及夹具设计是在学完了机械制图、机械制造技术基础、机械设计、机械工程材料等的基础下，进行的一个全面的考核。正确地解决一个零件在加工中的定位，夹紧以及工艺路线安排，工艺尺寸确定等问题，并设计出专用夹具，保证尺寸证零件的加工质量。本次设计也要培养自己的自学与创新能力。因此本次设计综合性和实践性强、涉及知识面广。所以在设计中既要注意基本概念、基本理论，又要注意生产实践的需要，只有将各种理论与生产实践相结合，才能很好的完成本次设计。本次设计水平有限，其中难免有缺点错误，敬请老师们批评指正。第2章 零件的分析2.1零件的形状题目给的零件是双联齿轮零件，主要作用是起连接作用。它主要用于轴与轴之间的连接，以传递动力和转矩。 双联齿轮主要用于一些机械设备变速箱中，通过与操作机构的结合，滑动齿轮从而实现变速。圆柱齿轮一般分为齿圈和轮体两部分，根据齿轮轮体的结构形状来划分可知上图中的双联齿轮为盘类齿轮，有两个齿圈，在齿圈上切出直齿齿形。零件的实际形状如上图所示，从零件图上看，该零件是典型的零件，结构比较简单。具体尺寸，公差如下图所示。2.2零件的工艺分析由零件图可知，具有较高强度，耐磨性，耐热性及减振性，适用于承受较大应力和要求耐磨零件。该零件属于齿轮类零件，形状规则，尺寸精度和形位精度要求均较高，零件的主要技术分析如下：（1）齿轮端面对准A的圆跳动公差不超过0.018mm，主要是保证端面平整光滑，双联是利用轴和孔进行配合定位，因此必须保证孔的尺寸精度。 双联齿轮之间啮合要求严格，要保证双联齿轮的齿形准确及同轴度较高。（2）由于零件是双联齿轮，轴向距离较小，根据生产纲领是选择合理的加工工艺。（3）齿轮要求加工精度高，要严格控制好定位（4）38H7孔是一比较重要的孔，也是以后机械加工各工序中的主要定位基准。因此加工孔的工序是比较重要的。要在夹具设计中考虑保证到此孔精度及粗糙度要求。双联齿轮零件主要加工表面为：1.车外圆及端面，表面粗糙度值为3.2。2.车外圆及端面，表面粗糙度值3.2。3.镗装配孔，表面粗糙度值3.2。4.半精车侧面，及表面粗糙度值3.2。5.两侧面粗糙度值1.6。第3章 工艺规程设计本双联齿轮假设年产量为10万台，每台需要该零件1个，备品率为111%，废品率为0.25%，每日工作班次为2班。考虑到零件在工作时要有高的耐磨性，所以选择锻造。依据设计要求Q=100000件/年，n=1件/台；结合生产实际，备品率和 废品率分别取111%和0.25%代入公式得该工件的生产纲领 N=2XQn(1+)（1+)=23134115件/年3.1 确定毛坯的制造形式 由于零件结构简单，尺寸较小，且有台阶轴，力学性能要求较高，精度较高且要进行大量生产所以选用模锻件，其加工余量小，表面质量好，机械强度高，生存率高。工件材料选用40Cr钢，毛坯的尺寸精度要求为IT1112级3.2定位基准的选择零件表面加工方法的选择待加工的两零件是盘状零件，孔是设计基准（也是装配基准和测量基准），为避免由于基准不重合而产生的误差，应选孔为定位基准，即遵循“基准重合”的原则。具体而言，即选一端面作为精基准。由于待加工的两零件全部表面都需加工，而孔作为精基准应先进行加工，对主动端而言，应选面积较大的外圆及其端面为粗基准；对从动端而言，应选面积较大190mm的外圆及其端面为粗基准。3.3 制定工艺路线制定工艺路线的出发点，应当是使零件的几何形状、尺寸精度及位置精度等技术要求能得到合理的保证。在生产纲领已经确定为成批生产的条件下，可以考虑采用万能性机床配以专用夹具，并尽量使工序集中来提高生产率。除此以外，还应当考虑经济效果，以便使生产成本尽量下降。 工艺路线一：010锻造锻造020热处理正火，去应力退火030粗车三爪装夹左端毛坯,车右端面以及72外圆，留精加工余量040粗车掉头，三爪装夹右端外圆,车左端面以及84外圆，留精加工余量050精车车右端面以及72外圆及倒角，达到图纸尺寸060精车车车左端面以及84外圆及倒角，达到图纸尺寸070扩扩30的通孔至36080镗镗38H7孔，达到图纸尺寸090镗镗50孔100滚齿滚齿（Z=26)110滚齿滚齿（Z=22)120钳去毛刺130检验140入库工艺路线二：010锻造锻造020热处理正火，去应力退火030粗车三爪装夹左端毛坯,车右端面以及72外圆，留精加工余量040粗车掉头，三爪装夹右端外圆,车左端面以及84外圆，留精加工余量050精车车右端面以及72外圆及倒角，达到图纸尺寸060精车车车左端面以及84外圆及倒角，达到图纸尺寸070滚齿滚齿（Z=26)080滚齿滚齿（Z=22)090扩扩30的通孔至36100镗镗38H7孔，达到图纸尺寸110镗镗50孔120钳去毛刺130检验140入库工艺方案一与方案二的比较：方案二把滚齿加工放到钻中心孔的加工之前，这样就导致加工时夹具的定位和加紧不好确定，也不好保证一个对A基准线的圆跳动误差。最终确定的工艺方案：010锻造锻造020热处理正火，去应力退火030粗车三爪装夹左端毛坯,车右端面以及72外圆，留精加工余量040粗车掉头，三爪装夹右端外圆,车左端面以及84外圆，留精加工余量050精车车右端面以及72外圆及倒角，达到图纸尺寸060精车车车左端面以及84外圆及倒角，达到图纸尺寸070扩扩30的通孔至36080镗镗38H7孔，达到图纸尺寸090镗镗50孔100滚齿滚齿（Z=26)110滚齿滚齿（Z=22)120钳去毛刺130检验140入库3.4 选择加工设备和工艺装备3.4.1 机床选用.工序和工序是粗车、粗镗和半精车、半精镗。各工序的工步数不多，成批量生产，故选用卧式车床就能满足要求。本零件外轮廓尺寸不大，精度要求属于中等要求，选用最常用的CA6140卧式车床。参考根据机械制造设计工工艺简明手册表4.2-7。.工序是钻孔，选用Z525摇臂钻床。 工序都为CA6140卧式车床。由于加工的零件外廓尺寸不大，又是回转体，故宜在车床上镗孔。由于要求的精度较高，表面粗糙度较小，需选用较精密的机床才能满足要求，因此选用CA6140卧式车床（表5-134）。3.4.2 选择刀具.在车床上加工的工序,一般选用硬质合金车刀和镗刀。加工刀具选用YG6类硬质合金车刀，它的主要应用范围为普通铸铁、冷硬铸铁、高温合金的精加工和半精加工。为提高生产率及经济性,可选用可转位车刀(GB5343.1-134,GB5343.2-134)。.钻孔时选用高速钢麻花钻，参考机械加工工艺手册（主编 孟少农），第二卷表10.21-47及表10.2-53可得到所有参数。3.4.3 选择量具本零件属于成批量生产，一般均采用通常量具。选择量具的方法有两种：一是按计量器具的不确定度选择；二是按计量器的测量方法极限误差选择。采用其中的一种方法即可。3.5 机械加工余量、工序尺寸及毛坯尺寸的确定“双联齿轮” 零件材料为40Cr，查机械加工工艺手册（以后简称工艺手册），表2.2-17 各种合金钢的性能比较，硬度HB为1432611，表2.2-23的物理性能，密度=7.27.3（），计算零件毛坯的重量约为2。表3-1 机械加工车间的生产性质生产类别同类零件的年产量件重型（零件重2000kg）中型（零件重1002000kg）轻型（零件重100kg）单件生产5以下10以下100以下小批生产510010200100500中批生产1003002005005005000大批生产30010005005000500050000大量生产1000以上5000以上50000以上根据所发的任务书上的数据，该零件的月工序数不低于3050，毛坯重量21000MPs的合金钢，切削速度=117m/min。切削速度的修正系数查参考文献7表1.40得：，其余的修正系数均为1，故：V=1170.811.15=110.4m/min=178r/min查参考文献6表4.2-8选择C1100-1机床的转速为： n=1134r/min=3.08r/s则实际切削速度v=1.56m/s半精加工，机床功率也可不校验。最后确定的切削用量为：=0.75mm, f=0.3mm/r, n=1134r/min=3.08r/s, v=1.56m/s=113.6m/min。车左端面以及84外圆及倒角，达到图纸尺寸确定半精车主动端端面的切削用量。采用车外圆相同的刀具加工，切削用量为：,f=0.3mm/r,n=1134r/min=3.08r/s, v=1.56m/s=113.6m/min。4.3.2 切削用量确定精车基本时间： =52s4.4 工序切削用量及基本时间的确定镗38H7孔，达到图纸尺寸，镗50孔选刀具为YT30硬质合金、主偏角、直径为12mm的圆形镗刀。其耐用度T=110min。=0.25mmf=0.15mm/rv=1.4=230.77mm/min=1837.3r/min参考文献1表5-56，根据C6140车床的转速表，选择n=1400r/min=23.3r/s,则实际切削速度v=4.118m/s。=16s滚齿加工由文献2表10-174V=312/T0.33S0.5N=0.124s0.9m1.7/D又由文献2表10-175,10-177S=2.5，T=240min，m=4代入上式得V=32.4m/min，N=0.27kw（2）插齿加工21齿由文献2表10-174V=49/T0.2s0.5m0.3N=17910-4sm2/20.11又由文献2表10-189,10-192S=0.32，T=300min，代入上式得V=18.3m/min，N=0.062kw由（1）、（2）计算它们均小于机床所能提供的功率，故符合要求。总 结毕业设计即将结束了，时间虽然短暂但是它对我们来说受益菲浅的，通过这次的设计使我们不再是只知道书本上的空理论，不再是纸上谈兵，而是将理论和实践相结合进行实实在在的设计，使我们不但巩固了理论知识而且掌握了设计的步骤和要领，使我们更好的利用图书馆的资料，更好的更熟练的利用我们手中的各种设计手册和AUTOCAD等制图软件，为我们踏入社会打下了好的基础。毕业设计使我们认识到了只努力的学好书本上的知识是不够的，还应该更好的做到理论和实践的结合。因此我们非常感谢老师给我们的辛勤指导，使我们学到了很多，也非常珍惜大学给我们的这次设计的机会，它将是我们毕业设计完成的更出色的关键一步。致 谢这次毕业设计使我收益不小，为我今后的学习和工作打下了坚实和良好的基础。但是，查阅资料尤其是在查阅切削用量手册时，数据存在大量的重复和重叠，由于经验不足，在选取数据上存在一些问题，不过我的指导老师每次都很有耐心地帮我提出宝贵的意见，在我遇到难题时给我指明了方向，最终我很顺利的完成了毕业设计。这次毕业设计成绩的取得，与指导老师的细心指导是分不开的。在此，我衷心感谢我的指导老师，特别是每次都放下他的休息时间，耐心地帮助我解决技术上的一些难题，她严肃的科学态度，严谨的治学精神，精益求精的工作作风，深深地感染和激励着我。从题目的选择到项目的最终完成，他都始终给予我细心的指导和不懈的支持。多少个日日夜夜，他不仅在学业上给我以精心指导，同时还在思想、生活上给我以无微不至的关怀，除了敬佩指导老师的专业水平外，他的治学严谨和科学研究的精神也是我永远学习的榜样，并将积极影响我今后的学习和工作。在此谨向指导老师致以诚挚的谢意和崇高的敬意。参 考 文 献1 东北重型机械学院，洛阳农业机械学院，长春汽车厂工人大学，机床夹具设计手册M，上海：上海科学技术出版社，111134。2 张进生。机械制造工艺与夹具设计指导。机械工业出版社，111115。3 李庆寿。机床夹具设计。机械工业出版社，111111。4 李洪。机械加工工艺手册。北京出版社，111134。5 上海市金属切削技术协会。金属切削手册。上海科学技术出版社，2544。6 黄如林，刘新佳，汪群。切削加工简明实用手册。化学工业出版社，2544。7 余光国，马俊，张兴发，机床夹具设计M，重庆：重庆大学出版社，111115。8 周永强，高等学校毕业设计指导M，北京：中国建材工业出版社，2540。11刘文剑，曹天河，赵维，夹具工程师手册M，哈尔滨：黑龙江科学技术出版社，111134。10 王光斗，王春福。机床夹具设计手册。上海科学技术出版社，2540。11 东北重型机械学院，洛阳农业机械学院，长春汽车厂工人大学。机床夹具设计手册.上海科学技术出版社，11184。 12 李庆寿，机械制造工艺装备设计适用手册M，银州：宁夏人民出版社，111111。11 廖念钊，莫雨松，李硕根，互换性与技术测量M，中国计量出版社，2540：11-111。14 王光斗，王春福，机床夹具设计手册M，上海科学技术出版社，2540。15 乐兑谦，金属切削刀具，机械工业出版社，25HT150：4-17An order tracking technique for the gear fault diagnosis using local meandecomposition methodJunsheng Cheng, Kang Zhang, Yu YangState Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, PR ChinaCollege of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, PR Chinaa r t i c l ei n f oa b s t r a c tArticle history:Received 17 November 2010Received in revised form 13 December 2011Accepted 30 April 2012Available online 28 May 2012Local mean decomposition (LMD) is a new self-adaptive timefrequency analysis method,which is particularly suitable for the processing of multi-component amplitude-modulatedand frequency-modulated (AMFM) signals. By using LMD, any complicated signal can bedecomposed into a number of product functions (PFs), each of which is the product of anenvelope signal and a purely frequency modulated signal from which physically meaningfulinstantaneous frequencies can be obtained. Theoretically, each PF is exactly a mono-componentAMFM signal. Therefore, the procedure of LMD can be regarded as the process of demodulation.While fault occurs in gear, the vibration signals would exactly present AMFM characteristics.Therefore, targeting the modulation feature of gear fault vibration signal in run-ups and run-downs and the fact that fault characteristics found in gear vibration signal could often be relatedto revolution of the shaft in the transient process, a gear fault diagnosis method in which ordertracking technique and local mean decomposition is put forward. The analysis results from thepractical gearbox vibration signal demonstrate that the proposed algorithm is effective in gearfault feature extraction. 2012 Elsevier Ltd. All rights reserved.Keywords:Order tracking techniqueLocal mean decompositionDemodulationGearFault diagnosis1. IntroductionGears are the important and frequently encountered components in the rotating machines that find widespread industrialapplications. Therefore, the corresponding gear fault diagnosis has been the subject of extensive research.The key step of gear fault diagnosis is the extraction of fault feature. On the one hand, the conventional gear fault diagnosismethods focus on examining the frequency spectrum analysis of vibration signal at a fixed rotation speed. Unfortunately, theinformation obtained thus is only partial because some faults maybe do not respond significantly at the fixed operation speed.Since faults commonly found in gear could often be related to revolution of the shaft, more comprehensive information may beacquired by measuring the gear vibration signal in the process of run-up and run-down 1. In addition, vibration signals derivedfrom gear in the transient process that are speed-dependent always display non-stationary feature. If frequency spectrum analysisis directly applied to the non-stationary vibration signal, frequency mixing would occur inevitably, which will bring undesirableeffect to the fault feature extraction. In past research, order-tracking technique, which normally exploits a vibration signalsupplemented with information of shaft speed of rotating machinery, has become one of the significant approaches for faultdiagnosis in rotating machinery 2,3. Essentially, order-tracking technique can transform a non-stationary signal in time domaininto stationary one in angular domain, which can highlight the vibration information related to rotation speed and restrain theunrelated information. Therefore, order tracking is a desirable method to extract gear fault feature in the process of run-up andrun-down.Mechanism and Machine Theory 55 (2012) 6776 Corresponding author at: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, PR China.Tel.: +86 731 88664008; fax: +86 731 88711911.E-mail address: signalp (J. Cheng).0094-114X/$ see front matter 2012 Elsevier Ltd. All rights reserved.doi:10.1016/j.mechmachtheory.2012.04.008Contents lists available at SciVerse ScienceDirectMechanism and Machine Theoryjournal homepage: /locate/mechmtOn the other hand, while faults occur in gears, the vibration signal picked up in run-up and run-down process always presentthe characteristics of amplitude-modulated and frequency-modulated (AMFM). In order to extract the modulation featureof gear fault vibration signals, demodulation analysis is one of the most popular methods 4,5. However, conventionaldemodulation approaches such as Hilbert transform demodulation and traditional envelope analysis have their own limitations6. These drawbacks include two aspects: (1) in practice most gear fault vibration signals are all multi-component AMFMsignals. For these signals, in conventional demodulation approaches, they are usually decomposed into single component AMFMsignals by band-pass filter and then demodulated to extract frequencies and amplitudes information. However, both the numberof the carrier frequency components and the magnitude of the carrier frequency are hard to be determined in practice, so theselection of central frequency of band-pass filter carries great subjectivity that would bring demodulation error and make itineffective to extract the characteristic of machinery fault vibration signal; (2) owing to the inevitable window effect of Hilberttransform, when Hilbert transform is used to extract the modulate information, the demodulation results present non-instantaneous response characteristic, that is, at the two ends of the modulated signal which has been demodulated as well as themiddle part with break would produce modulation again, which makes the amplitude get fluctuation in an exponentialattenuation way, and then the demodulation error would increase 7. In order to overcome the first drawback, an appropriatedecomposition method should be looked for to separate multi-component signal into a number of single component AMFMsignals before the envelope analysis. Since EMD (Empirical mode decomposition) could adaptively decompose a complicatedmulti-component signal into a sum of intrinsic mode functions (IMFs) whose instantaneous frequencies have physicalsignificance 8,9, order tracking method based on EMD has been widely used in the gear fault diagnosis 1013. However, therestill exist many deficiencies in EMD such as the end effects 14 and modes mixing 15 that are still underway. In addition, afterthe original signal is decomposed by EMD, the drawback produced by Hilbert transform (above mentioned) is inevitable whenIMF is performed envelope analysis by Hilbert transform. Moreover, sometimes the unexplainable negative instantaneousfrequency would appear when calculating instantaneous frequency by performing Hilbert transform to each IMF 16.Local mean decomposition (LMD) is a novel demodulation analysis method, which is particularly suitable for the processing ofmulti-component amplitude-modulated and frequency-modulated (AMFM) signals 16. By using LMD, any complicated signalcan be decomposed into a number of product functions (PFs), each of which is the product of an envelope signal (obtaineddirectly by the decomposition) from which instantaneous amplitude of the PF can be obtained and a purely frequency modulatedsignal from which a well-defined instantaneous frequency could be calculated. In essence, each PF is exactly a mono-componentAMFM signal. Therefore, the procedure of LMD could be, in fact, regarded as the process of demodulation. Modulationinformation can be extracted by performing spectrum analysis to the instantaneous amplitude (envelope signal, obtained directlyby the decomposition) of each PF component rather than by performing Hilbert transform to the PF components. Hence, whenLMD and EMD are applied to the demodulation analysis respectively, compared with EMD, the prominent advantage of LMD is toavoid the Hilbert transform. In addition, the LMD iteration process which uses smoothed local means and local magnitudes avoidsthe cubic spline approach used in EMD, which maybe bring the envelope errors and influence on the precision of theinstantaneous frequency and amplitude. Moreover, compared with EMD the end effect is not obvious in LMD approach because offaster algorithm speed and less iterative times 17.Based upon the above analysis, order-tracking analysis and the recent development of demodulation techniques, LMD, arecombined and applied to the gear fault diagnosis of various shaft speeds process. Firstly, order tracking technique is used totransform the gear vibration signals from time domain to angular domain. Secondly, decompose the re-sampling signal of angulardomain by LMD, thus s series PF components and corresponding instantaneous amplitudes and instantaneous frequencies can beobtained. Finally, spectrum analysis is carried out to the instantaneous amplitudes of the PF component containing dominant faultinformation. The analysis results from the experimental vibration signal show that the proposed method can extract fault featureof the gear effectively and classify working condition accurately.This paper is organized as follows. A theory of the LMD approach is given in Section 2. In Section 3 a gear fault diagnosisapproach in which order tracking technique and LMD are combined is put forward and the practice applications of proposedmethod are demonstrated. In addition, the comparison between LMD-based and EMD-based method is also given in Section 3.Finally, we offer the conclusion in Section 4.2. LMD analysis methodAs mentioned above, the nature of LMD is to demodulate AMFM signals. By using LMD a complicated signal can bedecomposed into a set of product functions, each of which is the product of an envelope signal and a purely frequency modulatedsignal. Furthermore, the completed timefrequency distribution of the original signal can be obtained. For any signal x(t), it can bedecomposed as follows 16:(1) Determine all local extrema niof the original signal x(t), and then the mean value miof two successive extrema niand ni+1can be calculated bymini ni121All mean value miof two successive extreme are connected by straight lines, and then local mean function m11(t)can be formed by using moving averaging to smooth the local means mi.68J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 6776(2) A corresponding envelope estimate aiis given byainini1?22Similarly, the envelope estimate aiis smoothed in the same way and the corresponding envelope function a11(t) isformed.(3) The local mean function m11(t) is subtracted from the original signal x(t) and the resulting signal h11(t) is given byh11t x t m11t 3(4) h11(t) can be amplitude demodulated by dividing it by envelope function a11(t)s11t h11t =a11t 4Ideally, s11(t) is a purely frequency modulated signal, namely, the envelope function a12(t) of s11(t) should satisfya12(t)=1. If a12(t)1, then s11(t) is regarded as the original signal and the above procedure needs to be repeateduntil a purely frequency modulated signal s1n(t) that meets 1s1n(t)1 is derived. In other words, envelopefunction a1(n+1)(t) of the resulting s1n(t) should satisfy a1(n+1)(t)=1. Thereforeh11t x t m11t h12 s11t m12t h1nt s1 n1t m1nt 8:5in which,s11t h11t =a11t s12t h12t =a12t s1nt h1nt =a1nt 8:6where the objective is thatlimna1nt 17In practice, a variation can be determined in advance. If 1a1(n+1)(t)1+ and 1s1n(t)1, then iterativeprocess would be stopped.(5) Envelope signal a1(t), namely, instantaneous amplitude function, can be derived by multiplying together the successiveenvelope estimate functions that are acquired during the iterative process described above.a1t a11t a12t a1nt nq1a1qt 8where q is the times of the iterative process.(6) Multiplying envelope signal a1(t) by the purely frequency modulated signal s1n(t) the first product function PF1of theoriginal signal can be obtained.PF1t a1t s1nt 9PF1contains the highest frequency oscillations of the original signal. Meantime, it is a mono-component AMFMsignal, whose instantaneous amplitude is exactly the envelope signal a1(t) and instantaneous frequency is definedfrom the purely frequency modulated signal s1n(t) asf1t 12d arccos s1nt ?dt10(7) Subtract the first PF component PF1(t) from the original signal x(t) and we have a new signal u1(t), which becomes the neworiginal signaland the whole of the above procedure is repeated,i.e. up tok times,until ukbecomes monotonic functionu1t x t PF1t u2t u1t PF2t ukt uk1t PFkt 8:1169J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 6776Thus, the original signal x(t) was decomposed into k-product and a monotonic function ukx t Xkp1PFpt ukt 12where p is the number of the product function.Furthermore, the corresponding complete timefrequency distribution could be obtained by assembling the instantaneousamplitude and instantaneous frequency of all PF components.3. The gear fault diagnosis method based on order tracking technique and LMD3.1. Order tracking analysis and the corresponding fault diagnosis methodOrder-tracking technique could transform a non-stationary signal in time domain into a stationary signal in angular domain byapplying equi-angular re-sampling to vibration signal with reference to shaft speed. Furthermore, order spectrum can be obtainedby using spectrum analysis to stationary signal in angular domain, thus the information related to rotation speed can behighlighted and the unrelated one could be restrained. Therefore, order-tracking is suitable for the vibration signal analysis ofrotation machine.There are three popular techniques for producing synchronously sampled data: a traditional hardware solution, computedorder tracking (COT) and order tracking based on estimation of instantaneous frequency 1820. The traditional hardwareapproach, which uses specialized hardware to dynamically adapt the sample rate, is only suitable for the case that rotating speedof shaft is relatively smooth, thus resulting to a high cost. The method of order tracking based on estimation of instantaneousfrequency has no need for specialized hardware and thus cost is relatively low, however, it has failed to analyze multiplecomponent signal. While in practice most gear fault vibration signals exactly present the characteristic of multi-component.Therefore, this technique has little practice significance. COT technique realized equi-angular re-sampling by software, thereforeit not only requires no specialized hardware, but also have no limitation for analysis signal that means it is more flexible and moreaccurate. Just for this reason, COT is introduced into the gear fault detection in this paper.The step of the gear fault diagnosis method based on order tracking technique and LMD can be listed as follows:(1) The vibration signals and a tachometer signal are asynchronously sampled, that is, they are sampled conventionally atequal time incrementst;(2) Calculate the time series ticorresponding to equi-angular increments by tachometer signals;(3) According to the time series ti, apply interpolation to the vibration signals, thus the synchronous sampling signal, namely,stationary signal in angular domain, can be obtained;(4) Use LMD to decompose the equi-angular re-sampling signal, thus s series PF components and corresponding instantaneousamplitudes and instantaneous frequencies can be acquired;(5) Apply spectrum analysis to the instantaneous amplitude of each PF component, and then we have the order spectrum.3.2. ApplicationSince the gear fault vibration signal in run-up and run-down process are always multiple component AMFM signals and faultfeature frequency would vary with rotation speed, the fault diagnosis method in which order tracking technique and LMD arecombined would be suitable for gear fault detection.To verify the effectiveness of the proposed method, the fault diagnosis method based on order tracking technique and LMDwas applied to the experimental gear vibration signals analysis. An experiment has been carried out on the rotating machinerytest rig that is used for modeling different gear faults 21. Here we consider three working conditions that are gear with normalcondition, with cracked tooth and with broken tooth. Standard gears with teeth number z=55 and z=75 are used on input andoutput shafts respectively, in which the crack fault is introduced into the gear on the input shaft by cutting slot with laser in theroot of tooth, and the width of the slot is 0.15 mm, as well as its depth is 0.3 mm. Therefore, the mesh order is xm=55 and thefault feature order is xc=1. Figs. 1 and 2 give the rotation speed signal r(t) picked up by a tachometer and vibration accelerationsignal s(t) of the gear with crack fault collected by a piezoelectric acceleration sensor respectively, in which the sample frequencyis 8192 Hz and total sample time is 20 s, and from which we know the speed of input shaft increased gradually from 150 rpm to1410 rpm, then decreased to 820 rpm. Meantime, the amplitude of vibration acceleration signal accordingly changed, from whicha section of signal s1(t) of 5 s7 s in the run-up progress is intercepted for further analysis. Fig. 3 gives the spectrum of s1(t) byapplying spectrum analysis directly to vibration signal. For the rotation speed changes with time, the frequency mixing arises.Therefore, it is impossible to find meshing frequency and fault feature frequency in Fig. 3. As a result, actual gear workingcondition cannot be identified. Replace direct spectrum analysis by the order tracking method. Firstly, assume sample point perrotation is 400, namely, the maximum analysis order is 200. Secondly, angular domain signal j1() shown in Fig. 4 can be obtainedby performing order re-sampling to s1(t), in which horizontal ordinate has changed from time to radian. Thirdly, thecorresponding order spectrum of j1() can be calculated that is illustrated in Fig. 5, from which we can find obvious spectral peak70J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 6776values at order O=55 and O=110 corresponding to gear meshing order and the double. Thus it means that frequency aliasingphenomenon has been eliminated to a large degree. However, j1() is still a multiple component MAMF signal. Therefore, sidefrequency band reflecting fault feature frequency is indistinct. To extract fault characteristic effectively, apply LMD to j1(), thusseven PF components and a residue can be obtained shown in Fig. 6, which means LMD is a demodulation progress. Therefore, it ispossible to extract gear fault feature by utilizing spectrum analysis to the instantaneous amplitude of PF component containingdominant fault information. By analysis, we know that the main failure information is included in the first PF component.Therefore, Figs. 7 and 8 give instantaneous amplitude a1() of the first PF component PF1() and the corresponding orderspectrum of a1(), from which it is clear that there are distinct spectral peak value at the 1st order (O=1) corresponding to gearfault feature order xc, which accords with the actual working condition of the gear.Figs. 9 and 10 show the rotation speed signal n(t) and the time domain waveform of vibration acceleration signal s(t) of thegear with broken tooth respectively, in which the sample rate is 8192 Hz and total sample time is 20 s. The broken tooth fault isintroduced into the gear on the input shaft by cutting slot with laser in the root of tooth. Firstly, a section of signal s1(t) of 5 s7 sin the run-up progress is intercepted for further analysis; secondly, assume sample point per rotation is 400; thirdly, angulardomain signal j1() shown in Fig. 11 can be obtained by performing order re-sampling to s1(t); fourthly, apply LMD to j1();finally, the corresponding order spectrum shown in Fig. 12 of instantaneous amplitude of the first PF component PF1() can beacquired, from which it is clear that there are distinct spectral peak value (it is bigger than that in Fig. 8) at the 1st order (O=1)corresponding to gear fault feature order xc, which accords with the actual working condition of the gear.Similarly, we can do likewise for the normal gear. The rotation speed signal n(t) and the time domain waveform of vibrationacceleration signal s(t) of the normal gear are listed in Figs. 13 and 14 respectively, in which the sample rate is 8192 Hz and totalsample time is 20 s. After the same method mentioned above is applied to the original signal shown in Fig. 14, the results areshown in Figs. 15 and 16. Fig. 15 shows the angular domain signal j1() after performing order re-sampling to the section (5 s7 sin the run-up progress) of the original signal. Fig. 16 shows the corresponding order spectrum of instantaneous amplitude of thefirst PF component, from which it is difficult to find gear fault feature order, which also accords with the actual working conditionof the gear.At present, another competing demodulation method for multi-component AMFM signal, namely, empirical modedecomposition (EMD), already exist and have been widely used in signal demodulation analysis7,22. In order to compare twoapproaches, replacing LMD by EMD, we can do likewise using EMD for the re-sampling signals shown in Figs. 4, 11 and 15Fig. 2. The vibration acceleration signal s(t) of the gear with crack fault.Fig. 3. The spectrum of vibration signal of the gear with crack fault.Fig. 1. The input shaft speed r(t) of the cracked gear in the run-up and run-down process.71J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 6776respectively, thus a series IMF component can be obtained. Furthermore, the corresponding instantaneous amplitude andinstantaneous frequency of each IMF component can be calculated by Hilbert transform. By analysis, we know that the dominantfeature information is included in the first IMF component. Therefore, spectrum analysis is only applied to the instantaneousamplitude of the first IMF component. Figs. 1719 give the order spectrum corresponding to three vibration signals of crackedfault, broken tooth fault and normal gear, respectively, from which it is clear that order tracking analysis based on EMD can alsoextract gear fault feature and identify gear working condition. Although both EMD and LMD can decompose the original signaleffectively, the difference between two methods still exists. Comparing to EMD method, as mentioned in Section 1, LMD have moreadvantages such as less iterative times, unobvious end effect and less phoniness components of the instantaneous frequency, whichmake it possible to use for more applications in practice.Fig. 4. The corresponding vibration acceleration signalj1() in angular domain by applying order re-sampling tos(t) shown in Fig. 2.Fig. 5. The order spectrum of j1().Fig. 6. The decomposition results of j1() by LMD.72J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 6776Fig. 8. The order spectrum of the first PF component shown in Fig. 6.Fig. 9. The input shaft speed r(t) of the gear with broken tooth in the run-up and run-down process.Fig. 7. The instantaneous amplitude a1() of PF1().Fig. 10. The vibration acceleration signal s(t) of the gear with broken tooth.Fig. 11. The corresponding vibration acceleration signalj1() in angular domain by applying order re-sampling tos(t) shown in Fig. 10.73J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 6776Fig. 12. The order spectrum of the first PF component of the broken gear fault vibration signal.Fig. 13. The input shaft speed r(t) of the normal gear in the process of the run-up and run-down.Fig. 14. The vibration acceleration signal s(t) of a gear under normal state.Fig. 15. The corresponding vibration acceleration signal j1() in angular domain by applying order re-sampling to s(t) shown in Fig. 14.Fig. 16. The order spectrum of the first PF component of the normal gear vibration signal.74J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 67764. ConclusionIn gear fault diagnostic technology, order tracking is a well-known technique that can be used for fault detection of rotationmachinery by using vibration signals. Targeting the modulation feature of gear fault vibration signal in run-ups and run-downsand the fact that faults found in gear could often be related to shaft speed in the transient process, order tracking technique andLMD are combined to use for the gear fault diagnosis. From the theory analysis and experiment results the following points can beconcluded:(1) When vibration signal under various shaft speed condition is processed, frequency mixing resulted from conventionalspectrum analysis can be overcome by introducing order tracking technique, which make the resulting spectrum linereadable.(2) Considering that the corresponding vibration signal often displays the AMFM feature when faults occur in gear, LMDapproach is applied to demodulation. By using LMD, signal can be decomposed into a number of product functions.Meantime instantaneous amplitude and instantaneous frequency of each PF component can be obtained, thusdemodulation of original signal eventually is realized. Furthermore, gear fault feature can be extracted accurately byapplying spectrum analysis to the instantaneous amplitude of certain PF component including dominant featureinformation. In the proposed method, since the instantaneous amplitude can be obtained directly from the process of LMDFig. 17. The order spectrum of the first IMF component of the gear with cracked tooth by using EMD.Fig. 18. The order spectrum of the first IMF component of the gear with broken tooth by using EMD.Fig. 19. The order spectrum of the first IMF component of the normal gear by using EMD.75J. Cheng et al. / Mechanism and Machine Theory 55 (2012) 6776other than using Hilbert transform, the limitations which is produced by Hilbert transform (mentioned in Section 1) can beavoided.(3) The analysis results from experimental signals with normal and defective gears show that the diagnosis approach proposedcould identify gear status-with or without fault accurately and effectively.AcknowledgmentsThis work was supported by the Chinese National Science Foundation Grant (no. 50775068, no. 51075131), Hunan ProvincialNaturalScienceFoundationofChina(no.11JJ2026